Related papers: Lambda constant and Ground states of Perelman's W-…

In this paper we define a class of Boolean and generalized Boolean functions defined on $\mathbb{F}_2^n$ with values in $\mathbb{Z}_q$ (mostly, we consider $q=2^k$), which we call landscape functions (whose class containing generalized…

We study Fermi liquids with a Fermi surface that lacks continuous rotational invariance, and in the presence of an arbitrary quartic interaction. We obtain the expressions of the generalized static susceptibilities that measure the linear…

We consider the ground state of the quantum Ising model with transverse field $h$ in one dimension in a finite volume \[ \Lambda{_{m}:=\{-m,-m+1,\ldots,m+L\}\ .}% \] For $h$ sufficiently large we prove a bound for the entanglement of the…

We study the ground-state entanglement Hamiltonian of free nonrelativistic fermions for semi-infinite domains in one dimension. This is encoded in the two-point correlations projected onto the subsystem, an operator that commutes with the…

Numerical results are presented for a generalized resonance valence bond state which includes both ionic and covalent contributions in each bond ; non nearest-neighbor bonds are also considered. Variational calculations have been performed…

We study the nonlinear Schr\"odinger equation for systems of $N$ orthonormal functions. We prove the existence of ground states for all $N$ when the exponent $p$ of the non linearity is not too large, and for an infinite sequence $N_j$…

A general field-theoretical description of many-fermion systems, with or without quenched disorder, is developed. Starting from the Grassmannian action for interacting fermions, we first bosonize the theory by introducing composite matrix…

The paper addresses questions of existence and regularity of solutions to linear partial differential equations whose coefficients are generalized functions or generalized constants in the sense of Colombeau. We introduce various new…

In an attempt to progress towards proving the conjecture the numerical range W (A) is a 2--spectral set for the matrix A, we propose a study of various constants. We review some partial results, many problems are still open. We describe our…

We extend General Relativity by promoting Planck scale and the cosmological constant into integration constants, interpreted as fluxes of $4$-forms hiding in the theory. When we include the charges of the $4$-forms, these `constants' can…

In this paper we investigate the Margulis-Ruelle inequality for general Riemannian manifolds (possibly noncompact and with boundary) and show that it always holds under integrable condition.

We consider Landau Hamiltonians with a weak coupling random electric potential of breather type. Under appropriate assumptions we prove a Wegner estimate. It implies the Hoelder continuity of the integrated density of states. The main…

In this paper, we exhibit upper and lower bounds with explicit constants for some objects related to entire $L$-functions in the critical strip, under the generalized Riemann hypothesis. The examples include the entire Dirichlet…

In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence…

We consider a generalized Burger's equation (dtu = dxxu - udxu + up - {\lambda}u)in a subdomain of R, under various boundary conditions. First, using some phase plane arguments, we study the existence of stationary solutions under Dirichlet…

We define a generalized Golomb--Dickman constant $\lambda_{\theta}$ as the limiting expected proportion of the longest cycle in random permutations under the Ewens measure with parameter $\theta > 0$. Exploiting the independence properties…

While dealing with a class of generalized Bargmann spaces, we rederive their reproducing kernels from the knowledge of an orthonormal basis by using an addition formula for Laguerre polynomials involving the disk polynomials. We construct…

We consider a generalized steady Stokes system with discontinuous coefficients in a nonsmooth domain when the inhomogeneous term belongs to a weighted $L^q$ space for $2<q<\infty$. We prove the global weighted $L^q$-estimates for the…

The authors introduce generalized Campanato space with regularized condition over non-homogeneous space, and study its basic properties including the John-Nirenberg inequality and equivalent characterizations. As applications, the…

In this paper, we develop the theory of weighted Bergman space and obtain a general representation formula of the Bergman kernel function for the spaces on the Reinhardt domain containing the origin. As applications, we calculate the…