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We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
We extend the work of Galatos (2004) on nested sums, originally called generalised ordinal sums, of residuated lattices. We show that the nested sum of an odd quasi relation algebra (qRA) satisfying certain conditions and an arbitrary qRA…
In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…
In this paper, we are mainly concerned with studying arbitrary unbounded square roots of linear operators as well as some of their basic properties. The paper contains many examples and counterexamples. As an illustration, we give explicit…
In the present paper we characterize the existence and uniqueness of maximal Lp-regular solutions of high order convolution operator equations. Particularly, we get coercive uniform estimates with respect to spectral parameter and we show…
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…
Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a…
We prove that the algebraic sum of unbounded normal operators satisfies the square root problem of Kato under appropriate hypotheses. As application, we consider perturbed Schrodinger operators.
We study nonlinear wave equations on $\mathbb R^{2+1}$ with quadratic derivative nonlinearities, which include in particular nonlinearities exhibiting a null form structure, with random initial data in $H_x^1\times L^2_x$. In contrast to…
While quantum circuits built from two-particle dual-unitary (maximally entangled) operators serve as minimal models of typically nonintegrable many-body systems, the construction and characterization of dual-unitary operators themselves are…
We study a system of fully nonlinear elliptic equations, depending on a small parameter $\eps$, that models long-range segregation of populations. The diffusion is governed by the negative Pucci operator. In the linear case, this system was…
We consider a non-commutative polynomial in several independent $N$-dimensional random unitary matrices, uniformly distributed over the unitary, orthogonal or symmetric groups, and assume that the coefficients are $n$-dimensional matrices.…
We introduce the notion of ideally supported achievement sets for a series of real numbers. We analize their complexity and topological properties. We compare the notion of ideal achievement sets with the notion of ideally supported sum…
This paper investigates the consensus problem in almost sure sense for uncertain multi-agent systems with noises and fixed topology. By combining the tools of stochastic analysis, algebraic graph theory, and matrix theory, we analyze the…
Of crucial importance to the development of quantum computing and information has been the construction of a quantum operations formalism that admits a description of quantum noise while simultaneously revealing the behavior of an open…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis is given. The main result is that any operator with the above property must have a…
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…
Lists, multisets, and sets are well-known data structures whose usefulness is widely recognized in various areas of Computer Science. These data structures have been analyzed from an axiomatic point of view with a parametric approach in (*)…
In this paper, the necessity theory for commutators of multilinear singular integral operators on weighted Lebesgue spaces is investigated. The results relax the restriction of the weights class to the general multiple weights, which can be…