Related papers: Maximal generalization of Lanczos' derivative usin…
We study right tail large deviations of the logarithm of the partition function for directed lattice paths in i.i.d. random potentials. The main purpose is the derivation of explicit formulas for the $1+1$-dimensional exactly solvable case…
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
Methods for generating new distributions from old can be thought of as techniques for simplifying integrals used in reverse. Hence integrating a probability density function (pdf) by parts provides a new way of modifying distributions; the…
In this paper, a general integral identity for convex functions is derived. Then, we establish new some inequalities of the Simpson and the Hermite-Hadamard's type for functions whose absolute values of derivatives are convex. Some…
We introduce and solve an infinite class of loop integrals which generalises the well-known ladder series. The integrals are described in terms of single-valued polylogarithmic functions which satisfy certain differential equations. The…
Integral transforms are invaluable mathematical tools to map functions into spaces where they are easier to characterize. We introduce the hyperdimensional transform as a new kind of integral transform. It converts square-integrable…
An algorithm for integration of polynomial functions with variable weight is considered. It provides extension of the Gaussian integration, with appropriate scaling of the abscissas and weights. Method is a good alternative to usually…
The subdifferential of a function is a generalization for nonsmooth functions of the concept of gradient. It is frequently used in variational analysis, particularly in the context of nonsmooth optimization. The present work proposes…
We present a closed-form finite-dimensional projection method for regularizing a function defined by a discrete set of measurement data, which have been contaminated by random, zero mean errors, and for estimating the derivative and…
How do we take repeated derivatives of composed multivariate functions? for one-dimensional functions, the common tools consist of the Fa\'a di Bruno formula with Bell polynomials; while there are extensions of the Fa\'a di Bruno formula,…
We examined the properties of the coefficients of the \cite{lanczos1964} approximation of the $\Gamma$-function with complex values of the free parameter together with the convergence properties of the approximation when using these…
Let $f: B^n \rightarrow {\mathbb R}$ be a $d+1$ times continuously differentiable function on the unit ball $B^n$, with $\max_{z\in B^n} \| f(z) \|=1$. A well-known fact is that if $f$ vanishes on a set $Z\subset B^n$ with a non-empty…
We propose another interpretation of well-known derivatives computations from regular expressions, due to Brzozowski, Antimirov or Lombardy and Sakarovitch, in order to abstract the underlying data structures (e.g. sets or linear…
A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…
This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are…
The derivative expansion of the effective action is considered in the model with two interacting real scalar fields in curved spacetime. Using the functional approach and local momentum representation, the coefficient of the derivative term…
The paper is devoted to discretization of integral norms of functions from a given finite dimensional subspace. This problem is very important in applications but there is no systematic study of it. We present here a new technique, which…
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating…
Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a…
The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…