Extending the idea of Even and Lehrer (2014) [3], we discuss a general approach to integration based on a given decomposition system equipped with a weighting function, and a decomposition of the integrated function. We distinguish two type of decompositions: sub-decomposition based integrals (in economics linked with optimization problems to maximize the possible profit) and super-decompositio...

We consider nonlinear stochastic integrals of Itô-type w.r.t. a family of semimartingales which depend on a spatial parameter. These integrals were introduced by Carmona and Nualart [2], Kunita [8], and Le Jan [9]. The extension of the elementary nonlinear integral is based on the condition that the semimartingale kernel has nice continuity properties in the spatial parameter. We investigate th...

‎In this paper‎, ‎we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for‎ ‎irreducible admissible representations of orthogonal groups‎, ‎or unitary groups‎. ‎One family is that of local integrals of the doubling method‎, ‎and the other family is‎ ‎that of local integrals expressed in terms of sph...

An efficient automatic quadrature procedure is developed for numerically computing the integrals 0 , where the function is smooth and nonoscillatory at infinity and is the Bessel functions of order ν =1,0 and 1/4. The procedure involves the use of an automatic integration scheme of modified FFT used for evaluating Fourier integrals and product type integration, and the modified W-transformation...

This paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy set. It also presents basic ideas on fuzzy integrals defined using these fuzzy measures. Definitions of new types of fuzzy measures and integrals are motivated by our research on generalized quantifiers. Several useful properties of fuzzy measures and fuzzy integrals are stated and proved. Definitio...

S U M M A R Y Fundamental to complex analysis is the Cauchy integral theorem, and the derivation of Cauchytype integrals. For over 40 yr, Cauchy-type integrals have been used to describe analytical continuation, establish the location of singular points, and study non-single-valued solutions of inverse problems in 2-D potential field theory. In this paper, we revive this interesting and fundame...

Some new Grüss type inequalities in inner product spaces and applications for integrals are given.

In this paper, some new Gronwall type inequalities involving iterated integrals are given.

This paper aims at developing Bode-type integrals for control systems over additive white Gaussian noise channels, by way of deriving information theoretic equalities and inequalities. The integrals characterize the fundamental performance trade-offs of such networked feedback systems with linear time-invariant plants and causal stabilizing controllers. We propose two new notions to facilitate ...

We present an efficient scheme to evaluate the [O](m) integrals that arise in many ab initio quantum chemical two-electron integral algorithms. The total number of floating-point operations (FLOPS) required by the scheme has been carefully minimized, both for cases where multipole expansions of the integrals are admissable and for cases where this is not so. The algorithm is based on the use of...