We prove that pointwise and global Hölder regularity can be characterized using the coefficients on Haar tight frame obtained by a finite union of shifted bases, despite fact elements composing are discontinuous.

This paper gives a qualitative description how Young tableaux can be used to perform a Clebsch-Gordan decomposition of tensor products in SU(3) and how this can be generalized to SU(N).

This essay describes the development of groups used for the specification of symmetries from ordinary and magnetic point groups to Fedorov and magnetic space groups, as well as other varieties of groups useful in the study of symmetric objects. In particular, we consider the problem of some incorrectness in Vol. A of the International Tables for Crystallography. Some results of tensor calculus ...

in the present paper the linear oscillator in r3 with z =constanthas been considered. the aim is to determine the necessary conditions forthe persistence of periodic solutions under discontinuous perturbations. a newapproach based on a computational method has been used. at the end weapply our method on an example.

Linear systems with large differences between coefficients (“discontinuous coefficients”) arise in many cases in which partial differential equations model physical phenomena involving heterogeneous media. The standard approach to solving such problems is to use domain decomposition (DD) techniques, with domain boundaries conforming to the boundaries between the different media. This approach c...

In the paper we consider a second order elliptic problem with discontinuous anisotropic coefficients defined on a polygonal region Ω . The problem is discretized by a Discontinuous Galerkin (DG) finite element method with triangular elements and piecewise linear functions. Our goal is to design and analyze an additive Schwarz method (ASM), see the book by Toselli and Widlund [4], for solving th...

In this work, we propose a numerical method to handle discontinuous fluxes arising in transport-like equations. More precisely, we study hyperbolic PDEs with flux transmission conditions at interfaces between subdomains where coefficients are discontinuous. A dedicated finite volume scheme with a limited high order enhancement is adapted to treat the discontinuities arising at interfaces. The v...

We propose a rigorous procedure to obtain the adjoint-based gradient representation of cost functionals for the optimal control of discontinuous solutions of conservation laws. Hereby, it is not necessary to introduce adjoint variables for the shock positions. Our approach is based on stability properties of the adjoint equation. We give a complete analysis for the case of convex scalar conserv...

A discontinuous Galerkin method, with hp-adaptivity based on the approximate solution of appropriate dual problems, is employed for highly-accurate eigenvalue computations on a collection of benchmark examples. After demonstrating the effectivity of our computed error estimates on a few well-studied examples, we present results for several examples in which the coefficients of the partial-diffe...

The paper discusses the properties of dynamo models with discontinuous distribution of the induction coefficients, showing that no additional source terms appear due to the discontinuities. The apparent contradiction between Parker’s (1971) result for his !-dynamo model and later results, which gave rise to the introduction of additional terms by Ruzmaikin et al (1979), is shown to be due to mi...