Non-empirical quadratic-integrand double-hybrid (QIDH) functionals
2023Juan-Carlos Sancho-García +3 more
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Quadrature over a Simplex: Part 1. A Representation for the Integrand Function
SIAM Journal on Numerical Analysis, 1978The basic purpose of the analysis is to derive an n-dimensional analogue of the Euler Maclaurin expansion valid for any quadrature role Q for the simplex.We choose for our calculation the simplex $S_n :x_i > 0;\Sigma _{i = 1}^n x_i < 1$ which lies within the hypercube $H_n :0 < x_i < 1$.
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A counter-example in homogenization of functional with polynomial integrand
1995The author considers the classical problem of homogenization in the calculus of variations \[ f_{\hom}(\xi)= \inf\Biggl\{\int_Y f(x,Du(x)) dx\mid u\in W^{1,p}_{\text{loc}}(\mathbb{R}^n), Du\text{ is }Y\text{-periodic}, \langle Du\rangle= \xi\Biggr\}, \] where \(Y\) denotes the unit cube in \(\mathbb{R}^n\) and \(\langle\cdots\rangle\) denotes the ...
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Evaluating the Superposition Integrals by Retaining the Singularity Functions in the Integrands
IEEE Transactions on Education, 1963This paper shows how the superposition integrals can be evaluated without recourse to changing the limits of integration, when the integrands are zero over a range, through the use of singularity functions. This method avoids the need for sketching the integrands and illustrates the concepts involved in the superposition integrals without restricting ...
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Integrative oncology: Addressing the global challenges of cancer prevention and treatment
Ca-A Cancer Journal for Clinicians, 2022Jun J Mao,, Msce +2 more
exaly
A COUNTEREXAMPLE IN HOMOGENIZATION OF FUNCTIONALS WITH ANALYTIC INTEGRAND
1994We prove that the homogenization in Calculus of Variations of the functional represented by the integrand f (x, xi) = a(x) \xi\(4), where xi epsilon R(2) and a is a measurable periodic and positive real valued function on R(2), has an integrand f(infinity):R(2) --> R which is not a polynomial.
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Relaxation of autonomous functionals with discontinuous integrands
ANNALI DELL UNIVERSITA DI FERRARA, 1988openaire +1 more source
Semicontinuity of integral functionals with integrands defined in infinite dimensional spaces
1990The paper is concerned with some abstract sequential lower semicontinuity results for integral functionals defined on functions taking values in infinite-dimensional spaces. The results obtained are also applied to get sequential lower semicontinuity results for functionals defined on the set \({\mathcal A} ([0,1 ],V)\) of the absolutely continuous ...
CALIGARIS, OTTAVIO, OLIVA, PIETRO
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??-convergence of integral functionals with degenerate integrands in periodically perforated domains
2017We consider a sequence of integral functionals with degenerate integrands in perforated domains of periodic structure. We establish the ??-convergence of the sequence under consideration to an integral functional defined on a limit weighted Sobolev space. A representation formula for the integrand of the ??-limit functional is given.
Kovalevsky, A.A., Rudakova, O.A.
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Reduction of Hyperbolic Integrands to Jacobian Elliptic Functions
1954Paul F. Byrd, Morris D. Friedman
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