An interesting integral originally obtained by Tefera (“A multiple integral evaluation inspired by the multi-WZ method,” Electron. J. Combin., 1999, #N2) via the WZ method is proved using calculus and basic probability. General recursions for a class of such integrals are derived and associated combinatorial identities are mentioned. 1 Background The integral in question reads

In this paper, some generalized integral inequalities which originate from an open problem posed in [F. Qi, Several integral inequalities, J. Inequal. Pure Appl. Math., 1(2) (2000), Art. 19] are established.

An experimental investigation dealing with failure characterization of 63/37 soldercopper interfaces is presented. The method of moird interferometry is used for mapping elasto-plastic deformations in bimaterials subjected to predominantly tensile loading. A method for quantifying the fracture parameter--the J-integral--using full-field measurement of crack opening displacements has been develo...

By applying p-adic integral on the set of integers in [27] (Interpolation Functions for New Classes Special Numbers and Polynomials via Applications Integrals Derivative Operator, Montes Taurus J. Pure Appl. Math. 3 (1), ...--..., 2021 Article ID: MTJPAM-D-20-00000), we constructed generating function special numbers polynomials involving following combinatorial sum numbers: y(n,\lambda )=\sum_...

Abstract When $k\geqslant 4$ and $0\leqslant d\leqslant (k-2)/4$ , we consider the system of Diophantine equations \begin{align*}x_1^j+\ldots +x_k^j=y_1^j+\ldots +y_k^j\quad (1\leqslant j\leqslant k,\, j\ne k-d).\end{align*} We show that in this cousin a Vinogradov system, there is paucity non-diagonal positive integral solutions. Our quantitative estimates are particularly sharp when $d=o\!\le...

in this paper, the mixed-mode dynamic fracture analysis of a fgm plate is performed using mlpg method also the effect of changes in value and angle of material gradation on the dynamic stress intensity fctor(sif) of mode i, ii, and effective are investigated. to solve time dependent equations that discretized by mlpg method, the central difference method (cdm) and the newmark method are used. a...

Following the ideas of the axiomatic characterization of the Choquet integral due to [D. Schmeidler, Integral representation without additivity, Proc. Amer. Math. Soc. 97 (1986) 255–261] and of the Sugeno integral given in [J.-L. Marichal, An axiomatic approach of the discrete Sugeno integral as a tool to aggregate interacting criteria in a qualitative framework, IEEE Trans. Fuzzy Syst. 9 (2001...

(The present proof of this old result roughly follows the proof given in Hörmander's An Introduction to Complex Analysis in Several Variables, which I believe roughly follows Hartogs' original argument.) Theorem: Let f be a C-valued function defined in an open set U ⊂ C n. Suppose that f is analytic in each variable z j when the other coordinates z k for k = j are fixed. Then f is analytic as a...