Related papers: Factorization conditions for nonlinear second-orde…
Nonlinear PDE's having {\bf given} conditional symmetries are constructed. They are obtained starting from the invariants of the "conditional symmetry" generator and imposing the extra condition given by the characteristic of the symmetry.…
We study the case of Hermite subdivision operators satisfying a spectral condition of order greater than their size. We show that this can be characterized by operator factorizations involving Taylor operators and difference factorizations…
We propose a localized divide and conquer algorithm for inverse factorization $S^{-1} = ZZ^*$ of Hermitian positive definite matrices $S$ with localized structure, e.g. exponential decay with respect to some given distance function on the…
In this paper we study ground states of the following fractional Schr\"odinger equation (- \Delta)^{s} u + V(x) u = f(x, u) \, \mbox{ in } \, \R^{N}, u\in \H^{s}(\R^{N}) where $s\in (0,1)$, $N>2s$ and $f$ is a continuous function satisfying…
For an $m \times n$ complex matrix $X$ of rank $r$ with Schur multiplier $S_X$ we show that there exist an $ r \times m $ complex matrix $L$ and an $ r\times n $ complex matrix $R$ such that $X = L^*R$ and $\|S_X\|\, =\, \|\mathrm{diag}…
The algebraic theory of third-order tensors under the $t$-product is naturally formulated over the complex field via Fourier block diagonalization. However, many applications require real-valued representations. In this paper, we…
We investigate random minimal factorizations of the $n$-cycle, that is, factorizations of the permutation $(1 \, 2 \cdots n)$ into a product of cycles $\tau_1, \ldots, \tau_k$ whose lengths $\ell(\tau_1), \ldots, \ell(\tau_k)$ verify the…
In this thesis we present an introduction to Soft-Collinear Effective Theory, which can be used to prove (or disprove) factorization theorems to all orders in the strong coupling constant for some B decays into light and energetic…
A recently-established necessary condition for polynomials that preserve the class of entrywise nonnegative matrices of a fixed order is shown to be necessary and sufficient for the class of nonnegative monomial matrices. Along the way, we…
Most numerical methods developed for solving nonlinear programming problems are designed to find points that satisfy certain optimality conditions. While the Karush-Kuhn-Tucker conditions are well-known, they become invalid when constraint…
The method of factorization, based on the model of unstable particles with a smeared mass, is applied to the processes with an unstable particle in the intermediate state. It was shown, that in the framework of the method suggested, the…
Sequential optimality conditions play an important role in constrained optimization since they provide necessary conditions without requiring constraint qualifications (CQs). This paper introduces a second-order extension of the Approximate…
We consider a nonlinear elliptic equation driven by a nonhomogeneous differential operator plus an indefinite potential. On the reaction term we impose conditions only near zero. Using variational methods, together with truncation and…
Let $r$ be a prime power and $q=r^m$. For $0\le i\le m-1$, let $f_i\in \mathbb{F}_r[x]$ be $q$-linearized and $a_i\in \mathbb{F}_q$. Assume that $z\in \mathbb{\bar{F}}_r$ satisfies the equation $\sum_{i=0}^{m-1}a_if_i(z)^{r^i}=0$, where…
We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and…
Let G be a block matrix function with one diagonal block A being positive definite and the off diagonal blocks complex conjugates of each other. Conditions are obtained for G to be factorable (in particular, with zero partial indices) in…
By investigating path-distribution dependent stochastic differential equations, the following type of nonlinear Fokker--Planck equations for probability measures $(\mu_t)_{t \geq 0}$ on the path space $\mathcal C:=C([-r_0,0];\mathbb R^d),$…
In this paper, we consider finite difference approximations of the second order wave equation. We use finite difference operators satisfying the summation-by-parts property to discretize the equation in space. Boundary conditions and grid…
Schemes with the second-order approximation in time are considered for numerical solving the Cauchy problem for an evolutionary equation of first order with a self-adjoint operator. The implicit two-level scheme based on the Pad\'{e}…
We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial…