相关论文: About some properties of simple trigonometric spli…
The integration by parts recurrence relations allow to reduce some Feynman integrals to more simple ones (with some lines missing). Nevertheless the possibility of such reduction for the given particular integral was unclear. The recently…
This paper considers the extension of classical Lagrange interpolation in one real or complex variable to "polynomials of one quaternionic variable". To do this we develop some aspects of the theory of such polynomials. We then give a…
The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of $\sigma$-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras. One of the key notions, that of…
In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…
Splint of root system for simple Lie algebra appears naturally in studies of (regular) embeddings of reductive subalgebras. Splint can be used to construct branching rules. We demonstrate that splint properties implementation drastically…
Mean value interpolation is a method for fitting a smooth function to piecewise-linear data prescribed on the boundary of a polygon of arbitrary shape, and has applications in computer graphics and curve and surface modelling. The method…
In this paper, we investigate the problem of designing compact support interpolation kernels for a given class of signals. By using calculus of variations, we simplify the optimization problem from an infinite nonlinear problem to a finite…
It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general points. We prove a generalization of this to higher dimensional varieties, showing that smooth varieties of minimal degree can be interpolated…
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
Most characterizations of interpolating sequences for Bergman spaces include the condition that the sequence be uniformly discrete in the hyperbolic metric. We show that if the notion of interpolation is suitably generalized, two of these…
In this article, we consider some generalizations of polynomial and exponential B-splines. Firstly, the extension from integral to complex orders is reviewed and presented. The second generalization involves the construction of uncountable…
Thom polynomials provide universal formulas for the fundamental class of singularity loci in terms of characteristic classes. Ohmoto extended this notion to SSM-Thom polynomials, which refine this description by capturing the richer…
Complete intersections may be unexpectedly simple over fields of positive characteristic: for instance, they may be unirational despite being of general type. One explanation is given by profiles, structure that tracks the special shape of…
In this work, we study the Hermite interpolation on $n$-dimensional non-equally spaced, rectilinear grids over a field $\Bbbk $ of characteristic zero, given the values of the function at each point of the grid and the partial derivatives…
We consider combinatorial properties of the Mills' ratio, and explore the interplay between a continued fraction expansion for the Mills' ratio, the Laplace polynomials and a new family of combinatorial identities.
A new efficient orthogonalization of the B-spline basis is proposed and contrasted with some previous orthogonalized methods. The resulting orthogonal basis of splines is best visualized as a net of functions rather than a sequence of them.…
We obtain a result concerning the stability under the interpolation with functional parameter method for the approximation spaces of Lorentz-Marcinkiewicz type and also for the approximation spaces generated by symmetric norming functions…
Scalar curvature constraints can be studied by means of splitting procedures. The success of this strategy depends on the control we can get on its splitting factors. We introduce canonical so-called minimal splitting factors. They have…
In this note we show that the degree of the interpolation polynomial for equidistant base points is characterized by the regularity of matrices of combinatorical type.
We give an explicit formula for the motivic integrals related to the Milnor number over spaces of parametrised arcs on the plane with fixed tangency orders with the axis. These integrals are rational functions of the parameters and the…