Results 171 to 180 of about 3,790 (213)

Reduction of Algebraic Integrands to Jacobian Elliptic Functions

1954
The most general elliptic integral encountered in practice may appear in the form 200.00 (200.00) where R1, R2, R3 and R4 are rational integral functions of t, and where P is a polynomial of the third or fourth degree with real coefficients and no repeated factors.
Paul F. Byrd, Morris D. Friedman
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Lower Semicontinuity of Integral Functionals with Nonconvex Integrands by Relaxation-Compactification

SIAM Journal on Control and Optimization, 1981
A new approach to the lower semicontinuity of integral functionals is presented. By a topological embedding of the “control” and “state” spaces in the Hilbert cube and a simultaneous relaxation of the “control functions,” a powerful approach emerges whose main features include: (i) A generalized convexity condition is imposed upon the integrand of ...
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Approximation of certain functions given by integrals with highly oscillatory integrands

IEEE Transactions on Antennas and Propagation, 1994
There is often a need to approximate integrals of highly oscillatory functions when studying scattering and diffraction of electromagnetic waves. This paper presents a method of estimating certain types of these integrals by evaluating one interpolating function and performing one or two relatively easy numerical integrations.
B. Drachman, J. Ross, D. Nyquist
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Integral functionals, normal integrands and measurable selections

1976
Abstract : A fundamental notion in many areas of mathematics, including optimal control, stochastic programming, and the study of partial differential equations, is that of an integral functional. By this is meant an expression of the form If(x) = integral over S of f(s,x(s))mu(DS), x is a member of X where X is a linear space of measurable functions ...
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Minimization with integrands composed of minimum of convex functions

Nonlinear Analysis: Theory, Methods & Applications, 2001
Let \(\Omega\) be a smooth bounded domain of \({\mathbb R}^n\). Then the paper is concerned with minimization problems of the form \[ \alpha=\inf\left\{\int_\Omega\min\{f(v,Dv),g(v,Dv)\}dx : v\in H^1(\Omega;{\mathbb R}^m)\right\}, \] under the assumption that the two integral functionals \[ v\to\int_\Omega f(v,Dv)dx\;\text{ and } v\to\int_\Omega g(v,Dv)
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Two-Scale Convergence of Integral Functionals with Convex, Periodic and Nonstandard Growth Integrands

Acta Applicandae Mathematicae, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tachago, Joel Fotso, Nnang, Hubert
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Convergence of Conditional Expectations for Unbounded Random Sets, Integrands, and Integral Functionals

Mathematics of Operations Research, 1991
Given a sequence of unbounded convex random sets, we study under which conditions Fatou's lemma for the weak upper limit of their conditional expectations holds. We also give multivalued versions of dominated and monotone convergence theorems, and we discuss the special case of the integral.
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Convergence of minima of integral functionals and multiplicative perturbations of the integrands

Annali di Matematica Pura ed Applicata, 1988
Considered is a sequence of functions \[ f_ h: (x,z)\in R^ n\times R^ n\to f_ h(x,z)\in [0,+\infty [,\quad h=1,2,...,\infty \] measurable in x, convex in z such that \[ | z|^ p\leq f_ h(x,z)\leq \Lambda (1+| z|^ p),\quad \Lambda \geq 1,\quad p>1 \] and verifying a standard consequence of \(\Gamma\)-convergence theory, i.e., for every bounded open set \(
De Arcangelis, Riccardo, Donato, Patrizia   +1 more
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On functionals with convex Carathéodory integrands with a linear growth condition

Journal of Mathematical Analysis and Applications, 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Minimization of functional with integrand expressed as minimum of quasiconvex functions –- general and special cases

Banach Center Publications, 2014
We present a method of optimization a coercive integral functional J with integrand being a minimum of quasiconvex functions. The method is further applied to the minimization of functional with integrand expressed as a minimum of two quadratic functions. This is done by approximating the original nonconvex problem by appropriate convex ones.
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