Results 251 to 260 of about 1,347,601 (289)
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Sensitivity Equations and Variational Equations
1987We assume an undisturbed state q i 0 , which satisfies the relationship (1.2.1) in a general phase space R n . The system of first-order differential equations q i = F i which correspond to a mechanical system and are basic to Eqs. (1.2.1), can, for example, be given by the set of canonical Hamilton differential equations.
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VECTOR FIELDS, VARIATIONAL EQUATIONS AND COMMUTATORS
International Journal of Bifurcation and Chaos, 2012We study autonomous systems of first order ordinary differential equations, their corresponding vector fields and the autonomous system corresponding to the vector field of the commutator of two such autonomous systems. These vector fields form a Lie algebra.
Willi-Hans Steeb +2 more
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Variational Principle for Eigenvalue Equations
Journal of Mathematical Physics, 1967A variational principle is developed to provide an estimate of an arbitrary functional of the eigen-functions of a set of eigenvalue equations. It is shown that the variational formalism is equivalent to a functional Taylor series expansion of the desired functional about the trial functions.
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Mathematical Inequalities & Applications, 2004
Summary: The main result proved in this article is the following. There is an \(\overline{x}\in X\) such that \[ g(\overline{x})\in C(\overline{x})\;\text{and}\;\sup_{y\in C(\overline{x})} \Psi(\overline{x}, y)=\Psi(\overline{x}, g(\overline{x}))\] where \(C: X\to 2^Y\) is a correspondence (\(g\) is a function defined over \(X\) in \(Y\)) and a ...
Nessah, Rabia, Chu, Chengbin
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Summary: The main result proved in this article is the following. There is an \(\overline{x}\in X\) such that \[ g(\overline{x})\in C(\overline{x})\;\text{and}\;\sup_{y\in C(\overline{x})} \Psi(\overline{x}, y)=\Psi(\overline{x}, g(\overline{x}))\] where \(C: X\to 2^Y\) is a correspondence (\(g\) is a function defined over \(X\) in \(Y\)) and a ...
Nessah, Rabia, Chu, Chengbin
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Variational Equations and Inequalities
2012In this chapter we review some standard results for boundary value and initial–boundary value problems, paying particular attention to weak or variational formulations. The first section will be concerned with elliptic variational equations, and this will be followed by a review of some material on elliptic variational inequalities.
Weimin Han, B. Daya Reddy
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The geometry of variational equations
AIP Conference Proceedings, 2004This lecture brings a survey of topics and results concerning differential equations which arise as equations for extremals of higher‐order variational functionals on fibered manifolds.
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Constitutive equations and variational elasticity
2008A rather brief introduction to the non-linear theory of elasticity is given. In the presentation most of mechanical and mathematical concepts used are introduced from scratch.
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1987
We shall assume that the time t does not appear explicitly in the functions F i in the right-hand side of (1.2.1). In this case, the process described by q i 0 (t) is autonomous. In addition, we select the stationary state as the undisturbed state, for which q i 0 = 0 holds.
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We shall assume that the time t does not appear explicitly in the functions F i in the right-hand side of (1.2.1). In this case, the process described by q i 0 (t) is autonomous. In addition, we select the stationary state as the undisturbed state, for which q i 0 = 0 holds.
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Variational solutions of the liouville equation
Il Nuovo Cimento B Series 10, 1968Arthurs, A. M., Anderson, N.
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