相关论文: A New Form of Williamson's Product Theorem
We consider the question of the boundedness of matrix products $A_{n}B_{n}\cdots A_{1}B_{1}$ with factors from two sets of matrices, $A_{i}\in\mathscr{A}$ and $B_{i}\in\mathscr{B}$, due to an appropriate choice of matrices $\{B_{i}\}$. It…
We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…
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…
We present a general formulation of the matrix product ansatz for exactly integrable chains on periodic lattices. This new formulation extends the matrix product ansatz present on our previous articles (F. C. Alcaraz and M. J. Lazo J. Phys.…
We study the recurrence of the product of n functions, each of which satisfies the same recurrence relation.
We investigate the Mal'tsev product $\mathcal{V} \circ \mathcal{W}$ of two varieties $\mathcal{V}$ and $\mathcal{W}$ of the same similarity type. Such a product is usually a quasivariety but not necessarily a variety. We give an equational…
A systematic theory is introduced for calculating the derivatives of quaternion matrix function with respect to quaternion matrix variables. The proposed methodology is equipped with the matrix product rule and chain rule and it is able to…
We carry on the investigation initiated in [15] : we describe new shuffle products coming from some special functions and group them, along with other products encountered in the literature, in a class of products, which we name…
We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.
Let $\mathbf{k}$ denote the totally ordered set (or chain) on $k$ elements. The product $\mathbf{k}^t=\mathbf{k}\times\cdots\times\mathbf{k}$ is a poset called a grid. This paper discusses several loosely related results on the Ramsey…
There is a famous multiplication table of types of tensor product of two von Neumann algebras. We filled out the multiplication table of graded tensor product of two graded von Neumann algebras in special cases.
In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…
We define and study a lift of the Boardman-Vogt tensor product of operads to bimodules over operads.
We give an elementary proof of low rank cases of the conjecture that the tensor product of two semistable Euclidean lattices is again semistable.
New results on comparison of distributions of Gaussian quadratic forms are presented
In this paper, we prove a theorem which adds a new member to the famous G\"oellnitz-Gordon identities. We construct a "new system of recurrence formulas" in order to prove it.
Fillmore Theorem says that if $A$ is a nonscalar matrix of order $n$ over a field $\mathbb{F}$ and $\gamma_1,\ldots,\gamma_n\in \mathbb{F}$ are such that $\gamma_1+\cdots+\gamma_n=\text{tr} \, A$, then there is a matrix $B$ similar to $A$…
We introduce an elementary argument to the theory of distribution of sequences modulo one.
By means of a modified hypervirial theorem we derive simple expressions for the integrals of products of Airy functions. Present results contain earlier ones as particular cases.
We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…