Math, Chemistry, and Physics | The National Academies Press

<!doctype html> <html lang="en"> <head> <meta charset="UTF-8"> <meta http-equiv="X-UA-Compatible" content="IE=edge"> <meta name="viewport" content="width=device-width, initial-scale=1.0"> <meta http-equiv="cache-control" content="no-cache"/> <title>Math, Chemistry, and Physics | The National Academies Press</title> <meta name="description" content="Browse 427 science publications on Math, Chemistry, and Physics from the National Academies Press."> <meta name="og:title" content="Math, Chemistry, and Physics"> <meta name="og:site_name" content="The National Academies Press"> <meta name="og:url" content="https://nap.nationalacademies.org/topic/topic/290/math-chemistry-and-physics"> <meta name="og:description" content="Browse 427 science publications on Math, Chemistry, and Physics from the National Academies Press."> <meta name="og:image" content="https://nap.nationalacademies.org/images/topics/290.png"> <meta name="twitter:card" content="summary"> <meta name="twitter:site" content="@theNASEM"> <meta name="twitter:title" content="Math, Chemistry, and Physics"> <meta name="twitter:description" content="Browse 427 science publications on Math, Chemistry, and Physics from the National Academies Press."> <meta name="twitter:image" content="https://nap.nationalacademies.org/images/topics/290.png"> <meta name="twitter:url" content="https://nap.nationalacademies.org/topic/topic/290/math-chemistry-and-physics"> <link rel="canonical" href="https://nap.nationalacademies.org/topic/topic/290/math-chemistry-and-physics"> <script> // if (document.location.hostname.search(/nap\.edu$/) < 0) { // url = "http://www.na" + "p.edu" + document.location.pathname + document.location.search // document.location.replace(url); // } </script>  <meta name="alexaVerifyID" content="02J2SepmgvpkhVXcfeE98cX3HKs" /> <link href="//nap.nationalacademies.org/stylesheets/nasem-nap.css" rel="stylesheet" type="text/css"> <link href="//nap.nationalacademies.org/stylesheets/topnav-lite-min.css" rel="stylesheet" type="text/css" /> <link href="//nap.nationalacademies.org/stylesheets/component.css" rel="stylesheet" type="text/css" />  <script src="/includes/js/jquery-3.5.1.min.js"></script> <script src="/includes/js/jquery.dotdotdot.min.js" type="text/javascript"></script>    <script type="text/javascript"> var $mcGoal = {'settings':{'uuid':'eaea39b6442dc4e0d08e6aa4a','dc':'us4'}}; (function() { var sp = document.createElement('script'); sp.type = 'text/javascript'; sp.async = true; sp.defer = true; sp.src = ('https:' == document.location.protocol ? 'https://s3.amazonaws.com/downloads.mailchimp.com' : 'http://downloads.mailchimp.com') + '/js/goal.min.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(sp, s); })(); </script>  <script> window.dataLayer = window.dataLayer || [];dataLayer.push({ 'pageTitle' : "Math, Chemistry, and Physics", 'bookTopic' : "Math, Chemistry, and Physics", 'loginStatus' : "guest", 'form' : "subscribe" }); </script> <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-N9MJ23');</script>  <script async src="https://www.googletagmanager.com/gtag/js?id=AW-1071160892"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'AW-1071160892'); gtag('config', 'AW-1071160892'); </script> <script id="mcjs">!function(c,h,i,m,p){m=c.createElement(h),p=c.getElementsByTagName(h)[0],m.async=1,m.src=i,p.parentNode.insertBefore(m,p)}(document,"script","https://chimpstatic.com/mcjs-connected/js/users/eaea39b6442dc4e0d08e6aa4a/208cb1a4b431cae38b54bdb6f.js");</script> <link rel="stylesheet" href="/stylesheets/vendor/bootstrap-3.0.3/bootstrap.min.css"> <link rel="stylesheet" href="/stylesheets/naphome.css" /> <style> body { background: #fff; } .top-rows { background: #F3F1EA; padding-bottom: 30px; } .topicindexicon { margin-right: 10px; } .report-type { padding-left: 10px; } h1.topic-hdr { padding-left: 0px; font-size: 30px; padding-bottom: 30px; } .topic-img { margin-top: 20px; } .nav-tabs > li > a { margin-right: 2px; line-height: 1.42857; border: 1px solid transparent; border-radius: 4px 4px 0px 0px; background: #1d1646; color: #fff; } .nav-tabs > li > a:hover { margin-right: 2px; line-height: 1.42857; border: 1px solid transparent; border-radius: 4px 4px 0px 0px; background: #4148c2; color: #fff; } .book-row.row { background: #fff; } #inputsearch { width:73%; } .btn-searchhome { height: 44px; padding: 1rem; } </style> <style>pre { background-color: transparent !important; }</style> </head> <body>  <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-N9MJ23" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript>  <a name="top" id="top"></a> <a href="#content" class="sr-only sr-only-focusable">Skip to main content</a> <style> body { overflow-x: hidden; } #lowerMenu { background: #fff } .global-nav--local .mega-menu { display: block; -webkit-transform: translateY(0em); transform: translateY(0em); } .global-nav--local.search-is-hidden .mega-menu { display: none; -webkit-transform: translateY(0em); transform: translateY(0em); } .global-nav .container:not(.mega-menu__header) { padding: 0rem; padding-top: 0rem; padding-right: 0rem; padding-top: 0.5rem; padding-right: 1rem; } .global-nav__controls { top: .3rem; padding-right: 20px; } .global-nav--local .global-nav__links { -webkit-transform: translateY(0); transform: translateY(0); max-width: 75%; float: right; background: #fff; } .global-nav__links ul { display: -webkit-flex; display: flex; -webkit-justify-content: flex-end; justify-content: flex-end; margin-top: .5rem; } .global-nav--local.menu-is-hidden .global-nav__links { opacity: 0; -webkit-transform: translateY(0.5em); transform: translateY(0.5em); visibility: hidden; } #header-large { max-width: 1180px; margin: 0; padding: 0 0; -webkit-box-shadow: none; -moz-box-shadow: none; box-shadow: none; flex-wrap: nowrap; position: absolute; top: 113px; text-align: right; width: 100%; right: 0; } #header-large .user-links { white-space: nowrap; display: inline-flex; margin: 0; padding: 0; background: #fff; z-index: 0; list-style: none; min-width:500px; } .user-links li { margin-right: 7%; } .user-links li a { font-size: 10px; text-align: left; text-transform: uppercase; color: #000; } #header-large a.site-links { margin-right: 15px; color: #000; padding-left: 0px; padding-right: 5px; font-size: 12px; text-transform: uppercase; } .site-links:hover { text-decoration: underline; } nav#sitelinks-wide { position: absolute; top: 16px; } #sitelinks-wide ul { display: flex; justify-content: space-between; margin: 0; padding: 0; } #sitelinks-wide ul li { #sitelinks-mobile { display: none; } white-space: nowrap; } #sitelinks-mobile { display: none; } .user-links li a:hover { text-decoration: underline; } .dropdown-menu { position: absolute; top: 100%; left: 10px; z-index: 9999999; display: none; float: left; min-width: 160px; padding: 5px 0; margin: 2px 0 0; list-style: none; font-size: 14px; background-color: #ffffff; border: 1px solid #cccccc; border: 1px solid rgba(0, 0, 0, 0.15); border-radius: 4px; -webkit-box-shadow: 0 6px 12px rgba(0, 0, 0, 0.175); box-shadow: 0 6px 12px rgba(0, 0, 0, 0.175); background-clip: padding-box; } #dropdownMenuButton { border: 1px solid #ccc; font-size: 14px; font-weight: 700; } .dropdown #dropdownMenuButton:after { content: '\02795'; /* Unicode character for "plus" sign (+) */ font-size: 13px; color: #777; float: right; margin-left: 5px; } .dropdown.open #dropdownMenuButton:after { content: "\2796"; /* Unicode character for "minus" sign (-) */ } li.naphelp { display: block;} @media (max-width: 930px) { #header-large { right: 80px; } #header-large .user-links { min-width:100px; } nav#sitelinks-wide { display: none; } #sitelinks-mobile { display: block; position: absolute; top: -10px; left: 107px; } #sitelinks-wide ul { display: block; } #sitelinks-wide ul li { margin-right: 0%; white-space: nowrap; } .dropdown-item { display: block; width: 100%; padding: .25rem 1.5rem; clear: both; font-weight: 400; color: #212529; text-align: inherit; white-space: nowrap; background-color: transparent; border: 0; text-align: left; } .dropdown.nap-mega-menu.mega-dropdown { display: none;} li.naphelp { display: none;} } .global-nav__links { display: none; opacity: 1; transition: opacity .15s, -webkit-transform .15s; transition: opacity .15s, transform .15s; transition: opacity .15s, transform .15s, -webkit-transform .15s; } .global-nav--local .global-nav__links { -webkit-transform: translateY(0); transform: translateY(0); } .global-nav--local.menu-is-hidden .global-nav__links { opacity: 0; -webkit-transform: translateY(0.5em); transform: translateY(0.5em); } .global-nav__links ul { display: -webkit-flex; display: flex; -webkit-justify-content: flex-end; justify-content: flex-end; margin-top: 1rem; } .global-nav__links li:hover .global-nav__link>span::before, .global-nav__links li:focus-within .global-nav__link>span::before, .global-nav__links .global-nav__link.is-active>span::before, .global-nav__links .global-nav__link:hover>span::before, .global-nav__links .global-nav__link:focus>span::before { background-color: #1C143D; ; } .global-nav__links li:hover .global-nav__link>span::before::after, .global-nav__links li:focus-within .global-nav__link>span::before::after, .global-nav__links .global-nav__link.is-active>span::before::after, .global-nav__links .global-nav__link:hover>span::before::after, .global-nav__links .global-nav__link:focus>span::before::after { opacity: 1; } @media screen and (min-width: 65em) { .global-nav__links { display: block; } .global-nav__links>ul>li:last-of-type .global-nav__link { margin-right: -1.25em; } } .global-nav__link { position: relative; display: block; padding: .75em 1.5em .5em; color: rgb(34, 34, 34); color: var(--color-neutral--charcoal); border-bottom: 5px solid transparent; /*font-size: .885rem;*/ font-weight: 700; font-weight: var(--lato--bold); text-decoration: none; transition: color .15s; } .global-nav__link>span { position: relative; } .global-nav__link>span::before { content: ""; position: absolute; bottom: -.5em; left: 0; width: 100%; height: 5px; background-color: transparent; transition: background-color .15s; } .global-nav__dropdown { position: absolute; top: calc(100% + 1em); left: 50%; display: none; width: 600px; background-color: rgb(255, 255, 255); background-color: var(--color-neutral--white); box-shadow: 0 5px 15px rgba(34, 34, 34, .25); box-shadow: 0 5px 15px var(--box-shadow--charcoal); -webkit-transform: translateX(-50%); transform: translateX(-50%); z-index: 20; } .global-nav__dropdown::before { content: ""; position: absolute; top: -1em; left: 0; display: block; width: 100%; height: 1em; } .global-nav__dropdown .dropdown__left { position: relative; min-height: 260px; width: 40%; padding: 1.5rem; background: rgb(255,255,255); background: -moz-linear-gradient(180deg, rgba(255,255,255,1) 0%, rgba(73,69,104,1) 0%, rgba(0,0,0,1) 100%, rgba(195,228,228,1) 100%); background: -webkit-linear-gradient(180deg, rgba(255,255,255,1) 0%, rgba(73,69,104,1) 0%, rgba(0,0,0,1) 100%, rgba(195,228,228,1) 100%); background: linear-gradient(180deg, rgba(255,255,255,1) 0%, rgba(73,69,104,1) 0%, rgba(0,0,0,1) 100%, rgba(195,228,228,1) 100%); filter: progid:DXImageTransform.Microsoft.gradient(startColorstr="#ffffff",endColorstr="#c3e4e4",GradientType=1); } .global-nav__dropdown .dropdown__left a { display: block; color: rgb(255, 255, 255); color: var(--color-neutral--white); font-weight: 400; font-weight: var(--lato--regular); transition: color .15s; font-size: 16px; } .global-nav__dropdown .dropdown__left a:hover, .global-nav__dropdown .dropdown__left a:focus, .global-nav__dropdown .dropdown__left a:active { color: rgb(246,210,0); color: var(--color-yellow--pure); } .global-nav__dropdown .dropdown__left ul { -webkit-flex-direction: column; flex-direction: column; } .global-nav__dropdown .dropdown__left li a { padding: .5em 0; line-height: 1.4; } .global-nav__dropdown .dropdown__left--default { position: absolute; top: 0; right: 0; bottom: 0; left: 0; overflow: hidden; background-color: rgb(243, 241, 235); background-color: var(--color-brown--bone); } .global-nav__dropdown .dropdown__left--default img { width: 100%; height: auto; /* stylelint-disable max-nesting-depth */ /* stylelint-enable max-nesting-depth */ } @supports (object-fit: cover) { .global-nav__dropdown .dropdown__left--default img { height: 100%; object-fit: cover; } } .global-nav__dropdown .dropdown__right { width: 60%; padding: 1.5rem; } .global-nav__dropdown .dropdown__right .button { margin-top: 2em; text-shadow: none; } .global-nav__dropdown .dropdown__right a { color: rgb(0, 89, 145); color: var(--color-blue--bahama); text-decoration: none; transition: color .15s; } .global-nav__dropdown .dropdown__right a:hover, .global-nav__dropdown .dropdown__right a:focus { color: rgb(33,23,71); color: var(--color-blue--imperial); text-decoration: underline; } .rm-dropdown:hover::after, .rm-dropdown:focus::after { visibility: hidden; } .has-dropdown { position: relative; } .has-dropdown::after { content: ""; position: absolute; top: calc(100% + 3px); left: 50%; width: 26px; height: 15px; background-image: url(data:image/png;base64,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); background-repeat: no-repeat; -webkit-transform: translateX(-50%); transform: translateX(-50%); visibility: hidden; } .has-dropdown:hover::after, .has-dropdown:focus::after { visibility: visible; } .has-dropdown:hover .global-nav__dropdown { display: -webkit-flex; display: flex; } .has-dropdown:focus-within .global-nav__dropdown { display: -webkit-flex; display: flex; } .has-dropdown:nth-last-of-type(-n+3) .global-nav__dropdown { left: auto; -webkit-transform: none; transform: none; } .has-dropdown:nth-last-of-type(3) .global-nav__dropdown { right: -200%; } .has-dropdown:nth-last-of-type(2) .global-nav__dropdown { right: -90%; } .has-dropdown:last-of-type .global-nav__dropdown { right: 5%; } .global-nav__links { z-index: 5; } header.global-nav { height: 150px; } .button.button--secondary.button--outline.button--icon { font-size: 12px; padding-right: 40px; } .button.button--icon svg { height: 2.5em; position: absolute; top: 50%; left: 60%; -webkit-transform: translate(-50%, -50%); transform: translate(-50%, -50%); width: 24px; } .controls__search, .controls__menu, .controls__nav { font-size: 12px; } .global-nav__menus--upper { display: -webkit-flex; display: flex; -webkit-justify-content: space-between; justify-content: space-between; margin-bottom: 2rem; } .global-nav__link { font-size: 16px; } .global-nav__links ul { display: -webkit-flex; display: flex; -webkit-justify-content: flex-end; justify-content: flex-end; margin-top: 5px; list-style: none; } .invert { background: #000; color: #fff; } .controls__nav .menu-off { display: inline; } .controls__nav .menu-on { display: none; } .controls__nav.invert .menu-off { display: none } .controls__nav.invert .menu-on { display: inline; } .mega-menu { background-color: rgb(243, 241, 235); background-color: var(--color-brown--bone); position: fixed; top: 0; right: 0; bottom: 0; left: 0; overflow: scroll; z-index: 9999999; } .mega-menu .mega-menu__header { display: -webkit-flex; display: flex; -webkit-justify-content: space-between; justify-content: space-between; -webkit-align-items: center; align-items: center; padding-top: 1rem; } .mega-menu__content .search-form__container { position: relative; max-width: 70em; margin: 0 auto; } #search .global-nav__logo { position: absolute; top: 1em; } .sf-top { margin-top: 50px; } #searchFormNAP { display: block; height: 100px; } a:hover, a:focus { color: #1C143D; text-decoration: underline; } #fixedfooter a:hover, #fixedfooter a:focus { color: #fff; text-decoration: underline; } .btn-blueflat.btn-searchhome.hide-xs { display: none; } .mega-menu__content { margin-top: 50px; margin-left: 7px; } .accordion__title.faq__accordion__title .flex.justify-between { display: inherit; } .global-nav__logo { margin: 0px !important; position: absolute; left: 15px; top: 25px; height: 55px; } .global-nav__link:hover { text-decoration: none; } @media screen and (min-width: 65em) { .mega-menu__content .search-form { padding: 1em 0px 3em 0em; } } @media (min-width: 45rem) { .global-nav__logo {} } @media (max-width: 480px) { .global-nav__logo { margin: 0px !important; position: absolute; left: 15px; top: 12px; } } /* Style the buttons that are used to open and close the accordion panel */ #mobile-menu button.accordion, #mobile-menu button.no-accordion { letter-spacing: 1px; text-align: left; color: #4148C2; font-size: 1.1em; font-weight: 700 !important; font-family: 'lato', helvetica, sans-serif; padding: 15px 0px 15px 0px; border-top: none !important; border-bottom: .5px solid rgb(221, 213, 199) !important; cursor: pointer; width: 100%; } .mega-menu__content .accordion { border: 0; font-weight: 700; } #mobile-menu .accordion:after { content: '\02795'; /* Unicode character for "plus" sign (+) */ font-size: 13px; color: #777; float: right; margin-left: 5px; } #mobile-menu button.active:after { content: "\2796"; /* Unicode character for "minus" sign (-) */ } /* Add a background color to the button if it is clicked on (add the .active class with JS), and when you move the mouse over it (hover) */ #mobile-menu button.active, #mobile-menu button.accordion:hover { background-color: transparent; } /* Style the accordion panel. Note: hidden by default */ #mobile-menu .panel { padding: 0 0; background-color: transparent; max-height: 0; box-shadow: 0 !important; overflow: hidden; transition: max-height 0.2s ease-out; margin: 0px !important; border: 0 !important; } #mobile-menu .panel ul li { margin: 0px 0px; padding-left: 0px; } #mobile-menu .panel ul { margin-top: 10px; margin-bottom: 10px; padding-left: 0px; } #mobile-menu .panel ul li { line-height: 2; } #mobile-menu .panel ul li a { color: #000; text-decoration: underline; cursor: pointer; } .controls__menu-mobile { text-transform: uppercase; } .controls__menu-mobile svg { fill: #222; fill: var(--color-neutral--charcoal); width: 1.75rem; height: 1.75rem; } .cart-badge { display: inline-block; text-align: center; line-height: 1; background: #7899F2; color: white; font-weight: bold; border-radius: 20px; padding: 3px 6px; margin-left: 3px; } @media screen and (min-width: 65em) { #mobile-menu .controls__menu { display: inline; } } @media screen and (max-width: 65em) { #mobile-menu .controls__menu svg { display: inline; } } /*NAP mega menu dropdown*/ li.nap-mega-menu.mega-dropdown { position: static !important; width:100% !important; } .nap-mega-menu .mega-dropdown-menu { padding: 20px 0px; box-shadow: none; -webkit-box-shadow: none; margin-top: 10px !important; box-shadow: 0 5px 15px var(--box-shadow--charcoal); transform: none !important; top: 100% !important; } .nap-mega-menu .mega-dropdown-menu > li > ul.browse-col { padding: 0; margin: 0; width: 100%; } .nap-mega-menu .mega-dropdown-menu > li > ul > li { list-style: none; } .nap-mega-menu .mega-dropdown-menu > li > ul > li > a { display: block; padding: 3px 20px; clear: both; font-weight: normal; line-height: 1.428571429; color: #4148C2; white-space: normal; font-size: 14px; text-transform: none; } .nap-mega-menu .mega-dropdown-menu > li ul > li > a:hover, .nap-mega-menu .mega-dropdown-menu > li ul > li > a:focus { text-decoration: none; color: #444; background-color: #f5f5f5; } .nap-mega-menu .mega-dropdown-menu .dropdown-header a { color: #4148C2; font-size: 14px; font-weight: 900 !important; text-align: left; text-transform: uppercase !important; padding: 0px; margin-bottom: 7px; } .nap-mega-menu .mega-dropdown-menu form { margin:3px 20px; } .nap-mega-menu .mega-dropdown-menu .form-group { margin-bottom: 3px; } .nap-mega-menu .vertical-divider { border-left: 1px solid #ccc; } .nap-mega-menu .mega-dropdown-menu > li.d-flex { display: inline-flex !important; margin-right: 0 !important; justify-content: space-between; flex-wrap: nowrap !important; flex-direction: row !important; } #nap-mega-menu-inner { justify-content: space-between; align-content:start; } #nap-mega-menu-inner li.browse-col { width: 22%; } </style> <header class="global-nav global-nav--local menu-is-hidden search-is-hidden" id="lowerMenu"> <div class="container flex justify-between">  <div aria-hidden="true" class="mega-menu" id="search"> <div data-lock=""> <div class="container mega-menu__header"> <div class="global-nav__logo"> <a class="navbar-brand js-scroll-trigger" href="https://www.nationalacademies.org/"> <svg xmlns="http://www.w3.org/2000/svg" id="nasemLogo" data-name="nasemLogo" viewBox="0 0 360 66.64"> <defs/> <path d="m4.26 8.63 19.56 20.49V1.72h-3.47v18.93L.8.16v27.32h3.46V8.63zM32.55 27.48h3.83l8.15-19.2 7.93 18.99.09.21h3.82L44.62 0 32.55 27.48zM175.05 27.48h3.83l8.16-19.2 7.93 18.99.08.21h3.83L187.12 0l-12.07 27.48zM68.23 27.48h3.47V5.03h7.72V1.72H60.51v3.31h7.72v22.45zM90.08 1.72h3.46v25.76h-3.46z" class="cls-2"/> <path d="M157.14 38.67A13.39 13.39 0 1 0 143.75 52a13.21 13.21 0 0 0 13.39-13.33Zm-3.54 0a9.85 9.85 0 1 1-9.85-10 9.93 9.93 0 0 1 9.85 10Z" class="cls-2" transform="translate(-24.97 -24.05)"/> <path d="m146.56 8.63 19.56 20.49V1.72h-3.47v18.93L143.1.16v27.32h3.46V8.63zM210.95 1.72h-3.46v25.76h13.8v-3.31h-10.34V1.72z" class="cls-2"/> <path d="M67.41 63A13.13 13.13 0 0 0 54 76.37a13 13 0 0 0 13.26 13.24A13.48 13.48 0 0 0 75 87.1l.14-.1v-4.46l-.58.58a10.91 10.91 0 0 1-2.81 2 10 10 0 0 1-4.51 1.13c-6.74 0-9.77-5.78-9.77-9.89a9.82 9.82 0 0 1 9.74-10.11 10.44 10.44 0 0 1 4.18.94 12 12 0 0 1 3.17 2.27l.58.58v-4.41l-.13-.1a12.1 12.1 0 0 0-7.6-2.53ZM130 66.4a14 14 0 0 0-9.47-3h-5.45v25.75h5.42c4.25 0 6.88-.83 9.39-3a12.32 12.32 0 0 0 4.52-9.89A12.54 12.54 0 0 0 130 66.4Zm-2.39 17.26a10.37 10.37 0 0 1-7 2.18h-2.11V66.7h2.11c6.21 0 10.22 3.77 10.22 9.59a9.23 9.23 0 0 1-3.25 7.37Z" class="cls-2" transform="translate(-24.97 -24.05)"/> <path d="M119.94 65.11h15.33V61.8h-11.86v-9.07h10.38v-3.31h-10.38v-6.76h11.86v-3.32h-15.33v25.77zM201.26 65.11h15.33V61.8h-11.86v-9.07h10.37v-3.31h-10.37v-6.76h11.86v-3.32h-15.33v25.77zM158.66 58.65l-9.79-21.53-4.42 27.99h3.56l2.36-16.59 8.25 18.12 8.35-18.12 2.25 16.59h3.56l-4.14-28.03-9.98 21.57zM184.29 39.34h3.46V65.1h-3.46z" class="cls-2"/> <path d="M263.7 76.76a12.7 12.7 0 0 0-4-2.44l-2.42-1a8 8 0 0 1-2.53-1.51 2.32 2.32 0 0 1-.83-1.94c0-2.11 1.56-3.53 3.87-3.53a4.18 4.18 0 0 1 2.61.79 5.51 5.51 0 0 1 1.37 1.77l.17.34 2.8-1.85-.14-.27a7.79 7.79 0 0 0-2.56-2.91 7.16 7.16 0 0 0-4.18-1.21c-4.34 0-7.37 2.8-7.37 6.8a5.53 5.53 0 0 0 1.83 4.35 10.74 10.74 0 0 0 3.24 2l2.44 1.17a10.81 10.81 0 0 1 2.94 1.68 3.39 3.39 0 0 1 1.13 2.68A4.8 4.8 0 0 1 254 85a5.6 5.6 0 0 1-1.42-3l-.05-.39-3.4.94.07.32a9.51 9.51 0 0 0 2.43 4.61 7.73 7.73 0 0 0 5.69 2.13 7.9 7.9 0 0 0 8.28-8 6.38 6.38 0 0 0-1.9-4.85Z" class="cls-2" transform="translate(-24.97 -24.05)"/> <path d="M0 65.11h3.83l8.16-19.21 7.92 19 .09.21h3.83L12.07 37.63 0 65.11zM57.37 65.11h3.83l8.15-19.21 7.93 19 .08.21h3.83L69.44 37.63 57.37 65.11z" class="cls-2"/> <path d="M292 26.45a3.91 3.91 0 0 0-1.07-.14 2.94 2.94 0 0 0-1.74.52 1.71 1.71 0 0 0-.72 1.47 2.36 2.36 0 0 0 .63 1.7 9.45 9.45 0 0 0 1.9 1.38 15.52 15.52 0 0 1 1.45 1 4.28 4.28 0 0 1 .94 1.12 2.87 2.87 0 0 1 .38 1.51 3.57 3.57 0 0 1-.57 2 3.79 3.79 0 0 1-1.6 1.34 5.79 5.79 0 0 1-2.39.47 9.63 9.63 0 0 1-2.22-.25 4.15 4.15 0 0 1-1.41-.52l.39-2.49H287l.11 1.84a2.93 2.93 0 0 0 .92.39 5 5 0 0 0 1.16.14 3.39 3.39 0 0 0 2-.6 1.94 1.94 0 0 0 .83-1.68 2.25 2.25 0 0 0-.56-1.54 7.66 7.66 0 0 0-1.7-1.32c-.6-.39-1.1-.75-1.51-1.07a4.43 4.43 0 0 1-1-1.2 2.94 2.94 0 0 1-.43-1.59 3.08 3.08 0 0 1 .57-1.85 3.58 3.58 0 0 1 1.55-1.23 5.17 5.17 0 0 1 2.13-.43 7.84 7.84 0 0 1 2 .21 4 4 0 0 1 1.25.51l-.4 2.31h-.95l-.14-1.68a2.39 2.39 0 0 0-.83-.32ZM300.27 29.79a2.2 2.2 0 0 0-1.53.62 4.15 4.15 0 0 0-1.06 1.74 8 8 0 0 0-.38 2.55 4.11 4.11 0 0 0 .5 2.24 1.6 1.6 0 0 0 1.42.74 2.71 2.71 0 0 0 1.25-.27 5.56 5.56 0 0 0 1.15-.81l.35.64a4.42 4.42 0 0 1-1.31 1.08 3.78 3.78 0 0 1-2 .5 2.76 2.76 0 0 1-2.31-1 4.51 4.51 0 0 1-.83-2.9 7.35 7.35 0 0 1 .6-2.87 6 6 0 0 1 1.77-2.38 4.27 4.27 0 0 1 2.77-.95 5.7 5.7 0 0 1 1.06.11 3.31 3.31 0 0 1 .92.3l-.48 1.7-.29-.11a2.91 2.91 0 0 0-1.6-.93ZM306.13 37.31a.54.54 0 0 0 .08.33.22.22 0 0 0 .2.11.74.74 0 0 0 .39-.12 2.88 2.88 0 0 0 .5-.4l.23.42a3.34 3.34 0 0 1-.78.77 2 2 0 0 1-1.23.4 1.3 1.3 0 0 1-.89-.27.9.9 0 0 1-.26-.81c0-.3.18-1.43.46-3.41q.24-1.59.6-4.23l-1.09-.4.11-.6 2.49-.4.38.19-1.17 8.25Zm-.08-10.8a1 1 0 0 1-.27-.69 1.24 1.24 0 0 1 .34-.89 1.07 1.07 0 0 1 .82-.37.94.94 0 0 1 .7.27.93.93 0 0 1 .26.66 1.35 1.35 0 0 1-.33.92 1.14 1.14 0 0 1-.88.38.9.9 0 0 1-.64-.28ZM315.15 38.24a4.26 4.26 0 0 1-2.23.6 3.45 3.45 0 0 1-2-.53 3.23 3.23 0 0 1-1.15-1.41 4.83 4.83 0 0 1-.36-1.87 7.38 7.38 0 0 1 .67-3.14 5.91 5.91 0 0 1 1.92-2.33 4.33 4.33 0 0 1 2.62-.88 2.64 2.64 0 0 1 1.88.6 2.06 2.06 0 0 1 .63 1.56 2.66 2.66 0 0 1-1 2.11 6.62 6.62 0 0 1-2.37 1.28 9.48 9.48 0 0 1-2.46.45 3.85 3.85 0 0 0 .42 2.13 1.68 1.68 0 0 0 1.6.91 3.61 3.61 0 0 0 1.54-.36 4.41 4.41 0 0 0 1.39-1l.38.65a4.39 4.39 0 0 1-1.48 1.23Zm-2.41-8a4.82 4.82 0 0 0-1 1.65 7.41 7.41 0 0 0-.44 1.94 5.85 5.85 0 0 0 1.86-.39 4.34 4.34 0 0 0 1.6-1 2 2 0 0 0 .65-1.46 1.5 1.5 0 0 0-.33-1.05 1.14 1.14 0 0 0-.88-.35 2 2 0 0 0-1.46.67ZM323.42 29.32a3.62 3.62 0 0 1 2-.64 1.89 1.89 0 0 1 1.51.6 2.93 2.93 0 0 1 .53 1.95 16.77 16.77 0 0 1-.39 2.68l-.07.4-.14.85a12.6 12.6 0 0 0-.28 2.12c0 .32.08.47.23.47a1.35 1.35 0 0 0 .82-.44l.21.46a1.7 1.7 0 0 1-.36.4 2.81 2.81 0 0 1-.7.45 1.92 1.92 0 0 1-.9.2c-.74 0-1.11-.35-1.11-1.07a14.6 14.6 0 0 1 .32-2.14l.16-.84.07-.42c.11-.63.21-1.18.28-1.66a9 9 0 0 0 .1-1.32 2 2 0 0 0-.23-1.12 1 1 0 0 0-.84-.3 2.63 2.63 0 0 0-1.57.69 6.6 6.6 0 0 0-1.48 1.67l-.86 6.34H319l1.13-8.49-.86-.42.14-.67 2.14-.39.37.2-.23 2.1a6.56 6.56 0 0 1 1.73-1.66ZM334.3 29.79a2.22 2.22 0 0 0-1.53.62 4.14 4.14 0 0 0-1 1.74 7.68 7.68 0 0 0-.38 2.55 4.11 4.11 0 0 0 .49 2.24 1.61 1.61 0 0 0 1.42.74 2.78 2.78 0 0 0 1.26-.27 5.52 5.52 0 0 0 1.14-.81l.36.64a4.56 4.56 0 0 1-1.31 1.08 3.85 3.85 0 0 1-2 .5 2.79 2.79 0 0 1-2.31-1 4.57 4.57 0 0 1-.83-2.9 7.19 7.19 0 0 1 .61-2.87 5.94 5.94 0 0 1 1.77-2.38 4.24 4.24 0 0 1 2.76-.95 5.7 5.7 0 0 1 1.06.11 3.2 3.2 0 0 1 .92.3l-.47 1.7-.3-.11a2.91 2.91 0 0 0-1.66-.93ZM343.32 38.24a4.26 4.26 0 0 1-2.23.6 3.42 3.42 0 0 1-1.95-.53A3.17 3.17 0 0 1 338 36.9a4.66 4.66 0 0 1-.37-1.87 7.53 7.53 0 0 1 .67-3.14 6 6 0 0 1 1.86-2.33 4.36 4.36 0 0 1 2.63-.88 2.65 2.65 0 0 1 1.88.6 2.06 2.06 0 0 1 .63 1.56 2.69 2.69 0 0 1-1 2.11 6.66 6.66 0 0 1-2.38 1.28 9.33 9.33 0 0 1-2.46.45 4 4 0 0 0 .42 2.13 1.68 1.68 0 0 0 1.6.91 3.65 3.65 0 0 0 1.55-.36 4.37 4.37 0 0 0 1.38-1l.39.65a4.43 4.43 0 0 1-1.48 1.23Zm-2.4-8a4.67 4.67 0 0 0-1 1.65 7 7 0 0 0-.44 1.94 5.79 5.79 0 0 0 1.85-.39 4.25 4.25 0 0 0 1.6-1 2 2 0 0 0 .65-1.46 1.5 1.5 0 0 0-.32-1.05 1.17 1.17 0 0 0-.89-.35 1.93 1.93 0 0 0-1.45.67ZM351.91 29.91a3.08 3.08 0 0 0-1.24-.24 2.15 2.15 0 0 0-1.3.35 1.18 1.18 0 0 0-.49 1 1.54 1.54 0 0 0 .4 1.06 6.17 6.17 0 0 0 1.13 1c.42.33.76.61 1 .85a3.35 3.35 0 0 1 .67.87 2.38 2.38 0 0 1 .3 1.2 2.4 2.4 0 0 1-1 2.07 4.21 4.21 0 0 1-2.53.73 7.55 7.55 0 0 1-1.57-.17 2.73 2.73 0 0 1-1-.39l.29-1.21a3.77 3.77 0 0 0 1 .5 3.94 3.94 0 0 0 1.36.24 2.47 2.47 0 0 0 1.31-.33 1.14 1.14 0 0 0 .55-1.06 1.58 1.58 0 0 0-.43-1.09 8 8 0 0 0-1.26-1 3.53 3.53 0 0 1-1.81-2.86 2.43 2.43 0 0 1 .46-1.45 2.92 2.92 0 0 1 1.25-1 4.48 4.48 0 0 1 1.75-.34 7.2 7.2 0 0 1 1.29.12 4.56 4.56 0 0 1 .92.22l-.3 1.33a1.83 1.83 0 0 0-.75-.4ZM287 50.81h8.32l-.12 2.79h-1l-.28-1.84-4-.14-.67 5 4.07-.14-.12 1.32-4-.14-.81 5.34 4.95-.21 1-2.12 1 .19-.71 3h-9.33l.07-.68 1.32-.21 1.4-11.19-1.19-.2ZM301.65 54.52a3.52 3.52 0 0 1 2-.64 1.89 1.89 0 0 1 1.51.6 2.89 2.89 0 0 1 .53 1.94 16.85 16.85 0 0 1-.39 2.69l-.07.4-.14.84a12.68 12.68 0 0 0-.28 2.13c0 .31.07.47.23.47a1.41 1.41 0 0 0 .82-.44l.14.49a1.76 1.76 0 0 1-.37.4 3.17 3.17 0 0 1-.69.45 2 2 0 0 1-.9.2A1 1 0 0 1 303 63a14.6 14.6 0 0 1 .32-2.14l.16-.84.07-.42c.11-.64.21-1.19.28-1.66a9.18 9.18 0 0 0 .1-1.33 2 2 0 0 0-.23-1.11 1 1 0 0 0-.84-.31 2.59 2.59 0 0 0-1.57.7 6.6 6.6 0 0 0-1.48 1.67l-.86 6.33h-1.67l1.13-8.49-.86-.42.14-.66 2.14-.39.37.19-.23 2.11a6.56 6.56 0 0 1 1.68-1.71ZM313.74 66.64a4.23 4.23 0 0 1-1.77 1.2 5.86 5.86 0 0 1-2 .37 7.37 7.37 0 0 1-1.13-.09 4.89 4.89 0 0 1-.87-.22l.37-1.42a6.44 6.44 0 0 0 1 .39 4.29 4.29 0 0 0 1.22.18 2.62 2.62 0 0 0 1.66-.43 2.58 2.58 0 0 0 .71-1.62l.33-2.33a4.25 4.25 0 0 1-1.18 1 3 3 0 0 1-1.52.39 2.52 2.52 0 0 1-2.17-1 4.5 4.5 0 0 1-.72-2.68 7.33 7.33 0 0 1 .66-3 6.45 6.45 0 0 1 1.95-2.49 4.73 4.73 0 0 1 3-1 5.1 5.1 0 0 1 1 .11 5.19 5.19 0 0 1 .91.28l1.09-.39-1.58 10.63a3.73 3.73 0 0 1-.96 2.12ZM313 54.81a2.66 2.66 0 0 0-2 .85 5.43 5.43 0 0 0-1.22 2.11 7.91 7.91 0 0 0-.4 2.46 3.81 3.81 0 0 0 .42 2 1.31 1.31 0 0 0 1.17.71 2.42 2.42 0 0 0 1.37-.44 3.83 3.83 0 0 0 1-1l.93-6.28a2.13 2.13 0 0 0-1.27-.41ZM320.16 62.51a.56.56 0 0 0 .08.32.24.24 0 0 0 .2.12.8.8 0 0 0 .4-.12 4.16 4.16 0 0 0 .5-.41l.23.42a3.57 3.57 0 0 1-.78.78 2 2 0 0 1-1.24.4 1.32 1.32 0 0 1-.89-.27.92.92 0 0 1-.25-.82c0-.29.18-1.43.46-3.4.16-1.07.36-2.48.59-4.23l-1.09-.4.11-.6 2.49-.4.39.19-1.18 8.25Zm-.08-10.81a.93.93 0 0 1-.27-.68 1.25 1.25 0 0 1 .35-.89 1 1 0 0 1 .81-.37.93.93 0 0 1 .7.27.9.9 0 0 1 .27.66 1.36 1.36 0 0 1-.34.92 1.11 1.11 0 0 1-.88.37.87.87 0 0 1-.64-.28ZM328.56 54.52a3.54 3.54 0 0 1 2-.64 1.89 1.89 0 0 1 1.51.6 2.89 2.89 0 0 1 .53 1.94 16.85 16.85 0 0 1-.39 2.69l-.07.4-.14.84a12.68 12.68 0 0 0-.28 2.13c0 .31.08.47.23.47a1.41 1.41 0 0 0 .82-.44l.23.49a1.76 1.76 0 0 1-.37.4 3.17 3.17 0 0 1-.69.45 2 2 0 0 1-.9.2 1 1 0 0 1-1.16-1.05 14.6 14.6 0 0 1 .32-2.14l.16-.84.07-.42c.11-.64.21-1.19.28-1.66a9.18 9.18 0 0 0 .1-1.33 2 2 0 0 0-.23-1.11 1 1 0 0 0-.84-.31 2.59 2.59 0 0 0-1.57.7 6.6 6.6 0 0 0-1.48 1.67l-.86 6.33h-1.67l1.13-8.49-.86-.42.14-.66 2.14-.39.37.19-.23 2.11a6.56 6.56 0 0 1 1.71-1.71ZM340.41 63.44a4.26 4.26 0 0 1-2.23.6 3.35 3.35 0 0 1-1.95-.54 3 3 0 0 1-1.15-1.4 4.66 4.66 0 0 1-.37-1.87 7.38 7.38 0 0 1 .67-3.14 5.91 5.91 0 0 1 1.86-2.33 4.29 4.29 0 0 1 2.62-.88 2.62 2.62 0 0 1 1.88.6 2 2 0 0 1 .63 1.56 2.63 2.63 0 0 1-1 2.1 6.47 6.47 0 0 1-2.37 1.28 9.38 9.38 0 0 1-2.46.46A4 4 0 0 0 337 62a1.69 1.69 0 0 0 1.6.9 3.61 3.61 0 0 0 1.54-.36 4.27 4.27 0 0 0 1.39-1l.39.65a4.68 4.68 0 0 1-1.51 1.25Zm-2.4-8a4.53 4.53 0 0 0-1 1.65 6.69 6.69 0 0 0-.44 1.94 6.13 6.13 0 0 0 1.85-.39 4.25 4.25 0 0 0 1.6-1 2 2 0 0 0 .65-1.46 1.55 1.55 0 0 0-.32-1.05 1.14 1.14 0 0 0-.89-.36 2 2 0 0 0-1.46.68ZM349.39 63.44a4.26 4.26 0 0 1-2.23.6 3.35 3.35 0 0 1-2-.54 3.09 3.09 0 0 1-1.15-1.4 4.66 4.66 0 0 1-.37-1.87 7.38 7.38 0 0 1 .68-3.14 5.91 5.91 0 0 1 1.86-2.33 4.25 4.25 0 0 1 2.62-.88 2.65 2.65 0 0 1 1.88.6 2 2 0 0 1 .63 1.56 2.66 2.66 0 0 1-1 2.1 6.51 6.51 0 0 1-2.31 1.28 9.38 9.38 0 0 1-2.46.46 3.94 3.94 0 0 0 .43 2.13 1.66 1.66 0 0 0 1.59.9 3.65 3.65 0 0 0 1.55-.36 4.34 4.34 0 0 0 1.38-1l.39.65a4.68 4.68 0 0 1-1.49 1.24Zm-2.4-8a4.67 4.67 0 0 0-1 1.65 7 7 0 0 0-.44 1.94 6.07 6.07 0 0 0 1.85-.39 4.38 4.38 0 0 0 1.61-1 2 2 0 0 0 .65-1.46 1.5 1.5 0 0 0-.33-1.05 1.14 1.14 0 0 0-.89-.36 2 2 0 0 0-1.44.68ZM356.34 55.24a4.21 4.21 0 0 1 1.13-1 2.81 2.81 0 0 1 1.4-.38.93.93 0 0 1 .56.12l-.37 1.86a1.64 1.64 0 0 0-.86-.18 2.68 2.68 0 0 0-1.48.5 3.31 3.31 0 0 0-1.14 1.4l-.8 6.24h-1.69l1.11-8.45-.88-.44.12-.65 2.07-.4.35.21-.12 1.56-.08.7a3.9 3.9 0 0 1 .68-1.09ZM362.32 62.51a.56.56 0 0 0 .08.32.23.23 0 0 0 .2.12.8.8 0 0 0 .4-.12 4.16 4.16 0 0 0 .5-.41l.22.42a3.18 3.18 0 0 1-.78.78 2 2 0 0 1-1.23.4 1.3 1.3 0 0 1-.89-.27.92.92 0 0 1-.25-.82c0-.29.17-1.43.45-3.4.17-1.07.36-2.48.6-4.23l-1.09-.4.11-.6 2.49-.4.38.19-1.17 8.25Zm-.08-10.81a.93.93 0 0 1-.24-.7 1.24 1.24 0 0 1 .34-.89 1.07 1.07 0 0 1 .82-.37.94.94 0 0 1 .7.27.93.93 0 0 1 .26.66 1.35 1.35 0 0 1-.33.92 1.12 1.12 0 0 1-.88.37.86.86 0 0 1-.67-.26ZM370.36 54.52a3.55 3.55 0 0 1 2-.64 1.91 1.91 0 0 1 1.51.6 2.89 2.89 0 0 1 .52 1.94 17.7 17.7 0 0 1-.38 2.69l-.07.4-.14.84a12.68 12.68 0 0 0-.28 2.13c0 .31.07.47.22.47a1.4 1.4 0 0 0 .83-.44l.21.46a1.76 1.76 0 0 1-.37.4 3.74 3.74 0 0 1-.69.45 2.13 2.13 0 0 1-.91.2 1 1 0 0 1-1.1-1.07 14.1 14.1 0 0 1 .31-2.14l.16-.84.07-.42c.12-.64.21-1.19.28-1.66a9.27 9.27 0 0 0 .11-1.33 1.88 1.88 0 0 0-.24-1.11 1 1 0 0 0-.83-.31 2.59 2.59 0 0 0-1.57.7 6.6 6.6 0 0 0-1.48 1.67l-.86 6.33H366l1.12-8.49-.86-.42.14-.66 2.14-.39.37.19-.23 2.11a6.72 6.72 0 0 1 1.68-1.66ZM382.46 66.64a4.23 4.23 0 0 1-1.77 1.2 5.87 5.87 0 0 1-2 .37 7.34 7.34 0 0 1-1.12-.09 4.82 4.82 0 0 1-.88-.22l.37-1.42a6.58 6.58 0 0 0 1 .39 4.24 4.24 0 0 0 1.22.18 2.57 2.57 0 0 0 1.65-.43 2.53 2.53 0 0 0 .72-1.62l.33-2.33a4.25 4.25 0 0 1-1.18 1 3.07 3.07 0 0 1-1.52.39 2.52 2.52 0 0 1-2.17-1 4.5 4.5 0 0 1-.73-2.68 7.35 7.35 0 0 1 .67-3 6.27 6.27 0 0 1 1.95-2.51 4.71 4.71 0 0 1 3-1 5.1 5.1 0 0 1 1 .11 5.47 5.47 0 0 1 .91.28l1.09-.39-1.58 10.63a3.86 3.86 0 0 1-.96 2.14Zm-.7-11.83a2.62 2.62 0 0 0-2 .85 5.31 5.31 0 0 0-1.22 2.11 7.93 7.93 0 0 0-.41 2.46 3.7 3.7 0 0 0 .43 2 1.31 1.31 0 0 0 1.17.71 2.42 2.42 0 0 0 1.37-.44 3.79 3.79 0 0 0 1-1l.93-6.28a2.08 2.08 0 0 0-1.27-.41ZM295.85 80.3q1.44-3.12 1.89-4.29h3.76l-.07.75-1.56.19-.34 11.2 1.49.21-.02.64h-4.82l.07-.68 1.6-.21.4-7.76.23-3.56L297.1 80l-4.1 9.08-.94.12-1.44-9-.55-3.33-.71 3.4-1.88 7.9 1.77.21-.07.68h-4.53l.07-.68 1.46-.21L289 77l-1.62-.19.11-.75h4.07l1.35 8.56.23 1.79.77-1.76q.49-1.22 1.94-4.35ZM308 88.64a4.35 4.35 0 0 1-2.23.59 3.38 3.38 0 0 1-2-.53 3.26 3.26 0 0 1-1.15-1.4 4.87 4.87 0 0 1-.36-1.87 7.34 7.34 0 0 1 .67-3.14 6 6 0 0 1 1.91-2.29 4.32 4.32 0 0 1 2.62-.87 2.63 2.63 0 0 1 1.88.59 2.06 2.06 0 0 1 .63 1.56 2.65 2.65 0 0 1-1 2.11 6.62 6.62 0 0 1-2.37 1.28 10 10 0 0 1-2.46.46 3.89 3.89 0 0 0 .42 2.13 1.69 1.69 0 0 0 1.6.9 3.61 3.61 0 0 0 1.54-.36 4.3 4.3 0 0 0 1.39-1l.38.65a4.52 4.52 0 0 1-1.47 1.19Zm-2.41-8a4.68 4.68 0 0 0-1 1.64 7.5 7.5 0 0 0-.44 1.94 6.11 6.11 0 0 0 1.86-.38 4.61 4.61 0 0 0 1.6-1 2 2 0 0 0 .65-1.47 1.54 1.54 0 0 0-.32-1 1.15 1.15 0 0 0-.89-.36 2 2 0 0 0-1.45.64ZM318.78 87.71c0 .29.09.44.26.44a1.42 1.42 0 0 0 .81-.44l.24.44a3.31 3.31 0 0 1-.76.71 1.9 1.9 0 0 1-1.15.36c-.69 0-1-.38-1-1.13v-.38a4.57 4.57 0 0 1-1.23 1.07 3.18 3.18 0 0 1-1.65.44 2.46 2.46 0 0 1-2.14-1 4.54 4.54 0 0 1-.72-2.68 7.24 7.24 0 0 1 .67-3 6.3 6.3 0 0 1 1.89-2.48 4.67 4.67 0 0 1 3-1 4.42 4.42 0 0 1 1.31.21l.48-3.16-1.16-.3.14-.61 2.47-.32.39.23-1.83 12.4a.59.59 0 0 0-.02.2Zm-2-7.7a2.62 2.62 0 0 0-2 .85 5.14 5.14 0 0 0-1.21 2.1 8 8 0 0 0-.4 2.47 3.83 3.83 0 0 0 .42 2 1.27 1.27 0 0 0 1.16.7 2.39 2.39 0 0 0 1.4-.46 3.7 3.7 0 0 0 1-1l.95-6.19a2.2 2.2 0 0 0-1.32-.48ZM324.44 87.71a.56.56 0 0 0 .08.32.25.25 0 0 0 .21.12.79.79 0 0 0 .39-.13 3.18 3.18 0 0 0 .5-.4l.23.42a3.35 3.35 0 0 1-.78.77 2 2 0 0 1-1.24.41 1.34 1.34 0 0 1-.89-.28.92.92 0 0 1-.25-.81c0-.29.18-1.43.46-3.41.16-1.06.36-2.47.59-4.22l-1.08-.41.1-.59 2.49-.41.39.2-1.18 8.24Zm-.07-10.81a1 1 0 0 1-.28-.68 1.29 1.29 0 0 1 .35-.9 1.1 1.1 0 0 1 .81-.37.92.92 0 0 1 1 .93 1.29 1.29 0 0 1-.34.92 1.11 1.11 0 0 1-.87.38.84.84 0 0 1-.67-.28ZM332.76 80.18a2.22 2.22 0 0 0-1.53.62 4.15 4.15 0 0 0-1.06 1.74 8 8 0 0 0-.37 2.55 4.09 4.09 0 0 0 .49 2.24 1.59 1.59 0 0 0 1.42.75 2.71 2.71 0 0 0 1.29-.28 5.56 5.56 0 0 0 1.15-.81l.35.65a4.84 4.84 0 0 1-1.3 1.08 3.94 3.94 0 0 1-2 .5 2.78 2.78 0 0 1-2.31-1 4.49 4.49 0 0 1-.83-2.9 7.35 7.35 0 0 1 .6-2.87 6.1 6.1 0 0 1 1.72-2.45 4.26 4.26 0 0 1 2.77-.94 5.66 5.66 0 0 1 1.06.1 3.31 3.31 0 0 1 .92.3l-.47 1.7-.3-.1a2.88 2.88 0 0 0-1.6-.88ZM338.88 87.71a.56.56 0 0 0 .12.29.23.23 0 0 0 .2.12.82.82 0 0 0 .4-.13 3.18 3.18 0 0 0 .5-.4l.23.42a3.56 3.56 0 0 1-.78.77 2 2 0 0 1-1.24.41 1.32 1.32 0 0 1-.89-.28.9.9 0 0 1-.25-.81c0-.29.18-1.43.46-3.41.16-1.06.36-2.47.59-4.22l-1.09-.41.11-.59 2.49-.41.39.2-1.18 8.24Zm-.08-10.81a1 1 0 0 1-.27-.68 1.29 1.29 0 0 1 .35-.9 1.07 1.07 0 0 1 .81-.37.92.92 0 0 1 1 .93 1.34 1.34 0 0 1-.34.92 1.11 1.11 0 0 1-.88.38.87.87 0 0 1-.67-.28ZM347.19 79.72a3.54 3.54 0 0 1 2-.64 1.89 1.89 0 0 1 1.51.59 2.93 2.93 0 0 1 .53 2 16.77 16.77 0 0 1-.39 2.68l-.07.41-.14.84a12.6 12.6 0 0 0-.28 2.12c0 .32.08.48.23.48a1.38 1.38 0 0 0 .82-.44l.21.45a1.91 1.91 0 0 1-.36.41 3.11 3.11 0 0 1-.7.44 1.93 1.93 0 0 1-.9.21 1 1 0 0 1-1.11-1.07 14.24 14.24 0 0 1 .32-2.14l.16-.85.07-.42c.11-.63.21-1.18.28-1.66a9 9 0 0 0 .1-1.32 1.87 1.87 0 0 0-.23-1.11 1 1 0 0 0-.84-.31 2.66 2.66 0 0 0-1.57.69 6.48 6.48 0 0 0-1.48 1.68l-.89 6.24h-1.66l1.12-8.49-.86-.42.14-.67 2.14-.38.37.19-.23 2.1a6.52 6.52 0 0 1 1.71-1.61ZM359 88.64a4.35 4.35 0 0 1-2.23.59 3.34 3.34 0 0 1-1.95-.53 3.19 3.19 0 0 1-1.15-1.4 4.69 4.69 0 0 1-.37-1.87 7.34 7.34 0 0 1 .67-3.14 6 6 0 0 1 1.9-2.29 4.35 4.35 0 0 1 2.63-.87 2.61 2.61 0 0 1 1.87.59 2 2 0 0 1 .64 1.56 2.68 2.68 0 0 1-1 2.11 6.75 6.75 0 0 1-2.38 1.28 9.81 9.81 0 0 1-2.46.46 4.08 4.08 0 0 0 .42 2.13 1.69 1.69 0 0 0 1.6.9 3.65 3.65 0 0 0 1.55-.36 4.37 4.37 0 0 0 1.38-1l.39.65a4.57 4.57 0 0 1-1.51 1.19Zm-2.4-8a4.54 4.54 0 0 0-1 1.64 6.76 6.76 0 0 0-.44 1.94 6 6 0 0 0 1.85-.38 4.52 4.52 0 0 0 1.6-1 2 2 0 0 0 .65-1.47 1.49 1.49 0 0 0-.32-1 1.14 1.14 0 0 0-.89-.36 2 2 0 0 0-1.41.64Z" class="cls-2" transform="translate(-24.97 -24.05)"/> </svg> </a></div> <div class="global-nav__controls"><button class="controls__search" style="display: none;"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""><path d="M13.8 21.6a7.8 7.8 0 110-15.6 7.8 7.8 0 010 15.6zm0-2a5.8 5.8 0 100-11.6 5.8 5.8 0 000 11.6z"></path><path d="M17.899 19.325l1.414-1.414 4.322 4.322-1.414 1.414z"></path></svg></button> <button class="controls__close" onclick="toggleSearch()"><span class="menus__close-label"> Close </span> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""><path fill-rule="evenodd" d="M20.728 8l1.818 1.818-5.455 5.455 5.455 5.455-1.818 1.818-5.455-5.455-5.455 5.455L8 20.728l5.455-5.455L8 9.818 9.818 8l5.455 5.455z"></path></svg></button></div></div> <div class="mega-menu__content"> <div class="search-form sf-top" > <div class="search-form__container"> <label for="inputsearch"> Search for Publications Only </label> <form id="searchFormNAP" action="/search" enctype="application/x-www-form-urlencoded"> <input id="inputsearch" name="term" type="text" placeholder="Type a title, topic, ISBN, or DOI and hit enter"> <input type="hidden" name="v:project" value="uweb_proj_ext"> <button class="search-form__submit"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""> <path d="M13.8 21.6a7.8 7.8 0 110-15.6 7.8 7.8 0 010 15.6zm0-2a5.8 5.8 0 100-11.6 5.8 5.8 0 000 11.6z"></path> <path d="M17.899 19.325l1.414-1.414 4.322 4.322-1.414 1.414z"></path> </svg> </button> </form> </div> </div> <div class="search-form"> <div class="search-form__container"> <label for="globalSearch"> Search All</label> <form id="searchForm" action="https://sparck.nationalacademies.org/vivisimo/cgi-bin/query-meta" enctype="application/x-www-form-urlencoded"> <input id="globalSearch" name="query" type="text" placeholder="Type anything and hit enter"> <input type="hidden" name="v:project" value="uweb_proj_ext"> <button class="search-form__submit"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""> <path d="M13.8 21.6a7.8 7.8 0 110-15.6 7.8 7.8 0 010 15.6zm0-2a5.8 5.8 0 100-11.6 5.8 5.8 0 000 11.6z"></path> <path d="M17.899 19.325l1.414-1.414 4.322 4.322-1.414 1.414z"></path> </svg> </button> </form> </div> </div> </div> </div> <div tabindex="0" aria-hidden="true"></div> </div>   <div aria-hidden="true" class="mega-menu" id="mobile-menu" style="display: none;"> <div data-lock=""> <div class="mega-menu__header"> <div class="global-nav__logo" style="padding-left: 10px;"> <a class="navbar-brand js-scroll-trigger" href="https://www.nationalacademies.org/"> <svg xmlns="http://www.w3.org/2000/svg" id="nasemLogo" data-name="nasemLogo" viewBox="0 0 360 66.64"> <defs/> <path d="m4.26 8.63 19.56 20.49V1.72h-3.47v18.93L.8.16v27.32h3.46V8.63zM32.55 27.48h3.83l8.15-19.2 7.93 18.99.09.21h3.82L44.62 0 32.55 27.48zM175.05 27.48h3.83l8.16-19.2 7.93 18.99.08.21h3.83L187.12 0l-12.07 27.48zM68.23 27.48h3.47V5.03h7.72V1.72H60.51v3.31h7.72v22.45zM90.08 1.72h3.46v25.76h-3.46z" class="cls-2"/> <path d="M157.14 38.67A13.39 13.39 0 1 0 143.75 52a13.21 13.21 0 0 0 13.39-13.33Zm-3.54 0a9.85 9.85 0 1 1-9.85-10 9.93 9.93 0 0 1 9.85 10Z" class="cls-2" transform="translate(-24.97 -24.05)"/> <path d="m146.56 8.63 19.56 20.49V1.72h-3.47v18.93L143.1.16v27.32h3.46V8.63zM210.95 1.72h-3.46v25.76h13.8v-3.31h-10.34V1.72z" class="cls-2"/> <path d="M67.41 63A13.13 13.13 0 0 0 54 76.37a13 13 0 0 0 13.26 13.24A13.48 13.48 0 0 0 75 87.1l.14-.1v-4.46l-.58.58a10.91 10.91 0 0 1-2.81 2 10 10 0 0 1-4.51 1.13c-6.74 0-9.77-5.78-9.77-9.89a9.82 9.82 0 0 1 9.74-10.11 10.44 10.44 0 0 1 4.18.94 12 12 0 0 1 3.17 2.27l.58.58v-4.41l-.13-.1a12.1 12.1 0 0 0-7.6-2.53ZM130 66.4a14 14 0 0 0-9.47-3h-5.45v25.75h5.42c4.25 0 6.88-.83 9.39-3a12.32 12.32 0 0 0 4.52-9.89A12.54 12.54 0 0 0 130 66.4Zm-2.39 17.26a10.37 10.37 0 0 1-7 2.18h-2.11V66.7h2.11c6.21 0 10.22 3.77 10.22 9.59a9.23 9.23 0 0 1-3.25 7.37Z" class="cls-2" transform="translate(-24.97 -24.05)"/> <path d="M119.94 65.11h15.33V61.8h-11.86v-9.07h10.38v-3.31h-10.38v-6.76h11.86v-3.32h-15.33v25.77zM201.26 65.11h15.33V61.8h-11.86v-9.07h10.37v-3.31h-10.37v-6.76h11.86v-3.32h-15.33v25.77zM158.66 58.65l-9.79-21.53-4.42 27.99h3.56l2.36-16.59 8.25 18.12 8.35-18.12 2.25 16.59h3.56l-4.14-28.03-9.98 21.57zM184.29 39.34h3.46V65.1h-3.46z" class="cls-2"/> <path d="M263.7 76.76a12.7 12.7 0 0 0-4-2.44l-2.42-1a8 8 0 0 1-2.53-1.51 2.32 2.32 0 0 1-.83-1.94c0-2.11 1.56-3.53 3.87-3.53a4.18 4.18 0 0 1 2.61.79 5.51 5.51 0 0 1 1.37 1.77l.17.34 2.8-1.85-.14-.27a7.79 7.79 0 0 0-2.56-2.91 7.16 7.16 0 0 0-4.18-1.21c-4.34 0-7.37 2.8-7.37 6.8a5.53 5.53 0 0 0 1.83 4.35 10.74 10.74 0 0 0 3.24 2l2.44 1.17a10.81 10.81 0 0 1 2.94 1.68 3.39 3.39 0 0 1 1.13 2.68A4.8 4.8 0 0 1 254 85a5.6 5.6 0 0 1-1.42-3l-.05-.39-3.4.94.07.32a9.51 9.51 0 0 0 2.43 4.61 7.73 7.73 0 0 0 5.69 2.13 7.9 7.9 0 0 0 8.28-8 6.38 6.38 0 0 0-1.9-4.85Z" class="cls-2" transform="translate(-24.97 -24.05)"/> <path d="M0 65.11h3.83l8.16-19.21 7.92 19 .09.21h3.83L12.07 37.63 0 65.11zM57.37 65.11h3.83l8.15-19.21 7.93 19 .08.21h3.83L69.44 37.63 57.37 65.11z" class="cls-2"/> <path d="M292 26.45a3.91 3.91 0 0 0-1.07-.14 2.94 2.94 0 0 0-1.74.52 1.71 1.71 0 0 0-.72 1.47 2.36 2.36 0 0 0 .63 1.7 9.45 9.45 0 0 0 1.9 1.38 15.52 15.52 0 0 1 1.45 1 4.28 4.28 0 0 1 .94 1.12 2.87 2.87 0 0 1 .38 1.51 3.57 3.57 0 0 1-.57 2 3.79 3.79 0 0 1-1.6 1.34 5.79 5.79 0 0 1-2.39.47 9.63 9.63 0 0 1-2.22-.25 4.15 4.15 0 0 1-1.41-.52l.39-2.49H287l.11 1.84a2.93 2.93 0 0 0 .92.39 5 5 0 0 0 1.16.14 3.39 3.39 0 0 0 2-.6 1.94 1.94 0 0 0 .83-1.68 2.25 2.25 0 0 0-.56-1.54 7.66 7.66 0 0 0-1.7-1.32c-.6-.39-1.1-.75-1.51-1.07a4.43 4.43 0 0 1-1-1.2 2.94 2.94 0 0 1-.43-1.59 3.08 3.08 0 0 1 .57-1.85 3.58 3.58 0 0 1 1.55-1.23 5.17 5.17 0 0 1 2.13-.43 7.84 7.84 0 0 1 2 .21 4 4 0 0 1 1.25.51l-.4 2.31h-.95l-.14-1.68a2.39 2.39 0 0 0-.83-.32ZM300.27 29.79a2.2 2.2 0 0 0-1.53.62 4.15 4.15 0 0 0-1.06 1.74 8 8 0 0 0-.38 2.55 4.11 4.11 0 0 0 .5 2.24 1.6 1.6 0 0 0 1.42.74 2.71 2.71 0 0 0 1.25-.27 5.56 5.56 0 0 0 1.15-.81l.35.64a4.42 4.42 0 0 1-1.31 1.08 3.78 3.78 0 0 1-2 .5 2.76 2.76 0 0 1-2.31-1 4.51 4.51 0 0 1-.83-2.9 7.35 7.35 0 0 1 .6-2.87 6 6 0 0 1 1.77-2.38 4.27 4.27 0 0 1 2.77-.95 5.7 5.7 0 0 1 1.06.11 3.31 3.31 0 0 1 .92.3l-.48 1.7-.29-.11a2.91 2.91 0 0 0-1.6-.93ZM306.13 37.31a.54.54 0 0 0 .08.33.22.22 0 0 0 .2.11.74.74 0 0 0 .39-.12 2.88 2.88 0 0 0 .5-.4l.23.42a3.34 3.34 0 0 1-.78.77 2 2 0 0 1-1.23.4 1.3 1.3 0 0 1-.89-.27.9.9 0 0 1-.26-.81c0-.3.18-1.43.46-3.41q.24-1.59.6-4.23l-1.09-.4.11-.6 2.49-.4.38.19-1.17 8.25Zm-.08-10.8a1 1 0 0 1-.27-.69 1.24 1.24 0 0 1 .34-.89 1.07 1.07 0 0 1 .82-.37.94.94 0 0 1 .7.27.93.93 0 0 1 .26.66 1.35 1.35 0 0 1-.33.92 1.14 1.14 0 0 1-.88.38.9.9 0 0 1-.64-.28ZM315.15 38.24a4.26 4.26 0 0 1-2.23.6 3.45 3.45 0 0 1-2-.53 3.23 3.23 0 0 1-1.15-1.41 4.83 4.83 0 0 1-.36-1.87 7.38 7.38 0 0 1 .67-3.14 5.91 5.91 0 0 1 1.92-2.33 4.33 4.33 0 0 1 2.62-.88 2.64 2.64 0 0 1 1.88.6 2.06 2.06 0 0 1 .63 1.56 2.66 2.66 0 0 1-1 2.11 6.62 6.62 0 0 1-2.37 1.28 9.48 9.48 0 0 1-2.46.45 3.85 3.85 0 0 0 .42 2.13 1.68 1.68 0 0 0 1.6.91 3.61 3.61 0 0 0 1.54-.36 4.41 4.41 0 0 0 1.39-1l.38.65a4.39 4.39 0 0 1-1.48 1.23Zm-2.41-8a4.82 4.82 0 0 0-1 1.65 7.41 7.41 0 0 0-.44 1.94 5.85 5.85 0 0 0 1.86-.39 4.34 4.34 0 0 0 1.6-1 2 2 0 0 0 .65-1.46 1.5 1.5 0 0 0-.33-1.05 1.14 1.14 0 0 0-.88-.35 2 2 0 0 0-1.46.67ZM323.42 29.32a3.62 3.62 0 0 1 2-.64 1.89 1.89 0 0 1 1.51.6 2.93 2.93 0 0 1 .53 1.95 16.77 16.77 0 0 1-.39 2.68l-.07.4-.14.85a12.6 12.6 0 0 0-.28 2.12c0 .32.08.47.23.47a1.35 1.35 0 0 0 .82-.44l.21.46a1.7 1.7 0 0 1-.36.4 2.81 2.81 0 0 1-.7.45 1.92 1.92 0 0 1-.9.2c-.74 0-1.11-.35-1.11-1.07a14.6 14.6 0 0 1 .32-2.14l.16-.84.07-.42c.11-.63.21-1.18.28-1.66a9 9 0 0 0 .1-1.32 2 2 0 0 0-.23-1.12 1 1 0 0 0-.84-.3 2.63 2.63 0 0 0-1.57.69 6.6 6.6 0 0 0-1.48 1.67l-.86 6.34H319l1.13-8.49-.86-.42.14-.67 2.14-.39.37.2-.23 2.1a6.56 6.56 0 0 1 1.73-1.66ZM334.3 29.79a2.22 2.22 0 0 0-1.53.62 4.14 4.14 0 0 0-1 1.74 7.68 7.68 0 0 0-.38 2.55 4.11 4.11 0 0 0 .49 2.24 1.61 1.61 0 0 0 1.42.74 2.78 2.78 0 0 0 1.26-.27 5.52 5.52 0 0 0 1.14-.81l.36.64a4.56 4.56 0 0 1-1.31 1.08 3.85 3.85 0 0 1-2 .5 2.79 2.79 0 0 1-2.31-1 4.57 4.57 0 0 1-.83-2.9 7.19 7.19 0 0 1 .61-2.87 5.94 5.94 0 0 1 1.77-2.38 4.24 4.24 0 0 1 2.76-.95 5.7 5.7 0 0 1 1.06.11 3.2 3.2 0 0 1 .92.3l-.47 1.7-.3-.11a2.91 2.91 0 0 0-1.66-.93ZM343.32 38.24a4.26 4.26 0 0 1-2.23.6 3.42 3.42 0 0 1-1.95-.53A3.17 3.17 0 0 1 338 36.9a4.66 4.66 0 0 1-.37-1.87 7.53 7.53 0 0 1 .67-3.14 6 6 0 0 1 1.86-2.33 4.36 4.36 0 0 1 2.63-.88 2.65 2.65 0 0 1 1.88.6 2.06 2.06 0 0 1 .63 1.56 2.69 2.69 0 0 1-1 2.11 6.66 6.66 0 0 1-2.38 1.28 9.33 9.33 0 0 1-2.46.45 4 4 0 0 0 .42 2.13 1.68 1.68 0 0 0 1.6.91 3.65 3.65 0 0 0 1.55-.36 4.37 4.37 0 0 0 1.38-1l.39.65a4.43 4.43 0 0 1-1.48 1.23Zm-2.4-8a4.67 4.67 0 0 0-1 1.65 7 7 0 0 0-.44 1.94 5.79 5.79 0 0 0 1.85-.39 4.25 4.25 0 0 0 1.6-1 2 2 0 0 0 .65-1.46 1.5 1.5 0 0 0-.32-1.05 1.17 1.17 0 0 0-.89-.35 1.93 1.93 0 0 0-1.45.67ZM351.91 29.91a3.08 3.08 0 0 0-1.24-.24 2.15 2.15 0 0 0-1.3.35 1.18 1.18 0 0 0-.49 1 1.54 1.54 0 0 0 .4 1.06 6.17 6.17 0 0 0 1.13 1c.42.33.76.61 1 .85a3.35 3.35 0 0 1 .67.87 2.38 2.38 0 0 1 .3 1.2 2.4 2.4 0 0 1-1 2.07 4.21 4.21 0 0 1-2.53.73 7.55 7.55 0 0 1-1.57-.17 2.73 2.73 0 0 1-1-.39l.29-1.21a3.77 3.77 0 0 0 1 .5 3.94 3.94 0 0 0 1.36.24 2.47 2.47 0 0 0 1.31-.33 1.14 1.14 0 0 0 .55-1.06 1.58 1.58 0 0 0-.43-1.09 8 8 0 0 0-1.26-1 3.53 3.53 0 0 1-1.81-2.86 2.43 2.43 0 0 1 .46-1.45 2.92 2.92 0 0 1 1.25-1 4.48 4.48 0 0 1 1.75-.34 7.2 7.2 0 0 1 1.29.12 4.56 4.56 0 0 1 .92.22l-.3 1.33a1.83 1.83 0 0 0-.75-.4ZM287 50.81h8.32l-.12 2.79h-1l-.28-1.84-4-.14-.67 5 4.07-.14-.12 1.32-4-.14-.81 5.34 4.95-.21 1-2.12 1 .19-.71 3h-9.33l.07-.68 1.32-.21 1.4-11.19-1.19-.2ZM301.65 54.52a3.52 3.52 0 0 1 2-.64 1.89 1.89 0 0 1 1.51.6 2.89 2.89 0 0 1 .53 1.94 16.85 16.85 0 0 1-.39 2.69l-.07.4-.14.84a12.68 12.68 0 0 0-.28 2.13c0 .31.07.47.23.47a1.41 1.41 0 0 0 .82-.44l.14.49a1.76 1.76 0 0 1-.37.4 3.17 3.17 0 0 1-.69.45 2 2 0 0 1-.9.2A1 1 0 0 1 303 63a14.6 14.6 0 0 1 .32-2.14l.16-.84.07-.42c.11-.64.21-1.19.28-1.66a9.18 9.18 0 0 0 .1-1.33 2 2 0 0 0-.23-1.11 1 1 0 0 0-.84-.31 2.59 2.59 0 0 0-1.57.7 6.6 6.6 0 0 0-1.48 1.67l-.86 6.33h-1.67l1.13-8.49-.86-.42.14-.66 2.14-.39.37.19-.23 2.11a6.56 6.56 0 0 1 1.68-1.71ZM313.74 66.64a4.23 4.23 0 0 1-1.77 1.2 5.86 5.86 0 0 1-2 .37 7.37 7.37 0 0 1-1.13-.09 4.89 4.89 0 0 1-.87-.22l.37-1.42a6.44 6.44 0 0 0 1 .39 4.29 4.29 0 0 0 1.22.18 2.62 2.62 0 0 0 1.66-.43 2.58 2.58 0 0 0 .71-1.62l.33-2.33a4.25 4.25 0 0 1-1.18 1 3 3 0 0 1-1.52.39 2.52 2.52 0 0 1-2.17-1 4.5 4.5 0 0 1-.72-2.68 7.33 7.33 0 0 1 .66-3 6.45 6.45 0 0 1 1.95-2.49 4.73 4.73 0 0 1 3-1 5.1 5.1 0 0 1 1 .11 5.19 5.19 0 0 1 .91.28l1.09-.39-1.58 10.63a3.73 3.73 0 0 1-.96 2.12ZM313 54.81a2.66 2.66 0 0 0-2 .85 5.43 5.43 0 0 0-1.22 2.11 7.91 7.91 0 0 0-.4 2.46 3.81 3.81 0 0 0 .42 2 1.31 1.31 0 0 0 1.17.71 2.42 2.42 0 0 0 1.37-.44 3.83 3.83 0 0 0 1-1l.93-6.28a2.13 2.13 0 0 0-1.27-.41ZM320.16 62.51a.56.56 0 0 0 .08.32.24.24 0 0 0 .2.12.8.8 0 0 0 .4-.12 4.16 4.16 0 0 0 .5-.41l.23.42a3.57 3.57 0 0 1-.78.78 2 2 0 0 1-1.24.4 1.32 1.32 0 0 1-.89-.27.92.92 0 0 1-.25-.82c0-.29.18-1.43.46-3.4.16-1.07.36-2.48.59-4.23l-1.09-.4.11-.6 2.49-.4.39.19-1.18 8.25Zm-.08-10.81a.93.93 0 0 1-.27-.68 1.25 1.25 0 0 1 .35-.89 1 1 0 0 1 .81-.37.93.93 0 0 1 .7.27.9.9 0 0 1 .27.66 1.36 1.36 0 0 1-.34.92 1.11 1.11 0 0 1-.88.37.87.87 0 0 1-.64-.28ZM328.56 54.52a3.54 3.54 0 0 1 2-.64 1.89 1.89 0 0 1 1.51.6 2.89 2.89 0 0 1 .53 1.94 16.85 16.85 0 0 1-.39 2.69l-.07.4-.14.84a12.68 12.68 0 0 0-.28 2.13c0 .31.08.47.23.47a1.41 1.41 0 0 0 .82-.44l.23.49a1.76 1.76 0 0 1-.37.4 3.17 3.17 0 0 1-.69.45 2 2 0 0 1-.9.2 1 1 0 0 1-1.16-1.05 14.6 14.6 0 0 1 .32-2.14l.16-.84.07-.42c.11-.64.21-1.19.28-1.66a9.18 9.18 0 0 0 .1-1.33 2 2 0 0 0-.23-1.11 1 1 0 0 0-.84-.31 2.59 2.59 0 0 0-1.57.7 6.6 6.6 0 0 0-1.48 1.67l-.86 6.33h-1.67l1.13-8.49-.86-.42.14-.66 2.14-.39.37.19-.23 2.11a6.56 6.56 0 0 1 1.71-1.71ZM340.41 63.44a4.26 4.26 0 0 1-2.23.6 3.35 3.35 0 0 1-1.95-.54 3 3 0 0 1-1.15-1.4 4.66 4.66 0 0 1-.37-1.87 7.38 7.38 0 0 1 .67-3.14 5.91 5.91 0 0 1 1.86-2.33 4.29 4.29 0 0 1 2.62-.88 2.62 2.62 0 0 1 1.88.6 2 2 0 0 1 .63 1.56 2.63 2.63 0 0 1-1 2.1 6.47 6.47 0 0 1-2.37 1.28 9.38 9.38 0 0 1-2.46.46A4 4 0 0 0 337 62a1.69 1.69 0 0 0 1.6.9 3.61 3.61 0 0 0 1.54-.36 4.27 4.27 0 0 0 1.39-1l.39.65a4.68 4.68 0 0 1-1.51 1.25Zm-2.4-8a4.53 4.53 0 0 0-1 1.65 6.69 6.69 0 0 0-.44 1.94 6.13 6.13 0 0 0 1.85-.39 4.25 4.25 0 0 0 1.6-1 2 2 0 0 0 .65-1.46 1.55 1.55 0 0 0-.32-1.05 1.14 1.14 0 0 0-.89-.36 2 2 0 0 0-1.46.68ZM349.39 63.44a4.26 4.26 0 0 1-2.23.6 3.35 3.35 0 0 1-2-.54 3.09 3.09 0 0 1-1.15-1.4 4.66 4.66 0 0 1-.37-1.87 7.38 7.38 0 0 1 .68-3.14 5.91 5.91 0 0 1 1.86-2.33 4.25 4.25 0 0 1 2.62-.88 2.65 2.65 0 0 1 1.88.6 2 2 0 0 1 .63 1.56 2.66 2.66 0 0 1-1 2.1 6.51 6.51 0 0 1-2.31 1.28 9.38 9.38 0 0 1-2.46.46 3.94 3.94 0 0 0 .43 2.13 1.66 1.66 0 0 0 1.59.9 3.65 3.65 0 0 0 1.55-.36 4.34 4.34 0 0 0 1.38-1l.39.65a4.68 4.68 0 0 1-1.49 1.24Zm-2.4-8a4.67 4.67 0 0 0-1 1.65 7 7 0 0 0-.44 1.94 6.07 6.07 0 0 0 1.85-.39 4.38 4.38 0 0 0 1.61-1 2 2 0 0 0 .65-1.46 1.5 1.5 0 0 0-.33-1.05 1.14 1.14 0 0 0-.89-.36 2 2 0 0 0-1.44.68ZM356.34 55.24a4.21 4.21 0 0 1 1.13-1 2.81 2.81 0 0 1 1.4-.38.93.93 0 0 1 .56.12l-.37 1.86a1.64 1.64 0 0 0-.86-.18 2.68 2.68 0 0 0-1.48.5 3.31 3.31 0 0 0-1.14 1.4l-.8 6.24h-1.69l1.11-8.45-.88-.44.12-.65 2.07-.4.35.21-.12 1.56-.08.7a3.9 3.9 0 0 1 .68-1.09ZM362.32 62.51a.56.56 0 0 0 .08.32.23.23 0 0 0 .2.12.8.8 0 0 0 .4-.12 4.16 4.16 0 0 0 .5-.41l.22.42a3.18 3.18 0 0 1-.78.78 2 2 0 0 1-1.23.4 1.3 1.3 0 0 1-.89-.27.92.92 0 0 1-.25-.82c0-.29.17-1.43.45-3.4.17-1.07.36-2.48.6-4.23l-1.09-.4.11-.6 2.49-.4.38.19-1.17 8.25Zm-.08-10.81a.93.93 0 0 1-.24-.7 1.24 1.24 0 0 1 .34-.89 1.07 1.07 0 0 1 .82-.37.94.94 0 0 1 .7.27.93.93 0 0 1 .26.66 1.35 1.35 0 0 1-.33.92 1.12 1.12 0 0 1-.88.37.86.86 0 0 1-.67-.26ZM370.36 54.52a3.55 3.55 0 0 1 2-.64 1.91 1.91 0 0 1 1.51.6 2.89 2.89 0 0 1 .52 1.94 17.7 17.7 0 0 1-.38 2.69l-.07.4-.14.84a12.68 12.68 0 0 0-.28 2.13c0 .31.07.47.22.47a1.4 1.4 0 0 0 .83-.44l.21.46a1.76 1.76 0 0 1-.37.4 3.74 3.74 0 0 1-.69.45 2.13 2.13 0 0 1-.91.2 1 1 0 0 1-1.1-1.07 14.1 14.1 0 0 1 .31-2.14l.16-.84.07-.42c.12-.64.21-1.19.28-1.66a9.27 9.27 0 0 0 .11-1.33 1.88 1.88 0 0 0-.24-1.11 1 1 0 0 0-.83-.31 2.59 2.59 0 0 0-1.57.7 6.6 6.6 0 0 0-1.48 1.67l-.86 6.33H366l1.12-8.49-.86-.42.14-.66 2.14-.39.37.19-.23 2.11a6.72 6.72 0 0 1 1.68-1.66ZM382.46 66.64a4.23 4.23 0 0 1-1.77 1.2 5.87 5.87 0 0 1-2 .37 7.34 7.34 0 0 1-1.12-.09 4.82 4.82 0 0 1-.88-.22l.37-1.42a6.58 6.58 0 0 0 1 .39 4.24 4.24 0 0 0 1.22.18 2.57 2.57 0 0 0 1.65-.43 2.53 2.53 0 0 0 .72-1.62l.33-2.33a4.25 4.25 0 0 1-1.18 1 3.07 3.07 0 0 1-1.52.39 2.52 2.52 0 0 1-2.17-1 4.5 4.5 0 0 1-.73-2.68 7.35 7.35 0 0 1 .67-3 6.27 6.27 0 0 1 1.95-2.51 4.71 4.71 0 0 1 3-1 5.1 5.1 0 0 1 1 .11 5.47 5.47 0 0 1 .91.28l1.09-.39-1.58 10.63a3.86 3.86 0 0 1-.96 2.14Zm-.7-11.83a2.62 2.62 0 0 0-2 .85 5.31 5.31 0 0 0-1.22 2.11 7.93 7.93 0 0 0-.41 2.46 3.7 3.7 0 0 0 .43 2 1.31 1.31 0 0 0 1.17.71 2.42 2.42 0 0 0 1.37-.44 3.79 3.79 0 0 0 1-1l.93-6.28a2.08 2.08 0 0 0-1.27-.41ZM295.85 80.3q1.44-3.12 1.89-4.29h3.76l-.07.75-1.56.19-.34 11.2 1.49.21-.02.64h-4.82l.07-.68 1.6-.21.4-7.76.23-3.56L297.1 80l-4.1 9.08-.94.12-1.44-9-.55-3.33-.71 3.4-1.88 7.9 1.77.21-.07.68h-4.53l.07-.68 1.46-.21L289 77l-1.62-.19.11-.75h4.07l1.35 8.56.23 1.79.77-1.76q.49-1.22 1.94-4.35ZM308 88.64a4.35 4.35 0 0 1-2.23.59 3.38 3.38 0 0 1-2-.53 3.26 3.26 0 0 1-1.15-1.4 4.87 4.87 0 0 1-.36-1.87 7.34 7.34 0 0 1 .67-3.14 6 6 0 0 1 1.91-2.29 4.32 4.32 0 0 1 2.62-.87 2.63 2.63 0 0 1 1.88.59 2.06 2.06 0 0 1 .63 1.56 2.65 2.65 0 0 1-1 2.11 6.62 6.62 0 0 1-2.37 1.28 10 10 0 0 1-2.46.46 3.89 3.89 0 0 0 .42 2.13 1.69 1.69 0 0 0 1.6.9 3.61 3.61 0 0 0 1.54-.36 4.3 4.3 0 0 0 1.39-1l.38.65a4.52 4.52 0 0 1-1.47 1.19Zm-2.41-8a4.68 4.68 0 0 0-1 1.64 7.5 7.5 0 0 0-.44 1.94 6.11 6.11 0 0 0 1.86-.38 4.61 4.61 0 0 0 1.6-1 2 2 0 0 0 .65-1.47 1.54 1.54 0 0 0-.32-1 1.15 1.15 0 0 0-.89-.36 2 2 0 0 0-1.45.64ZM318.78 87.71c0 .29.09.44.26.44a1.42 1.42 0 0 0 .81-.44l.24.44a3.31 3.31 0 0 1-.76.71 1.9 1.9 0 0 1-1.15.36c-.69 0-1-.38-1-1.13v-.38a4.57 4.57 0 0 1-1.23 1.07 3.18 3.18 0 0 1-1.65.44 2.46 2.46 0 0 1-2.14-1 4.54 4.54 0 0 1-.72-2.68 7.24 7.24 0 0 1 .67-3 6.3 6.3 0 0 1 1.89-2.48 4.67 4.67 0 0 1 3-1 4.42 4.42 0 0 1 1.31.21l.48-3.16-1.16-.3.14-.61 2.47-.32.39.23-1.83 12.4a.59.59 0 0 0-.02.2Zm-2-7.7a2.62 2.62 0 0 0-2 .85 5.14 5.14 0 0 0-1.21 2.1 8 8 0 0 0-.4 2.47 3.83 3.83 0 0 0 .42 2 1.27 1.27 0 0 0 1.16.7 2.39 2.39 0 0 0 1.4-.46 3.7 3.7 0 0 0 1-1l.95-6.19a2.2 2.2 0 0 0-1.32-.48ZM324.44 87.71a.56.56 0 0 0 .08.32.25.25 0 0 0 .21.12.79.79 0 0 0 .39-.13 3.18 3.18 0 0 0 .5-.4l.23.42a3.35 3.35 0 0 1-.78.77 2 2 0 0 1-1.24.41 1.34 1.34 0 0 1-.89-.28.92.92 0 0 1-.25-.81c0-.29.18-1.43.46-3.41.16-1.06.36-2.47.59-4.22l-1.08-.41.1-.59 2.49-.41.39.2-1.18 8.24Zm-.07-10.81a1 1 0 0 1-.28-.68 1.29 1.29 0 0 1 .35-.9 1.1 1.1 0 0 1 .81-.37.92.92 0 0 1 1 .93 1.29 1.29 0 0 1-.34.92 1.11 1.11 0 0 1-.87.38.84.84 0 0 1-.67-.28ZM332.76 80.18a2.22 2.22 0 0 0-1.53.62 4.15 4.15 0 0 0-1.06 1.74 8 8 0 0 0-.37 2.55 4.09 4.09 0 0 0 .49 2.24 1.59 1.59 0 0 0 1.42.75 2.71 2.71 0 0 0 1.29-.28 5.56 5.56 0 0 0 1.15-.81l.35.65a4.84 4.84 0 0 1-1.3 1.08 3.94 3.94 0 0 1-2 .5 2.78 2.78 0 0 1-2.31-1 4.49 4.49 0 0 1-.83-2.9 7.35 7.35 0 0 1 .6-2.87 6.1 6.1 0 0 1 1.72-2.45 4.26 4.26 0 0 1 2.77-.94 5.66 5.66 0 0 1 1.06.1 3.31 3.31 0 0 1 .92.3l-.47 1.7-.3-.1a2.88 2.88 0 0 0-1.6-.88ZM338.88 87.71a.56.56 0 0 0 .12.29.23.23 0 0 0 .2.12.82.82 0 0 0 .4-.13 3.18 3.18 0 0 0 .5-.4l.23.42a3.56 3.56 0 0 1-.78.77 2 2 0 0 1-1.24.41 1.32 1.32 0 0 1-.89-.28.9.9 0 0 1-.25-.81c0-.29.18-1.43.46-3.41.16-1.06.36-2.47.59-4.22l-1.09-.41.11-.59 2.49-.41.39.2-1.18 8.24Zm-.08-10.81a1 1 0 0 1-.27-.68 1.29 1.29 0 0 1 .35-.9 1.07 1.07 0 0 1 .81-.37.92.92 0 0 1 1 .93 1.34 1.34 0 0 1-.34.92 1.11 1.11 0 0 1-.88.38.87.87 0 0 1-.67-.28ZM347.19 79.72a3.54 3.54 0 0 1 2-.64 1.89 1.89 0 0 1 1.51.59 2.93 2.93 0 0 1 .53 2 16.77 16.77 0 0 1-.39 2.68l-.07.41-.14.84a12.6 12.6 0 0 0-.28 2.12c0 .32.08.48.23.48a1.38 1.38 0 0 0 .82-.44l.21.45a1.91 1.91 0 0 1-.36.41 3.11 3.11 0 0 1-.7.44 1.93 1.93 0 0 1-.9.21 1 1 0 0 1-1.11-1.07 14.24 14.24 0 0 1 .32-2.14l.16-.85.07-.42c.11-.63.21-1.18.28-1.66a9 9 0 0 0 .1-1.32 1.87 1.87 0 0 0-.23-1.11 1 1 0 0 0-.84-.31 2.66 2.66 0 0 0-1.57.69 6.48 6.48 0 0 0-1.48 1.68l-.89 6.24h-1.66l1.12-8.49-.86-.42.14-.67 2.14-.38.37.19-.23 2.1a6.52 6.52 0 0 1 1.71-1.61ZM359 88.64a4.35 4.35 0 0 1-2.23.59 3.34 3.34 0 0 1-1.95-.53 3.19 3.19 0 0 1-1.15-1.4 4.69 4.69 0 0 1-.37-1.87 7.34 7.34 0 0 1 .67-3.14 6 6 0 0 1 1.9-2.29 4.35 4.35 0 0 1 2.63-.87 2.61 2.61 0 0 1 1.87.59 2 2 0 0 1 .64 1.56 2.68 2.68 0 0 1-1 2.11 6.75 6.75 0 0 1-2.38 1.28 9.81 9.81 0 0 1-2.46.46 4.08 4.08 0 0 0 .42 2.13 1.69 1.69 0 0 0 1.6.9 3.65 3.65 0 0 0 1.55-.36 4.37 4.37 0 0 0 1.38-1l.39.65a4.57 4.57 0 0 1-1.51 1.19Zm-2.4-8a4.54 4.54 0 0 0-1 1.64 6.76 6.76 0 0 0-.44 1.94 6 6 0 0 0 1.85-.38 4.52 4.52 0 0 0 1.6-1 2 2 0 0 0 .65-1.47 1.49 1.49 0 0 0-.32-1 1.14 1.14 0 0 0-.89-.36 2 2 0 0 0-1.41.64Z" class="cls-2" transform="translate(-24.97 -24.05)"/> </svg> </a> </div> <div class="global-nav__controls"><button class="controls__menu"> Close <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""><path fill-rule="evenodd" d="M20.728 8l1.818 1.818-5.455 5.455 5.455 5.455-1.818 1.818-5.455-5.455-5.455 5.455L8 20.728l5.455-5.455L8 9.818 9.818 8l5.455 5.455z"></path></svg> </button> </div></div> <div class="mega-menu__content"><div> <button class="accordion">About Us</button> <div class="panel"><ul><li><a href="https://www.nationalacademies.org/about"> About Us </a></li><li><a href="https://www.nationalacademies.org/about/organization"> Our Program Divisions </a></li><li><a href="https://www.nationalacademies.org/about/the-national-academies"> Our Three Academies </a></li><li><a href="https://www.nationalacademies.org/about/leadership"> Leadership </a></li><li><a href="https://www.nationalacademies.org/newsroom"> Newsroom </a></li><li><a href="https://www.nationalacademies.org/ocga"> Government Affairs </a></li><li><a href="https://www.nationalacademies.org/giving"> Giving </a></li><li><a href="https://www.nationalacademies.org/about/institutional-policies-and-procedures/statement-on-diversity-and-inclusion"> Statement on Diversity and Inclusion </a></li></ul> </div> <button class="no-accordion"><a href="https://www.nationalacademies.org/events">Events</a></button> <button class="accordion">Our Work</button> <div class="panel"><ul><li><a href="https://www.nationalacademies.org/our-work"> Our Work </a></li><li><a href="https://www.nationalacademies.org/about/our-study-process"> Our Study Process </a></li><li><a href="https://www.nationalacademies.org/about/institutional-policies-and-procedures/conflict-of-interest-policies-and-procedures"> Conflict of Interest Policies and Procedures </a></li><li><a href="https://www.nationalacademies.org/about/institutional-policies-and-procedures/project-comments-and-information"> Project Comments and Information </a></li></ul> </div> <button class="accordion">Publications</button> <div class="panel"> <ul><li><a href="https://nap.nationalacademies.org/" target="_self"> Read Our Expert Reports and Published Proceedings </a></li><li><a href="https://www.pnas.org/" target="_self"> Explore PNAS, the Flagship Scientific Journal of NAS </a></li><li><a href="http://pubsindex.trb.org" target="_self"> Access Transportation Research Board Publications </a></li></ul> </div> <button class="accordion">Topics</button> <div class="panel"> <ul><li><a href="https://www.nationalacademies.org/topics/covid-19-resources"> Coronavirus Disease 2019 (COVID-19) </a></li><li><a href="https://www.nationalacademies.org/topics/resources-on-diversity-equity-and-inclusion"> Diversity, Equity, and Inclusion </a></li><li><a href="https://www.nationalacademies.org/topics/climate"> Climate </a></li><li><a href="https://www.nationalacademies.org/topics/economic-recovery"> Economic Recovery </a></li></ul> </div> <button class="no-accordion"><a href="https://www.nationalacademies.org/engagement">Engagement</a></button> <button class="accordion">Opportunities</button> <div class="panel"> <ul><li><a href="https://www.nationalacademies.org/careers"> Careers </a></li><li><a href="https://www.nationalacademies.org/fellowships-and-grants"> Fellowships and Grants </a></li><li><a href="https://www.nationalacademies.org/about/volunteers"> Volunteers </a></li><li><a href="https://www.nationalacademies.org/about/sponsors"> Sponsors </a></li><li><a href="https://www.nationalacademies.org/about/members"> Members </a></li></ul> </div> </div></div> </div> </div>  </div> <div class="container flex justify-between"> <div class="global-nav__logo" > <a class="navbar-brand js-scroll-trigger" aria-label="Logo of The National Academies" href="https://www.nationalacademies.org/home"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 315.11 58.33"> <defs><style>.cls-2{fill:#211747;}</style></defs><g id="Layer_2" data-name="Layer 2"><g id="Layer_1-2" data-name="Layer 1"><polygon class="cls-2" points="3.73 7.55 20.84 25.49 20.84 1.5 17.81 1.5 17.81 18.08 0.7 0.14 0.7 24.06 3.73 24.06 3.73 7.55"/><polygon class="cls-2" points="28.49 24.06 31.84 24.06 38.98 7.25 45.92 23.87 45.99 24.06 49.34 24.06 39.05 0 28.49 24.06"/><polygon class="cls-2" points="153.23 24.06 156.58 24.06 163.72 7.25 170.66 23.87 170.73 24.06 174.08 24.06 163.79 0 153.23 24.06"/><polygon class="cls-2" points="59.72 24.06 62.76 24.06 62.76 4.41 69.52 4.41 69.52 1.5 52.96 1.5 52.96 4.41 59.72 4.41 59.72 24.06"/><rect class="cls-2" x="78.85" y="1.5" width="3.03" height="22.55"/><path class="cls-2" d="M115.69,12.8a11.72,11.72,0,0,0-23.44,0,11.72,11.72,0,0,0,23.44,0m-3.09,0A8.63,8.63,0,1,1,104,4a8.7,8.7,0,0,1,8.63,8.76"/><polygon class="cls-2" points="128.29 7.55 145.4 25.49 145.4 1.5 142.37 1.5 142.37 18.08 125.25 0.14 125.25 24.06 128.29 24.06 128.29 7.55"/><polygon class="cls-2" points="184.65 1.5 181.62 1.5 181.62 24.06 193.7 24.06 193.7 21.16 184.65 21.16 184.65 1.5"/><path class="cls-2" d="M37.15,34.08A11.48,11.48,0,0,0,25.37,45.8,11.36,11.36,0,0,0,37,57.38a11.77,11.77,0,0,0,6.79-2.19l.13-.09V51.2l-.51.51A9.77,9.77,0,0,1,41,53.5a8.9,8.9,0,0,1-3.95,1A8.75,8.75,0,0,1,37,37a9.09,9.09,0,0,1,3.66.82,10.71,10.71,0,0,1,2.78,2l.51.5V36.4l-.12-.09a10.62,10.62,0,0,0-6.67-2.23"/><path class="cls-2" d="M91.91,37.08a12.19,12.19,0,0,0-8.29-2.64H78.85V57h4.74c3.72,0,6-.73,8.22-2.61a10.75,10.75,0,0,0,4-8.65,11,11,0,0,0-3.86-8.65m-2.09,15.1a9.11,9.11,0,0,1-6.1,1.91H81.88V37.34h1.84c5.44,0,9,3.29,9,8.39a8.09,8.09,0,0,1-2.85,6.45"/><polygon class="cls-2" points="104.99 56.99 118.4 56.99 118.4 54.09 108.02 54.09 108.02 46.16 117.11 46.16 117.11 43.26 108.02 43.26 108.02 37.34 118.4 37.34 118.4 34.44 104.99 34.44 104.99 56.99"/><polygon class="cls-2" points="176.17 56.99 189.58 56.99 189.58 54.09 179.2 54.09 179.2 46.16 188.28 46.16 188.28 43.26 179.2 43.26 179.2 37.34 189.58 37.34 189.58 34.44 176.17 34.44 176.17 56.99"/><polygon class="cls-2" points="138.88 51.34 130.31 32.49 126.44 56.99 129.55 56.99 131.62 42.47 138.84 58.33 146.15 42.47 148.13 56.99 151.23 56.99 147.61 32.45 138.88 51.34"/><rect class="cls-2" x="161.31" y="34.44" width="3.03" height="22.55"/><path class="cls-2" d="M209,46.15A10.78,10.78,0,0,0,205.49,44l-2.12-.92a6.8,6.8,0,0,1-2.21-1.33,2,2,0,0,1-.73-1.69A3.07,3.07,0,0,1,203.82,37a3.62,3.62,0,0,1,2.28.69,4.87,4.87,0,0,1,1.2,1.55l.15.3,2.45-1.62-.12-.24a7,7,0,0,0-2.24-2.55,6.34,6.34,0,0,0-3.69-1c-3.8,0-6.45,2.45-6.45,6a4.86,4.86,0,0,0,1.6,3.8,9.51,9.51,0,0,0,2.84,1.78l2.15,1a9.5,9.5,0,0,1,2.56,1.46,3,3,0,0,1,1,2.35,4.2,4.2,0,0,1-7.06,2.92,4.93,4.93,0,0,1-1.24-2.64l-.05-.33-3,.82.06.28a8.32,8.32,0,0,0,2.13,4,6.74,6.74,0,0,0,5,1.87,6.91,6.91,0,0,0,7.24-7A5.58,5.58,0,0,0,209,46.15"/><polygon class="cls-2" points="0 56.99 3.35 56.99 10.49 40.18 17.43 56.81 17.5 56.99 20.86 56.99 10.56 32.93 0 56.99"/><polygon class="cls-2" points="50.21 56.99 53.57 56.99 60.71 40.18 67.64 56.81 67.72 56.99 71.07 56.99 60.78 32.93 50.21 56.99"/><path class="cls-2" d="M233.74,2.1a3.34,3.34,0,0,0-.93-.11,2.53,2.53,0,0,0-1.52.45,1.48,1.48,0,0,0-.63,1.28,2,2,0,0,0,.54,1.44,7.94,7.94,0,0,0,1.64,1.26,13.5,13.5,0,0,1,1.26.89,3.76,3.76,0,0,1,.83,1,2.62,2.62,0,0,1,.33,1.33,3.06,3.06,0,0,1-.5,1.74,3.26,3.26,0,0,1-1.4,1.18,5.06,5.06,0,0,1-2.09.41,8.3,8.3,0,0,1-1.94-.22,3.51,3.51,0,0,1-1.24-.46l.34-2.18h.92l.09,1.62a2.53,2.53,0,0,0,.81.33,3.86,3.86,0,0,0,1,.13,2.93,2.93,0,0,0,1.77-.53,1.68,1.68,0,0,0,.73-1.47,1.91,1.91,0,0,0-.49-1.34,6.42,6.42,0,0,0-1.49-1.16c-.52-.34-1-.65-1.32-.94a3.76,3.76,0,0,1-.9-1,2.64,2.64,0,0,1-.37-1.4,2.64,2.64,0,0,1,.5-1.62,3.23,3.23,0,0,1,1.35-1.08,4.58,4.58,0,0,1,1.86-.37,7,7,0,0,1,1.72.18,3.31,3.31,0,0,1,1.09.45l-.35,2h-.83l-.12-1.47a2.39,2.39,0,0,0-.68-.3"/><path class="cls-2" d="M241,5a2,2,0,0,0-1.35.54,3.66,3.66,0,0,0-.92,1.52,7,7,0,0,0-.33,2.24,3.52,3.52,0,0,0,.43,1.95,1.39,1.39,0,0,0,1.24.66,2.38,2.38,0,0,0,1.1-.24,5.05,5.05,0,0,0,1-.72l.3.57a3.84,3.84,0,0,1-1.14.95,3.43,3.43,0,0,1-1.76.43,2.44,2.44,0,0,1-2-.91,4,4,0,0,1-.73-2.54A6.43,6.43,0,0,1,237.34,7a5.3,5.3,0,0,1,1.55-2.08,3.74,3.74,0,0,1,2.42-.83,5,5,0,0,1,.93.09,3.09,3.09,0,0,1,.81.26l-.42,1.49-.26-.09A2.53,2.53,0,0,0,241,5"/><path class="cls-2" d="M246.1,11.61a.56.56,0,0,0,.07.29.21.21,0,0,0,.18.1.65.65,0,0,0,.34-.11,2.64,2.64,0,0,0,.44-.35l.2.37a2.88,2.88,0,0,1-.68.67,1.71,1.71,0,0,1-1.08.35,1.14,1.14,0,0,1-.78-.23.8.8,0,0,1-.22-.72c0-.25.15-1.25.4-3,.14-.93.31-2.16.52-3.7l-1-.35.09-.52,2.18-.36.34.17-1,7.22ZM246,2.15a.84.84,0,0,1-.23-.59,1.13,1.13,0,0,1,.3-.79.94.94,0,0,1,.71-.32.79.79,0,0,1,.61.24.77.77,0,0,1,.23.57,1.15,1.15,0,0,1-.29.81,1,1,0,0,1-.77.33.75.75,0,0,1-.56-.25"/><path class="cls-2" d="M254,12.43a3.75,3.75,0,0,1-1.95.52,3,3,0,0,1-1.72-.47,2.74,2.74,0,0,1-1-1.23A4,4,0,0,1,249,9.62a6.35,6.35,0,0,1,.59-2.75,5.08,5.08,0,0,1,1.63-2,3.7,3.7,0,0,1,2.29-.77,2.27,2.27,0,0,1,1.64.52A1.79,1.79,0,0,1,255.72,6a2.34,2.34,0,0,1-.89,1.84,5.79,5.79,0,0,1-2.08,1.12,8.1,8.1,0,0,1-2.15.4,3.42,3.42,0,0,0,.37,1.87,1.48,1.48,0,0,0,1.4.79,3.18,3.18,0,0,0,1.35-.32,3.75,3.75,0,0,0,1.21-.9l.34.57A4,4,0,0,1,254,12.43m-2.11-7A4.1,4.1,0,0,0,251,6.88a5.9,5.9,0,0,0-.39,1.69,5.31,5.31,0,0,0,1.62-.33,4,4,0,0,0,1.41-.87,1.76,1.76,0,0,0,.57-1.28,1.33,1.33,0,0,0-.29-.92,1,1,0,0,0-.77-.31,1.74,1.74,0,0,0-1.28.57"/><path class="cls-2" d="M261.24,4.62A3.14,3.14,0,0,1,263,4.06a1.67,1.67,0,0,1,1.32.52,2.61,2.61,0,0,1,.46,1.71,15.44,15.44,0,0,1-.34,2.34l-.06.36-.13.74a11.51,11.51,0,0,0-.24,1.85c0,.28.06.42.2.42a1.22,1.22,0,0,0,.72-.39l.18.4a1.54,1.54,0,0,1-.32.36,2.92,2.92,0,0,1-.61.39,1.73,1.73,0,0,1-.79.17.84.84,0,0,1-1-.93,12.88,12.88,0,0,1,.27-1.88l.14-.73.06-.37c.1-.55.19-1,.25-1.45a8.17,8.17,0,0,0,.09-1.16,1.67,1.67,0,0,0-.21-1,.87.87,0,0,0-.73-.27,2.33,2.33,0,0,0-1.37.61,5.75,5.75,0,0,0-1.3,1.47l-.75,5.54h-1.46l1-7.43L257.62,5l.12-.58,1.88-.34.32.17-.2,1.84a5.72,5.72,0,0,1,1.5-1.45"/><path class="cls-2" d="M270.77,5a2,2,0,0,0-1.35.54,3.66,3.66,0,0,0-.92,1.52,7,7,0,0,0-.33,2.24,3.52,3.52,0,0,0,.43,1.95,1.39,1.39,0,0,0,1.24.66,2.38,2.38,0,0,0,1.1-.24,5.05,5.05,0,0,0,1-.72l.3.57a3.84,3.84,0,0,1-1.14.95,3.43,3.43,0,0,1-1.76.43,2.44,2.44,0,0,1-2-.91,4,4,0,0,1-.73-2.54A6.43,6.43,0,0,1,267.13,7a5.3,5.3,0,0,1,1.55-2.08,3.76,3.76,0,0,1,2.42-.83,5,5,0,0,1,.93.09,3,3,0,0,1,.81.26l-.42,1.49-.26-.09A2.53,2.53,0,0,0,270.77,5"/><path class="cls-2" d="M278.66,12.43a3.75,3.75,0,0,1-2,.52,3,3,0,0,1-1.71-.47,2.7,2.7,0,0,1-1-1.23,4.19,4.19,0,0,1-.32-1.63,6.35,6.35,0,0,1,.59-2.75,5.17,5.17,0,0,1,1.63-2,3.7,3.7,0,0,1,2.29-.77,2.32,2.32,0,0,1,1.65.52A1.82,1.82,0,0,1,280.38,6a2.34,2.34,0,0,1-.89,1.84,5.79,5.79,0,0,1-2.08,1.12,8,8,0,0,1-2.15.4,3.51,3.51,0,0,0,.37,1.87A1.48,1.48,0,0,0,277,12a3.18,3.18,0,0,0,1.35-.32,3.75,3.75,0,0,0,1.21-.9l.34.57a4,4,0,0,1-1.27,1.11m-2.11-7a4.25,4.25,0,0,0-.87,1.45,6.25,6.25,0,0,0-.39,1.69,5.44,5.44,0,0,0,1.63-.33,4.05,4.05,0,0,0,1.4-.87,1.76,1.76,0,0,0,.57-1.28,1.33,1.33,0,0,0-.29-.92,1,1,0,0,0-.77-.31,1.74,1.74,0,0,0-1.28.57"/><path class="cls-2" d="M286.18,5.13a2.75,2.75,0,0,0-1.09-.21,1.85,1.85,0,0,0-1.13.31,1,1,0,0,0-.43.89,1.43,1.43,0,0,0,.34.93,6.08,6.08,0,0,0,1,.88,10.43,10.43,0,0,1,.88.74,3.1,3.1,0,0,1,.6.76,2.15,2.15,0,0,1,.26,1.05,2.09,2.09,0,0,1-.9,1.81,3.71,3.71,0,0,1-2.22.64,6.32,6.32,0,0,1-1.37-.15,2.1,2.1,0,0,1-.9-.34l.24-1.06a3.41,3.41,0,0,0,.88.44,3.37,3.37,0,0,0,1.18.21,2.21,2.21,0,0,0,1.15-.29,1,1,0,0,0,.48-.92,1.37,1.37,0,0,0-.38-1,6.83,6.83,0,0,0-1.1-.89,3.07,3.07,0,0,1-1.58-2.5,2.16,2.16,0,0,1,.4-1.27,2.64,2.64,0,0,1,1.09-.84,3.81,3.81,0,0,1,1.54-.3,6.32,6.32,0,0,1,1.13.1,4.07,4.07,0,0,1,.8.19l-.26,1.17a1.55,1.55,0,0,0-.6-.39"/><polygon class="cls-2" points="229.34 23.43 236.61 23.43 236.51 25.87 235.6 25.87 235.35 24.25 231.87 24.13 231.29 28.48 234.85 28.36 234.74 29.51 231.21 29.38 230.58 34.05 234.91 33.87 235.77 32.01 236.63 32.18 236.01 34.84 227.85 34.84 227.91 34.24 229.06 34.05 230.29 24.25 229.24 24.09 229.34 23.43"/><path class="cls-2" d="M242.18,26.67a3.16,3.16,0,0,1,1.73-.56,1.67,1.67,0,0,1,1.32.53,2.51,2.51,0,0,1,.46,1.7,14.42,14.42,0,0,1-.34,2.35l-.06.35-.12.74a10.81,10.81,0,0,0-.25,1.86c0,.27.07.41.2.41a1.15,1.15,0,0,0,.72-.38l.19.4a1.54,1.54,0,0,1-.32.35,2.46,2.46,0,0,1-.61.39,1.76,1.76,0,0,1-.79.18c-.65,0-1-.31-1-.94a11.94,11.94,0,0,1,.28-1.87l.14-.74.06-.37c.1-.55.18-1,.24-1.45a8.14,8.14,0,0,0,.1-1.16,1.64,1.64,0,0,0-.21-1,.87.87,0,0,0-.73-.27,2.3,2.3,0,0,0-1.38.61,5.67,5.67,0,0,0-1.29,1.46l-.76,5.55h-1.45l1-7.44-.76-.36.13-.59,1.87-.34.32.17-.2,1.85a5.77,5.77,0,0,1,1.5-1.46"/><path class="cls-2" d="M252.77,37.29a4,4,0,0,1-1.55,1.05,5.36,5.36,0,0,1-1.78.32,5.69,5.69,0,0,1-1-.09,3.45,3.45,0,0,1-.76-.19l.32-1.24a5,5,0,0,0,.9.34,3.56,3.56,0,0,0,1.06.17,2.22,2.22,0,0,0,1.45-.39,2.12,2.12,0,0,0,.63-1.41l.29-2a3.73,3.73,0,0,1-1,.84A2.61,2.61,0,0,1,250,35a2.16,2.16,0,0,1-1.89-.88,3.9,3.9,0,0,1-.64-2.35,6.52,6.52,0,0,1,.58-2.6A5.62,5.62,0,0,1,249.73,27a4.15,4.15,0,0,1,2.61-.87,4.47,4.47,0,0,1,.87.1,5.15,5.15,0,0,1,.8.24l1-.34-1.38,9.31a3.37,3.37,0,0,1-.81,1.87m-.61-10.36a2.36,2.36,0,0,0-1.75.74,4.82,4.82,0,0,0-1.07,1.85,7.16,7.16,0,0,0-.35,2.15,3.3,3.3,0,0,0,.37,1.72,1.16,1.16,0,0,0,1,.62,2.09,2.09,0,0,0,1.2-.39,3.12,3.12,0,0,0,.9-.87l.82-5.5a1.85,1.85,0,0,0-1.15-.32"/><path class="cls-2" d="M258.39,33.67a.45.45,0,0,0,.07.28.19.19,0,0,0,.17.1.6.6,0,0,0,.35-.11,3.13,3.13,0,0,0,.44-.35l.2.37a3.17,3.17,0,0,1-.69.68,1.77,1.77,0,0,1-1.08.35,1.14,1.14,0,0,1-.78-.24.82.82,0,0,1-.22-.71c0-.26.16-1.25.4-3,.15-.93.32-2.17.52-3.7l-.95-.36.09-.52,2.19-.35.33.17-1,7.21Zm-.07-9.46a.81.81,0,0,1-.24-.6,1.09,1.09,0,0,1,.3-.78.94.94,0,0,1,.72-.33.81.81,0,0,1,.61.24.82.82,0,0,1,.23.58,1.17,1.17,0,0,1-.29.8,1,1,0,0,1-.77.33.76.76,0,0,1-.56-.24"/><path class="cls-2" d="M265.74,26.67a3.11,3.11,0,0,1,1.72-.56,1.65,1.65,0,0,1,1.32.53,2.5,2.5,0,0,1,.47,1.7,15.68,15.68,0,0,1-.34,2.35l-.06.35-.13.74a11.6,11.6,0,0,0-.24,1.86c0,.27.06.41.2.41a1.2,1.2,0,0,0,.72-.38l.18.4a1.54,1.54,0,0,1-.32.35,2.28,2.28,0,0,1-.61.39,1.73,1.73,0,0,1-.79.18.84.84,0,0,1-1-.94,12.8,12.8,0,0,1,.27-1.87l.14-.74.06-.37c.1-.55.19-1,.25-1.45a8.07,8.07,0,0,0,.09-1.16,1.64,1.64,0,0,0-.21-1,.87.87,0,0,0-.73-.27,2.27,2.27,0,0,0-1.37.61,5.7,5.7,0,0,0-1.3,1.46l-.75,5.55h-1.46l1-7.44-.75-.36.12-.59,1.88-.34.32.17-.2,1.85a5.77,5.77,0,0,1,1.5-1.46"/><path class="cls-2" d="M276.11,34.48a3.7,3.7,0,0,1-1.95.52,3,3,0,0,1-1.71-.46,2.87,2.87,0,0,1-1-1.23,4.24,4.24,0,0,1-.32-1.64,6.53,6.53,0,0,1,.59-2.75,5.17,5.17,0,0,1,1.63-2,3.76,3.76,0,0,1,2.29-.77,2.32,2.32,0,0,1,1.65.53,1.76,1.76,0,0,1,.55,1.36,2.31,2.31,0,0,1-.88,1.84A5.83,5.83,0,0,1,274.87,31a9.08,9.08,0,0,1-2.15.4,3.49,3.49,0,0,0,.36,1.86,1.48,1.48,0,0,0,1.4.79,3.16,3.16,0,0,0,1.35-.31,3.9,3.9,0,0,0,1.22-.9l.33.57a3.93,3.93,0,0,1-1.27,1.1m-2.1-7a4.12,4.12,0,0,0-.88,1.44,6.37,6.37,0,0,0-.38,1.7,5.17,5.17,0,0,0,1.62-.34,3.78,3.78,0,0,0,1.4-.87,1.74,1.74,0,0,0,.57-1.28,1.31,1.31,0,0,0-.28-.91,1,1,0,0,0-.78-.32,1.68,1.68,0,0,0-1.27.58"/><path class="cls-2" d="M284,34.48a3.7,3.7,0,0,1-2,.52,3,3,0,0,1-1.71-.46,2.87,2.87,0,0,1-1-1.23,4.24,4.24,0,0,1-.32-1.64,6.53,6.53,0,0,1,.59-2.75,5.26,5.26,0,0,1,1.63-2,3.79,3.79,0,0,1,2.3-.77,2.31,2.31,0,0,1,1.64.53,1.76,1.76,0,0,1,.55,1.36,2.31,2.31,0,0,1-.88,1.84A5.74,5.74,0,0,1,282.73,31a9.08,9.08,0,0,1-2.15.4,3.4,3.4,0,0,0,.37,1.86,1.45,1.45,0,0,0,1.39.79,3.2,3.2,0,0,0,1.36-.31,3.86,3.86,0,0,0,1.21-.9l.34.57a4,4,0,0,1-1.28,1.1m-2.1-7a4.12,4.12,0,0,0-.88,1.44,6.37,6.37,0,0,0-.38,1.7,5.17,5.17,0,0,0,1.62-.34,3.7,3.7,0,0,0,1.4-.87,1.74,1.74,0,0,0,.57-1.28,1.31,1.31,0,0,0-.28-.91,1,1,0,0,0-.78-.32,1.7,1.7,0,0,0-1.27.58"/><path class="cls-2" d="M290.05,27.3a3.77,3.77,0,0,1,1-.83,2.34,2.34,0,0,1,1.22-.34.83.83,0,0,1,.5.11l-.33,1.62a1.45,1.45,0,0,0-.75-.15,2.3,2.3,0,0,0-1.29.44,2.89,2.89,0,0,0-1,1.22l-.7,5.47h-1.48l1-7.41-.77-.38.11-.57,1.81-.35.31.18-.11,1.37-.08.61a4.09,4.09,0,0,1,.6-1"/><path class="cls-2" d="M295.29,33.67a.45.45,0,0,0,.07.28.19.19,0,0,0,.17.1.6.6,0,0,0,.35-.11,3.13,3.13,0,0,0,.44-.35l.2.37a3.17,3.17,0,0,1-.69.68,1.77,1.77,0,0,1-1.08.35,1.14,1.14,0,0,1-.78-.24.82.82,0,0,1-.22-.71c0-.26.16-1.25.4-3,.15-.93.32-2.17.52-3.7l-.95-.36.09-.52,2.19-.35.33.17-1,7.21Zm-.07-9.46a.81.81,0,0,1-.24-.6,1.09,1.09,0,0,1,.3-.78.94.94,0,0,1,.72-.33.81.81,0,0,1,.61.24.82.82,0,0,1,.23.58,1.17,1.17,0,0,1-.29.8,1,1,0,0,1-.77.33.76.76,0,0,1-.56-.24"/><path class="cls-2" d="M302.33,26.67a3.14,3.14,0,0,1,1.73-.56,1.67,1.67,0,0,1,1.32.53,2.56,2.56,0,0,1,.46,1.7,15.68,15.68,0,0,1-.34,2.35l-.06.35-.12.74a10.81,10.81,0,0,0-.25,1.86c0,.27.07.41.2.41a1.2,1.2,0,0,0,.72-.38l.19.4a1.64,1.64,0,0,1-.33.35,2.22,2.22,0,0,1-.6.39,1.76,1.76,0,0,1-.79.18c-.65,0-1-.31-1-.94a12.8,12.8,0,0,1,.27-1.87l.14-.74.06-.37c.11-.55.19-1,.25-1.45a8.07,8.07,0,0,0,.09-1.16,1.73,1.73,0,0,0-.2-1,.88.88,0,0,0-.73-.27,2.3,2.3,0,0,0-1.38.61,5.7,5.7,0,0,0-1.3,1.46l-.75,5.55h-1.46l1-7.44-.75-.36.13-.59,1.87-.34.32.17-.2,1.85a5.77,5.77,0,0,1,1.5-1.46"/><path class="cls-2" d="M312.92,37.29a4,4,0,0,1-1.55,1.05,5.36,5.36,0,0,1-1.78.32,5.69,5.69,0,0,1-1-.09,3.57,3.57,0,0,1-.77-.19l.33-1.24a5,5,0,0,0,.9.34,3.51,3.51,0,0,0,1.06.17,2.22,2.22,0,0,0,1.45-.39,2.11,2.11,0,0,0,.62-1.41l.3-2a3.73,3.73,0,0,1-1,.84,2.63,2.63,0,0,1-1.33.34,2.16,2.16,0,0,1-1.89-.88,3.9,3.9,0,0,1-.64-2.35,6.35,6.35,0,0,1,.58-2.6A5.62,5.62,0,0,1,309.88,27a4.11,4.11,0,0,1,2.61-.87,4.56,4.56,0,0,1,.87.1,5.15,5.15,0,0,1,.8.24l.95-.34-1.38,9.31a3.37,3.37,0,0,1-.81,1.87m-.62-10.36a2.35,2.35,0,0,0-1.74.74,4.7,4.7,0,0,0-1.07,1.85,7.16,7.16,0,0,0-.35,2.15,3.3,3.3,0,0,0,.37,1.72,1.14,1.14,0,0,0,1,.62,2,2,0,0,0,1.19-.39,3.3,3.3,0,0,0,.91-.87l.82-5.5a1.88,1.88,0,0,0-1.16-.32"/><path class="cls-2" d="M237.11,49.24c.83-1.82,1.39-3.07,1.65-3.76h3.29l-.06.66-1.37.17-.29,9.8,1.31.18-.07.6h-4.22l.06-.6,1.4-.18.35-6.79.2-3.12L238.2,49l-3.57,8-.83.11-1.26-7.89-.47-2.92-.63,3-1.64,6.91,1.55.18-.06.6h-4l.06-.6,1.28-.18,2.47-9.8-1.41-.17.09-.66h3.56L234.56,53l.2,1.57.67-1.53c.28-.69.84-1.95,1.68-3.77"/><path class="cls-2" d="M247.75,56.54a3.75,3.75,0,0,1-1.95.52,3,3,0,0,1-1.71-.47,2.7,2.7,0,0,1-1-1.23,4.19,4.19,0,0,1-.32-1.63,6.35,6.35,0,0,1,.59-2.75,5.17,5.17,0,0,1,1.63-2,3.7,3.7,0,0,1,2.29-.77,2.32,2.32,0,0,1,1.65.52,1.82,1.82,0,0,1,.55,1.37,2.34,2.34,0,0,1-.89,1.84A5.79,5.79,0,0,1,246.5,53a8,8,0,0,1-2.15.4,3.51,3.51,0,0,0,.37,1.87,1.48,1.48,0,0,0,1.4.79,3.18,3.18,0,0,0,1.35-.32,3.75,3.75,0,0,0,1.21-.9l.34.57a4,4,0,0,1-1.27,1.11m-2.11-7a4.25,4.25,0,0,0-.87,1.45,6.25,6.25,0,0,0-.39,1.69,5.44,5.44,0,0,0,1.63-.33,4.05,4.05,0,0,0,1.4-.87A1.76,1.76,0,0,0,248,50.2a1.33,1.33,0,0,0-.29-.92,1,1,0,0,0-.77-.31,1.74,1.74,0,0,0-1.28.57"/><path class="cls-2" d="M257.17,55.72q0,.39.24.39a1.19,1.19,0,0,0,.7-.39l.22.39a3.42,3.42,0,0,1-.67.62,1.68,1.68,0,0,1-1,.31c-.6,0-.9-.32-.9-1v-.34a3.94,3.94,0,0,1-1.08.94,2.72,2.72,0,0,1-1.44.38,2.13,2.13,0,0,1-1.87-.88,4,4,0,0,1-.63-2.34,6.41,6.41,0,0,1,.58-2.62A5.56,5.56,0,0,1,253,49a4.1,4.1,0,0,1,2.61-.86,4,4,0,0,1,1.15.18l.41-2.76-1-.26.13-.54,2.16-.28.34.2-1.6,10.84a.79.79,0,0,0,0,.17M255.42,49a2.32,2.32,0,0,0-1.74.75,4.64,4.64,0,0,0-1.06,1.84,7.15,7.15,0,0,0-.34,2.16,3.44,3.44,0,0,0,.36,1.72,1.12,1.12,0,0,0,1,.61,2.06,2.06,0,0,0,1.23-.41,3.11,3.11,0,0,0,.9-.91l.83-5.42a1.94,1.94,0,0,0-1.2-.34"/><path class="cls-2" d="M262.14,55.72a.57.57,0,0,0,.06.29.24.24,0,0,0,.18.1.71.71,0,0,0,.35-.11,3.84,3.84,0,0,0,.44-.35l.19.37a2.88,2.88,0,0,1-.68.67,1.71,1.71,0,0,1-1.08.35,1.19,1.19,0,0,1-.78-.23.8.8,0,0,1-.22-.72c0-.25.15-1.25.4-3,.14-.93.32-2.16.52-3.7l-.95-.35.09-.52,2.18-.36.34.17-1,7.22Zm-.07-9.46a.81.81,0,0,1-.24-.6,1.12,1.12,0,0,1,.3-.78,1,1,0,0,1,.71-.32.83.83,0,0,1,.62.24.81.81,0,0,1,.23.57,1.2,1.2,0,0,1-.29.81,1,1,0,0,1-.77.33.73.73,0,0,1-.56-.25"/><path class="cls-2" d="M269.42,49.14a2,2,0,0,0-1.35.54,3.6,3.6,0,0,0-.92,1.52,7,7,0,0,0-.33,2.24,3.52,3.52,0,0,0,.43,2,1.39,1.39,0,0,0,1.24.66,2.38,2.38,0,0,0,1.1-.24,5.05,5.05,0,0,0,1-.72l.3.57a4,4,0,0,1-1.14,1A3.43,3.43,0,0,1,268,57a2.44,2.44,0,0,1-2-.91,4,4,0,0,1-.73-2.54,6.43,6.43,0,0,1,.53-2.51A5.3,5.3,0,0,1,267.33,49a3.69,3.69,0,0,1,2.42-.83,5,5,0,0,1,.93.09,3.09,3.09,0,0,1,.81.26L271.07,50l-.26-.09a2.53,2.53,0,0,0-1.39-.78"/><path class="cls-2" d="M274.77,55.72a.56.56,0,0,0,.07.29.24.24,0,0,0,.18.1.71.71,0,0,0,.35-.11,3.15,3.15,0,0,0,.43-.35l.2.37a2.88,2.88,0,0,1-.68.67,1.71,1.71,0,0,1-1.08.35,1.19,1.19,0,0,1-.78-.23.8.8,0,0,1-.22-.72c0-.25.15-1.25.4-3,.14-.93.32-2.16.52-3.7l-1-.35.09-.52,2.18-.36.34.17-1,7.22Zm-.07-9.46a.85.85,0,0,1-.23-.6,1.12,1.12,0,0,1,.3-.78.94.94,0,0,1,.71-.32.79.79,0,0,1,.61.24.78.78,0,0,1,.24.57,1.16,1.16,0,0,1-.3.81,1,1,0,0,1-.76.33.75.75,0,0,1-.57-.25"/><path class="cls-2" d="M282,48.73a3.09,3.09,0,0,1,1.73-.56,1.65,1.65,0,0,1,1.32.52,2.54,2.54,0,0,1,.46,1.7,15.09,15.09,0,0,1-.33,2.35l-.07.36-.12.73a11.6,11.6,0,0,0-.24,1.86c0,.28.06.42.19.42a1.22,1.22,0,0,0,.73-.39l.18.4a1.77,1.77,0,0,1-.32.36,3.21,3.21,0,0,1-.61.39,1.86,1.86,0,0,1-.79.17c-.64,0-1-.31-1-.93a13.42,13.42,0,0,1,.28-1.88l.14-.73.06-.37c.1-.56.18-1,.25-1.45a8.17,8.17,0,0,0,.09-1.16,1.67,1.67,0,0,0-.21-1,.87.87,0,0,0-.73-.27,2.31,2.31,0,0,0-1.37.61,5.58,5.58,0,0,0-1.3,1.47l-.75,5.54H278.2l1-7.43-.75-.37.12-.58,1.87-.34.33.17-.2,1.84A5.85,5.85,0,0,1,282,48.73"/><path class="cls-2" d="M292.42,56.54a3.75,3.75,0,0,1-1.95.52,3,3,0,0,1-1.71-.47,2.7,2.7,0,0,1-1-1.23,4.19,4.19,0,0,1-.32-1.63A6.35,6.35,0,0,1,288,51a5.17,5.17,0,0,1,1.63-2,3.7,3.7,0,0,1,2.29-.77,2.32,2.32,0,0,1,1.65.52,1.82,1.82,0,0,1,.55,1.37,2.34,2.34,0,0,1-.89,1.84A5.79,5.79,0,0,1,291.17,53a8,8,0,0,1-2.15.4,3.51,3.51,0,0,0,.37,1.87,1.48,1.48,0,0,0,1.4.79,3.18,3.18,0,0,0,1.35-.32,3.75,3.75,0,0,0,1.21-.9l.34.57a4,4,0,0,1-1.27,1.11m-2.11-7a4.25,4.25,0,0,0-.87,1.45,6.25,6.25,0,0,0-.39,1.69,5.44,5.44,0,0,0,1.63-.33,4.05,4.05,0,0,0,1.4-.87,1.76,1.76,0,0,0,.57-1.28,1.33,1.33,0,0,0-.29-.92,1,1,0,0,0-.77-.31,1.74,1.74,0,0,0-1.28.57"/></g></g> </svg> </a> </div> <div class='global-nav-nap-menu' id="header-large"> <div class="dropdown" id="sitelinks-mobile"> <button class="btn btn-secondary dropdown-toggle" type="button" id="dropdownMenuButton" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> <span class="hidden-xxs">Navigate to</span> </button> <div class="dropdown-menu" aria-labelledby="dropdownMenuButton"> <a class="dropdown-item" href="/content/help">Help</a> <a class="dropdown-item" href="/content/help-with-ordering">Ordering Information</a> <a class="dropdown-item" href="/new" >New Releases</a> <a class="dropdown-item" href="/author">Browse by Division</a> <a class="dropdown-item" href="/topic" class="site-links"> Browse by Topic</a> </div> </div> <ul class="user-links"> <li><a href="/"><span class="icon-menu" data-icon=""> </span> NAP Home</a></li> <li class="dropdown nap-mega-menu mega-dropdown"> <a href="#" class="dropdown-toggle" data-toggle="dropdown"><span class="icon-menu" data-icon=""> </span> Browse <span class="caret"></span></a> <ul class="dropdown-menu mega-dropdown-menu row" id="nap-mega-menu-inner"> <li class="d-flex" > <ul class="browse-col" > <li class="dropdown-header"><a href="/author">Publications by Division</a></li> <li><a href="/author/DBASSE/">Division of Behavioral and Social Sciences and Education</a> </li> <li><a href="/author/DELS/">Division on Earth and Life Studies</a></li> <li><a href="/author/DEPS/">Division on Engineering and Physical Sciences</a> </li> <li><a href="/author/GRP/">Gulf Research Program</a></li> <li><a href="/author/HMD/">Health and Medicine Division</a></li> <li><a href="/author/PGA/">Policy and Global Affairs</a></li> <li><a href="/author/TRB/">Transportation Research Board</a></li> <li><hr style="margin-left: 21px; margin-right: 20px;"></li> <li><a href="/author/NAS">National Academy of Sciences</a></li> <li><a href="/author/NAE">National Academy of Engineering</a></li> <li><a href="/author/NAM">National Academy of Medicine</a></li> </ul> <ul class="browse-col" > <li class="dropdown-header"><a href="/topic">Publications by Topic</a></li> <li><a href="/topic/276">Agriculture</a></li> <li><a href="/topic/277">Behavioral and Social Sciences</a></li> <li><a href="/topic/292">Biography and Autobiography</a></li> <li><a href="/topic/278">Biology and Life Sciences</a></li> <li><a href="/topic/279">Computers and Information Technology</a></li> <li><a href="/topic/280">Conflict and Security Issues</a></li> <li><a href="/topic/281">Earth Sciences</a></li> <li><a href="/topic/282">Education</a></li> <li><a href="/topic/283">Energy and Energy Conservation</a></li> <li><a href="/topic/284">Engineering and Technology</a></li> </ul> <ul class="browse-col"> <li><br> </li> <li><a href="/topic/285">Environment and Environmental Studies</a></li> <li><a href="/topic/287">Food and Nutrition</a></li> <li><a href="/topic/288">Health and Medicine</a></li> <li><a href="/topic/289">Industry and Labor</a></li> <li><a href="/topic/290">Math, Chemistry, and Physics</a></li> <li><a href="/topic/423">Policy for Science and Technology</a></li> <li><a href="/topic/293">Space and Aeronautics</a></li> <li><a href="/topic/478">Surveys and Statistics</a></li> <li><a href="/topic/294">Transportation and Infrastructure</a></li> </ul> <ul class="browse-col vertical-divider"> <li class="dropdown-header"><br></li> <li><a href="/collection">Searchable Collections</a></li> <li><a href="/new">New Releases</a></li> </ul> </li> </ul> </li> <li class="dropdown"> <a class="dropdown-toggle" data-toggle="dropdown" href="#"><span class="icon-menu" data-icon=""> </span> MyNAP <span class="caret"></span></a> <ul class="dropdown-menu"> <li><a href="/login.php" class="userOff"><span class="icon-menu" data-icon=""> </span> Login</a></li> <li><a href="/login.php?action=new" class="register"><span class="icon-menu" data-icon=""> </span> Register</a></li> </ul> </li> <li class="naphelp"><a href="/content/help"><span class="icon-menu" data-icon=""> </span> HELP</a></li> <li> <a href="/cart/cart.php"> <span class="icon-menu" data-icon=""> </span> Cart </a> </li> </ul> </div> <div class="global-nav__menus"> <div class="global-nav__menus--upper"> <div class="global-nav__controls"> <div class="controls__social"></div> <button aria-label="Search" class="controls__search" onclick="toggleSearch()"><span class="search__label"> Search </span> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""> <path d="M13.8 21.6a7.8 7.8 0 110-15.6 7.8 7.8 0 010 15.6zm0-2a5.8 5.8 0 100-11.6 5.8 5.8 0 000 11.6z"></path> <path d="M17.899 19.325l1.414-1.414 4.322 4.322-1.414 1.414z"></path> </svg> </button> <button class="controls__menu"> Menu <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""> <path fill-rule="evenodd" d="M8 23h15v-2.5H8V23zm0-6.25h15v-2.5H8v2.5zM8 8v2.5h15V8H8z"></path> </svg> </button> <button class="controls__nav" onclick="toggleMenu(); myMenu(this)"> Global Menu <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class="menu-off"> <path fill-rule="evenodd" d="M8 23h15v-2.5H8V23zm0-6.25h15v-2.5H8v2.5zM8 8v2.5h15V8H8z"></path> </svg> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class="menu-on"><path fill-rule="evenodd" d="M20.728 8l1.818 1.818-5.455 5.455 5.455 5.455-1.818 1.818-5.455-5.455-5.455 5.455L8 20.728l5.455-5.455L8 9.818 9.818 8l5.455 5.455z"></path></svg> </button> </div> </div> <div class="global-nav__menus--lower" > <nav role="navigation" class="global-nav__links " > <ul role="menu"> <li role="none" class="has-dropdown"><a href="https://www.nationalacademies.org/about" target="_self" role="menuitem" class="global-nav__link"><span> About Us </span></a> <div class="global-nav__dropdown"> <div class="dropdown__left"> <ul class="global-nav__links-widget" type="nas-nav-links-widget"> <li><a rel="" title="" href="https://www.nationalacademies.org/about" target="_self"> About Us </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/about/organization" target="_self"> Our Program Divisions </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/about/the-national-academies" target="_self"> Our Three Academies </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/about/leadership" target="_self"> Leadership </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/newsroom" target="_self"> Newsroom </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/ocga" target="_self"> Government Affairs </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/giving" target="_self"> Giving </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/about/institutional-policies-and-procedures/statement-on-diversity-and-inclusion" target="_self"> Statement on Diversity and Inclusion </a></li> </ul> </div> <div class="dropdown__right"> <p> <p>The National Academies of Sciences, Engineering, and Medicine are private, nonprofit institutions that provide expert advice on some of the most pressing challenges facing the nation and world. Our work helps shape sound policies, inform public opinion, and advance the pursuit of science, engineering, and medicine.</p> </p> <a rel="" title="Learn More" href="https://www.nationalacademies.org/about" target="_self" role="menuitem" class="button button--secondary button--outline button--icon"> Learn More <span class="button__icon"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class="w2 h2"> <path d="M17.885 10.708a1 1 0 111.412-1.416l5.624 5.608-5.616 5.732a1 1 0 11-1.428-1.4l4.228-4.316-4.22-4.208z"></path> <path d="M23.07 14a1 1 0 010 2H7a1 1 0 010-2h16.07z"></path> </svg> </span></a></div> </div> </li> <li role="none" class="has-dropdown"><a href="https://www.nationalacademies.org/events" target="_self" role="menuitem" class="global-nav__link"><span> Events </span></a> <div class="global-nav__dropdown"> <div class="dropdown__left"><span class="dropdown__left--default"><img src="https://nasemoceprodcomm-nationalacademies.cec.ocp.oraclecloud.com/content/published/api/v1.1/assets/CONTC88C4C0CA7CE4E7FA8630DEF6E1B3A8F/native/NAS+Building.jpg?cb=_cache_a061&channelToken=d2dc71410b56f1d61406108f1738d0f4" alt=""></span></div> <div class="dropdown__right"> <p> <p>Throughout any given year, the National Academies convene hundreds of conferences, workshops, symposia, forums, roundtables, and other gatherings that attract the finest minds in academia and the public and private sectors. These venues for discussion and debate are essential for allowing the scientific process to unfold.</p> </p> <a rel="" title="See All Events" href="https://www.nationalacademies.org/events" target="_self" role="menuitem" class="button button--secondary button--outline button--icon"> See All Events <span class="button__icon"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class="w2 h2"> <path d="M17.885 10.708a1 1 0 111.412-1.416l5.624 5.608-5.616 5.732a1 1 0 11-1.428-1.4l4.228-4.316-4.22-4.208z"></path> <path d="M23.07 14a1 1 0 010 2H7a1 1 0 010-2h16.07z"></path> </svg> </span></a></div> </div> </li> <li role="none" class="has-dropdown"><a href="https://www.nationalacademies.org/our-work" target="_self" role="menuitem" class="global-nav__link"><span> Our Work </span></a> <div class="global-nav__dropdown"> <div class="dropdown__left"> <ul class="global-nav__links-widget" type="nas-nav-links-widget"> <li><a rel="" title="" href="https://www.nationalacademies.org/our-work" target="_self"> Our Work </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/about/our-study-process" target="_self"> Our Study Process </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/about/institutional-policies-and-procedures/conflict-of-interest-policies-and-procedures" target="_self"> Conflict of Interest Policies and Procedures </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/about/institutional-policies-and-procedures/project-comments-and-information" target="_self"> Project Comments and Information </a></li> </ul> </div> <div class="dropdown__right"> <p> <p>The National Academies of Sciences, Engineering, and Medicine are the nation's pre-eminent source of high-quality, objective advice on science, engineering, and health matters. <br> <br> Top experts participate in our projects, activities, and studies to examine and assemble evidence-based findings to address some of society's greatest challenges.</p> </p> <a rel="" title="Learn More" href="https://www.nationalacademies.org/our-work" target="_self" role="menuitem" class="button button--secondary button--outline button--icon"> Learn More <span class="button__icon"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class="w2 h2"> <path d="M17.885 10.708a1 1 0 111.412-1.416l5.624 5.608-5.616 5.732a1 1 0 11-1.428-1.4l4.228-4.316-4.22-4.208z"></path> <path d="M23.07 14a1 1 0 010 2H7a1 1 0 010-2h16.07z"></path> </svg> </span></a></div> </div> </li> <li role="none" class="has-dropdown"><a href="https://www.nationalacademies.org/publications" target="_self" role="menuitem" class="global-nav__link"><span> Publications </span></a> <div class="global-nav__dropdown"> <div class="dropdown__left"> <ul class="global-nav__links-widget" loadchildren="true" type="nas-nav-links-widget"> <li><a rel="" title="" href="https://nap.nationalacademies.org/" target="_self"> Read Our Expert Reports and Published Proceedings </a></li> <li><a rel="" title="" href="https://www.pnas.org/" target="_self"> Explore PNAS, the Flagship Scientific Journal of NAS </a></li> <li><a rel="" title="" href="http://pubsindex.trb.org/" target="_self"> Access Transportation Research Board Publications </a></li> </ul> </div> <div class="dropdown__right"> <p>Our peer-reviewed reports present the evidence-based consensus of committees of experts. Published proceedings record the presentations and discussions that take place at hundreds of conferences, workshops, symposia, forums, roundtables, and other gatherings every year. And, our prestigious journals publish the latest scientific findings on a wide range of topics.</p> <a rel="" title="Learn More" href="https://www.nationalacademies.org/publications" target="_self" role="menuitem" class="button button--secondary button--outline button--icon"> Learn More <span class="button__icon"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class="w2 h2"> <path d="M17.885 10.708a1 1 0 111.412-1.416l5.624 5.608-5.616 5.732a1 1 0 11-1.428-1.4l4.228-4.316-4.22-4.208z"></path> <path d="M23.07 14a1 1 0 010 2H7a1 1 0 010-2h16.07z"></path> </svg> </span></a></div> </div> </li> <li role="none" class="has-dropdown"><a href="https://www.nationalacademies.org/topics" target="_self" role="menuitem" class="global-nav__link"><span> Topics </span></a> <div class="global-nav__dropdown"> <div class="dropdown__left"> <ul class="global-nav__links-widget" type="nas-nav-links-widget"> <li><a rel="" title="" href="https://www.nationalacademies.org/topics/covid-19-resources" target="_self"> Coronavirus Disease 2019 (COVID-19) </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/topics/resources-on-diversity-equity-and-inclusion" target="_self"> Diversity, Equity, and Inclusion </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/topics/climate" target="_self"> Climate </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/topics/economic-recovery" target="_self"> Economic Recovery </a></li> </ul> </div> <div class="dropdown__right"> <p> <p>Discover what the National Academies are doing in various topic areas to strengthen the fields of science, engineering, and medicine and their capacity to contribute to the well-being of our nation and the world.</p> </p> <a rel="" title="See All Topics" href="https://www.nationalacademies.org/topics" target="_self" role="menuitem" class="button button--secondary button--outline button--icon"> See All Topics <span class="button__icon"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class="w2 h2"> <path d="M17.885 10.708a1 1 0 111.412-1.416l5.624 5.608-5.616 5.732a1 1 0 11-1.428-1.4l4.228-4.316-4.22-4.208z"></path> <path d="M23.07 14a1 1 0 010 2H7a1 1 0 010-2h16.07z"></path> </svg> </span></a></div> </div> </li> <li role="none" class="has-dropdown"><a href="https://www.nationalacademies.org/engagement" target="_self" role="menuitem" class="global-nav__link"><span> Engagement </span></a> <div class="global-nav__dropdown"> <div class="dropdown__left"><span class="dropdown__left--default"><img src="https://nasemoceprodcomm-nationalacademies.ocecdn.oraclecloud.com/content/published/api/v1.1/assets/CONTC267CED7812243AB86410D548C73D067/native/engagement-nav.jpg?cb=_cache_a061&channelToken=d2dc71410b56f1d61406108f1738d0f4" alt=""></span></div> <div class="dropdown__right"> <p> <p>A powerful way to foster appreciation for the impact of science and critical and innovative thinking is through art and the humanities. Learn more about the National Academies’ various programs designed to connect, engage, and inspire.</p> </p> <a rel="" title="Learn More" href="https://www.nationalacademies.org/engagement" target="_self" role="menuitem" class="button button--secondary button--outline button--icon"> Learn More <span class="button__icon"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class="w2 h2"> <path d="M17.885 10.708a1 1 0 111.412-1.416l5.624 5.608-5.616 5.732a1 1 0 11-1.428-1.4l4.228-4.316-4.22-4.208z"></path> <path d="M23.07 14a1 1 0 010 2H7a1 1 0 010-2h16.07z"></path> </svg> </span></a></div> </div> </li> <li role="none" class="has-dropdown"><a href="https://www.nationalacademies.org/opportunities" target="_self" role="menuitem" class="global-nav__link"><span> Opportunities </span></a> <div class="global-nav__dropdown"> <div class="dropdown__left"> <ul class="global-nav__links-widget" type="nas-nav-links-widget"> <li><a rel="" title="" href="https://www.nationalacademies.org/careers" target="_self"> Careers </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/fellowships-and-grants" target="_self"> Fellowships and Grants </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/about/volunteers" target="_self"> Volunteers </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/about/sponsors" target="_self"> Sponsors </a></li> <li><a rel="" title="" href="https://www.nationalacademies.org/about/members" target="_self"> Members </a></li> </ul> </div> <div class="dropdown__right"> <p>Make a real impact on the scientific, engineering, and health-related challenges facing society. Whether as a sponsor or donor, a member or volunteer, or an employee or fellow, you can make a difference.</p> <a rel="" title="Learn More" href="https://www.nationalacademies.org/opportunities" target="_self" role="menuitem" class="button button--secondary button--outline button--icon"> Learn More <span class="button__icon"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class="w2 h2"> <path d="M17.885 10.708a1 1 0 111.412-1.416l5.624 5.608-5.616 5.732a1 1 0 11-1.428-1.4l4.228-4.316-4.22-4.208z"></path> <path d="M23.07 14a1 1 0 010 2H7a1 1 0 010-2h16.07z"></path> </svg> </span></a></div> </div> </li> </ul> </nav> </div> </div> </div> </header> <a name="content"></a> <script> $(".controls__menu").click(function(){ $("#mobile-menu").toggle(); }); function toggleMenu() { var element = document.getElementById("lowerMenu"); element.classList.toggle("menu-is-hidden"); } function myMenu(x) { x.classList.toggle("invert"); } function toggleSearch() { var element = document.getElementById("lowerMenu"); element.classList.toggle("search-is-hidden"); } </script>  <script> var acc = document.getElementsByClassName("accordion"); var i; for (i = 0; i < acc.length; i++) { acc[i].addEventListener("click", function() { this.classList.toggle("active"); var panel = this.nextElementSibling; if (panel.style.maxHeight) { panel.style.maxHeight = null; } else { panel.style.maxHeight = panel.scrollHeight + "px"; } }); } </script> <div class="top-rows"> <div class="container"> <div class="row"> <div class="col-lg-10 topic-img"> <h1 class="topic-hdr"> <span class="topic-name">Math, Chemistry, and Physics</span> </h1> <div class="clearfix"></div> </div> </div> <div class="row"> <div class="col-lg-10"> <ul class="nav nav-tabs"> <li class="active"><a href="#searchtopic" data-toggle="tab" class="hidden-xs">Search Within This Topic</a></li> <li><a href="#topichome" data-toggle="tab" class="hidden-xs">Browse by Subtopic</a></li> <li class="hidden-xs"><a href="/topic">View All Topics</a></li> <div class="clearfix"></div> </ul> </div> <div class="col-lg-10"> <div class="tab-content "> <div class="tab-pane fade in active" id="searchtopic"> <div class=" searchouter"> <form class="search-form" role="form" action="//nap.nationalacademies.org/search" method="GET" title="Search NAP Books"> <div class="searchinput"> <label class="sr-only" for="inputsearch">Search Books</label> <input type="hidden" name="topic" value="290"> <div class="input-group"> <input type="text" name="term" id="inputsearch" placeholder="Search books in Math, Chemistry, and Physics" required value=""> <div class="input-group-append"> <button type="submit" class="btn-blueflat btn-searchhome"> <span class="visible-xxs"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 32 32"><path d="M 19 3 C 13.488281 3 9 7.488281 9 13 C 9 15.394531 9.839844 17.589844 11.25 19.3125 L 3.28125 27.28125 L 4.71875 28.71875 L 12.6875 20.75 C 14.410156 22.160156 16.605469 23 19 23 C 24.511719 23 29 18.511719 29 13 C 29 7.488281 24.511719 3 19 3 Z M 19 5 C 23.429688 5 27 8.570313 27 13 C 27 17.429688 23.429688 21 19 21 C 14.570313 21 11 17.429688 11 13 C 11 8.570313 14.570313 5 19 5 Z"/></svg></span> <span class="hidden-xxs">SEARCH</span> </button> </div> </div> </div> <div class="clearfix"></div> </form> </div> </div> <div class="tab-pane fade" id="topichome"> <ul class="browsetopics_inline"> <li class="link-subtopic"> <a href="/topic/409">Chemistry</a> </li> <li class="link-subtopic"> <a href="/topic/410">Math and Statistics</a> </li> <li class="link-subtopic"> <a href="/topic/411">Physics</a> </li> <li class="link-subtopic"> <a href="/topic/412">Policy, Reviews and Evaluations</a> </li> </ul> <div class="clearfix"></div> </div> </div> </div> </div> <div class="row visible-xs"> <div class="dropdown" style="margin-left: 10px"> <button class="btn btn-secondary dropdown-toggle" type="button" id="dropdownMenuButton" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Browse by subtopic </button> <div class="dropdown-menu" aria-labelledby="dropdownMenuButton"> <a href="/topic/409" class="dropdown-item">Chemistry</a> <a href="/topic/410" class="dropdown-item">Math and Statistics</a> <a href="/topic/411" class="dropdown-item">Physics</a> <a href="/topic/412" class="dropdown-item">Policy, Reviews and Evaluations</a> </div> <button class="btn btn-secondary" type="button" role="button"> <a href="/topic">View all topics</a> </button> </div> </div> </div> </div> <div class="container ft" style="margin-top: 10px;"> <div class="book-row row" data-title="Most Downloaded in Math, Chemistry, and Physics"> <div class="col-md-10"> <h2 class="row-title ft"> Most Downloaded in Math, Chemistry, and Physics <small> (last 7 days)</small> </h2> </div> <div class="books-flex-row"> <div class="book-tile col-sm-2 col-xs-5 "> <div class="well"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/27317/constructing-valid-geospatial-tools-for-environmental-justice" data-title="Constructing Valid Geospatial Tools for Environmental Justice" data-alias="cover"> <div class="img-container"> <img class="img-responsive" src="https://nap.nationalacademies.org/cover/27317/200" alt="Cover Image: Constructing Valid Geospatial Tools for Environmental Justice"> </div> </a> <h4 class="truncate"><a class="book-title truncate" href="https://nap.nationalacademies.org/catalog/27317/constructing-valid-geospatial-tools-for-environmental-justice" data-title="Constructing Valid Geospatial Tools for Environmental Justice" data-alias="title">Constructing Valid Geospatial Tools for Environmental Justice</a></h4> </div> </div> <div class="book-tile col-sm-2 col-xs-5 "> <div class="well"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/26894/foundational-research-gaps-and-future-directions-for-digital-twins" data-title="Foundational Research Gaps and Future Directions for Digital Twins" data-alias="cover"> <div class="img-container"> <img class="img-responsive" src="https://nap.nationalacademies.org/cover/26894/200" alt="Cover Image: Foundational Research Gaps and Future Directions for Digital Twins"> </div> </a> <h4 class="truncate"><a class="book-title truncate" href="https://nap.nationalacademies.org/catalog/26894/foundational-research-gaps-and-future-directions-for-digital-twins" data-title="Foundational Research Gaps and Future Directions for Digital Twins" data-alias="title">Foundational Research Gaps and Future Directions for Digital Twins</a></h4> </div> </div> <div class="book-tile col-sm-2 col-xs-5 "> <div class="well"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/27732/carbon-utilization-infrastructure-markets-and-research-and-development-a-final" data-title="Carbon Utilization Infrastructure, Markets, and Research and Development: A Final Report" data-alias="cover"> <div class="img-container"> <div class="prepubbanner hidden-xs hidden-sm">Prepublication</div> <img class="img-responsive" src="https://nap.nationalacademies.org/cover/27732/200" alt="Cover Image: Carbon Utilization Infrastructure, Markets, and Research and Development"> </div> </a> <h4 class="truncate"><a class="book-title truncate" href="https://nap.nationalacademies.org/catalog/27732/carbon-utilization-infrastructure-markets-and-research-and-development-a-final" data-title="Carbon Utilization Infrastructure, Markets, and Research and Development: A Final Report" data-alias="title">Carbon Utilization Infrastructure, Markets, and Research and Development: A Final Report</a></h4> </div> </div> <div class="book-tile col-sm-2 col-xs-5 "> <div class="well"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/12654/prudent-practices-in-the-laboratory-handling-and-management-of-chemical" data-title="Prudent Practices in the Laboratory: Handling and Management of Chemical Hazards, Updated Version" data-alias="cover"> <div class="img-container"> <img class="img-responsive" src="https://nap.nationalacademies.org/cover/12654/200" alt="Cover Image: Prudent Practices in the Laboratory"> </div> </a> <h4 class="truncate"><a class="book-title truncate" href="https://nap.nationalacademies.org/catalog/12654/prudent-practices-in-the-laboratory-handling-and-management-of-chemical" data-title="Prudent Practices in the Laboratory: Handling and Management of Chemical Hazards, Updated Version" data-alias="title">Prudent Practices in the Laboratory: Handling and Management of Chemical Hazards, Updated Version</a></h4> </div> </div> <div class="book-tile col-sm-2 col-xs-5 hidden-xs"> <div class="well"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/27830/the-current-status-and-future-direction-of-high-magnetic-field-science-and-technology-in-the-united-states" data-title="The Current Status and Future Direction of High-Magnetic-Field Science and Technology in the United States" data-alias="cover"> <div class="img-container"> <img class="img-responsive" src="https://nap.nationalacademies.org/cover/27830/200" alt="Cover Image: The Current Status and Future Direction of High-Magnetic-Field Science and Technology in the United States"> </div> </a> <h4 class="truncate"><a class="book-title truncate" href="https://nap.nationalacademies.org/catalog/27830/the-current-status-and-future-direction-of-high-magnetic-field-science-and-technology-in-the-united-states" data-title="The Current Status and Future Direction of High-Magnetic-Field Science and Technology in the United States" data-alias="title">The Current Status and Future Direction of High-Magnetic-Field Science and Technology in the United States</a></h4> </div> </div> </div> </div> </div> <div class="container"> <div class="row pagination-row pagination-row-top"> <div class="col-md-7 col-sm-6"> <h3 class="topics-results-hdr">Viewing 1 - 10 of 427 books in Math, Chemistry, and Physics</h3> </div> <div class="col-md-3 col-sm-4 pager-column"> <ul class="pagination"> <li class="active"><span>1</span></li> <li><a href="/topic/290?n=10&start=10">2</a></li> <li><a href="/topic/290?n=10&start=20">3</a></li> <li><a href="/topic/290?n=10&start=30">4</a></li> <li><a href="/topic/290?n=10&start=40">5</a></li> <li><a title="next page" href="/topic/290?n=10&start=10">&rsaquo;</a></li> </ul> </div> </div> <div id="recentreleases"> <div class="list-row row"> <div class=" col-xs-2"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/27939/statistical-and-data-driven-methods-for-additive-manufacturing-qualification-proceedings"> <img class="img-responsive img-cover150 " src="https://nap.nationalacademies.org/cover/27939/200" alt="Statistical and Data-Driven Methods for Additive Manufacturing Qualification: Proceedings of a Workshop"> <meta property="og:image" content="https://nap.nationalacademies.org/cover/27939/200" /> </a> </div> <div class=" col-xs-8"> <div class="results-author results-report-type"> <span data-placement="right" class="report-type" data-toggle="tooltip" data-container="body" title="Proceedings published by the National Academies of Sciences, Engineering, and Medicine chronicle the presentations and discussions at a workshop, symposium, or other event convened by the National Academies. The statements and opinions contained in proceedings are those of the participants and are not endorsed by other participants, the planning committee, or the National Academies."><em>Proceedings </em> </span> </div> <h4 class="results-title"> <a href="https://nap.nationalacademies.org/catalog/27939/statistical-and-data-driven-methods-for-additive-manufacturing-qualification-proceedings">Statistical and Data-Driven Methods for Additive Manufacturing Qualification: Proceedings of a Workshop</a>  (2024) </h4> <div class="results-metadata"> </div> <div class="results-actions"> <a href="https://nap.nationalacademies.org/read/27939" class="readit">Read Online</a> <a href="https://nap.nationalacademies.org/login.php?record_id=27939&page=https%3A%2F%2Fnap.nationalacademies.org%2Fdownload%2F27939" class="dloadit"> <span>Download Free PDF</span><span class="label downloads-label">158<span> downloads</span></span> </a> </div> <div class="clearfix"></div> </div> </div> <div class="list-row row"> <div class=" col-xs-2"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/27830/the-current-status-and-future-direction-of-high-magnetic-field-science-and-technology-in-the-united-states"> <img class="img-responsive img-cover150 " src="https://nap.nationalacademies.org/cover/27830/200" alt="The Current Status and Future Direction of High-Magnetic-Field Science and Technology in the United States"> <meta property="og:image" content="https://nap.nationalacademies.org/cover/27830/200" /> </a> </div> <div class=" col-xs-8"> <div class="results-author results-report-type"> <span data-placement="right" class="report-type" data-toggle="tooltip" data-container="body" title="Consensus Study Reports published by the National Academies of Sciences, Engineering, and Medicine document the evidence-based consensus on the study’s statement of task by an authoring committee of experts. Reports typically include findings, conclusions, and recommendations based on information gathered by the committee and the committee’s deliberations. Each report has been subjected to a rigorous and independent peer-review process and it represents the position of the National Academies on the statement of task."><em>Consensus Study Report </em> </span> </div> <h4 class="results-title"> <a href="https://nap.nationalacademies.org/catalog/27830/the-current-status-and-future-direction-of-high-magnetic-field-science-and-technology-in-the-united-states">The Current Status and Future Direction of High-Magnetic-Field Science and Technology in the United States</a>  (2024) </h4> <div class="results-metadata"> </div> <div class="results-actions"> <a href="https://nap.nationalacademies.org/read/27830" class="readit">Read Online</a> <a href="https://nap.nationalacademies.org/login.php?record_id=27830&page=https%3A%2F%2Fnap.nationalacademies.org%2Fdownload%2F27830" class="dloadit"> <span>Download Free PDF</span><span class="label downloads-label">980<span> downloads</span></span> </a> </div> <div class="clearfix"></div> </div> </div> <div class="list-row row"> <div class=" col-xs-2"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/27317/constructing-valid-geospatial-tools-for-environmental-justice"> <img class="img-responsive img-cover150 " src="https://nap.nationalacademies.org/cover/27317/200" alt="Constructing Valid Geospatial Tools for Environmental Justice"> <meta property="og:image" content="https://nap.nationalacademies.org/cover/27317/200" /> </a> </div> <div class=" col-xs-8"> <div class="results-author results-report-type"> <span data-placement="right" class="report-type" data-toggle="tooltip" data-container="body" title="Consensus Study Reports published by the National Academies of Sciences, Engineering, and Medicine document the evidence-based consensus on the study’s statement of task by an authoring committee of experts. Reports typically include findings, conclusions, and recommendations based on information gathered by the committee and the committee’s deliberations. Each report has been subjected to a rigorous and independent peer-review process and it represents the position of the National Academies on the statement of task."><em>Consensus Study Report </em> </span> </div> <h4 class="results-title"> <a href="https://nap.nationalacademies.org/catalog/27317/constructing-valid-geospatial-tools-for-environmental-justice">Constructing Valid Geospatial Tools for Environmental Justice</a>  (2024) </h4> <div class="results-metadata"> </div> <div class="results-actions"> <a href="https://nap.nationalacademies.org/read/27317" class="readit">Read Online</a> <a href="https://nap.nationalacademies.org/login.php?record_id=27317&page=https%3A%2F%2Fnap.nationalacademies.org%2Fdownload%2F27317" class="dloadit"> <span>Download Free PDF</span><span class="label downloads-label">1,990<span> downloads</span></span> </a> </div> <div class="clearfix"></div> </div> </div> <div class="list-row row"> <div class=" col-xs-2"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/27732/carbon-utilization-infrastructure-markets-and-research-and-development-a-final"> <img class="img-responsive img-cover150 " src="https://nap.nationalacademies.org/cover/27732/200" alt="Carbon Utilization Infrastructure, Markets, and Research and Development: A Final Report"> <meta property="og:image" content="https://nap.nationalacademies.org/cover/27732/200" /> <div class="prepubbanner hidden-xs hidden-sm">Prepublication</div> </a> <span class="prepub-label-sm visible-xs visible-sm hidden-md hidden-lg">Prepublication</span> </div> <div class=" col-xs-8"> <div class="results-author results-report-type"> <span data-placement="right" class="report-type" data-toggle="tooltip" data-container="body" title="Consensus Study Reports published by the National Academies of Sciences, Engineering, and Medicine document the evidence-based consensus on the study’s statement of task by an authoring committee of experts. Reports typically include findings, conclusions, and recommendations based on information gathered by the committee and the committee’s deliberations. Each report has been subjected to a rigorous and independent peer-review process and it represents the position of the National Academies on the statement of task."><em>Consensus Study Report </em> </span> </div> <h4 class="results-title"> <a href="https://nap.nationalacademies.org/catalog/27732/carbon-utilization-infrastructure-markets-and-research-and-development-a-final">Carbon Utilization Infrastructure, Markets, and Research and Development: A Final Report</a>  (2024) </h4> <div class="results-metadata"> </div> <div class="results-actions"> <a href="https://nap.nationalacademies.org/read/27732" class="readit">Read Online</a> <a href="https://nap.nationalacademies.org/login.php?record_id=27732&page=https%3A%2F%2Fnap.nationalacademies.org%2Fdownload%2F27732" class="dloadit"> <span>Download Free PDF</span><span class="label downloads-label">2,775<span> downloads</span></span> </a> </div> <div class="clearfix"></div> </div> </div> <div class="list-row row"> <div class=" col-xs-2"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/27745/risk-analysis-methods-for-nuclear-war-and-nuclear-terrorism-phase"> <img class="img-responsive img-cover150 " src="https://nap.nationalacademies.org/cover/27745/200" alt="Risk Analysis Methods for Nuclear War and Nuclear Terrorism: Phase II (Expanded Abbreviated Report of the CUI Version)"> <meta property="og:image" content="https://nap.nationalacademies.org/cover/27745/200" /> </a> </div> <div class=" col-xs-8"> <div class="results-author results-report-type"> <span data-placement="right" class="report-type" data-toggle="tooltip" data-container="body" title="Consensus Study Reports published by the National Academies of Sciences, Engineering, and Medicine document the evidence-based consensus on the study’s statement of task by an authoring committee of experts. Reports typically include findings, conclusions, and recommendations based on information gathered by the committee and the committee’s deliberations. Each report has been subjected to a rigorous and independent peer-review process and it represents the position of the National Academies on the statement of task."><em>Consensus Study Report </em> </span> </div> <h4 class="results-title"> <a href="https://nap.nationalacademies.org/catalog/27745/risk-analysis-methods-for-nuclear-war-and-nuclear-terrorism-phase">Risk Analysis Methods for Nuclear War and Nuclear Terrorism: Phase II (Expanded Abbreviated Report of the CUI Version)</a>  (2024) </h4> <div class="results-metadata"> </div> <div class="results-actions"> <a href="https://nap.nationalacademies.org/read/27745" class="readit">Read Online</a> <a href="https://nap.nationalacademies.org/login.php?record_id=27745&page=https%3A%2F%2Fnap.nationalacademies.org%2Fdownload%2F27745" class="dloadit"> <span>Download Free PDF</span><span class="label downloads-label">761<span> downloads</span></span> </a> </div> <div class="clearfix"></div> </div> </div> <div class="list-row row"> <div class=" col-xs-2"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/26443/poster-set-for-illustrating-the-impact-of-the-mathematical-sciences"> <img class="img-responsive img-cover150 " src="https://nap.nationalacademies.org/cover/26443/200" alt="Poster Set for Illustrating the Impact of the Mathematical Sciences"> <meta property="og:image" content="https://nap.nationalacademies.org/cover/26443/200" /> </a> </div> <div class=" col-xs-8"> <h4 class="results-title"> <a href="https://nap.nationalacademies.org/catalog/26443/poster-set-for-illustrating-the-impact-of-the-mathematical-sciences">Poster Set for Illustrating the Impact of the Mathematical Sciences</a>  (2024) </h4> <div class="results-metadata"> </div> <div class="results-actions"> </div> <div class="clearfix"></div> </div> </div> <div class="list-row row"> <div class=" col-xs-2"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/26894/foundational-research-gaps-and-future-directions-for-digital-twins"> <img class="img-responsive img-cover150 " src="https://nap.nationalacademies.org/cover/26894/200" alt="Foundational Research Gaps and Future Directions for Digital Twins"> <meta property="og:image" content="https://nap.nationalacademies.org/cover/26894/200" /> </a> </div> <div class=" col-xs-8"> <div class="results-author results-report-type"> <span data-placement="right" class="report-type" data-toggle="tooltip" data-container="body" title="Consensus Study Reports published by the National Academies of Sciences, Engineering, and Medicine document the evidence-based consensus on the study’s statement of task by an authoring committee of experts. Reports typically include findings, conclusions, and recommendations based on information gathered by the committee and the committee’s deliberations. Each report has been subjected to a rigorous and independent peer-review process and it represents the position of the National Academies on the statement of task."><em>Consensus Study Report </em> </span> </div> <h4 class="results-title"> <a href="https://nap.nationalacademies.org/catalog/26894/foundational-research-gaps-and-future-directions-for-digital-twins">Foundational Research Gaps and Future Directions for Digital Twins</a>  (2024) </h4> <div class="results-metadata"> </div> <div class="results-actions"> <a href="https://nap.nationalacademies.org/read/26894" class="readit">Read Online</a> <a href="https://nap.nationalacademies.org/login.php?record_id=26894&page=https%3A%2F%2Fnap.nationalacademies.org%2Fdownload%2F26894" class="dloadit"> <span>Download Free PDF</span><span class="label downloads-label">11,432<span> downloads</span></span> </a> </div> <div class="clearfix"></div> </div> </div> <div class="list-row row"> <div class=" col-xs-2"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/27393/risk-analysis-methods-for-nuclear-war-and-nuclear-terrorism-phase"> <img class="img-responsive img-cover150 " src="https://nap.nationalacademies.org/cover/27393/200" alt="Risk Analysis Methods for Nuclear War and Nuclear Terrorism: Phase II (Abbreviated Report of the CUI Version)"> <meta property="og:image" content="https://nap.nationalacademies.org/cover/27393/200" /> </a> </div> <div class=" col-xs-8"> <div class="results-author results-report-type"> <span data-placement="right" class="report-type" data-toggle="tooltip" data-container="body" title="Consensus Study Reports published by the National Academies of Sciences, Engineering, and Medicine document the evidence-based consensus on the study’s statement of task by an authoring committee of experts. Reports typically include findings, conclusions, and recommendations based on information gathered by the committee and the committee’s deliberations. Each report has been subjected to a rigorous and independent peer-review process and it represents the position of the National Academies on the statement of task."><em>Consensus Study Report </em> </span> </div> <h4 class="results-title"> <a href="https://nap.nationalacademies.org/catalog/27393/risk-analysis-methods-for-nuclear-war-and-nuclear-terrorism-phase">Risk Analysis Methods for Nuclear War and Nuclear Terrorism: Phase II (Abbreviated Report of the CUI Version)</a>  (2023) </h4> <div class="results-metadata"> </div> <div class="results-actions"> <a href="https://nap.nationalacademies.org/read/27393" class="readit">Read Online</a> <a href="https://nap.nationalacademies.org/login.php?record_id=27393&page=https%3A%2F%2Fnap.nationalacademies.org%2Fdownload%2F27393" class="dloadit"> <span>Download Free PDF</span><span class="label downloads-label">295<span> downloads</span></span> </a> </div> <div class="clearfix"></div> </div> </div> <div class="list-row row"> <div class=" col-xs-2"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/27161/innovations-in-catalysis-to-address-modern-challenges-proceedings-of-a"> <img class="img-responsive img-cover150 " src="https://nap.nationalacademies.org/cover/27161/200" alt="Innovations in Catalysis to Address Modern Challenges: Proceedings of a Workshop–in Brief"> <meta property="og:image" content="https://nap.nationalacademies.org/cover/27161/200" /> </a> </div> <div class=" col-xs-8"> <div class="results-author results-report-type"> <span data-placement="right" class="report-type" data-toggle="tooltip" data-container="body" title="Proceedings published by the National Academies of Sciences, Engineering, and Medicine chronicle the presentations and discussions at a workshop, symposium, or other event convened by the National Academies. The statements and opinions contained in proceedings are those of the participants and are not endorsed by other participants, the planning committee, or the National Academies."><em>Proceedings </em> </span> </div> <h4 class="results-title"> <a href="https://nap.nationalacademies.org/catalog/27161/innovations-in-catalysis-to-address-modern-challenges-proceedings-of-a">Innovations in Catalysis to Address Modern Challenges: Proceedings of a Workshop–in Brief</a>  (2023) </h4> <div class="results-metadata"> </div> <div class="results-actions"> <a href="https://nap.nationalacademies.org/read/27161" class="readit">Read Online</a> <a href="https://nap.nationalacademies.org/login.php?record_id=27161&page=https%3A%2F%2Fnap.nationalacademies.org%2Fdownload%2F27161" class="dloadit"> <span>Download Free PDF</span><span class="label downloads-label">154<span> downloads</span></span> </a> </div> <div class="clearfix"></div> </div> </div> <div class="list-row row"> <div class=" col-xs-2"> <a class="book-cover" href="https://nap.nationalacademies.org/catalog/27336/proposal-evaluation-for-allocation-of-supercomputing-time-for-the-study-of-molecular-dynamics"> <img class="img-responsive img-cover150 " src="https://nap.nationalacademies.org/cover/27336/200" alt="Proposal Evaluation for Allocation of Supercomputing Time for the Study of Molecular Dynamics: Fourteenth Round"> <meta property="og:image" content="https://nap.nationalacademies.org/cover/27336/200" /> </a> </div> <div class=" col-xs-8"> <h4 class="results-title"> <a href="https://nap.nationalacademies.org/catalog/27336/proposal-evaluation-for-allocation-of-supercomputing-time-for-the-study-of-molecular-dynamics">Proposal Evaluation for Allocation of Supercomputing Time for the Study of Molecular Dynamics: Fourteenth Round</a>  (2023) </h4> <div class="results-metadata"> </div> <div class="results-actions"> <a href="https://nap.nationalacademies.org/read/27336" class="readit">Read Online</a> <a href="https://nap.nationalacademies.org/login.php?record_id=27336&page=https%3A%2F%2Fnap.nationalacademies.org%2Fdownload%2F27336" class="dloadit"> <span>Download Free PDF</span><span class="label downloads-label">86<span> downloads</span></span> </a> </div> <div class="clearfix"></div> </div> </div> </div> <div class="row pagination-row pagination-row-bottom"> <div class="col-md-10 text-center"> <ul class="pagination"> <li class="active"><span>1</span></li> <li><a href="/topic/290?n=10&start=10">2</a></li> <li><a href="/topic/290?n=10&start=20">3</a></li> <li><a href="/topic/290?n=10&start=30">4</a></li> <li><a href="/topic/290?n=10&start=40">5</a></li> <li><a title="next page" href="/topic/290?n=10&start=10">&rsaquo;</a></li> </ul> </div> </div> </div>  <footer class="global-footer" style="background: #211747; border-top: none" id="global-footer-nap"> <div class="container"> <div class="global-footer__orgs"> <div class="global-footer__logo"> <a href="https://nap.nationalacademies.org"><img src="/images/footer-nap-text.png" alt="National Academies Press: Washington, DC | Home" class="img-responsive"></a> </div> <div> <form id="subscribe-form" action="/updates/" method="POST"> <input type="hidden" name="action" value="subscribe"> <div class="input-group"> <label for="email" class="sr-only">Email Address</label> <input type="hidden" name="SOURCE" value="homepage"> <input class="subscribe-input form-control" type="text" name="EMAIL" id="email" placeholder="Sign up for e-mail updates" title="Enter your e-mail address to subscribe to updates from NAP."> <span class="subscribe-button"> <button type="submit" class="btn btn-subscribe">Subscribe</button> </span> </div> </form></div></div> <div class="global-footer__links"> <ul class="global-footer__nav"> <li> <h6>NAP Quick Links</h6> <ul> <li><a href="/">Home</a></li> <li><a href="/content/about-the-national-academies-press">About</a></li> <li><a href="https://notes.nap.edu/">Notes from NAP</a></li> </ul> <h6>Request A</h6> <ul> <li><a href="/content/request-desk-copies">Desk Copy</a> </li> <li><a href="/content/request/exam_copy.html">Exam Copy </a></li> <li><a href="/content/request-review-copies">Review Copy</a></li> <li><a href="/content/request-rights-and-permissions">Reprint Permission</a></li> </ul> </li> <li> <h6>Browse Publications</h6> <ul> <li><a href="/author">By Division</a></li> <li><a href="/new/">By New Releases</a></li> <li><a href="/collection">By Searchable Collections</a></li> <li><a href="/topic">By Topic</a></li> </ul> </li> <li> <h6>NAP Ordering</h6> <ul> <li><a href="/content/contact-customer-service">Contact Customer Service</a></li> </ul> <h6>Using NAP.edu</h6> <ul> <li><a href="/content/searching-nap-publications">Tips for Searching</a> </li> <li><a href="/content/using-mynap">Help With MyNAP</a></li> <li><a href="/content/about-pdfs">Downloading and Reading PDFs</a> </li> </ul> </li> <li> <h6>NAP Information</h6> <ul> <li><a href="/content/help-with-discounts">Discounts</a></li> <li><a href="/content/information-for-book-trade-customers">Book Trade Customers</a></li> <li><a href="/content/request-rights-and-permissions">Rights and Permissions</a></li> <li><a href="/content/international-ordering-and-distribution">International Ordering and Distribution</a></li> <li><a href="/content/translation-rights">Translation Rights</a></li> </ul></li> </ul> </div></div></footer>  <footer class="global-footer" style="background: #666; border-top: none"><div class="container"><div class="global-footer__orgs"><div class="global-footer__logo"> <a aria-label="Logo of The National Academies" href="https://www.nationalacademies.org/home"> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 315.11 58.33"><defs><style>.cls-1{fill:#fff;}</style></defs><g id="Layer_2" data-name="Layer 2"><g id="Layer_1-2" data-name="Layer 1"><polygon class="cls-1" points="3.73 7.55 20.84 25.49 20.84 1.5 17.81 1.5 17.81 18.08 0.7 0.14 0.7 24.06 3.73 24.06 3.73 7.55"/><polygon class="cls-1" points="28.49 24.06 31.84 24.06 38.98 7.25 45.92 23.87 45.99 24.06 49.34 24.06 39.05 0 28.49 24.06"/><polygon class="cls-1" points="153.23 24.06 156.58 24.06 163.72 7.25 170.66 23.87 170.73 24.06 174.08 24.06 163.79 0 153.23 24.06"/><polygon class="cls-1" points="59.72 24.06 62.76 24.06 62.76 4.41 69.52 4.41 69.52 1.5 52.96 1.5 52.96 4.41 59.72 4.41 59.72 24.06"/><rect class="cls-1" x="78.85" y="1.5" width="3.03" height="22.55"/><path class="cls-1" d="M115.69,12.8a11.72,11.72,0,0,0-23.44,0,11.72,11.72,0,0,0,23.44,0m-3.09,0A8.63,8.63,0,1,1,104,4a8.7,8.7,0,0,1,8.63,8.76"/><polygon class="cls-1" points="128.29 7.55 145.4 25.49 145.4 1.5 142.37 1.5 142.37 18.08 125.25 0.14 125.25 24.06 128.29 24.06 128.29 7.55"/><polygon class="cls-1" points="184.65 1.5 181.62 1.5 181.62 24.06 193.7 24.06 193.7 21.16 184.65 21.16 184.65 1.5"/><path class="cls-1" d="M37.15,34.08A11.48,11.48,0,0,0,25.37,45.8,11.36,11.36,0,0,0,37,57.38a11.77,11.77,0,0,0,6.79-2.19l.13-.09V51.2l-.51.51A9.77,9.77,0,0,1,41,53.5a8.9,8.9,0,0,1-3.95,1A8.75,8.75,0,0,1,37,37a9.09,9.09,0,0,1,3.66.82,10.71,10.71,0,0,1,2.78,2l.51.5V36.4l-.12-.09a10.62,10.62,0,0,0-6.67-2.23"/><path class="cls-1" d="M91.91,37.08a12.19,12.19,0,0,0-8.29-2.64H78.85V57h4.74c3.72,0,6-.73,8.22-2.61a10.75,10.75,0,0,0,4-8.65,11,11,0,0,0-3.86-8.65m-2.09,15.1a9.11,9.11,0,0,1-6.1,1.91H81.88V37.34h1.84c5.44,0,9,3.29,9,8.39a8.09,8.09,0,0,1-2.85,6.45"/><polygon class="cls-1" points="104.99 56.99 118.4 56.99 118.4 54.09 108.02 54.09 108.02 46.16 117.11 46.16 117.11 43.26 108.02 43.26 108.02 37.34 118.4 37.34 118.4 34.44 104.99 34.44 104.99 56.99"/><polygon class="cls-1" points="176.17 56.99 189.58 56.99 189.58 54.09 179.2 54.09 179.2 46.16 188.28 46.16 188.28 43.26 179.2 43.26 179.2 37.34 189.58 37.34 189.58 34.44 176.17 34.44 176.17 56.99"/><polygon class="cls-1" points="138.88 51.34 130.31 32.49 126.44 56.99 129.55 56.99 131.62 42.47 138.84 58.33 146.15 42.47 148.13 56.99 151.23 56.99 147.61 32.45 138.88 51.34"/><rect class="cls-1" x="161.31" y="34.44" width="3.03" height="22.55"/><path class="cls-1" d="M209,46.15A10.78,10.78,0,0,0,205.49,44l-2.12-.92a6.8,6.8,0,0,1-2.21-1.33,2,2,0,0,1-.73-1.69A3.07,3.07,0,0,1,203.82,37a3.62,3.62,0,0,1,2.28.69,4.87,4.87,0,0,1,1.2,1.55l.15.3,2.45-1.62-.12-.24a7,7,0,0,0-2.24-2.55,6.34,6.34,0,0,0-3.69-1c-3.8,0-6.45,2.45-6.45,6a4.86,4.86,0,0,0,1.6,3.8,9.51,9.51,0,0,0,2.84,1.78l2.15,1a9.5,9.5,0,0,1,2.56,1.46,3,3,0,0,1,1,2.35,4.2,4.2,0,0,1-7.06,2.92,4.93,4.93,0,0,1-1.24-2.64l-.05-.33-3,.82.06.28a8.32,8.32,0,0,0,2.13,4,6.74,6.74,0,0,0,5,1.87,6.91,6.91,0,0,0,7.24-7A5.58,5.58,0,0,0,209,46.15"/><polygon class="cls-1" points="0 56.99 3.35 56.99 10.49 40.18 17.43 56.81 17.5 56.99 20.86 56.99 10.56 32.93 0 56.99"/><polygon class="cls-1" points="50.21 56.99 53.57 56.99 60.71 40.18 67.64 56.81 67.72 56.99 71.07 56.99 60.78 32.93 50.21 56.99"/><path class="cls-1" d="M233.74,2.1a3.34,3.34,0,0,0-.93-.11,2.53,2.53,0,0,0-1.52.45,1.48,1.48,0,0,0-.63,1.28,2,2,0,0,0,.54,1.44,7.94,7.94,0,0,0,1.64,1.26,13.5,13.5,0,0,1,1.26.89,3.76,3.76,0,0,1,.83,1,2.62,2.62,0,0,1,.33,1.33,3.06,3.06,0,0,1-.5,1.74,3.26,3.26,0,0,1-1.4,1.18,5.06,5.06,0,0,1-2.09.41,8.3,8.3,0,0,1-1.94-.22,3.51,3.51,0,0,1-1.24-.46l.34-2.18h.92l.09,1.62a2.53,2.53,0,0,0,.81.33,3.86,3.86,0,0,0,1,.13,2.93,2.93,0,0,0,1.77-.53,1.68,1.68,0,0,0,.73-1.47,1.91,1.91,0,0,0-.49-1.34,6.42,6.42,0,0,0-1.49-1.16c-.52-.34-1-.65-1.32-.94a3.76,3.76,0,0,1-.9-1,2.64,2.64,0,0,1-.37-1.4,2.64,2.64,0,0,1,.5-1.62,3.23,3.23,0,0,1,1.35-1.08,4.58,4.58,0,0,1,1.86-.37,7,7,0,0,1,1.72.18,3.31,3.31,0,0,1,1.09.45l-.35,2h-.83l-.12-1.47a2.39,2.39,0,0,0-.68-.3"/><path class="cls-1" d="M241,5a2,2,0,0,0-1.35.54,3.66,3.66,0,0,0-.92,1.52,7,7,0,0,0-.33,2.24,3.52,3.52,0,0,0,.43,1.95,1.39,1.39,0,0,0,1.24.66,2.38,2.38,0,0,0,1.1-.24,5.05,5.05,0,0,0,1-.72l.3.57a3.84,3.84,0,0,1-1.14.95,3.43,3.43,0,0,1-1.76.43,2.44,2.44,0,0,1-2-.91,4,4,0,0,1-.73-2.54A6.43,6.43,0,0,1,237.34,7a5.3,5.3,0,0,1,1.55-2.08,3.74,3.74,0,0,1,2.42-.83,5,5,0,0,1,.93.09,3.09,3.09,0,0,1,.81.26l-.42,1.49-.26-.09A2.53,2.53,0,0,0,241,5"/><path class="cls-1" d="M246.1,11.61a.56.56,0,0,0,.07.29.21.21,0,0,0,.18.1.65.65,0,0,0,.34-.11,2.64,2.64,0,0,0,.44-.35l.2.37a2.88,2.88,0,0,1-.68.67,1.71,1.71,0,0,1-1.08.35,1.14,1.14,0,0,1-.78-.23.8.8,0,0,1-.22-.72c0-.25.15-1.25.4-3,.14-.93.31-2.16.52-3.7l-1-.35.09-.52,2.18-.36.34.17-1,7.22ZM246,2.15a.84.84,0,0,1-.23-.59,1.13,1.13,0,0,1,.3-.79.94.94,0,0,1,.71-.32.79.79,0,0,1,.61.24.77.77,0,0,1,.23.57,1.15,1.15,0,0,1-.29.81,1,1,0,0,1-.77.33.75.75,0,0,1-.56-.25"/><path class="cls-1" d="M254,12.43a3.75,3.75,0,0,1-1.95.52,3,3,0,0,1-1.72-.47,2.74,2.74,0,0,1-1-1.23A4,4,0,0,1,249,9.62a6.35,6.35,0,0,1,.59-2.75,5.08,5.08,0,0,1,1.63-2,3.7,3.7,0,0,1,2.29-.77,2.27,2.27,0,0,1,1.64.52A1.79,1.79,0,0,1,255.72,6a2.34,2.34,0,0,1-.89,1.84,5.79,5.79,0,0,1-2.08,1.12,8.1,8.1,0,0,1-2.15.4,3.42,3.42,0,0,0,.37,1.87,1.48,1.48,0,0,0,1.4.79,3.18,3.18,0,0,0,1.35-.32,3.75,3.75,0,0,0,1.21-.9l.34.57A4,4,0,0,1,254,12.43m-2.11-7A4.1,4.1,0,0,0,251,6.88a5.9,5.9,0,0,0-.39,1.69,5.31,5.31,0,0,0,1.62-.33,4,4,0,0,0,1.41-.87,1.76,1.76,0,0,0,.57-1.28,1.33,1.33,0,0,0-.29-.92,1,1,0,0,0-.77-.31,1.74,1.74,0,0,0-1.28.57"/><path class="cls-1" d="M261.24,4.62A3.14,3.14,0,0,1,263,4.06a1.67,1.67,0,0,1,1.32.52,2.61,2.61,0,0,1,.46,1.71,15.44,15.44,0,0,1-.34,2.34l-.06.36-.13.74a11.51,11.51,0,0,0-.24,1.85c0,.28.06.42.2.42a1.22,1.22,0,0,0,.72-.39l.18.4a1.54,1.54,0,0,1-.32.36,2.92,2.92,0,0,1-.61.39,1.73,1.73,0,0,1-.79.17.84.84,0,0,1-1-.93,12.88,12.88,0,0,1,.27-1.88l.14-.73.06-.37c.1-.55.19-1,.25-1.45a8.17,8.17,0,0,0,.09-1.16,1.67,1.67,0,0,0-.21-1,.87.87,0,0,0-.73-.27,2.33,2.33,0,0,0-1.37.61,5.75,5.75,0,0,0-1.3,1.47l-.75,5.54h-1.46l1-7.43L257.62,5l.12-.58,1.88-.34.32.17-.2,1.84a5.72,5.72,0,0,1,1.5-1.45"/><path class="cls-1" d="M270.77,5a2,2,0,0,0-1.35.54,3.66,3.66,0,0,0-.92,1.52,7,7,0,0,0-.33,2.24,3.52,3.52,0,0,0,.43,1.95,1.39,1.39,0,0,0,1.24.66,2.38,2.38,0,0,0,1.1-.24,5.05,5.05,0,0,0,1-.72l.3.57a3.84,3.84,0,0,1-1.14.95,3.43,3.43,0,0,1-1.76.43,2.44,2.44,0,0,1-2-.91,4,4,0,0,1-.73-2.54A6.43,6.43,0,0,1,267.13,7a5.3,5.3,0,0,1,1.55-2.08,3.76,3.76,0,0,1,2.42-.83,5,5,0,0,1,.93.09,3,3,0,0,1,.81.26l-.42,1.49-.26-.09A2.53,2.53,0,0,0,270.77,5"/><path class="cls-1" d="M278.66,12.43a3.75,3.75,0,0,1-2,.52,3,3,0,0,1-1.71-.47,2.7,2.7,0,0,1-1-1.23,4.19,4.19,0,0,1-.32-1.63,6.35,6.35,0,0,1,.59-2.75,5.17,5.17,0,0,1,1.63-2,3.7,3.7,0,0,1,2.29-.77,2.32,2.32,0,0,1,1.65.52A1.82,1.82,0,0,1,280.38,6a2.34,2.34,0,0,1-.89,1.84,5.79,5.79,0,0,1-2.08,1.12,8,8,0,0,1-2.15.4,3.51,3.51,0,0,0,.37,1.87A1.48,1.48,0,0,0,277,12a3.18,3.18,0,0,0,1.35-.32,3.75,3.75,0,0,0,1.21-.9l.34.57a4,4,0,0,1-1.27,1.11m-2.11-7a4.25,4.25,0,0,0-.87,1.45,6.25,6.25,0,0,0-.39,1.69,5.44,5.44,0,0,0,1.63-.33,4.05,4.05,0,0,0,1.4-.87,1.76,1.76,0,0,0,.57-1.28,1.33,1.33,0,0,0-.29-.92,1,1,0,0,0-.77-.31,1.74,1.74,0,0,0-1.28.57"/><path class="cls-1" d="M286.18,5.13a2.75,2.75,0,0,0-1.09-.21,1.85,1.85,0,0,0-1.13.31,1,1,0,0,0-.43.89,1.43,1.43,0,0,0,.34.93,6.08,6.08,0,0,0,1,.88,10.43,10.43,0,0,1,.88.74,3.1,3.1,0,0,1,.6.76,2.15,2.15,0,0,1,.26,1.05,2.09,2.09,0,0,1-.9,1.81,3.71,3.71,0,0,1-2.22.64,6.32,6.32,0,0,1-1.37-.15,2.1,2.1,0,0,1-.9-.34l.24-1.06a3.41,3.41,0,0,0,.88.44,3.37,3.37,0,0,0,1.18.21,2.21,2.21,0,0,0,1.15-.29,1,1,0,0,0,.48-.92,1.37,1.37,0,0,0-.38-1,6.83,6.83,0,0,0-1.1-.89,3.07,3.07,0,0,1-1.58-2.5,2.16,2.16,0,0,1,.4-1.27,2.64,2.64,0,0,1,1.09-.84,3.81,3.81,0,0,1,1.54-.3,6.32,6.32,0,0,1,1.13.1,4.07,4.07,0,0,1,.8.19l-.26,1.17a1.55,1.55,0,0,0-.6-.39"/><polygon class="cls-1" points="229.34 23.43 236.61 23.43 236.51 25.87 235.6 25.87 235.35 24.25 231.87 24.13 231.29 28.48 234.85 28.36 234.74 29.51 231.21 29.38 230.58 34.05 234.91 33.87 235.77 32.01 236.63 32.18 236.01 34.84 227.85 34.84 227.91 34.24 229.06 34.05 230.29 24.25 229.24 24.09 229.34 23.43"/><path class="cls-1" d="M242.18,26.67a3.16,3.16,0,0,1,1.73-.56,1.67,1.67,0,0,1,1.32.53,2.51,2.51,0,0,1,.46,1.7,14.42,14.42,0,0,1-.34,2.35l-.06.35-.12.74a10.81,10.81,0,0,0-.25,1.86c0,.27.07.41.2.41a1.15,1.15,0,0,0,.72-.38l.19.4a1.54,1.54,0,0,1-.32.35,2.46,2.46,0,0,1-.61.39,1.76,1.76,0,0,1-.79.18c-.65,0-1-.31-1-.94a11.94,11.94,0,0,1,.28-1.87l.14-.74.06-.37c.1-.55.18-1,.24-1.45a8.14,8.14,0,0,0,.1-1.16,1.64,1.64,0,0,0-.21-1,.87.87,0,0,0-.73-.27,2.3,2.3,0,0,0-1.38.61,5.67,5.67,0,0,0-1.29,1.46l-.76,5.55h-1.45l1-7.44-.76-.36.13-.59,1.87-.34.32.17-.2,1.85a5.77,5.77,0,0,1,1.5-1.46"/><path class="cls-1" d="M252.77,37.29a4,4,0,0,1-1.55,1.05,5.36,5.36,0,0,1-1.78.32,5.69,5.69,0,0,1-1-.09,3.45,3.45,0,0,1-.76-.19l.32-1.24a5,5,0,0,0,.9.34,3.56,3.56,0,0,0,1.06.17,2.22,2.22,0,0,0,1.45-.39,2.12,2.12,0,0,0,.63-1.41l.29-2a3.73,3.73,0,0,1-1,.84A2.61,2.61,0,0,1,250,35a2.16,2.16,0,0,1-1.89-.88,3.9,3.9,0,0,1-.64-2.35,6.52,6.52,0,0,1,.58-2.6A5.62,5.62,0,0,1,249.73,27a4.15,4.15,0,0,1,2.61-.87,4.47,4.47,0,0,1,.87.1,5.15,5.15,0,0,1,.8.24l1-.34-1.38,9.31a3.37,3.37,0,0,1-.81,1.87m-.61-10.36a2.36,2.36,0,0,0-1.75.74,4.82,4.82,0,0,0-1.07,1.85,7.16,7.16,0,0,0-.35,2.15,3.3,3.3,0,0,0,.37,1.72,1.16,1.16,0,0,0,1,.62,2.09,2.09,0,0,0,1.2-.39,3.12,3.12,0,0,0,.9-.87l.82-5.5a1.85,1.85,0,0,0-1.15-.32"/><path class="cls-1" d="M258.39,33.67a.45.45,0,0,0,.07.28.19.19,0,0,0,.17.1.6.6,0,0,0,.35-.11,3.13,3.13,0,0,0,.44-.35l.2.37a3.17,3.17,0,0,1-.69.68,1.77,1.77,0,0,1-1.08.35,1.14,1.14,0,0,1-.78-.24.82.82,0,0,1-.22-.71c0-.26.16-1.25.4-3,.15-.93.32-2.17.52-3.7l-.95-.36.09-.52,2.19-.35.33.17-1,7.21Zm-.07-9.46a.81.81,0,0,1-.24-.6,1.09,1.09,0,0,1,.3-.78.94.94,0,0,1,.72-.33.81.81,0,0,1,.61.24.82.82,0,0,1,.23.58,1.17,1.17,0,0,1-.29.8,1,1,0,0,1-.77.33.76.76,0,0,1-.56-.24"/><path class="cls-1" d="M265.74,26.67a3.11,3.11,0,0,1,1.72-.56,1.65,1.65,0,0,1,1.32.53,2.5,2.5,0,0,1,.47,1.7,15.68,15.68,0,0,1-.34,2.35l-.06.35-.13.74a11.6,11.6,0,0,0-.24,1.86c0,.27.06.41.2.41a1.2,1.2,0,0,0,.72-.38l.18.4a1.54,1.54,0,0,1-.32.35,2.28,2.28,0,0,1-.61.39,1.73,1.73,0,0,1-.79.18.84.84,0,0,1-1-.94,12.8,12.8,0,0,1,.27-1.87l.14-.74.06-.37c.1-.55.19-1,.25-1.45a8.07,8.07,0,0,0,.09-1.16,1.64,1.64,0,0,0-.21-1,.87.87,0,0,0-.73-.27,2.27,2.27,0,0,0-1.37.61,5.7,5.7,0,0,0-1.3,1.46l-.75,5.55h-1.46l1-7.44-.75-.36.12-.59,1.88-.34.32.17-.2,1.85a5.77,5.77,0,0,1,1.5-1.46"/><path class="cls-1" d="M276.11,34.48a3.7,3.7,0,0,1-1.95.52,3,3,0,0,1-1.71-.46,2.87,2.87,0,0,1-1-1.23,4.24,4.24,0,0,1-.32-1.64,6.53,6.53,0,0,1,.59-2.75,5.17,5.17,0,0,1,1.63-2,3.76,3.76,0,0,1,2.29-.77,2.32,2.32,0,0,1,1.65.53,1.76,1.76,0,0,1,.55,1.36,2.31,2.31,0,0,1-.88,1.84A5.83,5.83,0,0,1,274.87,31a9.08,9.08,0,0,1-2.15.4,3.49,3.49,0,0,0,.36,1.86,1.48,1.48,0,0,0,1.4.79,3.16,3.16,0,0,0,1.35-.31,3.9,3.9,0,0,0,1.22-.9l.33.57a3.93,3.93,0,0,1-1.27,1.1m-2.1-7a4.12,4.12,0,0,0-.88,1.44,6.37,6.37,0,0,0-.38,1.7,5.17,5.17,0,0,0,1.62-.34,3.78,3.78,0,0,0,1.4-.87,1.74,1.74,0,0,0,.57-1.28,1.31,1.31,0,0,0-.28-.91,1,1,0,0,0-.78-.32,1.68,1.68,0,0,0-1.27.58"/><path class="cls-1" d="M284,34.48a3.7,3.7,0,0,1-2,.52,3,3,0,0,1-1.71-.46,2.87,2.87,0,0,1-1-1.23,4.24,4.24,0,0,1-.32-1.64,6.53,6.53,0,0,1,.59-2.75,5.26,5.26,0,0,1,1.63-2,3.79,3.79,0,0,1,2.3-.77,2.31,2.31,0,0,1,1.64.53,1.76,1.76,0,0,1,.55,1.36,2.31,2.31,0,0,1-.88,1.84A5.74,5.74,0,0,1,282.73,31a9.08,9.08,0,0,1-2.15.4,3.4,3.4,0,0,0,.37,1.86,1.45,1.45,0,0,0,1.39.79,3.2,3.2,0,0,0,1.36-.31,3.86,3.86,0,0,0,1.21-.9l.34.57a4,4,0,0,1-1.28,1.1m-2.1-7a4.12,4.12,0,0,0-.88,1.44,6.37,6.37,0,0,0-.38,1.7,5.17,5.17,0,0,0,1.62-.34,3.7,3.7,0,0,0,1.4-.87,1.74,1.74,0,0,0,.57-1.28,1.31,1.31,0,0,0-.28-.91,1,1,0,0,0-.78-.32,1.7,1.7,0,0,0-1.27.58"/><path class="cls-1" d="M290.05,27.3a3.77,3.77,0,0,1,1-.83,2.34,2.34,0,0,1,1.22-.34.83.83,0,0,1,.5.11l-.33,1.62a1.45,1.45,0,0,0-.75-.15,2.3,2.3,0,0,0-1.29.44,2.89,2.89,0,0,0-1,1.22l-.7,5.47h-1.48l1-7.41-.77-.38.11-.57,1.81-.35.31.18-.11,1.37-.08.61a4.09,4.09,0,0,1,.6-1"/><path class="cls-1" d="M295.29,33.67a.45.45,0,0,0,.07.28.19.19,0,0,0,.17.1.6.6,0,0,0,.35-.11,3.13,3.13,0,0,0,.44-.35l.2.37a3.17,3.17,0,0,1-.69.68,1.77,1.77,0,0,1-1.08.35,1.14,1.14,0,0,1-.78-.24.82.82,0,0,1-.22-.71c0-.26.16-1.25.4-3,.15-.93.32-2.17.52-3.7l-.95-.36.09-.52,2.19-.35.33.17-1,7.21Zm-.07-9.46a.81.81,0,0,1-.24-.6,1.09,1.09,0,0,1,.3-.78.94.94,0,0,1,.72-.33.81.81,0,0,1,.61.24.82.82,0,0,1,.23.58,1.17,1.17,0,0,1-.29.8,1,1,0,0,1-.77.33.76.76,0,0,1-.56-.24"/><path class="cls-1" d="M302.33,26.67a3.14,3.14,0,0,1,1.73-.56,1.67,1.67,0,0,1,1.32.53,2.56,2.56,0,0,1,.46,1.7,15.68,15.68,0,0,1-.34,2.35l-.06.35-.12.74a10.81,10.81,0,0,0-.25,1.86c0,.27.07.41.2.41a1.2,1.2,0,0,0,.72-.38l.19.4a1.64,1.64,0,0,1-.33.35,2.22,2.22,0,0,1-.6.39,1.76,1.76,0,0,1-.79.18c-.65,0-1-.31-1-.94a12.8,12.8,0,0,1,.27-1.87l.14-.74.06-.37c.11-.55.19-1,.25-1.45a8.07,8.07,0,0,0,.09-1.16,1.73,1.73,0,0,0-.2-1,.88.88,0,0,0-.73-.27,2.3,2.3,0,0,0-1.38.61,5.7,5.7,0,0,0-1.3,1.46l-.75,5.55h-1.46l1-7.44-.75-.36.13-.59,1.87-.34.32.17-.2,1.85a5.77,5.77,0,0,1,1.5-1.46"/><path class="cls-1" d="M312.92,37.29a4,4,0,0,1-1.55,1.05,5.36,5.36,0,0,1-1.78.32,5.69,5.69,0,0,1-1-.09,3.57,3.57,0,0,1-.77-.19l.33-1.24a5,5,0,0,0,.9.34,3.51,3.51,0,0,0,1.06.17,2.22,2.22,0,0,0,1.45-.39,2.11,2.11,0,0,0,.62-1.41l.3-2a3.73,3.73,0,0,1-1,.84,2.63,2.63,0,0,1-1.33.34,2.16,2.16,0,0,1-1.89-.88,3.9,3.9,0,0,1-.64-2.35,6.35,6.35,0,0,1,.58-2.6A5.62,5.62,0,0,1,309.88,27a4.11,4.11,0,0,1,2.61-.87,4.56,4.56,0,0,1,.87.1,5.15,5.15,0,0,1,.8.24l.95-.34-1.38,9.31a3.37,3.37,0,0,1-.81,1.87m-.62-10.36a2.35,2.35,0,0,0-1.74.74,4.7,4.7,0,0,0-1.07,1.85,7.16,7.16,0,0,0-.35,2.15,3.3,3.3,0,0,0,.37,1.72,1.14,1.14,0,0,0,1,.62,2,2,0,0,0,1.19-.39,3.3,3.3,0,0,0,.91-.87l.82-5.5a1.88,1.88,0,0,0-1.16-.32"/><path class="cls-1" d="M237.11,49.24c.83-1.82,1.39-3.07,1.65-3.76h3.29l-.06.66-1.37.17-.29,9.8,1.31.18-.07.6h-4.22l.06-.6,1.4-.18.35-6.79.2-3.12L238.2,49l-3.57,8-.83.11-1.26-7.89-.47-2.92-.63,3-1.64,6.91,1.55.18-.06.6h-4l.06-.6,1.28-.18,2.47-9.8-1.41-.17.09-.66h3.56L234.56,53l.2,1.57.67-1.53c.28-.69.84-1.95,1.68-3.77"/><path class="cls-1" d="M247.75,56.54a3.75,3.75,0,0,1-1.95.52,3,3,0,0,1-1.71-.47,2.7,2.7,0,0,1-1-1.23,4.19,4.19,0,0,1-.32-1.63,6.35,6.35,0,0,1,.59-2.75,5.17,5.17,0,0,1,1.63-2,3.7,3.7,0,0,1,2.29-.77,2.32,2.32,0,0,1,1.65.52,1.82,1.82,0,0,1,.55,1.37,2.34,2.34,0,0,1-.89,1.84A5.79,5.79,0,0,1,246.5,53a8,8,0,0,1-2.15.4,3.51,3.51,0,0,0,.37,1.87,1.48,1.48,0,0,0,1.4.79,3.18,3.18,0,0,0,1.35-.32,3.75,3.75,0,0,0,1.21-.9l.34.57a4,4,0,0,1-1.27,1.11m-2.11-7a4.25,4.25,0,0,0-.87,1.45,6.25,6.25,0,0,0-.39,1.69,5.44,5.44,0,0,0,1.63-.33,4.05,4.05,0,0,0,1.4-.87A1.76,1.76,0,0,0,248,50.2a1.33,1.33,0,0,0-.29-.92,1,1,0,0,0-.77-.31,1.74,1.74,0,0,0-1.28.57"/><path class="cls-1" d="M257.17,55.72q0,.39.24.39a1.19,1.19,0,0,0,.7-.39l.22.39a3.42,3.42,0,0,1-.67.62,1.68,1.68,0,0,1-1,.31c-.6,0-.9-.32-.9-1v-.34a3.94,3.94,0,0,1-1.08.94,2.72,2.72,0,0,1-1.44.38,2.13,2.13,0,0,1-1.87-.88,4,4,0,0,1-.63-2.34,6.41,6.41,0,0,1,.58-2.62A5.56,5.56,0,0,1,253,49a4.1,4.1,0,0,1,2.61-.86,4,4,0,0,1,1.15.18l.41-2.76-1-.26.13-.54,2.16-.28.34.2-1.6,10.84a.79.79,0,0,0,0,.17M255.42,49a2.32,2.32,0,0,0-1.74.75,4.64,4.64,0,0,0-1.06,1.84,7.15,7.15,0,0,0-.34,2.16,3.44,3.44,0,0,0,.36,1.72,1.12,1.12,0,0,0,1,.61,2.06,2.06,0,0,0,1.23-.41,3.11,3.11,0,0,0,.9-.91l.83-5.42a1.94,1.94,0,0,0-1.2-.34"/><path class="cls-1" d="M262.14,55.72a.57.57,0,0,0,.06.29.24.24,0,0,0,.18.1.71.71,0,0,0,.35-.11,3.84,3.84,0,0,0,.44-.35l.19.37a2.88,2.88,0,0,1-.68.67,1.71,1.71,0,0,1-1.08.35,1.19,1.19,0,0,1-.78-.23.8.8,0,0,1-.22-.72c0-.25.15-1.25.4-3,.14-.93.32-2.16.52-3.7l-.95-.35.09-.52,2.18-.36.34.17-1,7.22Zm-.07-9.46a.81.81,0,0,1-.24-.6,1.12,1.12,0,0,1,.3-.78,1,1,0,0,1,.71-.32.83.83,0,0,1,.62.24.81.81,0,0,1,.23.57,1.2,1.2,0,0,1-.29.81,1,1,0,0,1-.77.33.73.73,0,0,1-.56-.25"/><path class="cls-1" d="M269.42,49.14a2,2,0,0,0-1.35.54,3.6,3.6,0,0,0-.92,1.52,7,7,0,0,0-.33,2.24,3.52,3.52,0,0,0,.43,2,1.39,1.39,0,0,0,1.24.66,2.38,2.38,0,0,0,1.1-.24,5.05,5.05,0,0,0,1-.72l.3.57a4,4,0,0,1-1.14,1A3.43,3.43,0,0,1,268,57a2.44,2.44,0,0,1-2-.91,4,4,0,0,1-.73-2.54,6.43,6.43,0,0,1,.53-2.51A5.3,5.3,0,0,1,267.33,49a3.69,3.69,0,0,1,2.42-.83,5,5,0,0,1,.93.09,3.09,3.09,0,0,1,.81.26L271.07,50l-.26-.09a2.53,2.53,0,0,0-1.39-.78"/><path class="cls-1" d="M274.77,55.72a.56.56,0,0,0,.07.29.24.24,0,0,0,.18.1.71.71,0,0,0,.35-.11,3.15,3.15,0,0,0,.43-.35l.2.37a2.88,2.88,0,0,1-.68.67,1.71,1.71,0,0,1-1.08.35,1.19,1.19,0,0,1-.78-.23.8.8,0,0,1-.22-.72c0-.25.15-1.25.4-3,.14-.93.32-2.16.52-3.7l-1-.35.09-.52,2.18-.36.34.17-1,7.22Zm-.07-9.46a.85.85,0,0,1-.23-.6,1.12,1.12,0,0,1,.3-.78.94.94,0,0,1,.71-.32.79.79,0,0,1,.61.24.78.78,0,0,1,.24.57,1.16,1.16,0,0,1-.3.81,1,1,0,0,1-.76.33.75.75,0,0,1-.57-.25"/><path class="cls-1" d="M282,48.73a3.09,3.09,0,0,1,1.73-.56,1.65,1.65,0,0,1,1.32.52,2.54,2.54,0,0,1,.46,1.7,15.09,15.09,0,0,1-.33,2.35l-.07.36-.12.73a11.6,11.6,0,0,0-.24,1.86c0,.28.06.42.19.42a1.22,1.22,0,0,0,.73-.39l.18.4a1.77,1.77,0,0,1-.32.36,3.21,3.21,0,0,1-.61.39,1.86,1.86,0,0,1-.79.17c-.64,0-1-.31-1-.93a13.42,13.42,0,0,1,.28-1.88l.14-.73.06-.37c.1-.56.18-1,.25-1.45a8.17,8.17,0,0,0,.09-1.16,1.67,1.67,0,0,0-.21-1,.87.87,0,0,0-.73-.27,2.31,2.31,0,0,0-1.37.61,5.58,5.58,0,0,0-1.3,1.47l-.75,5.54H278.2l1-7.43-.75-.37.12-.58,1.87-.34.33.17-.2,1.84A5.85,5.85,0,0,1,282,48.73"/><path class="cls-1" d="M292.42,56.54a3.75,3.75,0,0,1-1.95.52,3,3,0,0,1-1.71-.47,2.7,2.7,0,0,1-1-1.23,4.19,4.19,0,0,1-.32-1.63A6.35,6.35,0,0,1,288,51a5.17,5.17,0,0,1,1.63-2,3.7,3.7,0,0,1,2.29-.77,2.32,2.32,0,0,1,1.65.52,1.82,1.82,0,0,1,.55,1.37,2.34,2.34,0,0,1-.89,1.84A5.79,5.79,0,0,1,291.17,53a8,8,0,0,1-2.15.4,3.51,3.51,0,0,0,.37,1.87,1.48,1.48,0,0,0,1.4.79,3.18,3.18,0,0,0,1.35-.32,3.75,3.75,0,0,0,1.21-.9l.34.57a4,4,0,0,1-1.27,1.11m-2.11-7a4.25,4.25,0,0,0-.87,1.45,6.25,6.25,0,0,0-.39,1.69,5.44,5.44,0,0,0,1.63-.33,4.05,4.05,0,0,0,1.4-.87,1.76,1.76,0,0,0,.57-1.28,1.33,1.33,0,0,0-.29-.92,1,1,0,0,0-.77-.31,1.74,1.74,0,0,0-1.28.57"/></g></g></svg> </a> </div> <div><a href="http://www.nasonline.org/" rel="noreferrer" target="_blank" class="global-footer__org"><img src="data:image/png;base64,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" alt="NAS Logo" width="17" height="17"> <span> National Academy of Sciences </span></a> <a href="https://www.nae.edu/" rel="noreferrer" target="_blank" class="global-footer__org"><img src="data:image/png;base64,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" alt="NAE Logo" width="17" height="17"> <span> National Academy of Engineering </span></a> <a href="https://nam.edu/" rel="noreferrer" target="_blank" class="global-footer__org"><img src="data:image/png;base64,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" alt="NAM Logo" width="17" height="17"> <span> National Academy of Medicine </span></a></div></div> <div class="global-footer__links"><ul class="global-footer__nav"><li><a rel="" title="" href="//www.nationalacademies.org/about" target="_self"> About Us </a></li><li><a rel="" title="" href="//www.nationalacademies.org/our-work" target="_self"> Our Work </a></li><li><a rel="" title="" href="//www.nationalacademies.org/events" target="_self"> Events </a></li><li><a rel="" title="" href="//www.nationalacademies.org/contact-us" target="_self"> Contact Us </a></li><li><a rel="" title="" href="//www.nationalacademies.org/opportunities" target="_self"> Opportunities </a></li><li><a rel="" title="" href="//www.nationalacademies.org/publications" target="_self"> Publications </a></li><li><a rel="" title="" href="//www.nationalacademies.org/about/visiting-us" target="_self"> Visit </a></li><li><a rel="" title="" href="//www.nationalacademies.org/about/operating-status" target="_self"> Current Operating Status </a></li><li><a rel="" title="" href="//www.nationalacademies.org/subscribe" target="_self"> E-Newsletters </a></li></ul> <div class="global-footer__social"><p> Connect With Us </p> <ul><li><a href="https://www.facebook.com/NationalAcademies/" target="_self" class="connect-facebook"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""><path fill-rule="evenodd" d="M20 9.375h-2.222c-.334 0-1.111.531-1.111 1.125v2.25H20v3.375h-3.333V24h-3.334v-7.875H10V12.75h3.333V10.5c0-2.482 2.18-4.5 4.515-4.5H20v3.375"></path></svg></a></li><li><a href="https://twitter.com/TheNASEM" target="_self" class="connect-twitter"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""><path fill-rule="evenodd" d="M24 9.775a7.238 7.238 0 01-2.121.598 3.787 3.787 0 001.625-2.096 7.253 7.253 0 01-2.347.92A3.65 3.65 0 0018.461 8c-2.04 0-3.695 1.697-3.695 3.787 0 .298.033.586.096.863-3.07-.157-5.793-1.665-7.615-3.956a3.853 3.853 0 00-.499 1.904c0 1.313.853 2.472 1.845 3.151-.606-.02-1.473-.191-1.473-.475v.05c0 1.833 1.072 3.363 2.761 3.712-.31.086-.736.133-1.072.133a3.99 3.99 0 01-.746-.07c.47 1.505 1.81 2.6 3.425 2.632A7.343 7.343 0 016 21.299 10.277 10.277 0 0011.66 23c6.795 0 10.51-5.77 10.51-10.774 0-.163-.005-.328-.013-.491A7.588 7.588 0 0024 9.775"></path></svg></a></li><li><a href="https://www.linkedin.com/company/the-national-academies" target="_self" class="connect-linkedin"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""><path fill-rule="evenodd" d="M7 23V10.533h3.4V23H7zm12.467-12.467c2.558 0 4.533 2.034 4.533 5.665V23h-3.4v-6.347c0-1.586-.779-2.679-2.192-2.679-1.082 0-1.94.736-2.223 1.443-.097.251-.118.608-.118.959V23h-3.4s.088-11.333.035-12.467h3.365l-.04 2.267c.516-1.133 1.335-2.267 3.44-2.267zM10.4 7.7a1.7 1.7 0 11-3.4 0 1.7 1.7 0 013.4 0z"></path></svg></a></li><li><a href="http://www.nationalacademies.org/news.xml" target="_self" title="Share our site" class="connect-rss"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""><path d="M11.85 20.537a2.425 2.425 0 11-4.85 0 2.425 2.425 0 014.85 0zm6.65 1.79c-.316-5.854-5.005-10.548-10.864-10.865a.605.605 0 00-.636.605v1.82c0 .32.246.586.564.607a8.484 8.484 0 017.904 7.904c.02.318.288.564.607.564h1.82c.346 0 .624-.29.605-.636zm5.462.01C23.644 13.484 16.52 6.32 7.625 6A.605.605 0 007 6.606v1.82c0 .327.259.593.585.606 7.238.297 13.048 6.108 13.345 13.345.013.326.28.585.606.585h1.82a.605.605 0 00.606-.625z"></path></svg></a></li><li><a href="//www.nationalacademies.org/subscribe" target="_self" title="Subscribe" class="connect-email"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""><path fill-rule="evenodd" d="M6 12.964v4.569c0 .296.197.386.439.2l2.822-2.15c.243-.184.243-.484 0-.669l-2.822-2.15c-.242-.185-.439-.095-.439.2zM7.125 9C6.506 9 6 9.601 6 10.071l8.514 6.455a.775.775 0 00.882.002L24 10.07C24 9.601 23.494 9 22.875 9H7.125zm13.613 6.584l2.822 2.15c.243.185.44.095.44-.201v-4.569c0-.295-.197-.385-.44-.2l-2.822 2.15c-.242.185-.242.485 0 .67zM18.26 16.8l-2.822 2.15a.764.764 0 01-.879 0l-2.822-2.15a.765.765 0 00-.88-.001L6 20.495v.29c0 .471.506 1.072 1.125 1.072h15.75c.619 0 1.125-.6 1.125-1.071v-.29L19.141 16.8a.767.767 0 00-.88.001z"></path></svg></a></li></ul></div> <div class="global-footer__legal"><div><button class="button button--icon button--reverse button--secondary"> <a href="https://www8.nationalacademies.org/AcademyGiving/nas/nasform.aspx ">Donate Today</a> <span class="button__icon"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 30 30" class=""><path d="M17.885 10.708a1 1 0 111.412-1.416l5.624 5.608-5.616 5.732a1 1 0 11-1.428-1.4l4.228-4.316-4.22-4.208z"></path><path d="M23.07 14a1 1 0 010 2H7a1 1 0 010-2h16.07z"></path></svg></span></button></div> <div><ul><li><a rel="" title="" href="//www.nationalacademies.org/legal/privacy" target="_self"> Privacy Statement </a></li><li><a rel="" title="" href="//www.nationalacademies.org/legal/policy" target="_self"> DMCA Policy </a></li><li><a rel="" title="" href="//www.nationalacademies.org/legal/terms" target="_self"> Terms of Use </a></li><li><a rel="" title="" href="//www.nationalacademies.org/site-map" target="_self"> Site Map </a></li></ul> <p class="copyright"><a rel="" title="" href="//www.nationalacademies.org/legal" target="_self"> Copyright © <script type="text/javascript">  </script> National Academy of Sciences. All Rights Reserved. </a></p></div></div></div></div></footer> <script src="//nap.nationalacademies.org/includes/js/jquery.dlmenu.js"></script> <script src="//nap.nationalacademies.org/includes/js/jquery.placeholder.js"></script>  <script> // Save to MyNAP handler $('a.saveit').one('click', function(e) { e.preventDefault(); $.getJSON('/napsave.php', { type: 'shelf', r: $(this).data('recordid') }, function(response) { $(e.target) .toggleClass('saveit saveit_active') .attr('href', '/mynap.php') .text('Added to Bookshelf'); }); }); </script>  <script src="https://cdn.cookielaw.org/scripttemplates/otSDKStub.js" type="text/javascript" charset="UTF-8" data-domain-script="5639f7b9-d1de-4e1d-9f2f-e86c3f24727b" ></script> <script type="text/javascript"> function OptanonWrapper() { } </script>   <div class="modal fade" id="type-modal" tabindex="-1" role="dialog" aria-labelledby="typeModalLabel" aria-hidden="true"> <div class="modal-dialog"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal"><span aria-hidden="true">×</span><span class="sr-only">Close</span></button> <h4 class="modal-title">Types of Publications</h4> </div> <div class="modal-body"> <p><strong>Proceedings: </strong><br> Proceedings published by the National Academies of Sciences, Engineering, and Medicine chronicle the presentations and discussions at a workshop, symposium, or other event convened by the National Academies. The statements and opinions contained in proceedings are those of the participants and are not endorsed by other participants, the planning committee, or the National Academies.</p> <p><strong>Consensus Study Reports: </strong><br> Consensus Study Reports published by the National Academies of Sciences, Engineering, and Medicine document the evidence-based consensus on the study’s statement of task by an authoring committee of experts. Reports typically include findings, conclusions, and recommendations based on information gathered by the committee and the committee’s deliberations. Each report has been subjected to a rigorous and independent peer-review process and it represents the position of the National Academies on the statement of task.</p> <p><strong>Rapid Expert Consultation:</strong><br> Rapid Expert Consultations published by the National Academies of Sciences, Engineering, and Medicine are authored by subject-matter experts on narrowly focused topics that can be supported by a body of evidence. The discussions contained in rapid expert consultations are considered those of the authors and do not contain policy recommendations. Rapid expert consultations are reviewed by the institution before release.</p> </div> <div class="modal-footer"> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div>  <script src="https://cdnjs.cloudflare.com/ajax/libs/popper.js/1.16.0/umd/popper.min.js"></script> <script src="/vendor/bootstrap/3.1.1/bootstrap.min.js"></script> <script src="/includes/js/jquery.dotdotdot.min.js" type="text/javascript"></script> <script src="/includes/js/typeahead.bundle.min.js"></script> <script src="/includes/js/nap-typeahead.js"></script> <script> $("[data-toggle=tooltip").tooltip(); $('#dl-menu').dlmenu({ animationClasses: { classin: 'dl-animate-in-5', classout: 'dl-animate-out-5' } }); $('.truncate').dotdotdot({ after: 'a.readmore', watch: 'window', lastCharacter: { remove: [' ', ',', ';', '.', '!', '?'] } }); $(window).on('load', function() { $('.truncate').trigger('update'); }); var $input = $('#searchtopic #inputsearch'); var parameters = { t: 290 } initTypeahead($input, parameters); $('#searchtopic .btn-searchhome').appendTo('.twitter-typeahead'); </script> <link ref="preload" src="//s7.addthis.com/js/300/addthis_widget.js#pubid=napdigops" as="script"/> <script type="text/javascript" src="//s7.addthis.com/js/300/addthis_widget.js#pubid=napdigops"></script> <script type="text/javascript"> dataLayer.push({'addevent': true}); addthis.layers({ 'theme' : 'transparent', 'share' : { 'position' : 'left', 'numPreferredServices' : 4, 'services': 'facebook,twitter,linkedin,email,more' }, 'responsive' : { 'maxWidth': '1210px' } }); </script>  </body> </html>

CINXE.COM

Math, Chemistry, and Physics | The National Academies Press