We show that, in general, inequalities between integrands with respect to Brownian motion do not lead to majorization in the convex order for the corresponding stochastic integrals. Particular examples and counter-examples are discussed.

We obtain refined estimates of the triangle inequality in a normed space using integrals and the Tapia semi-product. The particular case of an inner product space is discussed in more detail.

Abstract We report on the new functionality of open-source MATHEMATICA package FEYNCALC relevant for multiloop calculations. In particular, we focus such tasks as topology identification by means Pak algorithm, search equivalent master integrals and their graph representations well automatic derivations Feynman parametric a wide class integrals. The functions described in this are expected to b...

We introduce a technique called "precomputation of integrals" that makes it possible to compute conditional expectations in dynamic stochastic models in the initial stage of the solution procedure. This technique can be applied to any set of equations that contains conditional expectations, in particular, to the Bellman and Euler equations. After the integrals are precomputed, we can solve stoc...

We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schrödinger equation for diatomic molecules. Our approach employs Neumann’s expansion of the Coulomb repulsion 1/jx yj, solves the resulting integrals symbolically in closed form and subsequently performs a numeric Taylor...

A companion of the Grüss inequality in the general setting of measurable spaces and abstract Lebesgue integrals is proven. Some particular inequalities are mentioned as well. An application for the moments of guessing mapping is also provided.

SecDec is a program which can be used for the evaluation of parametric integrals, in particular multi-loop integrals. For a given set of propagators defining the graph, the program constructs the graph polynomials, factorizes the endpoint singularities, and finally produces a Laurent series in the dimensional regularization parameter, whose coefficients are evaluated numerically. In this talk w...

Polarized ferrofluids, lipid monolayers and magnetic bubbles form domains with deformable boundaries. Stability analysis of these domains depends on a family of nontrivial integrals. We present a closed form evaluation of these integrals as a combination of Legendre functions. This result allows exact and explicit formulae for stability thresholds and growth rates of individual modes. We also e...

X iv :1 00 3. 45 53 v2 [ m at h. N T ] 6 J un 2 01 0 ON SOME LOWER BOUNDS OF SOME SYMMETRY INTEGRALS by G.Coppola Abstract. We study the “symmetry integral”, say If , of some arithmetic functions f : N → R; we obtain from lower bounds of If (for a large class of arithmetic functions f ) lower bounds for the “Selberg integral” of f , say Jf (both these integrals give informations about f in almo...

On the basis of method iterative summation path integrals (ISPI), we develop a numerically exact transfer-matrix to describe nonequilibrium properties interacting quantum-dot systems. For this, map ISPI scheme approach, which is more accessible physical interpretation, allows for transparent formulation theory, and substantially improves efficiency. In particular, stationary limit directly impl...