Related papers: Generalizations of R0 and SSM properties; Extended…
Let $n$ be a natural number and $\mathcal{M}$ a set of $n \times n$-matrices over the nonnegative integers such that the joint spectral radius of $\mathcal{M}$ is at most one. We show that if the zero matrix $0$ is a product of matrices in…
We proposed in this paper a new method, which we named the W4 method, to solve nonlinear equation systems. It may be regarded as an extension of the Newton-Raphson~(NR) method to be used when the method fails. Indeed our method can be…
We prove new monotonicity properties for joint and generalized spectral radius and their essential versions of weighted geometric symmetrizations of bounded sets of positive kernel operators on $L^2$. To our knowledge, several proved…
The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…
Let $(R,\m)$ and $(S,\n)$ be commutative Noetherian local rings, and let $\phi:R\to S$ be a flat local homomorphism such that $\m S = \n$ and the induced map on residue fields $R/\m \to S/\n$ is an isomorphism. Given a finitely generated…
In this paper a special semi-smooth equation associated to the second order cone is studied. It is shown that, under mild assumptions, the semi-smooth Newton method applied to this equation is well-defined and the generated sequence is…
A theory of simultaneous resolution of singularities for families of embedded varieties (over a field of characteristic zero) parametrized by the spectrum of a suitable artinian ring, and compatible with a given algorithm of resolution, is…
We introduce new times in the monodromy preserving equations. While the usual times related to the moduli of complex structures of Riemann curves such as coordinates of marked points, we consider the moduli of generalized complex structures…
A study of the linearised gravitational field (spin 2 zero-rest-mass field) on a Minkowski background close to spatial infinity is done. To this purpose, a certain representation of spatial infinity in which it is depicted as a cylinder is…
A real square matrix $A$ is called a $Q$-matrix if the linear complementarity problem $LCP(A,q)$ has a solution for all $q \in \mathbb{R}^n$. This means that for every vector $q$ there exists a vector $x$ such that $x \geq 0, y=Ax+q\geq 0$…
Matrix completion results deal with the question of when a partially specified symmetric matrix can be completed to a member of certain matrix cones. Results from positive semidefinite matrix completion and completely positive matrix…
In the present paper we consider the system {\Delta}u - W_u (u) = 0, where u: R^n to R^n, for a class of potentials W: R^n to R that possess several global minima and are invariant under a general finite reflection group G. We establish…
In this paper, we provide a negative answer to a long-standing open problem on the compatibility of Spearman's rho matrices. Following an equivalence of Spearman's rho matrices and linear correlation matrices for dimensions up to 9 in the…
Matrix-variate optimization plays a central role in advanced wireless system designs. In this paper, we aim to explore optimal solutions of matrix variables under two special structure constraints using complex matrix derivatives, including…
We derive the soliton matrices corresponding to an arbitrary number of higher-order normal zeros for the matrix Riemann-Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order…
The article presents a generalization of Sherman-Morrison-Woodbury (SMW) formula for the inversion of a matrix of the form A+sum(U)k)*V(k),k=1..N).
The subject is parametrices for semi-linear problems, based on parametrices for linear boundary problems and on non-linearities that decompose into solution-dependent linear operators acting on the solutions. Non-linearities of product type…
SMT solvers use sophisticated techniques for polynomial (linear or non-linear) integer arithmetic. In contrast, non-polynomial integer arithmetic has mostly been neglected so far. However, in the context of program verification, polynomials…
The main objective of this paper is to give a rigorous treatment of Wigner's and Eisenbud's $R$-matrix method for scattering matrices of scattering systems consisting of two selfadjoint extensions of the same symmetric operator with finite…
We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative…