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Showing 1 to 20 of 50 for “"calculus of variations"”.
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Analysis of Economic Models Through Calculus of Variations
This thesis is a combination of two science fields: Mathematics and Economics. Mathematics is often used to formulate a clear and concise solution to economic problems. In my observation calculus of variation has often been used in various macroeconomic problems. This mathematical method deals with …
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Calculus of Variations on Time Scales and Its Applications to Economics
The goal of time scale research is to progress the development of a harmonized theory that is all encompassing of the more commonly known specialized forms. The main results of this paper is the presentation of the Ramsey model which can be written using both the A and V operators, and solved using …
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A posteriori Error Estimators based on Duality Techniques from the Calculus of Variations
… error estimators for a quite general class of variational statements, involving a linear operator and two convex functionals. We merely require, that the linear operator be coercive and the corresponding functional be uniformly convex. As the second functional may be arbitrary, the theory …
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Using calculus of variations to optimize paths of descent through ski race courses
The goal of ski racing is to pass through a series of gates as quickly as possible. There are many paths from gate to gate, but there is only one path that is fastest. By knowing what the fastest path is, a racer could shave tenths of seconds off his or her time. That is a tremendous amount of time …
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The Determination of Optimum Paths in The Phase Plane for Dynamic Systemsusing Calculus of Variations Techniques
… in DSpace on 2014-12-04T21:03:20Z (GMT). No. of bitstreams: 1 6101621.pdf: 3067290 bytes, checksum: f1dd43834c4e9464df87077a5799b0e0 (MD5) Previous issue date: 1961
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New and old sub-Riemannian challenges bridging analysis and geometry
The aim of this thesis is to propose a systematic exposition of some analytic and geometric problems arising from the study of sub-Riemannian geometry, Carnot-Carathéodory spaces and, more broadly, anisotropic metric and differential structures. We deal with four main topics. 1 Calculus of …
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Application of a Numerical Method and Optimal Control Theory to a Partial Differential Equation Model for a Bacterial Infection in a Chronic Wound
<p>In this work, we study the application both of optimal control techniques and a numerical method to a system of partial differential equations arising from a problem in wound healing. Optimal control theory is a generalization of calculus of variations, as well as the method of Lagrange …
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Experimental Evidence for Mixed Reality States in an Interreality System, And, Generalized Resonant Forcing of Nonlinear Dynamics
This work also explores resonances of nonlinear systems. This includes time-discrete chaotic maps as well as generalized systems of nonlinear first order differential equations. The calculus of variations is used to determine the minimal additive forcing function that induces a desired terminal …
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Mappings Between Annuli of Smallest p-Harmonic Energy
<p>An important topic in the calculus of variations is the study of traction-free problems, in which deformations between given domains in $\mathbb{R}^n$ are allowed to slip on the boundary, without prescribing boundary values. For annuli $\A = \A(r, R)$ and $\A^* = \A(r_*, R_*)$, we seek the …
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Invariant functionals
The study of continuous groups of transformations in function space was begun by G. Kowalewski in 1911. Vessiot considered the conditions under which r parameter Volterra transformations form a group. L. L. Dines considered projective transformations in function space continuing Kowalewski's work. …
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STUDY OF THE LOADING OF PILES USING A SEMI-ANALYTICAL METHOD AND THE DIGITAL IMAGE CORRELATION TECHNIQUE
The response of single piles and pile groups to axial and lateral loading and the displacements induced in the soil by it are studied in this work using theoretical and experimental approaches. The theoretical solution for the loading of piles is based on idealized displacement forms, energy …
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Semilinear elliptic partial differential equations with the critical Sobolev exponent
… analysis are applied to solving certain types of semilinear elliptic partial differential equations (PDEs). The ultimate goal is to prove results on the existence and non-existence of solutions to the Semilinear Elliptic PDEs with the Critical Sobolev Exponent. To this end, we first recall some …
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Optimization of material flow in the nuclear fuel cycle using a cyclic multi-stage production-to-inventory model
… and inventory holding costs for all stages of the fuel cycle. The model allows for cyclic flow (feedback) of materials, material flow conversion factors at each stage, production lag times at each stage, and for escalating costs of uranium ore. It does not allow shortages to occur in …
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Variational Convex Analysis
… analysis. First we present the basic tools of analysis necessary to develop the core theory and applications. New results concerning duality principles for systems originally modeled by non-linear differential equations are shown in chapters 9 to 17. A key aspect of this work is that …
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Novel optimal control algorithms with application to the parallel hydraulic hybrid vehicle power train.
… over non-hybrid power trains. Optimal control of the parallel HHV power train is critical to overall vehicle performance and is largely responsible for gains in efficiency. The research presented in this thesis aims to answer the question of how to best operate the power train to achieve …
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The Q-closeness technique: an application to isoperimetric inequalities in 2-d lattices and to the Faber-Krahn inequality
… a classical topic in mathematical analysis and calculus of variations. In recent years, however, increasing attention has been devoted to the challenges arising when extending these problems to discrete settings, motivated by material science and crystallisation theory. In the thesis, we …
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Optimal control of impulsive systems using adaptive critic based neural networks
… tools for the optimal control synthesis of fixed-time and variable-time impulsive systems. Necessary conditions for optimality have been derived for a fixed-time and a variable-time impulsive system using the calculus of variations method. Properties of the costates and the states …
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Optimization for a Sturm--Liouville problem with the spectral parameter in the boundary condition
We find an optimal mass of a structure described by a Sturm-Liouville (S-L) problem with a spectral parameter in the boundary conditions. While previous work on the subject focused on a somewhat simplified model, we consider a more general S-L problem. We use the calculus of variations approach to …
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Numerically-based ducted propeller design using vortex lattice lifting line theory
… were considered, and a method based on calculus of variations was selected. The results of this model were compared with the MIT Propeller Lifting Line Program (PLL) output for the purpose of validation. Ducted propellers are prevalent in modem marine propulsion systems, and the …
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