Related papers: Bilinear quadratures for inner products

We introduce the notion of quadratic hull of a linear code, and give some of its properties. We then show that any symmetric bilinear multiplication algorithm for a finite-dimensional algebra over a field can be obtained by…

New quaternary Plotkin constructions are given and are used to obtain new families of quaternary codes. The parameters of the obtained codes, such as the length, the dimension and the minimum distance are studied. Using these constructions…

The search for multivariate quadrature rules of minimal size with a specified polynomial accuracy has been the topic of many years of research. Finding such a rule allows accurate integration of moments, which play a central role in many…

A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two characteristic boundary layers. Exponential splines are used…

We consider bilinear oscillatory integrals, i.e. pseudo-product operators whose symbol involves an oscillating factor. Lebesgue space inequalities are established, which give decay as the oscillation becomes stronger ; this extends the…

We explicitly construct a class of multivariate generalized hypergeometric series which is conjectured in our previous paper [Alkalaev & Mandrygin 2025] to calculate multipoint one-loop parametric conformal integrals in $D$ dimensions. Our…

Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among…

We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…

Bilevel programming problems frequently arise in real-world applications across various fields, including transportation, economics, energy markets and healthcare. These problems have been proven to be NP-hard even in the simplest form with…

In this paper we propose an algorithm for the formation of matrices of isogeometric Galerkin methods. The algorithm is based on three ideas. The first is that we perform the external loop over the rows of the matrix. The second is that we…

Two recently introduced quadrature schemes for weakly singular integrals [Calabr\`o et al. J. Comput. Appl. Math. 2018] are investigated in the context of boundary integral equations arising in the isogeometric formulation of Galerkin…

Let A be a finite set of integers. For a polynomial f(x_1,...,x_n) with integer coefficients, let f(A) = {f(a_1,...,a_n) : a_1,...,a_n \in A}. In this paper it is proved that for every pair of normalized binary linear forms f(x,y)=u_1x+v_1y…

Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We begin a study of the basic properties of polyhedral…

We discuss multiplicative properties of the binary quadratic form $a x^2 + b x y + c y^2$ by considering a ring of matrices which is closed under a triple product. We prove that the ring forms a ternary algebra in the sense of Hestenes, and…

We introduce a linear algebraic object called a bidiagonal triple. A bidiagonal triple consists of three diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the…

In this paper we study dual bases functions in subspaces. These are bases which are dual to functionals on larger linear space. Our goal is construct and derive properties of certain bases obtained from the construction, with primary focus…

Given a space X we study the topology of the space of embeddings of X into $\mathbb{R}^d$ through the combinatorics of triangulations of X. We give a simple combinatorial formula for upper bounds for the largest dimension of a sphere that…

In this article, we study properties of multilinear Fourier integral operators on weighted modulation spaces. In particular, using the theory of Gabor frames, we study boundedness of multilinear Fourier integral operators on products of…

This thesis is concerned with the theory of invariant bilinear differential pairings on parabolic geometries. It introduces the concept formally with the help of the jet bundle formalism and provides a detailed analysis. More precisely,…

In this note we recast the Geronimus transformation in the framework of polynomials orthogonal with respect to symmetric bilinear forms. We also show that the double Geronimus transformations lead to non-diagonal Sobolev type inner…