We consider equidistant discrete splines S(j), j ∈ Z, which may grow as O(|j|s) as |j| → ∞. Such splines present a relevant tool for digital signal processing. The Zak transforms of Bsplines yield the integral representation of discrete splines. We define the wavelet space as a weak orthogonal complement of the coarse-grid space in the fine-grid space. We establish the integral representation o...

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The problem of deformation a DCB sample, which is composition bodies bound by an adhesive layer finite thickness, considered. Based on the variational equilibrium equation containing thickness as linear parameter, element solution loading with normal discontinuity in plane strain state constructed. stresses averaged over are related to along boundary equations. form conditions for mating bodies...

Let f∗(z) = ∞ ∑ j=0 aj z j be a convergent series in which {aj}j=0 are known real numbers. In this paper, by referring to Osler’s lemma [8], we obtain explicit forms of the two bivariate series ∞ ∑ j=0 an j+m r j cos(α+ j)θ and ∞ ∑ j=0 an j+m r j sin(α+ j)θ, where r, θ are real variables, α ∈ R, n ∈ N and m ∈ {0, 1, . . . , n − 1}. With some illustrative examples, we also show how to obtain the...

We have performed measurements of the magnetic susceptibility of NaV2O5 between 2 and 400 K. The high temperature part is typical of spin 1/2 chains with a nearest–neighbour antiferromagnetic exchange integral J of 529 K. We develop a model for the susceptibility of a system with finite chains to account for the low temperature part of the data, which cannot be fitted by a standard Curie-Weiss ...

Let D be an integral domain with identity having quotient field K. This paper gives necessary and sufficient conditions on D in order that each integrally closed subring of O should belong to some subclass of the class of integrally closed domains ; some of the subclasses considered are the completely integrally closed domains, Prüfer domains, and Dedekind domains. 1. The class of integrally cl...

Let F be a Siegel cusp form of integral weight k on the Siegel modular group Sp 2 (Z) of genus 2 and denote by a(T) (T 2 Q (2;2) ; T > 0 half-integral) its Fourier coeecients. It is known (see BB ocherer & Raghavan, 1988 and Fomenko, 1987) that (1) X fT>0; det(T)=N g=GL2(Z) ja(T)j 2 ";F N k?3=32+" (" > 0) where the sum is over GL 2 (Z)-classes of T > 0 with det(T) = N: In the present note we sh...

Littlewood in his 1968 monograph “Some Problems in Real and Complex Analysis” [12, problem 22] poses the following research problem, which appears to still be open: Problem. “If the nj are integral and all different, what is the lower bound on the number of real zeros of PN j=1 cos(njθ)? Possibly N −1, or not much less.” No progress appears to have been made on this in the last half century. We...

* Correspondence: [email protected] School of Science, Shandong University of Technology, Zibo, Shandong 255049, China Full list of author information is available at the end of the article Abstract In this paper, some new nonlinear integral inequalities are established, which provide a handy tool for analyzing the global existence and boundedness of solutions of differential and integral eq...

This paper presents a new method for conducting a continuum shape sensitivity analysis of a crack in an isotropic, linear-elastic, functionally graded material. This method involves the material derivative concept from continuum mechanics, domain integral representation of the J-integral and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed to cal...