相关论文: The Varchenko Determinant for Apartments

We define arrangements of codimension-1 submanifolds in a smooth manifold which generalize arrangements of hyperplanes. When these submanifolds are removed the manifold breaks up into regions, each of which is homeomorphic to an open disc.…

Algorithms involving Gaussian processes or determinantal point processes typically require computing the determinant of a kernel matrix. Frequently, the latter is computed from the Cholesky decomposition, an algorithm of cubic complexity in…

Let $\mathcal{V}=\bigsqcup_{i=0}^n\mathcal{V}_i$ be the lattice of subspaces of the $n$-dimensional vector space over the finite field $\mathbb{F}_q$ and let $\mathcal{A}$ be the graded Gorenstein algebra defined over $\mathbb{Q}$ which has…

A hyperplane arrangement is said to satisfy the ``Riemann hypothesis'' if all roots of its characteristic polynomial have the same real part. This property was conjectured by Postnikov and Stanley for certain families of arrangements which…

We investigate the Helmholtz equation with suitable boundary conditions and uncertainties in the wavenumber. Thus the wavenumber is modeled as a random variable or a random field. We discretize the Helmholtz equation using finite…

Striped phases, in which spin, charge, and pairing correlations vary inhomogeneously in the CuO_2 planes, are a known experimental feature of cuprate superconductors, and are also found in a variety of numerical treatments of the two…

The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that…

In this paper, a new kind of resultant, called the determinantal resultant, is introduced. This operator computes the projection of a determinantal variety under suitable hypothesis. As a direct generalization of the resultant of a very…

The entanglement produced by a bilinear Hamiltonian in continuous variables has been thoroughly studied and widely used. In contrast, the physics of entanglement resulting from nonlinear interaction described by partially degenerate…

Let $F$ be a field of odd characteristic, $E$ be a finite extension of $F$ equipped an involution with subfield of fixed points $E_0$ containing $F$ and $V$ be a finite dimensional $E$-vector space with a non-degenerate hermitian form $h$.…

The results from the article [Strachan I.A.B., Szablikowski B.M., Stud. Appl. Math. 133 (2014), 84-117] are extended over consideration of central extensions allowing the introducing of additional independent variables. Algebraic conditions…

We evaluate the determinant of a matrix whose entries are elliptic hypergeometric terms and whose form is reminiscent of Sylvester matrices. A hypergeometric determinant evaluation of a matrix of this type has appeared in the context of…

The number-theoretic codes are a class of codes defined by single or multiple congruences and are mainly used for correcting insertion and deletion errors. Since the number-theoretic codes are generally non-linear, the analysis method for…

The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…

A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…

As well as arising naturally in the study of non-intersecting random paths, random spanning trees, and eigenvalues of random matrices, determinantal point processes (sometimes also called fermionic point processes) are relatively easy to…

An extended variational principle providing the equations of motion for a system consisting of interacting classical, quasiclassical and quantum components is presented, and applied to the model of bilinear coupling. The relevant dynamical…

In his work on the twenty vertex model, Di Francesco [Electron. J. Combin. 28(4) (2021), Paper No. 4.38] found a determinant formula for the number of configurations in a specific such model, and he conjectured a closed form product formula…

Backdoor adjustment is a technique in causal inference for estimating interventional quantities from purely observational data. For example, in medical settings, backdoor adjustment can be used to control for confounding and estimate the…

We develop certain combinatorial tools for the study of discriminants of general systems of polynomial equations. Applying these tools in a sequel paper, we completely classify components of such discriminants, generalizing the classical…