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order</title> <meta name="description" content="Search results for: weak order"> <meta name="keywords" content="weak order"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" 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style="font-size:.9rem"><span class="badge badge-info">14467</span> A Simple Recursive Framework to Generate Gray Codes for Weak Orders in Constant Amortized Time </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Marsden%20Jacques">Marsden Jacques</a>, <a href="https://publications.waset.org/abstracts/search?q=Dennis%20Wong"> Dennis Wong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A weak order is a way to rank n objects where ties are allowed. In this talk, we present a recursive framework to generate Gray codes for weak orders. We then describe a simple algorithm based on the framework that generates 2-Gray codes for weak orders in constant amortized time per string. This framework can easily be modified to generate other Gray codes for weak orders. We provide an example on using the framework to generate the first Shift Gray code for weak orders, also in constant amortized time, where consecutive strings differ by a shift or a symbol change. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=weak%20order" title="weak order">weak order</a>, <a href="https://publications.waset.org/abstracts/search?q=Cayley%20permutation" title=" Cayley permutation"> Cayley permutation</a>, <a href="https://publications.waset.org/abstracts/search?q=Gray%20code" title=" Gray code"> Gray code</a>, <a href="https://publications.waset.org/abstracts/search?q=shift%20Gray%20code" title=" shift Gray code"> shift Gray code</a> </p> <a href="https://publications.waset.org/abstracts/118752/a-simple-recursive-framework-to-generate-gray-codes-for-weak-orders-in-constant-amortized-time" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/118752.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">178</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14466</span> Weak Instability in Direct Integration Methods for Structural Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shuenn-Yih%20Chang">Shuenn-Yih Chang</a>, <a href="https://publications.waset.org/abstracts/search?q=Chiu-Li%20Huang"> Chiu-Li Huang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20analysis" title="dynamic analysis">dynamic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=high%20frequency" title=" high frequency"> high frequency</a>, <a href="https://publications.waset.org/abstracts/search?q=integration%20method" title=" integration method"> integration method</a>, <a href="https://publications.waset.org/abstracts/search?q=overshoot" title=" overshoot"> overshoot</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20instability" title=" weak instability"> weak instability</a> </p> <a href="https://publications.waset.org/abstracts/107364/weak-instability-in-direct-integration-methods-for-structural-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/107364.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">223</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14465</span> Refined Procedures for Second Order Asymptotic Theory</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gubhinder%20Kundhi">Gubhinder Kundhi</a>, <a href="https://publications.waset.org/abstracts/search?q=Paul%20Rilstone"> Paul Rilstone</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Refined procedures for higher-order asymptotic theory for non-linear models are developed. These include a new method for deriving stochastic expansions of arbitrary order, new methods for evaluating the moments of polynomials of sample averages, a new method for deriving the approximate moments of the stochastic expansions; an application of these techniques to gather improved inferences with the weak instruments problem is considered. It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. In our application, finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=edgeworth%20expansions" title="edgeworth expansions">edgeworth expansions</a>, <a href="https://publications.waset.org/abstracts/search?q=higher%20order%20asymptotics" title=" higher order asymptotics"> higher order asymptotics</a>, <a href="https://publications.waset.org/abstracts/search?q=saddlepoint%20expansions" title=" saddlepoint expansions"> saddlepoint expansions</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20instruments" title=" weak instruments"> weak instruments</a> </p> <a href="https://publications.waset.org/abstracts/68155/refined-procedures-for-second-order-asymptotic-theory" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/68155.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">277</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14464</span> Propagation of Weak Non-Linear Waves in Non-Equilibrium Flow</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=J.%20Jena">J. Jena</a>, <a href="https://publications.waset.org/abstracts/search?q=Monica%20Saxena"> Monica Saxena </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the propagation of weak nonlinear waves in non-equilibrium flow has been studied in detail using the perturbation method. The expansive action of receding piston undergoing infinite acceleration has been discussed. Central expansion fan, compression waves and shock fronts have been discussed and the solutions up to the first order in the characteristic plane and physical plane have been obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Characteristic%20wave%20front" title="Characteristic wave front">Characteristic wave front</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20non-linear%20waves" title=" weak non-linear waves"> weak non-linear waves</a>, <a href="https://publications.waset.org/abstracts/search?q=central%20expansion%20fan" title=" central expansion fan"> central expansion fan</a>, <a href="https://publications.waset.org/abstracts/search?q=compression%20waves" title=" compression waves"> compression waves</a> </p> <a href="https://publications.waset.org/abstracts/14207/propagation-of-weak-non-linear-waves-in-non-equilibrium-flow" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14207.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">369</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14463</span> Rings Characterized by Classes of Rad-plus-Supplemented Modules</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manoj%20Kumar%20Patel">Manoj Kumar Patel</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we introduce and give various properties of weak* Rad-plus-supplemented and cofinitely weak* Rad-plus-supplemented modules over some special kinds of rings, in particular, artinian serial ring and semiperfect ring. Also prove that ring R is artinian serial if and only if every right and left R-module is weak* Rad-plus-supplemented. We provide the counter example which proves that weak* Rad-plus-supplemented module is the generalization of plus-supplemented and Rad-plus-supplemented modules. Furthermore, as an application of above finding results of this research article, our main focus is to characterized the semisimple ring, artinian principal ideal ring, semilocal ring, semiperfect ring, perfect ring, commutative noetherian ring and Dedekind domain in terms of weak* Rad-plus-supplemented module. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cofinitely%20weak%2A%20Rad-plus-supplemented%20module" title="cofinitely weak* Rad-plus-supplemented module ">cofinitely weak* Rad-plus-supplemented module </a>, <a href="https://publications.waset.org/abstracts/search?q=Dedekind%20domain" title=" Dedekind domain"> Dedekind domain</a>, <a href="https://publications.waset.org/abstracts/search?q=Rad-plus-supplemented%20module" title=" Rad-plus-supplemented module"> Rad-plus-supplemented module</a>, <a href="https://publications.waset.org/abstracts/search?q=semiperfect%20ring" title=" semiperfect ring"> semiperfect ring</a> </p> <a href="https://publications.waset.org/abstracts/79173/rings-characterized-by-classes-of-rad-plus-supplemented-modules" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79173.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">261</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14462</span> Early Warning Signals: Role and Status of Risk Management in Small and Medium Enterprises</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alexander%20Kel%C3%AD%C5%A1ek">Alexander Kelíšek</a>, <a href="https://publications.waset.org/abstracts/search?q=Denisa%20Janasov%C3%A1"> Denisa Janasová</a>, <a href="https://publications.waset.org/abstracts/search?q=Veronika%20Mita%C5%A1ov%C3%A1"> Veronika Mitašová</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Weak signals using is often associated with early warning. It is possible to find a link between early warning, respectively early problems detection and risk management. The idea of early warning is very important in the context of crisis management because of the risk prevention possibility. Weak signals are likened to risk symptoms. Nowadays, their usefulness as a tool of proactive problems solving is emphasized. Based on it, it is possible to use weak signals not only in strategic planning, project management, or early warning system, but also as a subsidiary element in risk management. The main question is how to effectively integrate weak signals into risk management. The main aim of the paper is to point out the possibilities of weak signals using in small and medium enterprises risk management. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=early%20warning%20system" title="early warning system">early warning system</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20signals" title=" weak signals"> weak signals</a>, <a href="https://publications.waset.org/abstracts/search?q=risk%20management" title=" risk management"> risk management</a>, <a href="https://publications.waset.org/abstracts/search?q=small%20and%20medium%20enterprises%20%28SMEs%29" title=" small and medium enterprises (SMEs)"> small and medium enterprises (SMEs)</a> </p> <a href="https://publications.waset.org/abstracts/59504/early-warning-signals-role-and-status-of-risk-management-in-small-and-medium-enterprises" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59504.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">427</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14461</span> Finite Sample Inferences for Weak Instrument Models</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gubhinder%20Kundhi">Gubhinder Kundhi</a>, <a href="https://publications.waset.org/abstracts/search?q=Paul%20Rilstone"> Paul Rilstone</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is well established that Instrumental Variable (IV) estimators in the presence of weak instruments can be poorly behaved, in particular, be quite biased in finite samples. Finite sample approximations to the distributions of these estimators are obtained using Edgeworth and Saddlepoint expansions. Departures from normality of the distributions of these estimators are analyzed using higher order analytical corrections in these expansions. In a Monte-Carlo experiment, the performance of these expansions is compared to the first order approximation and other methods commonly used in finite samples such as the bootstrap. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bootstrap" title="bootstrap">bootstrap</a>, <a href="https://publications.waset.org/abstracts/search?q=Instrumental%20Variable" title=" Instrumental Variable"> Instrumental Variable</a>, <a href="https://publications.waset.org/abstracts/search?q=Edgeworth%20expansions" title=" Edgeworth expansions"> Edgeworth expansions</a>, <a href="https://publications.waset.org/abstracts/search?q=Saddlepoint%20expansions" title=" Saddlepoint expansions"> Saddlepoint expansions</a> </p> <a href="https://publications.waset.org/abstracts/46824/finite-sample-inferences-for-weak-instrument-models" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46824.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">310</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14460</span> On Unification of the Electromagnetic, Strong and Weak Interactions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hassan%20Youssef%20Mohamed">Hassan Youssef Mohamed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we show new wave equations, and by using the equations, we concluded that the strong force and the weak force are not fundamental, but they are quantum effects for electromagnetism. This result is different from the current scientific understanding about strong and weak interactions at all. So, we introduce three evidences for our theory. First, we prove the asymptotic freedom phenomenon in the strong force by using our model. Second, we derive the nuclear shell model as an approximation of our model. Third, we prove that the leptons do not participate in the strong interactions, and we prove the short ranges of weak and strong interactions. So, our model is consistent with the current understanding of physics. Finally, we introduce the electron-positron model as the basic ingredients for protons, neutrons, and all matters, so we can study all particles interactions and nuclear interaction as many-body problems of electrons and positrons. Also, we prove the violation of parity conservation in weak interaction as evidence of our theory in the weak interaction. Also, we calculate the average of the binding energy per nucleon. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=new%20wave%20equations" title="new wave equations">new wave equations</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20strong%20force" title=" the strong force"> the strong force</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20grand%20unification%20theory" title=" the grand unification theory"> the grand unification theory</a>, <a href="https://publications.waset.org/abstracts/search?q=hydrogen%20atom" title=" hydrogen atom"> hydrogen atom</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20force" title=" weak force"> weak force</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20nuclear%20shell%20model" title=" the nuclear shell model"> the nuclear shell model</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20asymptotic%20freedom" title=" the asymptotic freedom"> the asymptotic freedom</a>, <a href="https://publications.waset.org/abstracts/search?q=electron-positron%20model" title=" electron-positron model"> electron-positron model</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20violation%20of%20parity%20conservation" title=" the violation of parity conservation"> the violation of parity conservation</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20binding%20energy" title=" the binding energy"> the binding energy</a> </p> <a href="https://publications.waset.org/abstracts/146460/on-unification-of-the-electromagnetic-strong-and-weak-interactions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/146460.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">185</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14459</span> Economic and Ecological Implications in Agricultural Production Within the Strong and Weak Sustainability Framework</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mauricio%20Quintero%20Angel">Mauricio Quintero Angel</a>, <a href="https://publications.waset.org/abstracts/search?q=Andr%C3%A9s%20A.%20Duque%20Nivia"> Andrés A. Duque Nivia</a>, <a href="https://publications.waset.org/abstracts/search?q=Carlos%20H.%20Fajardo%20Toro"> Carlos H. Fajardo Toro</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper analyzes two approaches of sustainability, the weak and strong, considering a case of study of oil palm production for an industry of biodegradable detergent. In this case, a company demand the oil palm as the active element for washing and through its trademark aims to supply 10% of the Colombian market of washing powders. Under each approach the economic and ecological implications of the palm oil production and especially the implications for crop management are described. The crop production under the weak sustainability implies plantations, intensive use of agrochemicals and the inclusion of new areas of cultivation as the market grows. Under the strong sustainability the production system is limited by the productive vocation of the ecosystem, so that new approaches and creativity for making viable the nature conservancy and the business development are require. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=agriculture" title="agriculture">agriculture</a>, <a href="https://publications.waset.org/abstracts/search?q=environmental%20impacts" title=" environmental impacts"> environmental impacts</a>, <a href="https://publications.waset.org/abstracts/search?q=oil%20palm" title=" oil palm"> oil palm</a>, <a href="https://publications.waset.org/abstracts/search?q=strong%20sustainability" title=" strong sustainability"> strong sustainability</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20sustainability" title=" weak sustainability "> weak sustainability </a> </p> <a href="https://publications.waset.org/abstracts/29377/economic-and-ecological-implications-in-agricultural-production-within-the-strong-and-weak-sustainability-framework" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29377.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">431</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14458</span> Characterization of Monoids by a New Generalization of Flatness Property</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mahdiyeh%20Abbasi">Mahdiyeh Abbasi</a>, <a href="https://publications.waset.org/abstracts/search?q=Akbar%20Golchin"> Akbar Golchin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> It is well-known that, using principal weak flatness property, some important monoids are characterized, such as regular monoids, left almost regular monoids, and so on. In this article, we define a generalization of principal weak flatness called GP-Flatness, and will characterize monoids by this property of their right (Rees factor) acts. Also we investigate new classes of monoids called generally regular monoids and generally left almost regular monoids. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=G-left%20stabilizing" title="G-left stabilizing">G-left stabilizing</a>, <a href="https://publications.waset.org/abstracts/search?q=GP-flatness" title=" GP-flatness"> GP-flatness</a>, <a href="https://publications.waset.org/abstracts/search?q=generally%20regular" title=" generally regular"> generally regular</a>, <a href="https://publications.waset.org/abstracts/search?q=principal%20weak%20flatness" title=" principal weak flatness"> principal weak flatness</a> </p> <a href="https://publications.waset.org/abstracts/36458/characterization-of-monoids-by-a-new-generalization-of-flatness-property" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36458.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">336</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14457</span> Weak Convergence of Mann Iteration for a Hybrid Pair of Mappings in a Banach Space</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alemayehu%20Geremew%20Geremew">Alemayehu Geremew Geremew</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=common%20fixed%20point" title="common fixed point">common fixed point</a>, <a href="https://publications.waset.org/abstracts/search?q=Mann%20iteration" title=" Mann iteration"> Mann iteration</a>, <a href="https://publications.waset.org/abstracts/search?q=multivalued%20mapping" title=" multivalued mapping"> multivalued mapping</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20convergence" title=" weak convergence"> weak convergence</a> </p> <a href="https://publications.waset.org/abstracts/5913/weak-convergence-of-mann-iteration-for-a-hybrid-pair-of-mappings-in-a-banach-space" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5913.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">335</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14456</span> Tunnelling Concepts in Overstressed Weak Rocks</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Entfellner%20Manuel">Entfellner Manuel</a>, <a href="https://publications.waset.org/abstracts/search?q=Wannenmacher%20Helmut"> Wannenmacher Helmut</a>, <a href="https://publications.waset.org/abstracts/search?q=Reisenbauer%20Josef"> Reisenbauer Josef</a>, <a href="https://publications.waset.org/abstracts/search?q=Schubert%20Wulf"> Schubert Wulf</a> </p> <p class="card-text"><strong>Abstract:</strong></p> When tunnelling in overstressed weak rocks ("squeezing ground"), two basic design approaches are available: the resistance principle, and the yielding principle. The resistance principle relies on rigid support systems to withstand the ground pressure. Alternatively, the yielding principle prioritizes controlled deformation, allowing the ground to deform without compromising tunnel integrity. This paper highlights the beneficial factors of the yielding principle for conventionally excavated tunnels in overstressed weak rocks. Especially the application of a ductile shotcrete lining with yielding elements is analysed in detail. Construction costs, safety, short- and long-term stabilities are discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=squeezing%20ground" title="squeezing ground">squeezing ground</a>, <a href="https://publications.waset.org/abstracts/search?q=yielding%20principle" title=" yielding principle"> yielding principle</a>, <a href="https://publications.waset.org/abstracts/search?q=yielding%20element" title=" yielding element"> yielding element</a>, <a href="https://publications.waset.org/abstracts/search?q=conventional%20tunneling" title=" conventional tunneling"> conventional tunneling</a> </p> <a href="https://publications.waset.org/abstracts/176528/tunnelling-concepts-in-overstressed-weak-rocks" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/176528.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">71</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14455</span> Non-Differentiable Mond-Weir Type Symmetric Duality under Generalized Invexity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jai%20Prakash%20Verma">Jai Prakash Verma</a>, <a href="https://publications.waset.org/abstracts/search?q=Khushboo%20Verma"> Khushboo Verma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper, a pair of Mond-Weir type non-differentiable multiobjective second-order programming problems, involving two kernel functions, where each of the objective functions contains support function, is formulated. We prove weak, strong and converse duality theorem for the second-order symmetric dual programs under η-pseudoinvexity conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-differentiable%20multiobjective%20programming" title="non-differentiable multiobjective programming">non-differentiable multiobjective programming</a>, <a href="https://publications.waset.org/abstracts/search?q=second-order%20symmetric%20duality" title=" second-order symmetric duality"> second-order symmetric duality</a>, <a href="https://publications.waset.org/abstracts/search?q=efficiency" title=" efficiency"> efficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=support%20function" title=" support function"> support function</a>, <a href="https://publications.waset.org/abstracts/search?q=eta-pseudoinvexity" title=" eta-pseudoinvexity"> eta-pseudoinvexity</a> </p> <a href="https://publications.waset.org/abstracts/57852/non-differentiable-mond-weir-type-symmetric-duality-under-generalized-invexity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57852.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">249</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14454</span> Optimality Conditions for Weak Efficient Solutions Generated by a Set Q in Vector Spaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elham%20Kiyani">Elham Kiyani</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Mansour%20Vaezpour"> S. Mansour Vaezpour</a>, <a href="https://publications.waset.org/abstracts/search?q=Javad%20Tavakoli"> Javad Tavakoli</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we first introduce a new distance function in a linear space not necessarily endowed with a topology. The algebraic concepts of interior and closure are useful to study optimization problems without topology. So, we define Q-weak efficient solutions generated by the algebraic interior of a set Q, where Q is not necessarily convex. Studying nonconvex vector optimization is valuable since, for a convex cone K in topological spaces, we have int(K)=cor(K), which means that topological interior of a convex cone K is equal to the algebraic interior of K. Moreover, we used the scalarization technique including the distance function generated by the vectorial closure of a set to characterize these Q-weak efficient solutions. Scalarization is a useful approach for solving vector optimization problems. This technique reduces the optimization problem to a scalar problem which tends to be an optimization problem with a real-valued objective function. For instance, Q-weak efficient solutions of vector optimization problems can be characterized and computed as solutions of appropriate scalar optimization problems. In the convex case, linear functionals can be used as objective functionals of the scalar problems. But in the nonconvex case, we should present a suitable objective function. It is the aim of this paper to present a new distance function that be useful to obtain sufficient and necessary conditions for Q-weak efficient solutions of general optimization problems via scalarization. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=weak%20efficient" title="weak efficient">weak efficient</a>, <a href="https://publications.waset.org/abstracts/search?q=algebraic%20interior" title=" algebraic interior"> algebraic interior</a>, <a href="https://publications.waset.org/abstracts/search?q=vector%20closure" title=" vector closure"> vector closure</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20space" title=" linear space"> linear space</a> </p> <a href="https://publications.waset.org/abstracts/94737/optimality-conditions-for-weak-efficient-solutions-generated-by-a-set-q-in-vector-spaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/94737.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">228</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14453</span> Duality in Multiobjective Nonlinear Programming under Generalized Second Order (F, b, φ, ρ, θ)− Univex Functions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Meraj%20Ali%20Khan">Meraj Ali Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Falleh%20R.%20Al-Solamy"> Falleh R. Al-Solamy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present paper, second order duality for multiobjective nonlinear programming are investigated under the second order generalized (F, b, φ, ρ, θ)− univex functions. The weak, strong and converse duality theorems are proved. Further, we also illustrated an example of (F, b, φ, ρ, θ)− univex functions. Results obtained in this paper extend some previously known results of multiobjective nonlinear programming in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=duality" title="duality">duality</a>, <a href="https://publications.waset.org/abstracts/search?q=multiobjective%20programming" title=" multiobjective programming"> multiobjective programming</a>, <a href="https://publications.waset.org/abstracts/search?q=univex%20functions" title=" univex functions"> univex functions</a>, <a href="https://publications.waset.org/abstracts/search?q=univex" title=" univex"> univex</a> </p> <a href="https://publications.waset.org/abstracts/4320/duality-in-multiobjective-nonlinear-programming-under-generalized-second-order-f-b-f-r-th-univex-functions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4320.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">354</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14452</span> Finite Element Approximation of the Heat Equation under Axisymmetry Assumption</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Raphael%20Zanella">Raphael Zanella</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This works deals with the finite element approximation of axisymmetric problems. The weak formulation of the heat equation under the axisymmetry assumption is established for continuous finite elements. The weak formulation is implemented in a C++ solver with implicit march-in-time. The code is verified by space and time convergence tests using a manufactured solution. The solving of an example problem with an axisymmetric formulation is compared to that with a full-3D formulation. Both formulations lead to the same result, but the code based on the axisymmetric formulation is much faster due to the lower number of degrees of freedom. This confirms the correctness of our approach and the interest in using an axisymmetric formulation when it is possible. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=axisymmetric%20problem" title="axisymmetric problem">axisymmetric problem</a>, <a href="https://publications.waset.org/abstracts/search?q=continuous%20finite%20elements" title=" continuous finite elements"> continuous finite elements</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20equation" title=" heat equation"> heat equation</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20formulation" title=" weak formulation"> weak formulation</a> </p> <a href="https://publications.waset.org/abstracts/143012/finite-element-approximation-of-the-heat-equation-under-axisymmetry-assumption" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/143012.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">203</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14451</span> An Investigation of the Weak Localization, Electron-Electron Interaction and the Superconducting Fluctuations in a Weakly Disordered Granular Aluminum Film</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rukshana%20Pervin">Rukshana Pervin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We report a detailed study on the transport properties of a 40 nm thick granular aluminum film. As measured by temperature-dependent resistance R(T), a resistance peak is observed before the transition to superconductivity, which indicates that the diffusion channel is subjected to weak localization and electron-electron interaction, and the superconductor channel is subjected to SC fluctuations (SCFs). The zero-magnetic field transport measurement demonstrated that Electron-Electron Interaction (EEI), weak localization, and SCFs are closely related in this granular aluminum film. The characteristic temperature at which SCFs emerge on the sample is determined by measuring the R(T) during cooling. The SCF of the film is studied in terms of the direct contribution of the Aslamazov-Larkin's fluctuation Cooper pair density and the indirect contribution of the Maki-Thomson's quasiparticle pair density. In this sample, the rise in R(T) above the SCF characteristic temperature indicates the WL and/or EEI. Comparative analyses are conducted on how the EEI and WL contribute to the upturn in R(T). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fluctuation%20superconductivity" title="fluctuation superconductivity">fluctuation superconductivity</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20localization" title=" weak localization"> weak localization</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20deposition" title=" thermal deposition"> thermal deposition</a>, <a href="https://publications.waset.org/abstracts/search?q=electron-electron%20interaction" title=" electron-electron interaction"> electron-electron interaction</a> </p> <a href="https://publications.waset.org/abstracts/175740/an-investigation-of-the-weak-localization-electron-electron-interaction-and-the-superconducting-fluctuations-in-a-weakly-disordered-granular-aluminum-film" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/175740.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">56</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14450</span> Weak Mutually Unbiased Bases versus Mutually Unbiased Bases in Terms of T-Designs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Shalaby">Mohamed Shalaby</a>, <a href="https://publications.waset.org/abstracts/search?q=Yasser%20Kamal"> Yasser Kamal</a>, <a href="https://publications.waset.org/abstracts/search?q=Negm%20Shawky"> Negm Shawky</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Mutually unbiased bases (MUBs) have an important role in the field of quantum computation and information. A complete set of these bases can be constructed when the system dimension is the power of the prime. Constructing such complete set in composite dimensions is still an open problem. Recently, the concept of weak mutually unbiased bases (WMUBs) in composite dimensions was introduced. A complete set of such bases can be constructed by combining the MUBs in each subsystem. In this paper, we present a comparative study between MUBs and WMUBs in the context of complex projective t-design. Explicit proofs are presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=complex%20projective%20t-design" title="complex projective t-design">complex projective t-design</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20quantum%20systems" title=" finite quantum systems"> finite quantum systems</a>, <a href="https://publications.waset.org/abstracts/search?q=mutually%20unbiased%20bases" title=" mutually unbiased bases"> mutually unbiased bases</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20mutually%20unbiased%20bases" title=" weak mutually unbiased bases "> weak mutually unbiased bases </a> </p> <a href="https://publications.waset.org/abstracts/33996/weak-mutually-unbiased-bases-versus-mutually-unbiased-bases-in-terms-of-t-designs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33996.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">449</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14449</span> Testing the Weak Form Efficiency of Islamic Stock Market: Empirical Evidence from Indonesia</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Herjuno%20Bagus%20Wicaksono">Herjuno Bagus Wicaksono</a>, <a href="https://publications.waset.org/abstracts/search?q=Emma%20Almira%20Fauni"> Emma Almira Fauni</a>, <a href="https://publications.waset.org/abstracts/search?q=Salma%20Amelia%20Dina"> Salma Amelia Dina</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Efficient Market Hypothesis (EMH) states that, in an efficient capital market, price fully reflects the information available in the market. This theory has influenced many investors behavior in trading in the stock market. Advanced researches have been conducted to test the efficiency of the stock market in particular countries. Indonesia, as one of the emerging countries, has performed substantial growth in the past years. Hence, this paper aims to examine the efficiency of Islamic stock market in Indonesia in its weak form. The daily stock price data from Indonesia Sharia Stock Index (ISSI) for the period October 2015 to October 2016 were used to do the statistical tests: Run Test and Serial Correlation Test. The results show that there is no serial correlation between the current price with the past prices and the market follows the random walk. This research concludes that Indonesia Islamic stock market is weak form efficient. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=efficient%20market%20hypothesis" title="efficient market hypothesis">efficient market hypothesis</a>, <a href="https://publications.waset.org/abstracts/search?q=Indonesia%20sharia%20stock%20index" title=" Indonesia sharia stock index"> Indonesia sharia stock index</a>, <a href="https://publications.waset.org/abstracts/search?q=random%20walk" title=" random walk"> random walk</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20form%20efficiency" title=" weak form efficiency"> weak form efficiency</a> </p> <a href="https://publications.waset.org/abstracts/61095/testing-the-weak-form-efficiency-of-islamic-stock-market-empirical-evidence-from-indonesia" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/61095.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">460</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14448</span> Arithmetic Operations in Deterministic P Systems Based on the Weak Rule Priority</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chinedu%20Peter">Chinedu Peter</a>, <a href="https://publications.waset.org/abstracts/search?q=Dashrath%20Singh"> Dashrath Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Membrane computing is a computability model which abstracts its structures and functions from the biological cell. The main ingredient of membrane computing is the notion of a membrane structure, which consists of several cell-like membranes recurrently placed inside a unique skin membrane. The emergence of several variants of membrane computing gives rise to the notion of a P system. The paper presents a variant of P systems for arithmetic operations on non-negative integers based on the weak priorities for rule application. Consequently, we obtain deterministic P systems. Two membranes suffice. There are at most four objects for multiplication and five objects for division throughout the computation processes. The model is simple and has a potential for possible extension to non-negative integers and real numbers in general. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=P%20system" title="P system">P system</a>, <a href="https://publications.waset.org/abstracts/search?q=binary%20operation" title=" binary operation"> binary operation</a>, <a href="https://publications.waset.org/abstracts/search?q=determinism" title=" determinism"> determinism</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20rule%20priority" title=" weak rule priority"> weak rule priority</a> </p> <a href="https://publications.waset.org/abstracts/34826/arithmetic-operations-in-deterministic-p-systems-based-on-the-weak-rule-priority" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34826.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">445</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14447</span> Variability of L-Band GPS Scintillation over Auroral Region, Maitri, Antarctica </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Prakash%20Khatarkar">Prakash Khatarkar</a>, <a href="https://publications.waset.org/abstracts/search?q=P.%20A.%20Khan"> P. A. Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Shweta%20Mukherjee"> Shweta Mukherjee</a>, <a href="https://publications.waset.org/abstracts/search?q=Roshni%20Atulkar"> Roshni Atulkar</a>, <a href="https://publications.waset.org/abstracts/search?q=P.%20K.%20Purohit"> P. K. Purohit</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20K.%20Gwal"> A. K. Gwal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We have investigated the occurrence characteristics of ionospheric scintillations, using dual frequency GPS, installed and operated at Indian scientific base station Maitri (71.45S and 11.45E), Antarctica, during December 2009 to December 2010. The scintillation morphology is described in terms of S4 Index. The scintillations are classified into four main categories as Weak (0.2<S4<0.4), Moderate (0.4<S4<0.6), Strong (0.6<S4<1.0) and Saturated (S4>1.0). From the analysis we found that the percentage of weak, moderate, strong and saturated scintillations were 96%, 80%, 58% and 7%, respectively. The maximum percentage of all types of scintillation was observed in the summer season, followed by equinox and the least in winter season. As the year 2010 was a low solar activity period, consequently the maximum occurrences of scintillations were those of weak and moderate and only four cases of saturated scintillation were observed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=L-band%20scintillation" title="L-band scintillation">L-band scintillation</a>, <a href="https://publications.waset.org/abstracts/search?q=GPS" title=" GPS"> GPS</a>, <a href="https://publications.waset.org/abstracts/search?q=auroral%20region" title=" auroral region"> auroral region</a>, <a href="https://publications.waset.org/abstracts/search?q=low%20solar%20activity" title=" low solar activity"> low solar activity</a> </p> <a href="https://publications.waset.org/abstracts/11220/variability-of-l-band-gps-scintillation-over-auroral-region-maitri-antarctica" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11220.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">648</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14446</span> Features of Calculating Structures for Frequent Weak Earthquakes</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20S.%20Belashov">M. S. Belashov</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20V.%20Benin"> A. V. Benin</a>, <a href="https://publications.waset.org/abstracts/search?q=Lin%20Hong"> Lin Hong</a>, <a href="https://publications.waset.org/abstracts/search?q=Sh.%20Sh.%20Nazarova"> Sh. Sh. Nazarova</a>, <a href="https://publications.waset.org/abstracts/search?q=O.%20B.%20Sabirova"> O. B. Sabirova</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20M.%20Uzdin"> A. M. Uzdin</a>, <a href="https://publications.waset.org/abstracts/search?q=Lin%20Hong"> Lin Hong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The features of calculating structures for the action of weak earthquakes are analyzed. Earthquakes with a recurrence of 30 years and 50 years are considered. In the first case, the structure is to operate normally without damage after the earthquake. In the second case, damages are allowed that do not affect the possibility of the structure operation. Three issues are emphasized: setting elastic and damping characteristics of reinforced concrete, formalization of limit states, and combinations of loads. The dependence of damping on the reinforcement coefficient is estimated. When evaluating limit states, in addition to calculations for crack resistance and strength, a human factor, i.e., the possibility of panic among people, was considered. To avoid it, it is proposed to limit a floor-by-floor speed level in certain octave ranges. Proposals have been developed for estimating the coefficients of the combination of various loads with the seismic one. As an example, coefficients of combinations of seismic and ice loads are estimated. It is shown that for strong actions, the combination coefficients for different regions turn out to be close, while for weak actions, they may differ. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=weak%20earthquake" title="weak earthquake">weak earthquake</a>, <a href="https://publications.waset.org/abstracts/search?q=frequent%20earthquake" title=" frequent earthquake"> frequent earthquake</a>, <a href="https://publications.waset.org/abstracts/search?q=damage" title=" damage"> damage</a>, <a href="https://publications.waset.org/abstracts/search?q=limit%20state" title=" limit state"> limit state</a>, <a href="https://publications.waset.org/abstracts/search?q=reinforcement" title=" reinforcement"> reinforcement</a>, <a href="https://publications.waset.org/abstracts/search?q=crack%20resistance" title=" crack resistance"> crack resistance</a>, <a href="https://publications.waset.org/abstracts/search?q=strength%20resistance" title=" strength resistance"> strength resistance</a>, <a href="https://publications.waset.org/abstracts/search?q=a%20floor-by-floor%20velocity" title=" a floor-by-floor velocity"> a floor-by-floor velocity</a>, <a href="https://publications.waset.org/abstracts/search?q=combination%20coefficients" title=" combination coefficients"> combination coefficients</a> </p> <a href="https://publications.waset.org/abstracts/159990/features-of-calculating-structures-for-frequent-weak-earthquakes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/159990.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">88</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14445</span> Budget and the Performance of Public Enterprises: A Study of Selected Public Enterprises in Nasarawa State Nigeria (2009-2013)</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dalhatu">Dalhatu</a>, <a href="https://publications.waset.org/abstracts/search?q=Musa%20Yusha%E2%80%99u"> Musa Yusha’u</a>, <a href="https://publications.waset.org/abstracts/search?q=Shuaibu%20Sidi%20Safiyanu"> Shuaibu Sidi Safiyanu</a>, <a href="https://publications.waset.org/abstracts/search?q=Haliru%20Musa%20Hussaini"> Haliru Musa Hussaini</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study examined budget and performance of public enterprises in Nasarawa State, Nigeria in a period of 2009-2013. The study utilized secondary sources of data obtained from four selected parastatals’ budget allocation and revenue generation for the period under review. The simple correlation coefficient was used to analyze the extent of the relationship between budget allocation and revenue generation of the parastatals. Findings revealed varying results. There was positive (0.21) and weak correlation between expenditure and revenue of Nasarawa Investment and Property Development Company (NIPDC). However, the study further revealed that there was strong and weak negative relationship in the revenue and expenditure of the following parastatals over the period under review. Viz: Nasarawa State Water Board, -0.27 (weak), Nasarawa State Broadcasting Service, -0.52 (Strong) and Nasarawa State College of Agriculture, -0.36 (weak). The study therefore, recommends that government should increase its investments in NIPDC to enhance efficiency and profitability. It also recommends that government should strengthen its fiscal responsibility, accountability and transparency in public parastatals. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=budget" title="budget">budget</a>, <a href="https://publications.waset.org/abstracts/search?q=public%20enterprises" title=" public enterprises"> public enterprises</a>, <a href="https://publications.waset.org/abstracts/search?q=revenue" title=" revenue"> revenue</a>, <a href="https://publications.waset.org/abstracts/search?q=enterprise" title=" enterprise"> enterprise</a> </p> <a href="https://publications.waset.org/abstracts/37058/budget-and-the-performance-of-public-enterprises-a-study-of-selected-public-enterprises-in-nasarawa-state-nigeria-2009-2013" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37058.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">260</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14444</span> Applying Element Free Galerkin Method on Beam and Plate</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mahdad%20M%E2%80%99hamed">Mahdad M’hamed</a>, <a href="https://publications.waset.org/abstracts/search?q=Belaidi%20Idir"> Belaidi Idir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=numerical%20computation" title="numerical computation">numerical computation</a>, <a href="https://publications.waset.org/abstracts/search?q=element-free%20Galerkin%20%28EFG%29" title=" element-free Galerkin (EFG)"> element-free Galerkin (EFG)</a>, <a href="https://publications.waset.org/abstracts/search?q=moving%20least%20squares%20%28MLS%29" title=" moving least squares (MLS)"> moving least squares (MLS)</a>, <a href="https://publications.waset.org/abstracts/search?q=meshless%20methods" title=" meshless methods"> meshless methods</a> </p> <a href="https://publications.waset.org/abstracts/50344/applying-element-free-galerkin-method-on-beam-and-plate" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50344.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">283</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14443</span> Incorporating Polya’s Problem Solving Process: A Polytechnic Mathematics Module Case Study</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pei%20Chin%20Lim">Pei Chin Lim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> School of Mathematics and Science of Singapore Polytechnic offers a Basic Mathematics module to students who did not pass GCE O-Level Additional Mathematics. These students are weaker in Mathematics. In particular, they struggle with word problems and tend to leave them blank in tests and examinations. In order to improve students’ problem-solving skills, the school redesigned the Basic Mathematics module to incorporate Polya’s problem-solving methodology. During tutorial lessons, students have to work through learning activities designed to raise their metacognitive awareness by following Polya’s problem-solving process. To assess the effectiveness of the redesign, students’ working for a challenging word problem in the mid-semester test were analyzed. Sixty-five percent of students attempted to understand the problem by making sketches. Twenty-eight percent of students went on to devise a plan and implement it. Only five percent of the students still left the question blank. These preliminary results suggest that with regular exposure to an explicit and systematic problem-solving approach, weak students’ problem-solving skills can potentially be improved. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mathematics%20education" title="mathematics education">mathematics education</a>, <a href="https://publications.waset.org/abstracts/search?q=metacognition" title=" metacognition"> metacognition</a>, <a href="https://publications.waset.org/abstracts/search?q=problem%20solving" title=" problem solving"> problem solving</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20students" title=" weak students"> weak students</a> </p> <a href="https://publications.waset.org/abstracts/98195/incorporating-polyas-problem-solving-process-a-polytechnic-mathematics-module-case-study" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/98195.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">162</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14442</span> Histochemistry of Intestinal Enzymes of Juvenile Dourado Salminus brasiliensis Fed Bovine Colostrum</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Debora%20B.%20Moretti">Debora B. Moretti</a>, <a href="https://publications.waset.org/abstracts/search?q=Wiolene%20M.%20Nordi"> Wiolene M. Nordi</a>, <a href="https://publications.waset.org/abstracts/search?q=Thaline%20Maira%20P.%20Cruz"> Thaline Maira P. Cruz</a>, <a href="https://publications.waset.org/abstracts/search?q=Jos%C3%A9%20Eurico%20P.%20Cyrino"> José Eurico P. Cyrino</a>, <a href="https://publications.waset.org/abstracts/search?q=Raul%20Machado-Neto"> Raul Machado-Neto</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Enzyme activity was evaluated in the intestine of juvenile dourado (Salminus brasiliensis) fed with diets containing 0, 10 or 20% of lyophilized bovine colostrum (LBC) inclusion for either 30 or 60 days. The intestinal enzymes acid and alkaline phosphatase (ACP and ALP, respectively), non-specific esterase (NSE), lipase (LIP), dipeptidyl aminopeptidase IV (DAP IV) and leucine aminopeptidase (LAP) were studied using histochemistry in four intestinal segments (S1, S2, S3 and posterior intestine). Weak proteolitic activity was observed in all intestinal segments for DAP IV and LAP. The activity of NSE and LIP was also weak in all intestines, except for the moderate activity of NSE in the S2 of 20% LBC group after 30 days and in the S1 of 0% LBC group after 60 days. The ACP was detected only in the S2 and S3 of the 10% LBC group after 30 days. Moderate and strong staining was observed in the first three intestinal segments for ALP and weak activity in the posterior intestine. The activity of DAP IV, LAP and ALP were also present in the cytoplasm of the enterocytes. In the present results, bovine colostrum feeding did not cause alterations in activity of intestinal enzymes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=carnivorous%20fish" title="carnivorous fish">carnivorous fish</a>, <a href="https://publications.waset.org/abstracts/search?q=enterocyte" title=" enterocyte"> enterocyte</a>, <a href="https://publications.waset.org/abstracts/search?q=intestinal%20epithelium" title=" intestinal epithelium"> intestinal epithelium</a>, <a href="https://publications.waset.org/abstracts/search?q=teleost" title=" teleost"> teleost</a> </p> <a href="https://publications.waset.org/abstracts/9534/histochemistry-of-intestinal-enzymes-of-juvenile-dourado-salminus-brasiliensis-fed-bovine-colostrum" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9534.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">329</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14441</span> Challenging Weak Central Coherence: An Exploration of Neurological Evidence from Visual Processing and Linguistic Studies in Autism Spectrum Disorder</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jessica%20Scher%20Lisa">Jessica Scher Lisa</a>, <a href="https://publications.waset.org/abstracts/search?q=Eric%20Shyman"> Eric Shyman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Autism spectrum disorder (ASD) is a neuro-developmental disorder that is characterized by persistent deficits in social communication and social interaction (i.e. deficits in social-emotional reciprocity, nonverbal communicative behaviors, and establishing/maintaining social relationships), as well as by the presence of repetitive behaviors and perseverative areas of interest (i.e. stereotyped or receptive motor movements, use of objects, or speech, rigidity, restricted interests, and hypo or hyperactivity to sensory input or unusual interest in sensory aspects of the environment). Additionally, diagnoses of ASD require the presentation of symptoms in the early developmental period, marked impairments in adaptive functioning, and a lack of explanation by general intellectual impairment or global developmental delay (although these conditions may be co-occurring). Over the past several decades, many theories have been developed in an effort to explain the root cause of ASD in terms of atypical central cognitive processes. The field of neuroscience is increasingly finding structural and functional differences between autistic and neurotypical individuals using neuro-imaging technology. One main area this research has focused upon is in visuospatial processing, with specific attention to the notion of ‘weak central coherence’ (WCC). This paper offers an analysis of findings from selected studies in order to explore research that challenges the ‘deficit’ characterization of a weak central coherence theory as opposed to a ‘superiority’ characterization of strong local coherence. The weak central coherence theory has long been both supported and refuted in the ASD literature and has most recently been increasingly challenged by advances in neuroscience. The selected studies lend evidence to the notion of amplified localized perception rather than deficient global perception. In other words, WCC may represent superiority in ‘local processing’ rather than a deficit in global processing. Additionally, the right hemisphere and the specific area of the extrastriate appear to be key in both the visual and lexicosemantic process. Overactivity in the striate region seems to suggest inaccuracy in semantic language, which lends itself to support for the link between the striate region and the atypical organization of the lexicosemantic system in ASD. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=autism%20spectrum%20disorder" title="autism spectrum disorder">autism spectrum disorder</a>, <a href="https://publications.waset.org/abstracts/search?q=neurology" title=" neurology"> neurology</a>, <a href="https://publications.waset.org/abstracts/search?q=visual%20processing" title=" visual processing"> visual processing</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20coherence" title=" weak coherence"> weak coherence</a> </p> <a href="https://publications.waset.org/abstracts/115591/challenging-weak-central-coherence-an-exploration-of-neurological-evidence-from-visual-processing-and-linguistic-studies-in-autism-spectrum-disorder" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/115591.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">127</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14440</span> Fragile States as the Fertile Ground for Non-State Actors: Colombia and Somalia</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Giorgi%20Goguadze">Giorgi Goguadze</a>, <a href="https://publications.waset.org/abstracts/search?q=Jakub%20Zaj%C4%85czkowski"> Jakub Zajączkowski</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is written due to overview the connection between fragile states and non-state actors, we should take into account that fragile states may vary from weak, failing and failed. In this paper we will discuss about two countries, one of them is weak (Colombia/ second one is already failed- Somalia. We will try to understand what feeds ill non-state actors such as: terrorist organizations, criminal entities and other cells in these countries, what threats are they representing and how to eliminate these dangers in both national and international scope. This paper is mainly based on literature overview and personal attitude and doesn’t claim to be in scientific chain. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fragile%20States" title="fragile States">fragile States</a>, <a href="https://publications.waset.org/abstracts/search?q=terrorism" title=" terrorism"> terrorism</a>, <a href="https://publications.waset.org/abstracts/search?q=tribalism" title=" tribalism"> tribalism</a>, <a href="https://publications.waset.org/abstracts/search?q=Somalia" title=" Somalia"> Somalia</a> </p> <a href="https://publications.waset.org/abstracts/29056/fragile-states-as-the-fertile-ground-for-non-state-actors-colombia-and-somalia" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29056.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">367</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14439</span> Theoretical Analysis of Self-Starting Busemann Intake Family</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=N.%20Moradian">N. Moradian</a>, <a href="https://publications.waset.org/abstracts/search?q=E.%20Timofeev"> E. Timofeev</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Tahir"> R. Tahir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, startability of the Busemann intake family with weak/strong conical shock, as most efficient intakes, via overboard mass spillage method is theoretically analyzed. Masterix and Candifix codes are used to numerically simulate few models of this type of intake and verify the theoretical results. Portions of the intake corresponding to various flow capture angles are considered to have mass spillage in the starting process of this intake. This approach allows for overboard mass spillage via a V-shaped slot with the tip of V coinciding with the focal point of the Busemann flow. The theoretical results, achieved using two different theories, of self-started Busemann takes with weak/strong conical shock show that significant improve in intake startability using overboard spillage technique. The starting phenomena of Busemann intakes with weak conical shock and seven different capture angles are numerically simulated at freestream Mach number of 3 to find the minimum area ratios of self-started intakes. The numerical results confirm the theoretical ones achieved by authors. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Busemann%20intake" title="Busemann intake">Busemann intake</a>, <a href="https://publications.waset.org/abstracts/search?q=conical%20shock" title=" conical shock"> conical shock</a>, <a href="https://publications.waset.org/abstracts/search?q=overboard%20spillage" title=" overboard spillage"> overboard spillage</a>, <a href="https://publications.waset.org/abstracts/search?q=startability" title=" startability"> startability</a> </p> <a href="https://publications.waset.org/abstracts/57464/theoretical-analysis-of-self-starting-busemann-intake-family" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57464.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">205</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">14438</span> Improving Anchor Technology for Adapting the Weak Soil</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sang%20Hee%20Shin">Sang Hee Shin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The technical improving project is for using the domestic construction technology in the weak soil condition. The improved technology is applied directly under local construction site at OOO, OOO. Existing anchor technology was developed for the case of soft ground as N value 10 or less. In case of soft ground and heavy load, the attachment site per one strand is shortened due to the distributed interval so that the installation site is increased relatively and being economically infeasible. In addition, in case of high tensile load, adhesion phenomenon between wedge and block occurs. To solve these problems, it strengthens the function of the attached strands to treat a ‘bulbing’ on the strands. In the solution for minimizing the internal damage and strengthening the removal function, it induces lubricating action using the film and the attached film, and it makes the buffer structure using wedge lubricating structure and the spring. The technology is performed such as in-house testing and the field testing. The project can improve the reliability of the standardized quality technique. As a result, it intended to give the technical competitiveness. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=anchor" title="anchor">anchor</a>, <a href="https://publications.waset.org/abstracts/search?q=improving%20technology" title=" improving technology"> improving technology</a>, <a href="https://publications.waset.org/abstracts/search?q=removal%20anchor" title=" removal anchor"> removal anchor</a>, <a href="https://publications.waset.org/abstracts/search?q=soil%20reinforcement" title=" soil reinforcement"> soil reinforcement</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20soil" title=" weak soil"> weak soil</a> </p> <a href="https://publications.waset.org/abstracts/46616/improving-anchor-technology-for-adapting-the-weak-soil" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46616.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">210</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=weak%20order&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=weak%20order&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=weak%20order&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=weak%20order&page=5">5</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=weak%20order&page=6">6</a></li> <li class="page-item"><a class="page-link" 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