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principle</title> <meta name="description" content="Search results for: Hamilton's principle"> <meta name="keywords" content="Hamilton's principle"> <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 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="Hamilton's principle"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 1184</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: Hamilton's principle</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1184</span> Hamilton-Jacobi Treatment of Damped Motion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khaled%20I.%20Nawafleh">Khaled I. Nawafleh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we apply the method of Hamilton-Jacobi to obtain solutions of Hamiltonian systems in classical mechanics with two certain structures: the first structure plays a central role in the theory of time-dependent Hamiltonians, whilst the second is used to treat classical Hamiltonians, including dissipation terms. It is proved that the generalization of problems from the calculus of variation methods in the nonstationary case can be obtained naturally in Hamilton-Jacobi formalism. Then, another expression of geometry of the Hamilton Jacobi equation is retrieved for Hamiltonians with time-dependent and frictional terms. Both approaches shall be applied to many physical examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hamilton-Jacobi" title="Hamilton-Jacobi">Hamilton-Jacobi</a>, <a href="https://publications.waset.org/abstracts/search?q=time%20dependent%20lagrangians" title=" time dependent lagrangians"> time dependent lagrangians</a>, <a href="https://publications.waset.org/abstracts/search?q=dissipative%20systems" title=" dissipative systems"> dissipative systems</a>, <a href="https://publications.waset.org/abstracts/search?q=variational%20principle" title=" variational principle"> variational principle</a> </p> <a href="https://publications.waset.org/abstracts/127155/hamilton-jacobi-treatment-of-damped-motion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127155.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">179</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">1183</span> Adaptations to Hamilton's Rule in Human Populations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Monty%20Vacura">Monty Vacura</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Hamilton鈥檚 Rule is a universal law of biology expressed in protists, plants and animals. When applied to human populations, this model explains: 1) Origin of religion in society as a biopsychological need selected to increase population size; 2) Instincts of racism expressed through intergroup competition; 3) Simultaneous selection for human cooperation and conflict, love and hate; 4) Connection between sporting events and instinctive social messaging for stimulating offensive and defensive responses; 5) Pathway to reduce human sacrifice. This chapter discusses the deep psychological influences of Hamilton鈥檚 Rule. Suggestions are provided to reduce human deaths via our instinctive sacrificial behavior, by consciously monitoring Hamilton鈥檚 Rule variables highlighted throughout our media outlets. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=psychology" title="psychology">psychology</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton%E2%80%99s%20rule" title=" Hamilton鈥檚 rule"> Hamilton鈥檚 rule</a>, <a href="https://publications.waset.org/abstracts/search?q=evolution" title=" evolution"> evolution</a>, <a href="https://publications.waset.org/abstracts/search?q=human%20instincts" title=" human instincts"> human instincts</a> </p> <a href="https://publications.waset.org/abstracts/179985/adaptations-to-hamiltons-rule-in-human-populations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/179985.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">60</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">1182</span> A Lagrangian Hamiltonian Computational Method for Hyper-Elastic Structural Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hosein%20Falahaty">Hosein Falahaty</a>, <a href="https://publications.waset.org/abstracts/search?q=Hitoshi%20Gotoh"> Hitoshi Gotoh</a>, <a href="https://publications.waset.org/abstracts/search?q=Abbas%20Khayyer"> Abbas Khayyer</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hamilton%27s%20principle%20of%20least%20action" title="Hamilton's principle of least action">Hamilton's principle of least action</a>, <a href="https://publications.waset.org/abstracts/search?q=particle-based%20method" title=" particle-based method"> particle-based method</a>, <a href="https://publications.waset.org/abstracts/search?q=hyper-elasticity" title=" hyper-elasticity"> hyper-elasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=analysis%20of%20stability" title=" analysis of stability"> analysis of stability</a> </p> <a href="https://publications.waset.org/abstracts/50921/a-lagrangian-hamiltonian-computational-method-for-hyper-elastic-structural-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50921.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">341</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">1181</span> Vibration Analysis of Power Lines with Moving Dampers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Bukhari">Mohammad Bukhari</a>, <a href="https://publications.waset.org/abstracts/search?q=Oumar%20Barry"> Oumar Barry</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In order to reduce the Aeolian vibration of overhead transmission lines, the Stockbridge damper is usually attached. The efficiency of Stockbridge damper depends on its location on the conductor and its resonant frequencies. When the Stockbridge damper is located on a vibration node, it becomes inefficient. Hence, the static damper should be subrogated by a dynamic one. In the present study, a proposed dynamic absorber for transmission lines is studied. Hamilton鈥檚 principle is used to derive the governing equations, then the system of ordinary differential equations is solved numerically. Parametric studies are conducted to determine how certain parameters affect the performance of the absorber. The results demonstrate that replacing the static absorber by a dynamic one enhance the absorber performance for wider range of frequencies. The results also indicate that the maximum displacement decreases as the absorber speed and the forcing frequency increase. However, this reduction in maximum displacement is accompanying with increasing in the steady state vibration displacement. It is also indicated that the energy dissipation in moving absorber covers higher range of frequencies. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=absorber%20performance" title="absorber performance">absorber performance</a>, <a href="https://publications.waset.org/abstracts/search?q=Aeolian%20vibration" title=" Aeolian vibration"> Aeolian vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton%E2%80%99s%20principle" title=" Hamilton鈥檚 principle"> Hamilton鈥檚 principle</a>, <a href="https://publications.waset.org/abstracts/search?q=stockbridge%20damper" title=" stockbridge damper"> stockbridge damper</a> </p> <a href="https://publications.waset.org/abstracts/66478/vibration-analysis-of-power-lines-with-moving-dampers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66478.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">267</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">1180</span> Biological Expressions of Hamilton鈥檚 Rule in Human Populations: The Deep Psychological Influence of Defensive and Offensive Motivations Found in Human Conflicts and Sporting Events</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Monty%20Vacura">Monty Vacura</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Hamilton鈥檚 Rule is a universal law of biology expressed in protists, plants and animals. When applied to human populations, this model explains: 1) Origin of religion in society as a biopsychological need naturally selected to increase population size; 2) Instincts of racism expressed through intergroup competition; 3) Simultaneous selection for human cooperation and conflict, love and hate; 4) Places Dawkins鈥檚 selfish gene as the r, relationship variable; 5) Flipping the equation variable themes (close relationship to distant relationship, and benefit to threat) the new equation can now be used to identify the offensive and defensive sides of conflict; 6) Connection between sporting events and instinctive social messaging for stimulating offensive and defensive responses; 6) Pathway to reduce human sacrifice through manipulation of variables. This paper discusses the deep psychological influences of Hamilton鈥檚 Rule. Suggestions are provided to reduce human deaths via our instinctive sacrificial behavior, by consciously monitoring Hamilton鈥檚 Rule variables highlighted throughout our media outlets. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=psychology" title="psychology">psychology</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton%E2%80%99s%20rule" title=" Hamilton鈥檚 rule"> Hamilton鈥檚 rule</a>, <a href="https://publications.waset.org/abstracts/search?q=evolution" title=" evolution"> evolution</a>, <a href="https://publications.waset.org/abstracts/search?q=human%20instincts" title=" human instincts"> human instincts</a> </p> <a href="https://publications.waset.org/abstracts/187335/biological-expressions-of-hamiltons-rule-in-human-populations-the-deep-psychological-influence-of-defensive-and-offensive-motivations-found-in-human-conflicts-and-sporting-events" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/187335.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">50</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">1179</span> Solution for Thick Plate Resting on Winkler Foundation by Symplectic Geometry Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mei-Jie%20Xu">Mei-Jie Xu</a>, <a href="https://publications.waset.org/abstracts/search?q=Yang%20Zhong"> Yang Zhong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=symplectic%20geometry%20method" title="symplectic geometry method">symplectic geometry method</a>, <a href="https://publications.waset.org/abstracts/search?q=Winkler%20foundation" title=" Winkler foundation"> Winkler foundation</a>, <a href="https://publications.waset.org/abstracts/search?q=thick%20rectangular%20plate" title=" thick rectangular plate"> thick rectangular plate</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20separation%20method" title=" variable separation method"> variable separation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton%20system" title=" Hamilton system "> Hamilton system </a> </p> <a href="https://publications.waset.org/abstracts/6000/solution-for-thick-plate-resting-on-winkler-foundation-by-symplectic-geometry-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/6000.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">305</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">1178</span> A Study of Hamilton-Jacobi-Bellman Equation Systems Arising in Differential Game Models of Changing Society</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Weihua%20Ruan">Weihua Ruan</a>, <a href="https://publications.waset.org/abstracts/search?q=Kuan-Chou%20Chen"> Kuan-Chou Chen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hamilton-Jacobi-Bellman%20equations" title="Hamilton-Jacobi-Bellman equations">Hamilton-Jacobi-Bellman equations</a>, <a href="https://publications.waset.org/abstracts/search?q=infinite-horizon%20differential%20games" title=" infinite-horizon differential games"> infinite-horizon differential games</a>, <a href="https://publications.waset.org/abstracts/search?q=continuous%20and%20discrete%20state%20variables" title=" continuous and discrete state variables"> continuous and discrete state variables</a>, <a href="https://publications.waset.org/abstracts/search?q=political-economy%20models" title=" political-economy models"> political-economy models</a> </p> <a href="https://publications.waset.org/abstracts/69675/a-study-of-hamilton-jacobi-bellman-equation-systems-arising-in-differential-game-models-of-changing-society" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/69675.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">377</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">1177</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">70</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">1176</span> Geo-Spatial Methods to Better Understand Urban Food Deserts</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Brian%20Ceh">Brian Ceh</a>, <a href="https://publications.waset.org/abstracts/search?q=Alison%20Jackson-Holland"> Alison Jackson-Holland</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Food deserts are a reality in some cities. These deserts can be described as a shortage of healthy food options within close proximity of consumers. The shortage in this case is typically facilitated by a lack of stores in an urban area that provide adequate fruit and vegetable choices. This study explores new avenues to better understand food deserts by examining modes of transportation that are available to shoppers or consumers, e.g. walking, automobile, or public transit. Further, this study is unique in that it not only explores the location of large grocery stores, but small grocery and convenience stores too. In this study, the relationship between some socio-economic indicators, such as personal income, are also explored to determine any possible association with food deserts. In addition, to help facilitate our understanding of food deserts, complex network spatial models that are built on adequate algorithms are used to investigate the possibility of food deserts in the city of Hamilton, Canada. It is found that Hamilton, Canada is adequate serviced by retailers who provide healthy food choices and that the food desert phenomena is almost absent. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Canada" title="Canada">Canada</a>, <a href="https://publications.waset.org/abstracts/search?q=desert" title=" desert"> desert</a>, <a href="https://publications.waset.org/abstracts/search?q=food" title=" food"> food</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton" title=" Hamilton"> Hamilton</a>, <a href="https://publications.waset.org/abstracts/search?q=store" title=" store"> store</a> </p> <a href="https://publications.waset.org/abstracts/76750/geo-spatial-methods-to-better-understand-urban-food-deserts" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/76750.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">241</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">1175</span> Optimal Investment and Consumption Decision for an Investor with Ornstein-Uhlenbeck Stochastic Interest Rate Model through Utility Maximization</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Silas%20A.%20Ihedioha">Silas A. Ihedioha</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work; it is considered that an investor鈥檚 portfolio is comprised of two assets; a risky stock which price process is driven by the geometric Brownian motion and a risk-free asset with Ornstein-Uhlenbeck Stochastic interest rate of return, where consumption, taxes, transaction costs and dividends are involved. This paper aimed at the optimization of the investor鈥檚 expected utility of consumption and terminal return on his investment at the terminal time having power utility preference. Using dynamic optimization procedure of maximum principle, a second order nonlinear partial differential equation (PDE) (the Hamilton-Jacobi-Bellman equation HJB) was obtained from which an ordinary differential equation (ODE) obtained via elimination of variables. The solution to the ODE gave the closed form solution of the investor鈥檚 problem. It was found the optimal investment in the risky asset is horizon dependent and a ratio of the total amount available for investment and the relative risk aversion coefficient. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=optimal" title="optimal">optimal</a>, <a href="https://publications.waset.org/abstracts/search?q=investment" title=" investment"> investment</a>, <a href="https://publications.waset.org/abstracts/search?q=Ornstein-Uhlenbeck" title=" Ornstein-Uhlenbeck"> Ornstein-Uhlenbeck</a>, <a href="https://publications.waset.org/abstracts/search?q=utility%20maximization" title=" utility maximization"> utility maximization</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20interest%20rate" title=" stochastic interest rate"> stochastic interest rate</a>, <a href="https://publications.waset.org/abstracts/search?q=maximum%20principle" title=" maximum principle"> maximum principle</a> </p> <a href="https://publications.waset.org/abstracts/76818/optimal-investment-and-consumption-decision-for-an-investor-with-ornstein-uhlenbeck-stochastic-interest-rate-model-through-utility-maximization" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/76818.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">225</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">1174</span> Sustainable Development: The Human Rights Approach to Environmental Protection in South Africa</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=CM%20van%20der%20Bank">CM van der Bank</a>, <a href="https://publications.waset.org/abstracts/search?q=Marjon%C3%A9%20van%20der%20Bank"> Marjon茅 van der Bank</a> </p> <p class="card-text"><strong>Abstract:</strong></p> International and domestic environmental law has evolved quite rapidly in the last few decades. At the international level the Stockholm and Rio Declarations paved the way for a broad based consensus of the international community on environmental issues and principles. At the Domestic level also many states have incorporated environmental protection in their constitutions and even more states are doing the same at least in their domestic legislations. In this process of evolution environmental law has unleashed a number of novel principles such as; the participatory principle, the polluter pays principle, the precautionary principle, the inter-generational and intra-generational principles, the prevention principle, the sustainable development principle and so on. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=environment" title="environment">environment</a>, <a href="https://publications.waset.org/abstracts/search?q=human%20rights" title=" human rights"> human rights</a>, <a href="https://publications.waset.org/abstracts/search?q=international%20law" title=" international law"> international law</a>, <a href="https://publications.waset.org/abstracts/search?q=protection" title=" protection"> protection</a> </p> <a href="https://publications.waset.org/abstracts/15184/sustainable-development-the-human-rights-approach-to-environmental-protection-in-south-africa" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15184.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">463</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">1173</span> The Standard of Best Interest of the Child in Custody Adjudication under the Malaysian Laws</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Roslina%20Che%20Soh">Roslina Che Soh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Best interest of the child has been the prevailing principle of the custody legislations of most nations in the world. The tremendous shift from parental rights to parental responsibilities throughout the centuries had made the principle of best interests of the child as the utmost matter which parents must uphold in child upbringing. Despite the commitment to this principle is significantly enshrined in the United Nation Convention on Rights of the Child, the content and application of the principle differs across borders. Differences persist notwithstanding many countries have experienced a substantial shift over the last several decades in the types of custodial arrangements that are thought to best serve children鈥檚 interests. The laws in Malaysia similarly uphold this principle but do not provide further deliberation on the principle itself. The principle is entirely developed by the courts through decided cases. Thus, this paper seeks to discuss the extent of the application of best interest of the child principle in custody disputes. In doing so, it attempts to provide an overview of the current laws and the approach of the Civil and the Shariah courts in Malaysia in applying the principle in determining custody disputes. For purposes of comparison, it briefly examines the legislations and the courts practices in Australia and England on this matter. The purpose is to determine the best standard to be adopted by Malaysia and to propose improvement to the laws whenever appropriate. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=child%20custody" title="child custody">child custody</a>, <a href="https://publications.waset.org/abstracts/search?q=best%20interest" title=" best interest"> best interest</a>, <a href="https://publications.waset.org/abstracts/search?q=Malaysian%20law" title=" Malaysian law"> Malaysian law</a>, <a href="https://publications.waset.org/abstracts/search?q=bioinformatics" title=" bioinformatics"> bioinformatics</a>, <a href="https://publications.waset.org/abstracts/search?q=biomedicine" title=" biomedicine"> biomedicine</a> </p> <a href="https://publications.waset.org/abstracts/8863/the-standard-of-best-interest-of-the-child-in-custody-adjudication-under-the-malaysian-laws" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/8863.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">274</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">1172</span> Introducing the Accounting Reform of Public Finance in the Czech Republic</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Otrusinova">M. Otrusinova</a>, <a href="https://publications.waset.org/abstracts/search?q=E.%20Pastuszkova"> E. Pastuszkova</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The article is addressing the currently ongoing reform processes of transforming the public finance accounting based on cash flow principle to accrual principle. The presented analysis concerns the issues associated with the introduction of the state accounting from the perspective of municipal employees in compiling the opinions of financial experts in conditions of the Czech Republic. The aim of this paper is to present outcomes of analysis focused on currently discussed topics which are related to introducing the accrual principle into accounting of selected entities, especially municipalities and municipality-funded institutions. The output of the paper consists of comparing the application of the accrual principle in the financial reporting of municipalities in the Czech Republic and Slovakia. In conclusion and based on the survey, respondents from Slovak municipalities that have already adopted the accrual accounting principle show better opinion than Czech municipalities. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=accrual%20principle" title="accrual principle">accrual principle</a>, <a href="https://publications.waset.org/abstracts/search?q=accounting" title=" accounting"> accounting</a>, <a href="https://publications.waset.org/abstracts/search?q=accounting%20reform" title=" accounting reform"> accounting reform</a>, <a href="https://publications.waset.org/abstracts/search?q=Czech%20Republic" title=" Czech Republic"> Czech Republic</a>, <a href="https://publications.waset.org/abstracts/search?q=municipalities" title=" municipalities"> municipalities</a>, <a href="https://publications.waset.org/abstracts/search?q=public%20finance" title=" public finance "> public finance </a> </p> <a href="https://publications.waset.org/abstracts/18314/introducing-the-accounting-reform-of-public-finance-in-the-czech-republic" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/18314.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">262</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">1171</span> Deciding Graph Non-Hamiltonicity via a Closure Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=E.%20R.%20Swart">E. R. Swart</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20J.%20Gismondi"> S. J. Gismondi</a>, <a href="https://publications.waset.org/abstracts/search?q=N.%20R.%20Swart"> N. R. Swart</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20E.%20Bell"> C. E. Bell</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present an heuristic algorithm that decides graph non-Hamiltonicity. All graphs are directed, each undirected edge regarded as a pair of counter directed arcs. Each of the n! Hamilton cycles in a complete graph on n+1 vertices is mapped to an n-permutation matrix P where p(u,i)=1 if and only if the ith arc in a cycle enters vertex u, starting and ending at vertex n+1. We first create exclusion set E by noting all arcs (u, v) not in G, sufficient to code precisely all cycles excluded from G i.e. cycles not in G use at least one arc not in G. Members are pairs of components of P, {p(u,i),p(v,i+1)}, i=1, n-1. A doubly stochastic-like relaxed LP formulation of the Hamilton cycle decision problem is constructed. Each {p(u,i),p(v,i+1)} in E is coded as variable q(u,i,v,i+1)=0 i.e. shrinks the feasible region. We then implement the Weak Closure Algorithm (WCA) that tests necessary conditions of a matching, together with Boolean closure to decide 0/1 variable assignments. Each {p(u,i),p(v,j)} not in E is tested for membership in E, and if possible, added to E (q(u,i,v,j)=0) to iteratively maximize |E|. If the WCA constructs E to be maximal, the set of all {p(u,i),p(v,j)}, then G is decided non-Hamiltonian. Only non-Hamiltonian G share this maximal property. Ten non-Hamiltonian graphs (10 through 104 vertices) and 2000 randomized 31 vertex non-Hamiltonian graphs are tested and correctly decided non-Hamiltonian. For Hamiltonian G, the complement of E covers a matching, perhaps useful in searching for cycles. We also present an example where the WCA fails. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hamilton%20cycle%20decision%20problem" title="Hamilton cycle decision problem">Hamilton cycle decision problem</a>, <a href="https://publications.waset.org/abstracts/search?q=computational%20complexity%20theory" title=" computational complexity theory"> computational complexity theory</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20theory" title=" graph theory"> graph theory</a>, <a href="https://publications.waset.org/abstracts/search?q=theoretical%20computer%20science" title=" theoretical computer science"> theoretical computer science</a> </p> <a href="https://publications.waset.org/abstracts/6023/deciding-graph-non-hamiltonicity-via-a-closure-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/6023.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">373</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">1170</span> Melnikov Analysis for the Chaos of the Nonlocal Nanobeam Resting on Fractional-Order Softening Nonlinear Viscoelastic Foundations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Guy%20Joseph%20Eyebe">Guy Joseph Eyebe</a>, <a href="https://publications.waset.org/abstracts/search?q=Gambo%20Betchewe"> Gambo Betchewe</a>, <a href="https://publications.waset.org/abstracts/search?q=Alidou%20Mohamadou"> Alidou Mohamadou</a>, <a href="https://publications.waset.org/abstracts/search?q=Timoleon%20Crepin%20Kofane"> Timoleon Crepin Kofane</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chaos" title="chaos">chaos</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional-order" title=" fractional-order"> fractional-order</a>, <a href="https://publications.waset.org/abstracts/search?q=Melnikov%20method" title=" Melnikov method"> Melnikov method</a>, <a href="https://publications.waset.org/abstracts/search?q=nanobeam" title=" nanobeam"> nanobeam</a> </p> <a href="https://publications.waset.org/abstracts/102726/melnikov-analysis-for-the-chaos-of-the-nonlocal-nanobeam-resting-on-fractional-order-softening-nonlinear-viscoelastic-foundations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/102726.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">159</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">1169</span> Non Linear Dynamic Analysis of Cantilever Beam with Breathing Crack Using XFEM</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20Vigneshwaran">K. Vigneshwaran</a>, <a href="https://publications.waset.org/abstracts/search?q=Manoj%20Pandey"> Manoj Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, breathing crack is considered for the non linear dynamic analysis. The stiffness of the cracked beam is found out by using influence coefficients. The influence coefficients are calculated by using Castigliano鈥檚 theorem and strain energy release rate (SERR). The equation of motion of the beam was derived by using Hamilton鈥檚 principle. The stiffness and natural frequencies for the cracked beam has been calculated using XFEM and Eigen approach. It is seen that due to presence of cracks, the stiffness and natural frequency changes. The mode shapes and the FRF for the uncracked and breathing cracked cantilever beam also obtained and compared. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=breathing%20crack" title="breathing crack">breathing crack</a>, <a href="https://publications.waset.org/abstracts/search?q=XFEM" title=" XFEM"> XFEM</a>, <a href="https://publications.waset.org/abstracts/search?q=mode%20shape" title=" mode shape"> mode shape</a>, <a href="https://publications.waset.org/abstracts/search?q=FRF" title=" FRF"> FRF</a>, <a href="https://publications.waset.org/abstracts/search?q=non%20linear%20analysis" title=" non linear analysis"> non linear analysis</a> </p> <a href="https://publications.waset.org/abstracts/42956/non-linear-dynamic-analysis-of-cantilever-beam-with-breathing-crack-using-xfem" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42956.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">344</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">1168</span> Effect of Aerobics Exercise on the Patient with Anxiety Disorder</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20A.%20Abd%20El%20Rahim">Ahmed A. Abd El Rahim</a>, <a href="https://publications.waset.org/abstracts/search?q=Andrew%20Anis%20Fakhrey%20Mosaad"> Andrew Anis Fakhrey Mosaad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Background: An important psychological issue that has an impact on both mental and physical function is anxiety disorders. The general consensus is that aerobic exercise and physical activity are good for lowering anxiety and mood. Purpose: This study's goal was to look into how patients with anxiety disorders responded to aerobic exercise. Subjects: Anxiety disorders were identified in 30 individuals from the psychiatric hospital at Sohag University who were chosen based on inclusive criteria and had ages ranging from 25 to 45. Methods: Patients were split into two equal groups at random: For four weeks, three sessions per week, fifteen patients in group A (the study group), seven men and eight women, underwent medication therapy and aerobic exercise. Age (28.4 卤 2.11 years), weight (72.5 卤 10.06 kg), height (164.8 卤 9.64 cm), and BMI (26.65 卤 2.68 kg/m2) were all mean SD values. And in Group B (Control Group), only medication therapy was administered to 15 patients (9 males and 6 females). Age (29.6 卤 3.68), weight (75 卤 7.07 kg), height (166.9 卤 6.75) cm, and BMI (26.87 卤 1.11) kg/m2 were the mean SD values. Before and after the treatment, the Hamilton Anxiety Scale was used to gauge the patient's degree of anxiety. Results: Within the two groups, there were significant differences both before and after the treatment. Following therapy, there was a significant difference between the two groups; the study group displayed better improvement on the Hamilton Anxiety Scale. Conclusion: Patients with anxiety problems can benefit from aerobic activities and antianxiety drugs as effective treatments for lowering anxiety levels. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=aerobic%20exercises" title="aerobic exercises">aerobic exercises</a>, <a href="https://publications.waset.org/abstracts/search?q=anxiety%20disorders" title=" anxiety disorders"> anxiety disorders</a>, <a href="https://publications.waset.org/abstracts/search?q=antianxiety%20medications" title=" antianxiety medications"> antianxiety medications</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton%20anxiety%20scale" title=" Hamilton anxiety scale"> Hamilton anxiety scale</a> </p> <a href="https://publications.waset.org/abstracts/160453/effect-of-aerobics-exercise-on-the-patient-with-anxiety-disorder" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/160453.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">84</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">1167</span> Quantization of Damped Systems Based on the Doubling of Degrees of Freedom</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khaled%20I.%20Nawafleh">Khaled I. Nawafleh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, it provide the canonical approach for studying dissipated oscillators based on the doubling of degrees of freedom. Clearly, expressions for Lagrangians of the elementary modes of the system are given, which ends with the familiar classical equations of motion for the dissipative oscillator. The equation for one variable is the time reversed of the motion of the second variable. it discuss in detail the extended Bateman Lagrangian specifically for a dual extended damped oscillator time-dependent. A Hamilton-Jacobi analysis showing the equivalence with the Lagrangian approach is also obtained. For that purpose, the techniques of separation of variables were applied, and the quantization process was achieved. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=doubling%20of%20degrees%20of%20freedom" title="doubling of degrees of freedom">doubling of degrees of freedom</a>, <a href="https://publications.waset.org/abstracts/search?q=dissipated%20harmonic%20oscillator" title=" dissipated harmonic oscillator"> dissipated harmonic oscillator</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton-Jacobi" title=" Hamilton-Jacobi"> Hamilton-Jacobi</a>, <a href="https://publications.waset.org/abstracts/search?q=time-dependent%20lagrangians" title=" time-dependent lagrangians"> time-dependent lagrangians</a>, <a href="https://publications.waset.org/abstracts/search?q=quantization" title=" quantization"> quantization</a> </p> <a href="https://publications.waset.org/abstracts/171405/quantization-of-damped-systems-based-on-the-doubling-of-degrees-of-freedom" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171405.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">68</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">1166</span> Free Vibration Analysis of Symmetric Sandwich Beams</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ibnorachid%20Zakaria">Ibnorachid Zakaria</a>, <a href="https://publications.waset.org/abstracts/search?q=El%20Bikri%20Khalid"> El Bikri Khalid</a>, <a href="https://publications.waset.org/abstracts/search?q=Benamar%20Rhali"> Benamar Rhali</a>, <a href="https://publications.waset.org/abstracts/search?q=Farah%20Abdoun"> Farah Abdoun</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton鈥檚 principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20vibration" title="linear vibration">linear vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=sandwich" title=" sandwich"> sandwich</a>, <a href="https://publications.waset.org/abstracts/search?q=shear%20deformation" title=" shear deformation"> shear deformation</a>, <a href="https://publications.waset.org/abstracts/search?q=Timoshenko%20zig-zag%20model" title=" Timoshenko zig-zag model"> Timoshenko zig-zag model</a> </p> <a href="https://publications.waset.org/abstracts/20383/free-vibration-analysis-of-symmetric-sandwich-beams" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20383.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">474</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">1165</span> Geometrically Linear Symmetric Free Vibration Analysis of Sandwich Beam </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ibnorachid%20Zakaria">Ibnorachid Zakaria</a>, <a href="https://publications.waset.org/abstracts/search?q=El%20Bikri%20Khalid"> El Bikri Khalid</a>, <a href="https://publications.waset.org/abstracts/search?q=Benamar%20Rhali"> Benamar Rhali</a>, <a href="https://publications.waset.org/abstracts/search?q=Farah%20Abdoun"> Farah Abdoun</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton鈥檚 principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20vibration" title="linear vibration">linear vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=sandwich" title=" sandwich"> sandwich</a>, <a href="https://publications.waset.org/abstracts/search?q=shear%20deformation" title=" shear deformation"> shear deformation</a>, <a href="https://publications.waset.org/abstracts/search?q=Timoshenko%20zig-zag%20model" title=" Timoshenko zig-zag model"> Timoshenko zig-zag model</a> </p> <a href="https://publications.waset.org/abstracts/19506/geometrically-linear-symmetric-free-vibration-analysis-of-sandwich-beam" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19506.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">472</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">1164</span> Portfolio Selection with Constraints on Trading Frequency</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Min%20Dai">Min Dai</a>, <a href="https://publications.waset.org/abstracts/search?q=Hong%20Liu"> Hong Liu</a>, <a href="https://publications.waset.org/abstracts/search?q=Shuaijie%20Qian"> Shuaijie Qian</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We study a portfolio selection problem of an investor who faces constraints on rebalancing frequency, which is common in pension fund investment. We formulate it as a multiple optimal stopping problem and utilize the dynamic programming principle. By numerically solving the corresponding Hamilton-Jacobi-Bellman (HJB) equation, we find a series of free boundaries characterizing optimal strategy, and the constraints significantly impact the optimal strategy. Even in the absence of transaction costs, there is a no-trading region, depending on the number of the remaining trading chances. We also find that the equivalent wealth loss caused by the constraints is large. In conclusion, our model clarifies the impact of the constraints on transaction frequency on the optimal strategy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=portfolio%20selection" title="portfolio selection">portfolio selection</a>, <a href="https://publications.waset.org/abstracts/search?q=rebalancing%20frequency" title=" rebalancing frequency"> rebalancing frequency</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20strategy" title=" optimal strategy"> optimal strategy</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20boundary" title=" free boundary"> free boundary</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20stopping" title=" optimal stopping"> optimal stopping</a> </p> <a href="https://publications.waset.org/abstracts/171745/portfolio-selection-with-constraints-on-trading-frequency" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171745.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">1163</span> Max-Entropy Feed-Forward Clustering Neural Network</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xiaohan%20Bookman">Xiaohan Bookman</a>, <a href="https://publications.waset.org/abstracts/search?q=Xiaoyan%20Zhu"> Xiaoyan Zhu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The outputs of non-linear feed-forward neural network are positive, which could be treated as probability when they are normalized to one. If we take Entropy-Based Principle into consideration, the outputs for each sample could be represented as the distribution of this sample for different clusters. Entropy-Based Principle is the principle with which we could estimate the unknown distribution under some limited conditions. As this paper defines two processes in Feed-Forward Neural Network, our limited condition is the abstracted features of samples which are worked out in the abstraction process. And the final outputs are the probability distribution for different clusters in the clustering process. As Entropy-Based Principle is considered into the feed-forward neural network, a clustering method is born. We have conducted some experiments on six open UCI data sets, comparing with a few baselines and applied purity as the measurement. The results illustrate that our method outperforms all the other baselines that are most popular clustering methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=feed-forward%20neural%20network" title="feed-forward neural network">feed-forward neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=clustering" title=" clustering"> clustering</a>, <a href="https://publications.waset.org/abstracts/search?q=max-entropy%20principle" title=" max-entropy principle"> max-entropy principle</a>, <a href="https://publications.waset.org/abstracts/search?q=probabilistic%20models" title=" probabilistic models "> probabilistic models </a> </p> <a href="https://publications.waset.org/abstracts/26856/max-entropy-feed-forward-clustering-neural-network" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/26856.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">435</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">1162</span> Donoho-Stark鈥檚 and Hardy鈥檚 Uncertainty Principles for the Short-Time Quaternion Offset Linear Canonical Transform</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Younus%20Bhat">Mohammad Younus Bhat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The quaternion offset linear canonical transform (QOLCT), which isa time-shifted and frequency-modulated version of the quaternion linear canonical transform (QLCT), provides a more general framework of most existing signal processing tools. For the generalized QOLCT, the classical Heisenberg鈥檚 and Lieb鈥檚 uncertainty principles have been studied recently. In this paper, we first define the short-time quaternion offset linear canonical transform (ST-QOLCT) and drive its relationship with the quaternion Fourier transform (QFT). The crux of the paper lies in the generalization of several well-known uncertainty principles for the ST-QOLCT, including Donoho-Stark鈥檚 uncertainty principle, Hardy鈥檚 uncertainty principle, Beurling鈥檚 uncertainty principle, and the logarithmic uncertainty principle. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Quaternion%20Fourier%20transform" title="Quaternion Fourier transform">Quaternion Fourier transform</a>, <a href="https://publications.waset.org/abstracts/search?q=Quaternion%20offset%20linear%20canonical%20transform" title=" Quaternion offset linear canonical transform"> Quaternion offset linear canonical transform</a>, <a href="https://publications.waset.org/abstracts/search?q=short-time%20quaternion%20offset%20linear%20canonical%20transform" title=" short-time quaternion offset linear canonical transform"> short-time quaternion offset linear canonical transform</a>, <a href="https://publications.waset.org/abstracts/search?q=uncertainty%20principle" title=" uncertainty principle"> uncertainty principle</a> </p> <a href="https://publications.waset.org/abstracts/142375/donoho-starks-and-hardys-uncertainty-principles-for-the-short-time-quaternion-offset-linear-canonical-transform" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/142375.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">211</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">1161</span> Vibration Analysis of Functionally Graded Engesser-Timoshenko Beams Subjected to Axial Load Located on a Continuous Elastic Foundation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Karami%20Khorramabadi">M. Karami Khorramabadi</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20R.%20Nezamabadi"> A. R. Nezamabadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=functionally%20graded%20beam" title="functionally graded beam">functionally graded beam</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20vibration" title=" free vibration"> free vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=elastic%20foundation" title=" elastic foundation"> elastic foundation</a>, <a href="https://publications.waset.org/abstracts/search?q=Engesser-Timoshenko%20beam%20theory" title=" Engesser-Timoshenko beam theory"> Engesser-Timoshenko beam theory</a> </p> <a href="https://publications.waset.org/abstracts/15081/vibration-analysis-of-functionally-graded-engesser-timoshenko-beams-subjected-to-axial-load-located-on-a-continuous-elastic-foundation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15081.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">418</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">1160</span> Non-Linear Vibration and Stability Analysis of an Axially Moving Beam with Rotating-Prismatic Joint</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Najafi">M. Najafi</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Rahimi%20Dehgolan"> F. Rahimi Dehgolan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20vibration" title="non-linear vibration">non-linear vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=stability" title=" stability"> stability</a>, <a href="https://publications.waset.org/abstracts/search?q=axially%20moving%20beam" title=" axially moving beam"> axially moving beam</a>, <a href="https://publications.waset.org/abstracts/search?q=bifurcation" title=" bifurcation"> bifurcation</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20scales%20method" title=" multiple scales method"> multiple scales method</a> </p> <a href="https://publications.waset.org/abstracts/67244/non-linear-vibration-and-stability-analysis-of-an-axially-moving-beam-with-rotating-prismatic-joint" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67244.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">370</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">1159</span> Margin-Based Feed-Forward Neural Network Classifiers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xiaohan%20Bookman">Xiaohan Bookman</a>, <a href="https://publications.waset.org/abstracts/search?q=Xiaoyan%20Zhu"> Xiaoyan Zhu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Margin-Based Principle has been proposed for a long time, it has been proved that this principle could reduce the structural risk and improve the performance in both theoretical and practical aspects. Meanwhile, feed-forward neural network is a traditional classifier, which is very hot at present with a deeper architecture. However, the training algorithm of feed-forward neural network is developed and generated from Widrow-Hoff Principle that means to minimize the squared error. In this paper, we propose a new training algorithm for feed-forward neural networks based on Margin-Based Principle, which could effectively promote the accuracy and generalization ability of neural network classifiers with less labeled samples and flexible network. We have conducted experiments on four UCI open data sets and achieved good results as expected. In conclusion, our model could handle more sparse labeled and more high-dimension data set in a high accuracy while modification from old ANN method to our method is easy and almost free of work. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Max-Margin%20Principle" title="Max-Margin Principle">Max-Margin Principle</a>, <a href="https://publications.waset.org/abstracts/search?q=Feed-Forward%20Neural%20Network" title=" Feed-Forward Neural Network"> Feed-Forward Neural Network</a>, <a href="https://publications.waset.org/abstracts/search?q=classifier" title=" classifier"> classifier</a>, <a href="https://publications.waset.org/abstracts/search?q=structural%20risk" title=" structural risk"> structural risk</a> </p> <a href="https://publications.waset.org/abstracts/27178/margin-based-feed-forward-neural-network-classifiers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27178.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">341</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">1158</span> Chaotic Motion of Single-Walled Carbon Nanotube Subject to Damping Effect</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tai-Ping%20Chang">Tai-Ping Chang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton鈥檚 principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin鈥檚 method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chaotic%20motion" title="chaotic motion">chaotic motion</a>, <a href="https://publications.waset.org/abstracts/search?q=damping" title=" damping"> damping</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20exponents" title=" Lyapunov exponents"> Lyapunov exponents</a>, <a href="https://publications.waset.org/abstracts/search?q=single-walled%20carbon%20nanotube" title=" single-walled carbon nanotube"> single-walled carbon nanotube</a> </p> <a href="https://publications.waset.org/abstracts/43091/chaotic-motion-of-single-walled-carbon-nanotube-subject-to-damping-effect" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/43091.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">320</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">1157</span> Thermal Buckling Analysis of Functionally Graded Beams with Various Boundary Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gholamreza%20Koochaki">Gholamreza Koochaki</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents the buckling analysis of functionally graded beams with various boundary conditions. The first order shear deformation beam theory (Timoshenko beam theory) and the classical theory (Euler-Bernoulli beam theory) of Reddy have been applied to the functionally graded beams buckling analysis The material property gradient is assumed to be in thickness direction. The equilibrium and stability equations are derived using the total potential energy equations, classical theory and first order shear deformation theory assumption. The temperature difference and applied voltage are assumed to be constant. The critical buckling temperature of FG beams are upper than the isotropic ones. Also, the critical temperature is different for various boundary conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=buckling" title="buckling">buckling</a>, <a href="https://publications.waset.org/abstracts/search?q=functionally%20graded%20beams" title=" functionally graded beams"> functionally graded beams</a>, <a href="https://publications.waset.org/abstracts/search?q=Hamilton%27s%20principle" title=" Hamilton's principle"> Hamilton's principle</a>, <a href="https://publications.waset.org/abstracts/search?q=Euler-Bernoulli%20beam" title=" Euler-Bernoulli beam"> Euler-Bernoulli beam</a> </p> <a href="https://publications.waset.org/abstracts/30892/thermal-buckling-analysis-of-functionally-graded-beams-with-various-boundary-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30892.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">392</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">1156</span> Forced Vibration of an Auxetic Cylindrical Shell Containing Fluid Under the Influence of Shock Load</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Korosh%20Khorshidi">Korosh Khorshidi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Due to the increasing use of different materials, such as auxetic structures, it is necessary to investigate mechanical phenomena, such as vibration, in structures made of these types of materials. This paper examines the forced vibrations of a three-layer cylindrical shell containing inviscid fluid under shock load. All three layers are made of aluminum, and the central layer is made of a re-entrant honeycomb cell structure. Using high-order shear deformation theories (HSDT) and Hamilton鈥檚 principle, the governing equations of the system have been extracted and solved by the Galerkin weighted residual method. The outputs of the Abaqus finite element software are used to validate the results. The system is investigated with both simple and clamped support conditions. Finally, this study investigates the influence of the geometrical parameters of the shell and the auxetic structure, as well as the type, intensity, duration, and location of the load, and the effect of the fluid on the dynamic and time responses. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=force%20vibration" title="force vibration">force vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=cylindrical%20shell" title=" cylindrical shell"> cylindrical shell</a>, <a href="https://publications.waset.org/abstracts/search?q=auxetic%20structure" title=" auxetic structure"> auxetic structure</a>, <a href="https://publications.waset.org/abstracts/search?q=inviscid%20fluid" title=" inviscid fluid"> inviscid fluid</a> </p> <a href="https://publications.waset.org/abstracts/184704/forced-vibration-of-an-auxetic-cylindrical-shell-containing-fluid-under-the-influence-of-shock-load" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/184704.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">43</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">1155</span> Super Harmonic Nonlinear Lateral Vibration of an Axially Moving Beam with Rotating Prismatic Joint</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Najafi">M. Najafi</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Bab"> S. Bab</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Rahimi%20Dehgolan"> F. Rahimi Dehgolan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The motion of an axially moving beam with rotating prismatic joint with a tip mass on the end is analyzed to investigate the nonlinear vibration and dynamic stability of the beam. The beam is moving with a harmonic axially and rotating velocity about a constant mean velocity. A time-dependent partial differential equation and boundary conditions with the aid of the Hamilton principle are derived to describe the beam lateral deflection. After the partial differential equation is discretized by the Galerkin method, the method of multiple scales is applied to obtain analytical solutions. Frequency response curves are plotted for the super harmonic resonances of the first and the second modes. The effects of non-linear term and mean velocity are investigated on the steady state response of the axially moving beam. The results are validated with numerical simulations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=super%20harmonic%20resonances" title="super harmonic resonances">super harmonic resonances</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20vibration" title=" non-linear vibration"> non-linear vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=axially%20moving%20beam" title=" axially moving beam"> axially moving beam</a>, <a href="https://publications.waset.org/abstracts/search?q=Galerkin%20method" title=" Galerkin method"> Galerkin method</a> </p> <a href="https://publications.waset.org/abstracts/67098/super-harmonic-nonlinear-lateral-vibration-of-an-axially-moving-beam-with-rotating-prismatic-joint" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67098.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">391</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=Hamilton%27s%20principle&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Hamilton%27s%20principle&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Hamilton%27s%20principle&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=Hamilton%27s%20principle&page=5">5</a></li> <li class="page-item"><a class="page-link" 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