are obtained by integrating f with respect to the invariant measure on the conjugacy class of y. They are of considerable importance for the harmonic analysis of G(F). Invariant orbital integrals are also of interest because they occur on the geometric side of the trace formula, in the case of compact quotient. For the general trace formula, the analogous terms are weighted orbital integrals [3...

The paper introduces a new class of functions from [0,1]n to [0,n] called d-Choquet integrals. These are generalization the “standard” Choquet integral obtained by replacing difference in definition usual dissimilarity function. In particular, all integrals encompasses but use dissimilarities provides higher flexibility and generality. We show that some aggregation/pre-aggregation/averaging/fun...

this work deals with the calculation of franck-condon factors using hua potential function for the first time. the advantages of this function have been mentioned, and the numerical methods are used to obtain franck-condon factors for the following band systems: agreement between the values of this work and those obtained from other works is quite good that verifies the reliability of the prese...

We give a simple proof of an isomorphism between two C(t)-modules corresponding to bivariate polynomial H with non-degenerate highest homogeneous part: the module of relative cohomologies 2/dH ∧ 1 and the module of Abelian integrals. Using this isomorphism, we prove the existence and deduce some properties of the corresponding Picard–Fuchs system. Mathematics Subject Classification: 14D05, 32S4...

We describe methods for evaluating one-loop integrals in 4−2 dimensions. We give a recursion relation that expresses the scalar n-point integral as a cyclicly symmetric combination of (n− 1)point integrals. The computation of such integrals thus reduces to the calculation of box diagrams (n = 4). The tensor integrals required in gauge theory may be obtained by differentiating the scalar integra...

We consider Riemann sum approximations of stochastic integrals with respect to the fractional Browian motion index H≥1 2. show convergence these schemes at first and second order. The processes obtained in limit case are Rosenblatt process if H>3 4 standard Brownian otherwise. These results under assumption that integrand is a “controlled” process. provide many examples such processes, particul...

We extend Igusa ́s stationary phase method to the case of oscillatory integrals depending on several parameters. As a particular case, we obtain estimations for the modulus of Gaussian exponential sums depending on several parameters.

In a brief review, we discuss interrelations between arbitrary solutions of the loop equations that describe Hermitean one-matrix model and particular (multi-cut) solutions that describe concrete matrix integrals. These latter ones enjoy a series of specific properties and, in particular, are described in terms of Seiberg-Witten-Whitham theory. The simplest example of ordinary integral is consi...

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...