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data-dom-id="Pill-react-component-38a88d07-1a31-428e-8f07-35ebe8f72454"></div> <div id="Pill-react-component-38a88d07-1a31-428e-8f07-35ebe8f72454"></div> </a></div></div></div></div><div class="right-panel-container"><div class="user-content-wrapper"><div class="uploads-container" id="social-redesign-work-container"><div class="upload-header"><h2 class="ds2-5-heading-sans-serif-xs">Uploads</h2></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Bruno Carbonaro</h3></div><div class="js-work-strip profile--work_container" data-work-id="123274493"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/123274493/A_nonconservative_kinetic_framework_under_the_action_of_an_external_force_field_Theoretical_results_with_application_inspired_to_ecology"><img alt="Research paper thumbnail of A nonconservative kinetic framework under the action of an external force field: Theoretical results with application inspired to ecology" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/123274493/A_nonconservative_kinetic_framework_under_the_action_of_an_external_force_field_Theoretical_results_with_application_inspired_to_ecology">A nonconservative kinetic framework under the action of an external force field: Theoretical results with application inspired to ecology</a></div><div class="wp-workCard_item"><span>European Journal of Applied Mathematics</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The present paper deals with the kinetic-theoretic description of the evolution of systems consis...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The present paper deals with the kinetic-theoretic description of the evolution of systems consisting of many particles interacting not only with each other but also with the external world, so that the equation governing their evolution contains an additional term representing such interaction, called the ‘forcing term’. Firstly, the interactions between pairs of particles are both conservative and nonconservative; the latter represents, among others, birth/death rates. The ‘forcing term’ does not express a ‘classical’ force exerted by the external world on the particles, but a more general influence on the effects of mutual interactions of particles, for instance, climate changes, that increase or decrease the different agricultural productions at different times, thus altering the economic relationships between different subsystems, that in turn can be also perturbed by stock market fluctuations, sudden wars, periodic epidemics, and so on. Thus, the interest towards these problem...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="123274493"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="123274493"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 123274493; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=123274493]").text(description); $(".js-view-count[data-work-id=123274493]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 123274493; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='123274493']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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} }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115391918"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115391918/Modeling_epidemics_by_means_of_the_stochastic_description_of_complex_systems"><img alt="Research paper thumbnail of Modeling epidemics by means of the stochastic description of complex systems" class="work-thumbnail" src="https://attachments.academia-assets.com/111811797/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115391918/Modeling_epidemics_by_means_of_the_stochastic_description_of_complex_systems">Modeling epidemics by means of the stochastic description of complex systems</a></div><div class="wp-workCard_item"><span>Computational and mathematical methods</span><span>, Oct 25, 2021</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The aim of the present paper is to show a way in which the problem of predicting the evolution of...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The aim of the present paper is to show a way in which the problem of predicting the evolution of an epidemic may be tackled by describing it in the framework of Boltzmann's kinetic theory, as it has been developed and applied in the last years to complex systems by a suitable modification of the Boltzmann equation, a suitable re-interpretation of state variables and the introduction of the notion of functional subsystems. Accordingly, in this paper we model an arbitrary (national) population S as a complex system, split in two functional subsystems, the first containing all single individuals of S and the second containing the care tools , that are to be meant as available places in hospitals with a sufficient number of physicians and of equipments</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="62f64b0a59ffce2790af2161243a1e4b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":111811797,"asset_id":115391918,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/111811797/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115391918"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115391918"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115391918; 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Necessary and sufficient conditions to get common ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562443"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562443"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562443; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562443]").text(description); $(".js-view-count[data-work-id=111562443]").attr('title', description).tooltip(); 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=111562443]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":111562443,"title":"Some remarks on a modified fluid dynamics equation","internal_url":"https://www.academia.edu/111562443/Some_remarks_on_a_modified_fluid_dynamics_equation","owner_id":219146495,"coauthors_can_edit":true,"owner":{"id":219146495,"first_name":"Bruno","middle_initials":null,"last_name":"Carbonaro","page_name":"BrunoCarbonaro","domain_name":"independent","created_at":"2022-03-29T02:46:30.348-07:00","display_name":"Bruno Carbonaro","url":"https://independent.academia.edu/BrunoCarbonaro"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562442"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562442/The_mathematical_analysis_towards_the_dependence_on_the_initial_data_for_a_discrete_thermostatted_kinetic_framework_for_biological_systems_composed_of_interacting_entities"><img alt="Research paper thumbnail of The mathematical analysis towards the dependence on the initial data for a discrete thermostatted kinetic framework for biological systems composed of interacting entities" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562442/The_mathematical_analysis_towards_the_dependence_on_the_initial_data_for_a_discrete_thermostatted_kinetic_framework_for_biological_systems_composed_of_interacting_entities">The mathematical analysis towards the dependence on the initial data for a discrete thermostatted kinetic framework for biological systems composed of interacting entities</a></div><div class="wp-workCard_item"><span>AIMS biophysics</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper is devoted to a mathematical proof of the continuous dependence on the initial data fo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper is devoted to a mathematical proof of the continuous dependence on the initial data for the discrete thermostatted kinetic framework, for all T &gt; 0. This is a versatile model for describing the time-evolution of a biological complex system which is composed by a large number of interacting entities, called active particles, and is subjected to an external force field due to the environment. A thermostat term is introduced in order to keep the 2nd-order moment of the system, corresponding to the physical global activation energy, constant in time. This model is expressed by a system of nonlinear ordinary differential equations with quadratic nonlinearity.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562442"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562442"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562442; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562442]").text(description); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562441"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562441/On_the_work_and_energy_theorem_for_unbounded_elastic_bodies"><img alt="Research paper thumbnail of On the work and energy theorem for unbounded elastic bodies" class="work-thumbnail" src="https://attachments.academia-assets.com/109065222/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562441/On_the_work_and_energy_theorem_for_unbounded_elastic_bodies">On the work and energy theorem for unbounded elastic bodies</a></div><div class="wp-workCard_item"><span>Journal of Elasticity</span><span>, 1985</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The main scope of the paper is the statement and the proof of the "work and energy theorem" for e...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The main scope of the paper is the statement and the proof of the "work and energy theorem" for elastic bodies that occupy an unbounded region of space and whose acoustic tensor A may suitably grow at large spatial distance from a fixed origin.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9321d4936f190a9f4d3c55c14a7e7d2d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065222,"asset_id":111562441,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065222/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562441"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562441"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562441; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562440"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562440/Some_Theorems_in_Temperature_Rate_Dependent_Thermoelasticity_for_Unbounded_Domains"><img alt="Research paper thumbnail of Some Theorems in Temperature-Rate-Dependent Thermoelasticity for Unbounded Domains" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562440/Some_Theorems_in_Temperature_Rate_Dependent_Thermoelasticity_for_Unbounded_Domains">Some Theorems in Temperature-Rate-Dependent Thermoelasticity for Unbounded Domains</a></div><div class="wp-workCard_item"><span>Journal of Thermal Stresses</span><span>, 1987</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A domain of influence theorem, work and energy theorem, and reciprocity theorem are proved for a ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A domain of influence theorem, work and energy theorem, and reciprocity theorem are proved for a linear anisotropic nonhomogeneous temperature-rate-dependent thermoelastic unbounded body. The theorems cover the case where the constitutive fields may attain unbounded values at infinity, and they are based on a hypothesis from which it follows that a thermoelastic disturbance produced by an external ther-momechanical load of</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562440"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562440"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562440; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562440]").text(description); $(".js-view-count[data-work-id=111562440]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 111562440; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='111562440']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=111562440]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":111562440,"title":"Some Theorems in Temperature-Rate-Dependent Thermoelasticity for Unbounded Domains","internal_url":"https://www.academia.edu/111562440/Some_Theorems_in_Temperature_Rate_Dependent_Thermoelasticity_for_Unbounded_Domains","owner_id":219146495,"coauthors_can_edit":true,"owner":{"id":219146495,"first_name":"Bruno","middle_initials":null,"last_name":"Carbonaro","page_name":"BrunoCarbonaro","domain_name":"independent","created_at":"2022-03-29T02:46:30.348-07:00","display_name":"Bruno Carbonaro","url":"https://independent.academia.edu/BrunoCarbonaro"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562439"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562439/The_role_of_the_principle_of_inertia_in_KTAP_models"><img alt="Research paper thumbnail of The role of the principle of inertia in KTAP models" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562439/The_role_of_the_principle_of_inertia_in_KTAP_models">The role of the principle of inertia in KTAP models</a></div><div class="wp-workCard_item"><span>Journal of Mathematical Physics</span><span>, 2022</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The mathematical models for describing the evolution of complex systems in the framework of the K...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The mathematical models for describing the evolution of complex systems in the framework of the Kinetic Theory for Active Particles (KTAPs), based on suitable generalizations of Boltzmann’s kinetic theory of gases, nowadays seem to be the most versatile and effective ones to formulate in sufficiently precise and accurate terms, and possibly to solve, the most important and difficult problems not only of our everyday’s individual life but also of the life of human collectivities in the long term. In this connection, a simple examination of the application of KTAP to practical problems in which the state variables are not the usual position-velocity variables (and the kinetic state can, indeed, be completely disregarded), such as the prediction of the evolution of an epidemic in a given population in view of possible containment measures, suggests that the scheme is not always so general as it would be desirable for the simple reason that it is conditioned by the implicit (and natural) assumption of the principle of inertia, which in non-mechanical contexts should be rejected. Starting from this remark, this paper has a threefold aim: (1) to point out that KTAP equations make a tacit use of the principle of inertia; (2) to recall the reasons why the principle of inertia is naturally connected to the origin of KTAP models; and (3) to suggest a suitable modification of the KTAP general system, enabling the user to choose to adopt or reject the principle of inertia.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562439"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562439"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562439; 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It was originally planned as a "note added in proof" to [1], but when I received the galley proofs of [1], it was not yet ready. According to its nature of an "appendix" to [1], throughout this note we shall always refer to the notations and the formulae of the full paper. The reader should be then aware that, when quoting formula (,) or Section X or Remark Y, we mean formula (,) or Section X or Remark Y of[1]. The need of this addition to [1] may be easily understood by considering the following objection to the counterexamples given there. The one-dimensional model of the dynamical problem of linear elasticity is not quite suitable to sample the considered case in which a point o of the body B is allowed to be a singularity point for the material data. Indeed, the statement of the boundary-initial value problem, in its general form, requires that B is an "open connected set" (cf. Section 3): now, when dealing with a one-dimensional example, the presence of the singularity point o "breaks" the connection of B, which in this case turns out to be the join of two different bodies B l = (-x0, 0) and B 2 = (0, + o0) (cf. Section 5). Thus, at a first glance, it could seem that if we would construct an analogous example in the general case (i.e. in two or three dimensions), we should think, rather than of a single body B containing a singularity point o, of two different bodies B1 and B2 with a common boundary 7, where the material data are allowed to be singular. In such a problem, the dependence of the uniqueness of solutions on some conditions on 7 (e.g., the continuity of the displacement and/or the stress field across 7, or the validity of the Third Law of Dynamics for the contact interactions between B~ and B2) is to be</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f916a2624bd7781f5def0fa5e1e82872" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065148,"asset_id":111562438,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065148/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562438"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562438"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562438; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562437"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562437/Wave_Propagation_Uniqueness_and_Singularities_at_Infinity_for_an_Unbounded_Linearly_Viscoelastic_Material"><img alt="Research paper thumbnail of Wave Propagation, Uniqueness and Singularities at Infinity for an Unbounded Linearly Viscoelastic Material" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562437/Wave_Propagation_Uniqueness_and_Singularities_at_Infinity_for_an_Unbounded_Linearly_Viscoelastic_Material">Wave Propagation, Uniqueness and Singularities at Infinity for an Unbounded Linearly Viscoelastic Material</a></div><div class="wp-workCard_item"><span>Mathematical Models and Methods in Applied Sciences</span><span>, Dec 1, 1995</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Following a method used in two earlier papers,2,3 a general domain of dependence in equality is p...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Following a method used in two earlier papers,2,3 a general domain of dependence in equality is proved for inhomogeneous and anisotropic linearly viscoelastic solids, which furnishes the explicit link between the maximum propagation speed of disturbances in the body and the behavior at infinity of the acoustic tensor and the memory functions of the material, and allows to prove a global uniqueness theorem for the mixed problem of viscoelasticity in an unbounded reference configuration Ω. The method of proof applies regardless of whether the memory functions are assumed or not: moreover, no boundedness assumption is made on the material data.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562437"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562437"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562437; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562437]").text(description); $(".js-view-count[data-work-id=111562437]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 111562437; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='111562437']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=111562437]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":111562437,"title":"Wave Propagation, Uniqueness and Singularities at Infinity for an Unbounded Linearly Viscoelastic Material","internal_url":"https://www.academia.edu/111562437/Wave_Propagation_Uniqueness_and_Singularities_at_Infinity_for_an_Unbounded_Linearly_Viscoelastic_Material","owner_id":219146495,"coauthors_can_edit":true,"owner":{"id":219146495,"first_name":"Bruno","middle_initials":null,"last_name":"Carbonaro","page_name":"BrunoCarbonaro","domain_name":"independent","created_at":"2022-03-29T02:46:30.348-07:00","display_name":"Bruno Carbonaro","url":"https://independent.academia.edu/BrunoCarbonaro"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562436"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562436/Wave_propagation_and_uniqueness_in_magneto_elastodynamics"><img alt="Research paper thumbnail of Wave propagation and uniqueness in magneto-elastodynamics" class="work-thumbnail" src="https://attachments.academia-assets.com/109065220/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562436/Wave_propagation_and_uniqueness_in_magneto_elastodynamics">Wave propagation and uniqueness in magneto-elastodynamics</a></div><div class="wp-workCard_item"><span>International Journal of Engineering Science</span><span>, 1986</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">By using the method introduced in [ 11, some sufficient conditions on the acoustic tensor and on ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">By using the method introduced in [ 11, some sufficient conditions on the acoustic tensor and on the kinetic and magnetic fields are given in order that a perturbation initially confined in a proper subset of an unbounded magnetoelastic solid, propagate with finite speed. Moreover, a strong uniqueness theorem is proved for regular solutions to the initial-boundary-value problem of magnetoelastodynamics.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="59a921091867066ee0477fa2fd869588" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065220,"asset_id":111562436,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065220/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562436"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562436"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562436; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562435"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562435/On_the_Cauchy_Problem_of_Vectorial_Thermostatted_Kinetic_Frameworks"><img alt="Research paper thumbnail of On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks" class="work-thumbnail" src="https://attachments.academia-assets.com/109065137/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562435/On_the_Cauchy_Problem_of_Vectorial_Thermostatted_Kinetic_Frameworks">On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks</a></div><div class="wp-workCard_item"><span>Symmetry</span><span>, Apr 2, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic th...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose microscopic state includes a vectorial state variable. The mathematical analysis refers to the global existence and uniqueness of the solution of the related Cauchy problem. Specifically, the paper is divided in two parts. In the first part the thermostatted framework with a continuous vectorial variable is proposed and analyzed. The framework consists of a system of partial integro-differential equations with quadratic type nonlinearities. In the second part the thermostatted framework with a discrete vectorial variable is investigated. Real world applications, such as social systems and crowd dynamics, and future research directions are outlined in the paper.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cc45af057b1acecc08f4125c102374cd" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065137,"asset_id":111562435,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065137/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562435"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562435"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562435; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562434"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562434/On_the_modelling_of_complex_sociopsychological_systems_with_some_reasoning_about_Kate_Jules_and_Jim"><img alt="Research paper thumbnail of On the modelling of complex sociopsychological systems with some reasoning about Kate, Jules, and Jim" class="work-thumbnail" src="https://attachments.academia-assets.com/109065218/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562434/On_the_modelling_of_complex_sociopsychological_systems_with_some_reasoning_about_Kate_Jules_and_Jim">On the modelling of complex sociopsychological systems with some reasoning about Kate, Jules, and Jim</a></div><div class="wp-workCard_item"><span>Differential Equations and Nonlinear Mechanics</span><span>, 2006</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper deals with the modelling of complex sociopsychological games and reciprocal feelings i...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper deals with the modelling of complex sociopsychological games and reciprocal feelings involving interacting individuals. The modelling is based on suitable developments of the methods of mathematical kinetic theory of active particles with special attention to modelling multiple interactions. A first approach to complexity analysis is proposed referring to both computational and modelling aspects.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9d560a306e71b9764792246b362c7cf6" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065218,"asset_id":111562434,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065218/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562434"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562434"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562434; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562432"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562432/On_some_classical_theorems_in_micropolar_elasticity"><img alt="Research paper thumbnail of On some classical theorems in micropolar elasticity" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562432/On_some_classical_theorems_in_micropolar_elasticity">On some classical theorems in micropolar elasticity</a></div><div class="wp-workCard_item"><span>International Journal of Engineering Science</span><span>, 1985</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT By means of suitable a priori estimates, some classical theorems for the system of micro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT By means of suitable a priori estimates, some classical theorems for the system of micropolar elasticity are proved in arbitrary domains. No assumptions are made upon the behaviour of solutions at infinity and the coefficients of the equations may suitably grow at large spatial distance.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562432"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562432"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562432; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562432]").text(description); $(".js-view-count[data-work-id=111562432]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 111562432; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='111562432']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=111562432]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":111562432,"title":"On some classical theorems in micropolar elasticity","internal_url":"https://www.academia.edu/111562432/On_some_classical_theorems_in_micropolar_elasticity","owner_id":219146495,"coauthors_can_edit":true,"owner":{"id":219146495,"first_name":"Bruno","middle_initials":null,"last_name":"Carbonaro","page_name":"BrunoCarbonaro","domain_name":"independent","created_at":"2022-03-29T02:46:30.348-07:00","display_name":"Bruno Carbonaro","url":"https://independent.academia.edu/BrunoCarbonaro"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562431"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562431/On_Graffis_reciprocal_theorem_in_unbounded_domains"><img alt="Research paper thumbnail of On Graffi's reciprocal theorem in unbounded domains" class="work-thumbnail" src="https://attachments.academia-assets.com/109065223/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562431/On_Graffis_reciprocal_theorem_in_unbounded_domains">On Graffi's reciprocal theorem in unbounded domains</a></div><div class="wp-workCard_item"><span>Journal of Elasticity</span><span>, Mar 1, 1985</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A generalization of the reciprocal theorem of linear elastodynamics is proposed for a class of un...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A generalization of the reciprocal theorem of linear elastodynamics is proposed for a class of unbounded elastic bodies that may stiffen at infinity. It is achieved by means of some a-priori estimates derived in a previous paper of ours [1]. * A generalization based upon weak assumptions at infinity is given in [6]. * Recall that, denoting by Lin the space of the second-order tensors on V and by Sym the space of all the symmetric dements of Lin, C is a linear mapping from Lin into Sym such that C[A ] = 0, for any skew A. * Of course,/* is chosen so small as to assure D~, =~ ~. ** It is understood that [A(0, m)] ~< c 2, Vm ~ V, Iml =1.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b7348d912c9b0bc194171a7cc5c0d4de" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065223,"asset_id":111562431,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065223/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562431"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562431"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562431; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562430"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562430/Energy_inequalities_and_the_domain_of_influence_theorem_in_classical_elastodynamics"><img alt="Research paper thumbnail of Energy inequalities and the domain of influence theorem in classical elastodynamics" class="work-thumbnail" src="https://attachments.academia-assets.com/109065221/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562430/Energy_inequalities_and_the_domain_of_influence_theorem_in_classical_elastodynamics">Energy inequalities and the domain of influence theorem in classical elastodynamics</a></div><div class="wp-workCard_item"><span>Journal of Elasticity</span><span>, Jun 1, 1984</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we derive a number of a priori estimates for classical solutions of the system of l...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we derive a number of a priori estimates for classical solutions of the system of linear elastodynamics, and we prove an analogue of the classical domain of influence theorem for a class of unbounded elastic bodies that may stiffen at infinity. b~ CI(Q), (2.3) ,,* q(a,uT), s* G(a2uT), and we shall consider the class "-of regular solutions of (2.1)-(2,2), i.e. the fields u(x,t)~C2(Q)nC~(flx[O, TD with Vu~C2(fix]0, TD such that /*~Cl(fi ×]0, T D. Here, C~'(S), with S ___ E × [0, T], stands for the set of k-th order tensor functions whose components belong to C"(S), where the symbol C"(S) indicates the set of the scalar functions defined on S and within this domain differentiable up to the</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="29657bd6032b78395ffdf1fb9dd04031" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065221,"asset_id":111562430,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065221/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562430"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562430"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562430; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562430]").text(description); $(".js-view-count[data-work-id=111562430]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 111562430; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='111562430']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562429"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562429/Toward_a_mathematical_theory_of_living_systems_focusing_on_developmental_biology_and_evolution_A_review_and_perspectives_"><img alt="Research paper thumbnail of Toward a mathematical theory of living systems focusing on developmental biology and evolution: A review and perspectives☆" class="work-thumbnail" src="https://attachments.academia-assets.com/109065224/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562429/Toward_a_mathematical_theory_of_living_systems_focusing_on_developmental_biology_and_evolution_A_review_and_perspectives_">Toward a mathematical theory of living systems focusing on developmental biology and evolution: A review and perspectives☆</a></div><div class="wp-workCard_item"><span>Physics of Life Reviews</span><span>, Mar 1, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This review paper is devoted to present a personal perspective, based on a critical analysis of t...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This review paper is devoted to present a personal perspective, based on a critical analysis of the existing literature, about the conceptual difficulties that mathematics meets when attempting to describe the complexity of living matter focusing on the challenging goal of developing a mathematical theory for living systems. The authors propose a personal path, starting from the identification of a number of common features of living systems that can be viewed as sources of complexity, firstly in general, and subsequently focusing specifically on evolution problems. Further, three key questions are posed addressing to a mathematical theory. Finally, the tools of the kinetic theory of active particles are critically analyzed to understand how far this approach still is from the achievement of the afore said ambitious objective.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9d51a10f45d43dc54ea25e4dd5bd5f18" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065224,"asset_id":111562429,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065224/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562429"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562429"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562429; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562428"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562428/Dependence_on_the_Initial_Data_for_the_Continuous_Thermostatted_Framework"><img alt="Research paper thumbnail of Dependence on the Initial Data for the Continuous Thermostatted Framework" class="work-thumbnail" src="https://attachments.academia-assets.com/109065136/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562428/Dependence_on_the_Initial_Data_for_the_Continuous_Thermostatted_Framework">Dependence on the Initial Data for the Continuous Thermostatted Framework</a></div><div class="wp-workCard_item"><span>Mathematics</span><span>, Jul 6, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The paper deals with the problem of continuous dependence on initial data of solutions to the equ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The paper deals with the problem of continuous dependence on initial data of solutions to the equation describing the evolution of a complex system in the presence of an external force acting on the system and of a thermostat, simply identified with the condition that the second order moment of the activity variable (see Section 1) is a constant. We are able to prove that these solutions are stable with respect to the initial conditions in the Hadamard's sense. In this connection, two remarks spontaneously arise and must be carefully considered: first, one could complain the lack of information about the "distance" between solutions at any time t ∈ [0, +∞); next, one cannot expect any more complete information without taking into account the possible distribution of the transition probabiliy densities and the interaction rates (see Section 1 again). This work must be viewed as a first step of a research which will require many more steps to give a sufficiently complete picture of the relations between solutions (see Section 5).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cbce5b7783e66d805b57a0eb51f87975" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065136,"asset_id":111562428,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065136/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562428"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562428"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562428; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562427"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562427/The_work_and_energy_theorem_and_the_reciprocity_relation_in_asymmetric_magneto_elastodynamics"><img alt="Research paper thumbnail of The work and energy theorem and the reciprocity relation in asymmetric magneto-elastodynamics" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562427/The_work_and_energy_theorem_and_the_reciprocity_relation_in_asymmetric_magneto_elastodynamics">The work and energy theorem and the reciprocity relation in asymmetric magneto-elastodynamics</a></div><div class="wp-workCard_item"><span>International Journal of Engineering Science</span><span>, 1985</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">... of the Lemma and conditions (9). Ifp&amp;#x27;(VH)2 = o( 1&amp;quot;), .p&amp;#x27;(VH)2 = o1...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">... of the Lemma and conditions (9). Ifp&amp;#x27;(VH)2 = o( 1&amp;quot;), .p&amp;#x27;(VH)2 = o1&amp;quot;&amp;quot;) and udQ +oD, wdQ +w, HdQ +oo, Ja Ja Ja u&amp;#x27;odfK+co, M&amp;#x27;gdS2 +oo, Hl dQ +00, Ja Ja Ja 3 M 0 ... 0[Vw(fs)] ds Jo Jo and f&amp;quot; . r&amp;#x27;aii il(ts)it(s)ds= (ts)ii(s)ds Jo Jo as ft au =H(O.HoHoH(i)+ tl(ts)(s)ds Jo as r&amp;#x27; = H(0 Ho Ho H(0 ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562427"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562427"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562427; 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</script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="15261132" id="papers"><div class="js-work-strip profile--work_container" data-work-id="123274493"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/123274493/A_nonconservative_kinetic_framework_under_the_action_of_an_external_force_field_Theoretical_results_with_application_inspired_to_ecology"><img alt="Research paper thumbnail of A nonconservative kinetic framework under the action of an external force field: Theoretical results with application inspired to ecology" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/123274493/A_nonconservative_kinetic_framework_under_the_action_of_an_external_force_field_Theoretical_results_with_application_inspired_to_ecology">A nonconservative kinetic framework under the action of an external force field: Theoretical results with application inspired to ecology</a></div><div class="wp-workCard_item"><span>European Journal of Applied Mathematics</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The present paper deals with the kinetic-theoretic description of the evolution of systems consis...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The present paper deals with the kinetic-theoretic description of the evolution of systems consisting of many particles interacting not only with each other but also with the external world, so that the equation governing their evolution contains an additional term representing such interaction, called the ‘forcing term’. Firstly, the interactions between pairs of particles are both conservative and nonconservative; the latter represents, among others, birth/death rates. The ‘forcing term’ does not express a ‘classical’ force exerted by the external world on the particles, but a more general influence on the effects of mutual interactions of particles, for instance, climate changes, that increase or decrease the different agricultural productions at different times, thus altering the economic relationships between different subsystems, that in turn can be also perturbed by stock market fluctuations, sudden wars, periodic epidemics, and so on. Thus, the interest towards these problem...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="123274493"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="123274493"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 123274493; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=123274493]").text(description); $(".js-view-count[data-work-id=123274493]").attr('title', description).tooltip(); 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} }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="115391918"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/115391918/Modeling_epidemics_by_means_of_the_stochastic_description_of_complex_systems"><img alt="Research paper thumbnail of Modeling epidemics by means of the stochastic description of complex systems" class="work-thumbnail" src="https://attachments.academia-assets.com/111811797/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/115391918/Modeling_epidemics_by_means_of_the_stochastic_description_of_complex_systems">Modeling epidemics by means of the stochastic description of complex systems</a></div><div class="wp-workCard_item"><span>Computational and mathematical methods</span><span>, Oct 25, 2021</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The aim of the present paper is to show a way in which the problem of predicting the evolution of...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The aim of the present paper is to show a way in which the problem of predicting the evolution of an epidemic may be tackled by describing it in the framework of Boltzmann's kinetic theory, as it has been developed and applied in the last years to complex systems by a suitable modification of the Boltzmann equation, a suitable re-interpretation of state variables and the introduction of the notion of functional subsystems. Accordingly, in this paper we model an arbitrary (national) population S as a complex system, split in two functional subsystems, the first containing all single individuals of S and the second containing the care tools , that are to be meant as available places in hospitals with a sufficient number of physicians and of equipments</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="62f64b0a59ffce2790af2161243a1e4b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":111811797,"asset_id":115391918,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/111811797/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="115391918"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="115391918"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 115391918; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562443"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562443/Some_remarks_on_a_modified_fluid_dynamics_equation"><img alt="Research paper thumbnail of Some remarks on a modified fluid dynamics equation" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562443/Some_remarks_on_a_modified_fluid_dynamics_equation">Some remarks on a modified fluid dynamics equation</a></div><div class="wp-workCard_item"><span>Rendiconti Del Circolo Matematico Di Palermo</span><span>, 1981</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Abstract A modification of Navier-Stokes equation, recently suggested to overcome the well-known ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Abstract A modification of Navier-Stokes equation, recently suggested to overcome the well-known paradox about the sound diffusion with infinite velocity in viscous fluids, is compared with Navier-Stokes equation itself. Necessary and sufficient conditions to get common ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562443"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562443"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562443; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562443]").text(description); $(".js-view-count[data-work-id=111562443]").attr('title', description).tooltip(); 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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=111562443]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":111562443,"title":"Some remarks on a modified fluid dynamics equation","internal_url":"https://www.academia.edu/111562443/Some_remarks_on_a_modified_fluid_dynamics_equation","owner_id":219146495,"coauthors_can_edit":true,"owner":{"id":219146495,"first_name":"Bruno","middle_initials":null,"last_name":"Carbonaro","page_name":"BrunoCarbonaro","domain_name":"independent","created_at":"2022-03-29T02:46:30.348-07:00","display_name":"Bruno Carbonaro","url":"https://independent.academia.edu/BrunoCarbonaro"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562442"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562442/The_mathematical_analysis_towards_the_dependence_on_the_initial_data_for_a_discrete_thermostatted_kinetic_framework_for_biological_systems_composed_of_interacting_entities"><img alt="Research paper thumbnail of The mathematical analysis towards the dependence on the initial data for a discrete thermostatted kinetic framework for biological systems composed of interacting entities" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562442/The_mathematical_analysis_towards_the_dependence_on_the_initial_data_for_a_discrete_thermostatted_kinetic_framework_for_biological_systems_composed_of_interacting_entities">The mathematical analysis towards the dependence on the initial data for a discrete thermostatted kinetic framework for biological systems composed of interacting entities</a></div><div class="wp-workCard_item"><span>AIMS biophysics</span><span>, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper is devoted to a mathematical proof of the continuous dependence on the initial data fo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper is devoted to a mathematical proof of the continuous dependence on the initial data for the discrete thermostatted kinetic framework, for all T &gt; 0. This is a versatile model for describing the time-evolution of a biological complex system which is composed by a large number of interacting entities, called active particles, and is subjected to an external force field due to the environment. A thermostat term is introduced in order to keep the 2nd-order moment of the system, corresponding to the physical global activation energy, constant in time. This model is expressed by a system of nonlinear ordinary differential equations with quadratic nonlinearity.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562442"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562442"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562442; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562442]").text(description); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562441"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562441/On_the_work_and_energy_theorem_for_unbounded_elastic_bodies"><img alt="Research paper thumbnail of On the work and energy theorem for unbounded elastic bodies" class="work-thumbnail" src="https://attachments.academia-assets.com/109065222/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562441/On_the_work_and_energy_theorem_for_unbounded_elastic_bodies">On the work and energy theorem for unbounded elastic bodies</a></div><div class="wp-workCard_item"><span>Journal of Elasticity</span><span>, 1985</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The main scope of the paper is the statement and the proof of the "work and energy theorem" for e...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The main scope of the paper is the statement and the proof of the "work and energy theorem" for elastic bodies that occupy an unbounded region of space and whose acoustic tensor A may suitably grow at large spatial distance from a fixed origin.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9321d4936f190a9f4d3c55c14a7e7d2d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065222,"asset_id":111562441,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065222/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562441"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562441"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562441; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562440"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562440/Some_Theorems_in_Temperature_Rate_Dependent_Thermoelasticity_for_Unbounded_Domains"><img alt="Research paper thumbnail of Some Theorems in Temperature-Rate-Dependent Thermoelasticity for Unbounded Domains" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562440/Some_Theorems_in_Temperature_Rate_Dependent_Thermoelasticity_for_Unbounded_Domains">Some Theorems in Temperature-Rate-Dependent Thermoelasticity for Unbounded Domains</a></div><div class="wp-workCard_item"><span>Journal of Thermal Stresses</span><span>, 1987</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A domain of influence theorem, work and energy theorem, and reciprocity theorem are proved for a ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A domain of influence theorem, work and energy theorem, and reciprocity theorem are proved for a linear anisotropic nonhomogeneous temperature-rate-dependent thermoelastic unbounded body. The theorems cover the case where the constitutive fields may attain unbounded values at infinity, and they are based on a hypothesis from which it follows that a thermoelastic disturbance produced by an external ther-momechanical load of</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562440"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562440"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562440; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562440]").text(description); $(".js-view-count[data-work-id=111562440]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 111562440; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='111562440']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=111562440]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":111562440,"title":"Some Theorems in Temperature-Rate-Dependent Thermoelasticity for Unbounded Domains","internal_url":"https://www.academia.edu/111562440/Some_Theorems_in_Temperature_Rate_Dependent_Thermoelasticity_for_Unbounded_Domains","owner_id":219146495,"coauthors_can_edit":true,"owner":{"id":219146495,"first_name":"Bruno","middle_initials":null,"last_name":"Carbonaro","page_name":"BrunoCarbonaro","domain_name":"independent","created_at":"2022-03-29T02:46:30.348-07:00","display_name":"Bruno Carbonaro","url":"https://independent.academia.edu/BrunoCarbonaro"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562439"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562439/The_role_of_the_principle_of_inertia_in_KTAP_models"><img alt="Research paper thumbnail of The role of the principle of inertia in KTAP models" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562439/The_role_of_the_principle_of_inertia_in_KTAP_models">The role of the principle of inertia in KTAP models</a></div><div class="wp-workCard_item"><span>Journal of Mathematical Physics</span><span>, 2022</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The mathematical models for describing the evolution of complex systems in the framework of the K...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The mathematical models for describing the evolution of complex systems in the framework of the Kinetic Theory for Active Particles (KTAPs), based on suitable generalizations of Boltzmann’s kinetic theory of gases, nowadays seem to be the most versatile and effective ones to formulate in sufficiently precise and accurate terms, and possibly to solve, the most important and difficult problems not only of our everyday’s individual life but also of the life of human collectivities in the long term. In this connection, a simple examination of the application of KTAP to practical problems in which the state variables are not the usual position-velocity variables (and the kinetic state can, indeed, be completely disregarded), such as the prediction of the evolution of an epidemic in a given population in view of possible containment measures, suggests that the scheme is not always so general as it would be desirable for the simple reason that it is conditioned by the implicit (and natural) assumption of the principle of inertia, which in non-mechanical contexts should be rejected. Starting from this remark, this paper has a threefold aim: (1) to point out that KTAP equations make a tacit use of the principle of inertia; (2) to recall the reasons why the principle of inertia is naturally connected to the origin of KTAP models; and (3) to suggest a suitable modification of the KTAP general system, enabling the user to choose to adopt or reject the principle of inertia.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562439"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562439"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562439; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562439]").text(description); $(".js-view-count[data-work-id=111562439]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 111562439; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='111562439']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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It was originally planned as a "note added in proof" to [1], but when I received the galley proofs of [1], it was not yet ready. According to its nature of an "appendix" to [1], throughout this note we shall always refer to the notations and the formulae of the full paper. The reader should be then aware that, when quoting formula (,) or Section X or Remark Y, we mean formula (,) or Section X or Remark Y of[1]. The need of this addition to [1] may be easily understood by considering the following objection to the counterexamples given there. The one-dimensional model of the dynamical problem of linear elasticity is not quite suitable to sample the considered case in which a point o of the body B is allowed to be a singularity point for the material data. Indeed, the statement of the boundary-initial value problem, in its general form, requires that B is an "open connected set" (cf. Section 3): now, when dealing with a one-dimensional example, the presence of the singularity point o "breaks" the connection of B, which in this case turns out to be the join of two different bodies B l = (-x0, 0) and B 2 = (0, + o0) (cf. Section 5). Thus, at a first glance, it could seem that if we would construct an analogous example in the general case (i.e. in two or three dimensions), we should think, rather than of a single body B containing a singularity point o, of two different bodies B1 and B2 with a common boundary 7, where the material data are allowed to be singular. In such a problem, the dependence of the uniqueness of solutions on some conditions on 7 (e.g., the continuity of the displacement and/or the stress field across 7, or the validity of the Third Law of Dynamics for the contact interactions between B~ and B2) is to be</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="f916a2624bd7781f5def0fa5e1e82872" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065148,"asset_id":111562438,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065148/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562438"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562438"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562438; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562437"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562437/Wave_Propagation_Uniqueness_and_Singularities_at_Infinity_for_an_Unbounded_Linearly_Viscoelastic_Material"><img alt="Research paper thumbnail of Wave Propagation, Uniqueness and Singularities at Infinity for an Unbounded Linearly Viscoelastic Material" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562437/Wave_Propagation_Uniqueness_and_Singularities_at_Infinity_for_an_Unbounded_Linearly_Viscoelastic_Material">Wave Propagation, Uniqueness and Singularities at Infinity for an Unbounded Linearly Viscoelastic Material</a></div><div class="wp-workCard_item"><span>Mathematical Models and Methods in Applied Sciences</span><span>, Dec 1, 1995</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Following a method used in two earlier papers,2,3 a general domain of dependence in equality is p...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Following a method used in two earlier papers,2,3 a general domain of dependence in equality is proved for inhomogeneous and anisotropic linearly viscoelastic solids, which furnishes the explicit link between the maximum propagation speed of disturbances in the body and the behavior at infinity of the acoustic tensor and the memory functions of the material, and allows to prove a global uniqueness theorem for the mixed problem of viscoelasticity in an unbounded reference configuration Ω. The method of proof applies regardless of whether the memory functions are assumed or not: moreover, no boundedness assumption is made on the material data.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562437"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562437"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562437; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562437]").text(description); $(".js-view-count[data-work-id=111562437]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 111562437; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='111562437']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=111562437]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":111562437,"title":"Wave Propagation, Uniqueness and Singularities at Infinity for an Unbounded Linearly Viscoelastic Material","internal_url":"https://www.academia.edu/111562437/Wave_Propagation_Uniqueness_and_Singularities_at_Infinity_for_an_Unbounded_Linearly_Viscoelastic_Material","owner_id":219146495,"coauthors_can_edit":true,"owner":{"id":219146495,"first_name":"Bruno","middle_initials":null,"last_name":"Carbonaro","page_name":"BrunoCarbonaro","domain_name":"independent","created_at":"2022-03-29T02:46:30.348-07:00","display_name":"Bruno Carbonaro","url":"https://independent.academia.edu/BrunoCarbonaro"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562436"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562436/Wave_propagation_and_uniqueness_in_magneto_elastodynamics"><img alt="Research paper thumbnail of Wave propagation and uniqueness in magneto-elastodynamics" class="work-thumbnail" src="https://attachments.academia-assets.com/109065220/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562436/Wave_propagation_and_uniqueness_in_magneto_elastodynamics">Wave propagation and uniqueness in magneto-elastodynamics</a></div><div class="wp-workCard_item"><span>International Journal of Engineering Science</span><span>, 1986</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">By using the method introduced in [ 11, some sufficient conditions on the acoustic tensor and on ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">By using the method introduced in [ 11, some sufficient conditions on the acoustic tensor and on the kinetic and magnetic fields are given in order that a perturbation initially confined in a proper subset of an unbounded magnetoelastic solid, propagate with finite speed. Moreover, a strong uniqueness theorem is proved for regular solutions to the initial-boundary-value problem of magnetoelastodynamics.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="59a921091867066ee0477fa2fd869588" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065220,"asset_id":111562436,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065220/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562436"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562436"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562436; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562435"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562435/On_the_Cauchy_Problem_of_Vectorial_Thermostatted_Kinetic_Frameworks"><img alt="Research paper thumbnail of On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks" class="work-thumbnail" src="https://attachments.academia-assets.com/109065137/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562435/On_the_Cauchy_Problem_of_Vectorial_Thermostatted_Kinetic_Frameworks">On the Cauchy Problem of Vectorial Thermostatted Kinetic Frameworks</a></div><div class="wp-workCard_item"><span>Symmetry</span><span>, Apr 2, 2020</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic th...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper is devoted to the derivation and mathematical analysis of new thermostatted kinetic theory frameworks for the modeling of nonequilibrium complex systems composed by particles whose microscopic state includes a vectorial state variable. The mathematical analysis refers to the global existence and uniqueness of the solution of the related Cauchy problem. Specifically, the paper is divided in two parts. In the first part the thermostatted framework with a continuous vectorial variable is proposed and analyzed. The framework consists of a system of partial integro-differential equations with quadratic type nonlinearities. In the second part the thermostatted framework with a discrete vectorial variable is investigated. Real world applications, such as social systems and crowd dynamics, and future research directions are outlined in the paper.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cc45af057b1acecc08f4125c102374cd" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065137,"asset_id":111562435,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065137/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562435"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562435"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562435; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562434"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562434/On_the_modelling_of_complex_sociopsychological_systems_with_some_reasoning_about_Kate_Jules_and_Jim"><img alt="Research paper thumbnail of On the modelling of complex sociopsychological systems with some reasoning about Kate, Jules, and Jim" class="work-thumbnail" src="https://attachments.academia-assets.com/109065218/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562434/On_the_modelling_of_complex_sociopsychological_systems_with_some_reasoning_about_Kate_Jules_and_Jim">On the modelling of complex sociopsychological systems with some reasoning about Kate, Jules, and Jim</a></div><div class="wp-workCard_item"><span>Differential Equations and Nonlinear Mechanics</span><span>, 2006</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This paper deals with the modelling of complex sociopsychological games and reciprocal feelings i...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This paper deals with the modelling of complex sociopsychological games and reciprocal feelings involving interacting individuals. The modelling is based on suitable developments of the methods of mathematical kinetic theory of active particles with special attention to modelling multiple interactions. A first approach to complexity analysis is proposed referring to both computational and modelling aspects.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9d560a306e71b9764792246b362c7cf6" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065218,"asset_id":111562434,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065218/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562434"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562434"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562434; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562432"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562432/On_some_classical_theorems_in_micropolar_elasticity"><img alt="Research paper thumbnail of On some classical theorems in micropolar elasticity" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562432/On_some_classical_theorems_in_micropolar_elasticity">On some classical theorems in micropolar elasticity</a></div><div class="wp-workCard_item"><span>International Journal of Engineering Science</span><span>, 1985</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT By means of suitable a priori estimates, some classical theorems for the system of micro...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT By means of suitable a priori estimates, some classical theorems for the system of micropolar elasticity are proved in arbitrary domains. No assumptions are made upon the behaviour of solutions at infinity and the coefficients of the equations may suitably grow at large spatial distance.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562432"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562432"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562432; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562432]").text(description); $(".js-view-count[data-work-id=111562432]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 111562432; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='111562432']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=111562432]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":111562432,"title":"On some classical theorems in micropolar elasticity","internal_url":"https://www.academia.edu/111562432/On_some_classical_theorems_in_micropolar_elasticity","owner_id":219146495,"coauthors_can_edit":true,"owner":{"id":219146495,"first_name":"Bruno","middle_initials":null,"last_name":"Carbonaro","page_name":"BrunoCarbonaro","domain_name":"independent","created_at":"2022-03-29T02:46:30.348-07:00","display_name":"Bruno Carbonaro","url":"https://independent.academia.edu/BrunoCarbonaro"},"attachments":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562431"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562431/On_Graffis_reciprocal_theorem_in_unbounded_domains"><img alt="Research paper thumbnail of On Graffi's reciprocal theorem in unbounded domains" class="work-thumbnail" src="https://attachments.academia-assets.com/109065223/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562431/On_Graffis_reciprocal_theorem_in_unbounded_domains">On Graffi's reciprocal theorem in unbounded domains</a></div><div class="wp-workCard_item"><span>Journal of Elasticity</span><span>, Mar 1, 1985</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">A generalization of the reciprocal theorem of linear elastodynamics is proposed for a class of un...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">A generalization of the reciprocal theorem of linear elastodynamics is proposed for a class of unbounded elastic bodies that may stiffen at infinity. It is achieved by means of some a-priori estimates derived in a previous paper of ours [1]. * A generalization based upon weak assumptions at infinity is given in [6]. * Recall that, denoting by Lin the space of the second-order tensors on V and by Sym the space of all the symmetric dements of Lin, C is a linear mapping from Lin into Sym such that C[A ] = 0, for any skew A. * Of course,/* is chosen so small as to assure D~, =~ ~. ** It is understood that [A(0, m)] ~< c 2, Vm ~ V, Iml =1.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="b7348d912c9b0bc194171a7cc5c0d4de" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065223,"asset_id":111562431,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065223/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562431"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562431"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562431; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562430"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562430/Energy_inequalities_and_the_domain_of_influence_theorem_in_classical_elastodynamics"><img alt="Research paper thumbnail of Energy inequalities and the domain of influence theorem in classical elastodynamics" class="work-thumbnail" src="https://attachments.academia-assets.com/109065221/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562430/Energy_inequalities_and_the_domain_of_influence_theorem_in_classical_elastodynamics">Energy inequalities and the domain of influence theorem in classical elastodynamics</a></div><div class="wp-workCard_item"><span>Journal of Elasticity</span><span>, Jun 1, 1984</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we derive a number of a priori estimates for classical solutions of the system of l...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we derive a number of a priori estimates for classical solutions of the system of linear elastodynamics, and we prove an analogue of the classical domain of influence theorem for a class of unbounded elastic bodies that may stiffen at infinity. b~ CI(Q), (2.3) ,,* q(a,uT), s* G(a2uT), and we shall consider the class "-of regular solutions of (2.1)-(2,2), i.e. the fields u(x,t)~C2(Q)nC~(flx[O, TD with Vu~C2(fix]0, TD such that /*~Cl(fi ×]0, T D. Here, C~'(S), with S ___ E × [0, T], stands for the set of k-th order tensor functions whose components belong to C"(S), where the symbol C"(S) indicates the set of the scalar functions defined on S and within this domain differentiable up to the</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="29657bd6032b78395ffdf1fb9dd04031" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065221,"asset_id":111562430,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065221/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562430"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562430"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562430; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=111562430]").text(description); $(".js-view-count[data-work-id=111562430]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 111562430; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='111562430']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-a9bf3a2bc8c89fa2a77156577594264ee8a0f214d74241bc0fcd3f69f8d107ac.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562429"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562429/Toward_a_mathematical_theory_of_living_systems_focusing_on_developmental_biology_and_evolution_A_review_and_perspectives_"><img alt="Research paper thumbnail of Toward a mathematical theory of living systems focusing on developmental biology and evolution: A review and perspectives☆" class="work-thumbnail" src="https://attachments.academia-assets.com/109065224/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562429/Toward_a_mathematical_theory_of_living_systems_focusing_on_developmental_biology_and_evolution_A_review_and_perspectives_">Toward a mathematical theory of living systems focusing on developmental biology and evolution: A review and perspectives☆</a></div><div class="wp-workCard_item"><span>Physics of Life Reviews</span><span>, Mar 1, 2011</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">This review paper is devoted to present a personal perspective, based on a critical analysis of t...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">This review paper is devoted to present a personal perspective, based on a critical analysis of the existing literature, about the conceptual difficulties that mathematics meets when attempting to describe the complexity of living matter focusing on the challenging goal of developing a mathematical theory for living systems. The authors propose a personal path, starting from the identification of a number of common features of living systems that can be viewed as sources of complexity, firstly in general, and subsequently focusing specifically on evolution problems. Further, three key questions are posed addressing to a mathematical theory. Finally, the tools of the kinetic theory of active particles are critically analyzed to understand how far this approach still is from the achievement of the afore said ambitious objective.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9d51a10f45d43dc54ea25e4dd5bd5f18" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065224,"asset_id":111562429,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065224/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562429"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562429"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562429; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562428"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/111562428/Dependence_on_the_Initial_Data_for_the_Continuous_Thermostatted_Framework"><img alt="Research paper thumbnail of Dependence on the Initial Data for the Continuous Thermostatted Framework" class="work-thumbnail" src="https://attachments.academia-assets.com/109065136/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/111562428/Dependence_on_the_Initial_Data_for_the_Continuous_Thermostatted_Framework">Dependence on the Initial Data for the Continuous Thermostatted Framework</a></div><div class="wp-workCard_item"><span>Mathematics</span><span>, Jul 6, 2019</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">The paper deals with the problem of continuous dependence on initial data of solutions to the equ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">The paper deals with the problem of continuous dependence on initial data of solutions to the equation describing the evolution of a complex system in the presence of an external force acting on the system and of a thermostat, simply identified with the condition that the second order moment of the activity variable (see Section 1) is a constant. We are able to prove that these solutions are stable with respect to the initial conditions in the Hadamard's sense. In this connection, two remarks spontaneously arise and must be carefully considered: first, one could complain the lack of information about the "distance" between solutions at any time t ∈ [0, +∞); next, one cannot expect any more complete information without taking into account the possible distribution of the transition probabiliy densities and the interaction rates (see Section 1 again). This work must be viewed as a first step of a research which will require many more steps to give a sufficiently complete picture of the relations between solutions (see Section 5).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="cbce5b7783e66d805b57a0eb51f87975" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":109065136,"asset_id":111562428,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/109065136/download_file?s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562428"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562428"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562428; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="111562427"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" rel="nofollow" href="https://www.academia.edu/111562427/The_work_and_energy_theorem_and_the_reciprocity_relation_in_asymmetric_magneto_elastodynamics"><img alt="Research paper thumbnail of The work and energy theorem and the reciprocity relation in asymmetric magneto-elastodynamics" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" rel="nofollow" href="https://www.academia.edu/111562427/The_work_and_energy_theorem_and_the_reciprocity_relation_in_asymmetric_magneto_elastodynamics">The work and energy theorem and the reciprocity relation in asymmetric magneto-elastodynamics</a></div><div class="wp-workCard_item"><span>International Journal of Engineering Science</span><span>, 1985</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">... of the Lemma and conditions (9). Ifp&amp;#x27;(VH)2 = o( 1&amp;quot;), .p&amp;#x27;(VH)2 = o1...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">... of the Lemma and conditions (9). Ifp&amp;#x27;(VH)2 = o( 1&amp;quot;), .p&amp;#x27;(VH)2 = o1&amp;quot;&amp;quot;) and udQ +oD, wdQ +w, HdQ +oo, Ja Ja Ja u&amp;#x27;odfK+co, M&amp;#x27;gdS2 +oo, Hl dQ +00, Ja Ja Ja 3 M 0 ... 0[Vw(fs)] ds Jo Jo and f&amp;quot; . r&amp;#x27;aii il(ts)it(s)ds= (ts)ii(s)ds Jo Jo as ft au =H(O.HoHoH(i)+ tl(ts)(s)ds Jo as r&amp;#x27; = H(0 Ho Ho H(0 ...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="111562427"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="111562427"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 111562427; 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