Related papers: Applying numerosity to surreal integration
Euclidean quantum measure in Regge calculus with independent area tensors is considered using example of the Regge manifold of a simple structure. We go over to integrations along certain contours in the hyperplane of complex connection…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…
Taking into account the global one-dimensionality conjecture recently proposed by the author, the Cauchy-like analytical wave functional of the Wheeler-DeWitt theory is derived. The crucial point of the integration strategy is canceling of…
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial approximations, the proposed approach arises from exact…
Using the sign expansion of the surreal numbers, we give a possible notion of convergence for surreal sequences.
This paper investigates summability principles for multilinear summing operators. The main result presents a novel inclusion theorem for a class of summing operators, which generalizes several classical results. As applications, we derive…
A fundamental theme in classical Fourier analysis relates smoothness properties of functions to the growth and/or integrability of their Fourier transform. By using a suitable class of $L^{p}-$multipliers, a rather general inequality…
In this paper, we develop a sliding method for the fractional Laplacian. We first obtain the key ingredients needed in the sliding method either in a bounded domain or in the whole space, such as narrow region principles and maximum…
We study numerical integration of functions depending on an infinite number of variables. We provide lower error bounds for general deterministic linear algorithms and provide matching upper error bounds with the help of suitable multilevel…
We prove the curse of dimensionality in the worst case setting for multivariate numerical integration for various classes of smooth functions. We prove the results when the domains are isotropic convex bodies with small diameter satisfying…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…
The classical random matrix theory is mostly focused on asymptotic spectral properties of random matrices as their dimensions grow to infinity. At the same time many recent applications from convex geometry to functional analysis to…
We consider a large class of physical fields $u$ written as double inverse Fourier transforms of some functions $F$ of two complex variables. Such integrals occur very often in practice, especially in diffraction theory. Our aim is to…
We consider a neutral self-interacting massive scalar field defined in a d-dimensional Euclidean space. Assuming thermal equilibrium, we discuss the one-loop perturbative renormalization of this theory in the presence of rigid boundary…
A new approach to the solution of boundary value problems within the so-called fictitious domain methods philosophy is proposed which avoids well known shortcomings of other fictitious domain methods, including the need to generate…
We introduce a natural definition for sums of the form \[ \sum_{\nu=1}^x f(\nu) \] when the number of terms x is a rather arbitrary real or even complex number. The resulting theory includes the known interpolation of the factorial by the…
Let $\psi:{\mathcal{D}}\rightarrow{\mathbf{R}}$ be a harmonic function such that $\Delta\psi(x)=0$ for all $x\in\mathcal{D}\subset{\mathbf{R}}^{n}$. There are then many well-established classical results:the Dirichlet problem and Poisson…
The integration of data from multiple sources is increasingly used to achieve larger sample sizes and enhance population diversity. Our previous work established that, under random sampling from the same underlying population, integrating…
Employing numerical and theoretical methods, we investigate the structural characteristics of random sequential addition (RSA) of congruent spheres in $d$-dimensional Euclidean space $\mathbb{R}^d$ in the infinite-time or saturation limit…
We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited,…