Related papers: On pair correlation for generic diagonal forms
We completely determine cohomology groups of sections of homogeneous line bundles over a toroidal group.
Divergence-form operators with random coefficients homogenize over large scales. Over the last decade, an intensive research effort focused on turning this asymptotic statement into quantitative estimates. The goal of this note is to review…
Motivated by a problem in local differential geometry of Cauchy--Riemann (CR) structures of hypersurface type, we find a canonical form for pairs consisting of a nondegenerate Hermitian form and a self-adjoint antilinear operator, or,…
This paper shows how to build a formal analytical solution for a differential equation of arbitrary order and with variable coefficients. It proofs that the most known approximated solutions for such a problem can be derived from the…
Classical entanglement is a powerful tool which provides a neat numerical estimate for the study of classical correlations. Its experimental investigation, however, has been limited to special cases. Here, we demonstrate that the…
We employ the combinatorial atlas technology to prove new correlation inequalities for the number of linear extensions of finite posets. These include the approximate independence of probabilities and expectations of values of random linear…
This paper begins the exploration of what we call measures of association between two irreducible complex projective varieties of the same dimension. The idea is to study from various points of view the minimal complexity of correspondences…
Given a description of the stacking statistics of layered close-packed structures in the form of a hidden Markov model, we develop analytical expressions for the pairwise correlation functions between the layers. These may be calculated…
Via multilinear algebra, we formulate a criterion for connectedness in the parametric geometry of numbers in terms of pencils, which are certain algebraic varieties in the space of matrices. As a consequence, we obtain a connectedness…
A novel factorization for the sum of two single-pair matrices is established as product of lower-triangular, tridiagonal, and upper-triangular matrices, leading to semi-closed-form formulas for tridiagonal matrix inversion. Subsequent…
The aim of this paper is to present a simple way to generate proper monomial rational maps between generalized balls and via the relations between generalized balls and bounded symmetric domains of type I, we suggest new examples of proper…
We generalize the spherical harmonics for l=1 and give the differential equation that the generalized forms satisfy. The new forms have an obvious interpretation in the context of quantum mechanics.
We make several new contributions to the study of proper holomorphic mappings between balls. Our results include a degree estimate for rational proper maps, a new gap phenomenon for convex families of arbitrary proper maps, and an…
In this paper, we study discrete quasi-copulas associated with imprecise copulas. We focus on discrete imprecise copulas that are in correspondence with the Alternating Sign Matrices and provide some construction techniques of dual pairs.…
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation…
In this article we survey recent results on rigid dualizing complexes over commutative algebras. We begin by recalling what are dualizing complexes. Next we define rigid complexes, and explain their functorial properties. Due to the…
The paper summarizes the construction of pairings on some standard spectral sequences in algebraic topology.
We generalize the array orthogonality property for perfect autocorrelation sequences to $n$-dimensional arrays. The generalized array orthogonality property is used to derive a number of $n$-dimensional perfect array constructions.
We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived in \cite{Kusa} actually characterize them. Secondly, by…
The Particle Number Projected Generator Coordinate Method is formulated for the pairing Hamiltonian in a detailed way in the projection after variation and the variation after projection methods. The dependence of the wave functions on the…