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Special matrix functions have recently been investigated for regions of convergence, integral representations and the systems of matrix differential equation that these functions satisfy. In this paper, we find the recursion formulas for…

In this work, we investigate the problem of learning distance functions within the query-based learning framework, where a learner is able to pose triplet queries of the form: ``Is $x_i$ closer to $x_j$ or $x_k$?'' We establish formal…

Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…

We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove…

We exploit the parquet formalism to derive exact flow equations for the two-particle-reducible four-point vertices, the self-energy, and typical response functions, circumventing the reliance on higher-point vertices. This includes a…

Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis…

We use the recently introduced factorization of motion polynomials for constructing overconstrained spatial linkages with a straight line trajectory. Unlike previous examples, the end-effector motion is not translational and the link graph…

We give the new connection formula for the divergent bilateral basic hypergeometric series ${}_2\psi_2(a_1,a_2;b_1;q,x)$ by the using of the $q$-Borel-Laplace resummation method and Slater's formula. The connection coefficients are given by…

This paper is an adaptation of a method used in \cite{K} to the model of random quadrangulations. We prove local weak convergence of uniform measures on quadrangulations and show that the local growth of quadrangulation is governed by…

A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent…

For a given spectral curve, we construct a family of symplectic dual spectral curves for which we prove an explicit formula expressing the $n$-point functions produced by the topological recursion on these curves via the $n$-point functions…

Nearly 15 years ago, a set of qualitative spatial relations between oriented straight line segments (dipoles) was suggested by Schlieder. This work received substantial interest amongst the qualitative spatial reasoning community. However,…

In this paper we develop a new approach to the design of direct numerical methods for multidimensional problems of the calculus of variations. The approach is based on a transformation of the problem with the use of a new class of…

Derivative-matching approximations are constructed as power series built from functions. The method assumes the knowledge of special values of the Bell polynomials of the second kind, for which we refer to the literature. The presented…

Starting from the Lorentzian inversion formula, we derive a dispersion relation which computes a four-point function in 1d CFTs as an integral over its double discontinuity. The crossing symmetric kernel of the integral is given explicitly…

We study the relationship between the areas of the consecutive quadrilaterals cut from a convex quadrilateral in the plane by means of a finite or infinite number of straight lines intersecting two of its opposite sides. Moreover, we obtain…

The surface reconstruction problem from sets of planar parallel slices representing cross sections through 3D objects is presented. The final result of surface reconstruction is always based on the correct estimation of the structure of the…

It is well-known that direct analytic continuation of DGLAP evolution kernel (splitting functions) from space-like to time-like kinematics breaks down at three loops. We identify the origin of this breakdown as splitting functions are not…

In this work, approximations for real two variables function $f$ which has continuous partial $(n-1)$-derivatives $(n \ge 1)$ and has the $n$--th partial derivative of bounded bivariation or absolutely continuous are established. Explicit…

Starting from special near-bent functions in dimension 2t-1 we construct bent functions in dimension 2t having a specific derivative. We deduce new famillies of bent functions