Fuzzy measures were introduced by M Sugeno in in order to express a grade of fuzziness in the same way that probability measures express a grade of random ness The Sugeno fuzzy integrals are the functionals with monotonicity de ned by using fuzzy measures Later on Murofushi and Sugeno proposed another type of fuzzy integral the Choquet integral based on the Capacity Theory developed by G Choque...

It is well known that there are many analogies between the theories of difference equations and differential equations. The concept of time scales unifies these two situations but gives also solutions for problems on discrete sets with non-uniform step size or combinations of real and discrete intervals and many others. On the other hand, as it was seen in literature (beginning with [2]), the s...

The intertwining operators Ad = Ad(g) on the round sphere (Sn, g) are the conformal analogues of the power Laplacians 1d/2 on the flat Rn . To each metric ρg, conformally equivalent to g, we can naturally associate an operator Ad(ρg), which is compact, elliptic, pseudodifferential of order d, and which has eigenvalues λ j (ρ); the special case d = 2 gives precisely the conformal Laplacian in th...

New transformations for accelerating the convergence of infinite double series and infinite double integrals are presented. These transformations are generalizations of the univariate dand D-transformations. The D2transformation for infinite double integrals is efficient if the integrand satisfies a p.d.e. of a certain type. Similarly, the d2-transformation for double series works well for seri...

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 use Monte Carlo methods to directly evaluate D-dimensional SU(N) Yang-Mills partition functions reduced to zero Euclidean dimensions, with and without supersymmetry. In the non-supersymmetric case, we find that the integrals exist for D = 3, N ≥ 4 and D = 4, N ≥ 3 and, lastly, D ≥ 5, N ≥ 2. We conclude that the D = 3 and D = 4 integrals exist in the large N limit, and therefore lead to a wel...

We calculate 3-loop master integrals for heavy quark correlators and the 3-loop QCD corrections to the ρ-parameter. They obey non-factorizing differential equations of second order with more than three singularities, which cannot be factorized in Mellin-N space either. The solution of the homogeneous equations is possible in terms of convergent close integer power series as 2F1 Gauß hypergeomet...

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi,...