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We study the Sunyaev-Zeldovich effect for clusters of galaxies. We explore the relativistic corrections to the Kompaneets equation in terms of two different expansion approximation schemes, namely, the Fokker-Planck expansion approximation…
In this paper, we obtained some global approximation results for general Gamma type operators.
A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in this paper. Results are both, on the one hand, from a…
This paper establishes the Quantum Voronovskaya--Damasclin (QVD) Theorem, providing a complete asymptotic characterization of Quantum Neural Network Operators in the approximation of arbitrary quantum channels. The result extends the…
Kernel based methods provide a way to reconstruct potentially high-dimensional functions from meshfree samples, i.e., sampling points and corresponding target values. A crucial ingredient for this to be successful is the distribution of the…
In this work, wavelet-based filtering operators are constructed by introducing a basic function $D(t_1, t_2, t_3)$ using a general wavelet transform. The cardinal orthogonal scaling functions (COSF) provide an idea to derive the standard…
We present a theoretical analysis of the approximation properties of convolutional architectures when applied to the modeling of temporal sequences. Specifically, we prove an approximation rate estimate (Jackson-type result) and an inverse…
Kernel approximation with exponentials is useful in many problems with convolution quadrature and particle interactions such as integral-differential equations, molecular dynamics and machine learning. This paper proposes a weighted…
Vapnik--Chervonenkis' theorem is a seminal result in machine learning. It establishes sufficient conditions for empirical probabilities to converge to theoretical probabilities, uniformly over families of events. It also provides an…
We prove quantitative Runge type approximation results for spaces of smooth zero solutions of several classes of linear partial differential operators with constant coefficients. Among others, we establish such results for arbitrary…
We describe generalizations of the universal approximation theorem for neural networks to maps invariant or equivariant with respect to linear representations of groups. Our goal is to establish network-like computational models that are…
In this paper, we develop a multivariate framework for approximation by max-min neural network operators. Building on the recent advances in approximation theory by neural network operators, particularly, the univariate max-min operators,…
We study the family of intersection graphs of low density objects in low dimensional Euclidean space. This family is quite general, and includes planar graphs. We prove that such graphs have small separators. Next, we present efficient…
An asymmetric operator of generalised translation is introduced in this paper. Using this operator, we define a generalised modulus of smoothness and prove direct and inverse theorems of approximation theory for it.
We consider the eigenvalue equation for the largest eigenvalue of certain kinds of non-compact linear operators given as the sum of a multiplication and a kernel operator. It is shown that, under moderate conditions, such operators can be…
A wide range of numerical methods exists for computing polynomial approximations of solutions of ordinary differential equations based on Chebyshev series expansions or Chebyshev interpolation polynomials. We consider the application of…
We introduce an asymmetric operator of generalised translation, define the generalised modulus of smoothness by its means, and obtain the direct and inverse theorems in approximation theory for it.
We construct new rational approximants of Euler's constant that improve those of Aptekarev et al. (2007) and Rivoal (2009). The approximants are given in terms of certain (mixed type) multiple orthogonal polynomials associated with the…
Some sharp results related to the convergence of means and families of operators generated by the generalized Bochner-Riesz kernels are obtained. The exact order of approximation of functions by these methods via $K$-functional (or its…
We introduce and investigate a new notion of the theory of approximation-the so-called degenerate approximation, i.e. approximation of the function of two (and more) variables (kernel) by means of degenerate function (kernel). We apply…