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In this article, the approximation properties of the Szasz-Mirakjan type operators are studied for the function of two variables, and the rate of convergence of the bivariate operators is determined in terms of total and partial modulus of…
In this paper, we study Brownian-type operators, which are upper triangular $2\times 2$ block matrix operators with entries satisfying some algebraic constraints. We establish a lifting theorem stating that any Brownian-type operator with…
This paper is concerned with the accurate, conservative, and stable imposition of boundary conditions and inter-element coupling for multi-dimensional summation-by-parts (SBP) finite-difference operators. More precisely, the focus is on…
We define a class of deformed multimode oscillator algebras which possess number operators and can be mapped to multimode Bose algebra.We construct and discuss the states in the Fock space and the corresponding number operators.
This letter summarizes and proves the concept of bounded-input bounded-state (BIBS) stability for weight convergence of a broad family of in-parameter-linear nonlinear neural architectures as it generally applies to a broad family of…
A leading twist expansion in terms of bi-local operators is proposed for the structure functions of deeply inelastic scattering near the elastic limit $x \to 1$, which is also applicable to a range of other processes. Operators of…
We introduce here new generalized principal eigenvalues for linear parabolic operators with heterogeneous coefficients in space and time. We consider a bounded spatial domain and an unbounded time interval $I$ : $I=\mathbb{R},\…
How entangled is a randomly chosen bipartite stabilizer state? We show that if the number of qubits each party holds is large the state will be close to maximally entangled with probability exponentially close to one. We provide a similar…
We present a combinatorial method of constructing solutions to the normal ordering of boson operators. Generalizations of standard combinatorial notions - the Stirling and Bell numbers, Bell polynomials and Dobinski relations - lead to…
In this second paper on loop quantization of Gowdy model, we introduce the kinematical Hilbert space on which appropriate holonomies and fluxes are well represented. The quantization of the volume operator and the Gauss constraint is…
We extend and generalize the construction of Sturm-Liouville problems for a family of Hamiltonians constrained to fulfill a third-order shape-invariance condition and focusing on the "$-2x/3$" hierarchy of solutions to the fourth Painlev\'e…
Solutions of bilevel optimization problems tend to suffer from instability under changes to problem data. In the optimistic setting, we construct a lifted formulation that exhibits desirable stability properties under mild assumptions that…
Bayesian statistical inference for Generalized Linear Models (GLMs) with parameters lying on a constrained space is of general interest (e.g., in monotonic or convex regression), but often constructing valid prior distributions supported on…
The celebrated Brascamp-Lieb (BL) inequalities (and their extensions) are an important mathematical tool, unifying and generalizing numerous inequalities in analysis, convex geometry and information theory. While their structural theory is…
Qualitative and quantitative aspects for variational inequalities governed by strongly pseudomonotone operators on Hilbert space are investigated in this paper. First, we establish a global error bound for the solution set of the given…
Gaussian boson sampling (GBS) is a promising protocol for demonstrating quantum computational advantage. One of the key steps for proving classical hardness of GBS is the so-called ``hiding conjecture'', which asserts that one can ``hide''…
We use the concept of the algebra eigenstates that provides a unified description of the generalized coherent states (belonging to different sets) and of the intelligent states associated with a dynamical symmetry group. The formalism is…
In this paper, we introduce a class of backward stochastic equations (BSEs) that extend classical BSDEs and include many interesting examples of generalized BSDEs as well as semimartingale backward equations. We show that a BSE can be…
We introduce a class of multidimensional Schr\"odinger operators with elliptic potential which generalize the classical Lam\'e operator to higher dimensions. One natural example is the Calogero--Moser operator, others are related to the…
We construct a formal global quantization of the Poisson Sigma Model in the BV-BFV formalism using the perturbative quantization of AKSZ theories on manifolds with boundary and analyze the properties of the boundary BFV operator. Moreover,…