相关论文: A remark on natural constraints in variational met…

A new method of verifying the subnormality of unbounded Hilbert space operators based on an approximation technique is proposed. Diverse sufficient conditions for subnormality of unbounded weighted shifts on directed trees are established.…

The Lagrange problem is established in the discrete field theory subject to constraints with values in a Lie group. For the admissible sections that satisfy a certain regularity condition, we prove that the critical sections of such…

We consider the system -\Delta u_j + a(x)u_j = \mu_j u_j^3 + \be\sum_{k\ne j}u_k^2u_j, u_j>0, \qquad j=1,...,n, on a possibly unbounded domain $\Om\subset\R^N$, $N\le3$, with Dirichlet boundary conditions. The system appears in nonlinear…

In [15] we proposed a set of sufficient conditions for the approximate controllability of a discrete-spectrum bilinear Schr\"odinger equation. These conditions are expressed in terms of the controlled potential and of the eigenpairs of the…

The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…

We study the defocusing nonlinear Schr\"odinger equation on noncompact metric graphs under general self-adjoint vertex conditions ensuring the existence of a negative eigenvalue of the Hamiltonian operator. First, we focus on the existence…

We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light…

The extension of strongly anisotropic or dynamical scaling to local scale invariance is investigated. For the special case of an anisotropy or dynamical exponent $\theta=z=2$, the group of local scale transformation considered is the…

We study the existence or the nonexistence of classical solutions to a singular Gierer-Meinhardt system with Dirichlet boundary condition. The main feature of our model is that the activator and the inhibitor have different sources given by…

We determine under which conditions certain natural models of random constraint satisfaction problems have sharp thresholds of satisfiability. These models include graph and hypergraph homomorphism, the $(d,k,t)$-model, and binary…

We consider optimization problems with a disjunctive structure of the constraints. Prominent examples of such problems are mathematical programs with equilibrium constraints or vanishing constraints. Based on the concepts of directional…

We consider the variational problem with a mass constraint arising from the two-dimensional dispersion managed nonlinear Schr\"odinger equation with power-law type nonlinearity. We prove a threshold phenomenon with respect to mass for the…

Here we obtain bounds on the spectrum of that operator whose inverse, when it exists, gives the Green's function. We consider the wide of physical problems that can be cast in a form where a constitutive equation ${\bf J}({\bf x})={\bf…

We prove pathwise (hence strong) uniqueness of solutions to stochastic evolution equations in Hilbert spaces with merely measurable bounded drift and cylindrical Wiener noise, thus generalizing Veretennikov's fundamental result on…

We consider a family of self-adjoint Ornstein--Uhlenbeck operators $L_{\alpha} $ in an infinite dimensional Hilbert space H having the same gaussian invariant measure $\mu$ for all $\alpha \in [0,1]$. We study the Dirichlet problem for the…

The Newlander-Nirenberg theorem says that a formally integrable complex structure is locally equivalent to the standard complex structure in the complex Euclidean space. In this paper, we consider two natural generalizations of the…

We consider the Brenier-Schr{\"o}dinger problem on compact manifolds with boundary. In the spirit of a work by Arnaudon, Cruzeiro, L{\'e}onard and Zambrini, we study the kinetic property of regular solutions and obtain a link to the…

A numerical algorithm to solve the spectral problem for arbitrary self-adjoint extensions of 1D regular Schroedinger operators is presented. It is shown that the set of all self-adjoint extensions of 1D regular Schroedinger operators is in…

This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such…

In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…