Related papers: Inequalities for exchange Slater integrals
Under certain conditions on an integrable function f having a real-valued Fourier transform Tf=F, we obtain a certain estimate for the oscillation of F in the interval [-C||f'||/||f||,C||f'||/||f||] with C>0 an absolute constant. Given q>0…
This paper presents a matrix formulation of the scalar laws of radiative transfer. The method applies to coupled mixed boundary condition problems on general domains. Participating media can range from transparent to absorbing, emitting,…
Discretizations of differential equations are often studied through their modified equation. This is a differential equation, usually obtained as a power series, with solutions that exactly interpolate the discretization. By comparing the…
This paper derives exponential concentration inequalities and polynomial moment inequalities for the spectral norm of a random matrix. The analysis requires a matrix extension of the scalar concentration theory developed by Sourav…
Spectral morphisms between Banach algebras are useful for comparing their K-theory and their "noncommutative dimensions" as expressed by various notions of stable ranks. In practice, one often encounters situations where the spectral…
Various issues surrounding a recently proposed inequality among twist-two quark distributions in the nucleon are discussed. We provide a rigorous derivation of the inequality in QCD, including radiative corrections and scale dependence. We…
We prove optimal regularity results for solutions to linear kinetic Fokker-Planck equations in bounded domains. Our contributions are two-fold. First, we establish the sharp $C^{1/2}$ regularity for either diffuse reflection or prescribed…
We show that the exchange statistics have consequences in 1D systems with compact topology, contrary to the common opinion that exchange statistics is arbitrary in 1D. As examples of non-trivial statistical behavior we exactly calculate the…
The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor…
We study Hoeffding decomposable exchangeable sequences with values in a finite set D. We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, if the cardinality of D is strictly greater…
Inexact Newton regularization methods have been proposed by Hanke and Rieder for solving nonlinear ill-posed inverse problems. Every such a method consists of two components: an outer Newton iteration and an inner scheme providing…
Images obtained from coherent illumination processes are contaminated with speckle. A prominent example of such imagery systems is the polarimetric synthetic aperture radar (PolSAR). For such remote sensing tool the speckle interference…
An improved algorithm to evaluate the nonrelativistic three-electron Hylleraas-Configuration Interaction (Hy-CI) kinetic energy integrals over Slater orbitals and the Hamiltonian in Hylleraas coordinates is shown. The resulting analytical…
Reciprocal transformations mix the role of the dependent and independent variables of (nonlinear partial) differential equations to achieve simpler versions or even linearized versions of them. These transformations help in the…
We present applications of the recently introduced ``Generalized SIC-Slater'' scheme which provides a simple Self-Interaction Correction approximation in the framework of the Optimized Effective Potential. We focus on the computation of…
The Fokker-Planck equation needs to be modified when the diffusion parameters are not constant, in order to match it with the backward equation. It even becomes simpler, and the integration of the underlying stochastic differential equation…
A systematic derivation provides extended series of correlation inequalities in quantum systems. Each order in truncated Taylor expansion of the spectral representation for the Duhamel correlation function gives its lower and upper bounds.…
We analyze in detail the interaction correction to Full Counting Statistics (FCS) of electron transfer in a quantum contact originating from the electromagnetic environment surrounding the contact. The correction can be presented as a sum…
The translation operator $T^A$ associated with the special affine Fourier transform (SAFT) $\mathscr{F}_A$ is introduced from harmonic analysis point of view. The analogues of Wendel's theorem, Wiener theorem, Weiner-Tauberian theorem and…
In this paper, the linear differential expression of order $n \ge 2$ with distribution coefficients of various singularity orders is considered. We obtain the associated matrix for the regularization of this expression. Furthermore, we…