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We derive explicit formulas for the normal ordering of powers of arbitrary monomials of boson operators. These formulas lead to generalisations of conventional Bell and Stirling numbers and to appropriate generalisations of the Dobinski…
We discuss the appropriate techniques for modelling the geometry of open ended elastic polymer molecules. The molecule is assumed to have fixed endpoints on a boundary surface. In particular we discuss the concept of the winding number, a…
Feynman integrals that have been evaluated in dimensional regularization can be written in terms of generalized hypergeometric functions. It is well known that properties of these functions are revealed in the framework of intersection…
We show that Boolean matrix multiplication, computed as a sum of products of column vectors with row vectors, is essentially the same as Warshall's algorithm for computing the transitive closure matrix of a graph from its adjacency matrix.…
We study the global boundedness of bilinear and multilinear Fourier integral operators on Banach and quasi-Banach $L^p$ spaces, where the amplitudes of the operators are smooth or rough in the spatial variables. The results are obtained by…
Algorithm unfolding or unrolling is the technique of constructing a deep neural network (DNN) from an iterative algorithm. Unrolled DNNs often provide better interpretability and superior empirical performance over standard DNNs in signal…
This paper is concerned with general $n\times n$ upper triangular operator matrices with given diagonal entries. We characterize perturbations of the left (right) essential spectrum, the essential spectrum, as well as the left (right) the…
Brownian motions in the infinite-dimensional group of all unitary operators are studied under strong continuity assumption rather than norm continuity. Every such motion can be described in terms of a countable collection of independent…
The generalized density is a product of a density function and a weight function. For example, the average local brightness of an astronomical image is the probability of finding a galaxy times the mean brightness of the galaxy. We propose…
We extend the Colombeau algebra of generalized functions to arbitrary (infinitely differentiable, paracompact) n-dimensional manifolds M. Embedding of continuous functions and distributions is achieved with the help of a family of n-forms…
We study generalizations of the classical Bernstein operators on polynomial spaces, where instead of fixing $\mathbf{1}$ and $x$, we require that $\mathbf{1}$ and a strictly increasing polynomial $f_1$ be fixed. Via several examples, we…
We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…
A generalization of Gy's theory for the variance of the fundamental sampling error is reviewed. Practical situations where the generalized model potentially leads to more accurate variance estimates are identified as: clustering of…
Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…
We prove a uniform generalized gaussian bound for the powers of a discrete convolution operator in one space dimension. Our bound is derived under the assumption that the Fourier transform of the coefficients of the convolution operator is…
Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…
The mean shift algorithm is a popular way to find modes of some probability density functions taking a specific kernel-based shape, used for clustering or visual tracking. Since its introduction, it underwent several practical improvements…
In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…
We present a numerical implementation of generalized unitarity. We will show that we are able to obtain the box coefficients of any 1 loop gluonic amplitude, for an arbitrary helicity configuration and for any number of external particles.
Recently, a generalized Bernoulli process (GBP) was developed as a stationary binary sequence whose covariance function obeys a power law. In this paper, we further develop generalized Bernoulli processes, reveal their asymptotic behaviors,…