The ABC systems are a particular family of Lotka{Volterra systems in dimension 3. Their integrability has been studied these last years by many authors. In this paper we study the ABC systems which are algebraically integrable, i.e. the ABC systems having two independent algebraic rst integrals. For doing this we need to summarize all the known results about the polynomial and rational rst inte...

A combinatorial construction of the multiple stochastic integral is developed using sequences in Clifford (geometric) algebras. In particular, sequences of Berezin integrals in an ascending chain of geometric algebras converge in mean to the iterated stochastic integral. By embedding such chains within an infinite-dimensional Clifford algebra, an infinitedimensional analogue of the Berezin inte...

The systematic approach to solving the recurrence relations for multi-loop integrals is described. In particular, the criteria of their reducibility is suggested.

In this paper, we give a definition of the Fermi function, or so-called Woods-Saxon potential, well-known potential in nuclear physics; then, few its applications as examples. Some important integrals, which involve are computed discussing integrability and convergence these integrals. Following, derive formulae that encounter above-mentioned function to get generalized moments; radial Fourier ...

in this paper, quadratic rules for obtaining approximate solution of definite integrals as well as single and double integrals using spline quasi-interpolants will be illustrated. the method is applied to a few test examples to illustrate the accuracy and the implementation of the method

minkowski type inequalities for the seminormed fuzzy integrals on abstract spaces are studied in a rather general form. also related inequalities to minkowski type inequality for the seminormed fuzzy integrals on abstract spaces are studied. several examples are given to illustrate the validity of theorems. some results on chebyshev and minkowski type inequalities are obtained.

Inequalities of the majorisation type for convex functions and Stieltjes integrals are given. Applications for some particular convex functions of interest are also pointed out.

A bstract The method of canonical differential equations is an important tool in the calculation Feynman integrals quantum field theories. It has been realized that bases are closely related to d -dimensional log-form integrands. In this work, we explore generalized loop-by-loop Baikov representation, and clarify its relation difference with using language intersection theory. We then utilize r...

We extend the study of recently discovered Yangian symmetry massive Feynman integrals and its relation to momentum space conformal symmetry. After proving statements in detail at one two loop orders, we employ constraints bootstrap various one-loop examples integrals. In particular, explore interplay between hypergeometric expressions considered Based on these conjecture single series represent...

‎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...