Related papers: A New Form of Williamson's Product Theorem
We prove that the system of Gromov-Witten invariants of the product of two varieties is equal to the tensor product of the systems of Gromov-Witten invariants of the two factors.
A construction that generates Williamson matrices of order $2n$ from Williamson matrices of odd order $n$ is presented. The construction is completely constructive and only uses three simple sequence operations.
In this paper, we study the recently defined notion of the inverse along an element. An existence criterion for the inverse along a product is given in a ring. As applications, we present the equivalent conditions for the existence and…
Williamson's theorem is well known for symmetric matrices. In this paper, we state and re-derive some of the cases of Williamson's theorem for symmetric positive-semi definite matrices and symmetric matrices having negative index 1, due to…
This note simplifies the proof of a recent result on the oscillation of the prime product in Martens Theorem, and provides a quantitative expression for the error term. In addition, the corresponding oscillation results for the finite sums…
Wilson's Theorem states that the product of all nonzero elements of a finite field ${\mathbb F}_q$ is $-1$. In this article, we define some natural subsets $S \subset {\mathbb F}_q^\times$ and find formulas for the product of the elements…
We present a new kind of normalization theorem: linearization theorem for skew products. The normal form is a skew product again, with the fiber maps linear. It appears, that even in the smooth case, the conjugacy is only H\"older…
A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.
In this paper, we first give an expression for the Moore-Penrose inverse of the product of two tensors via the Einstein product. We then introduce a new generalized inverse of a tensor called product Moore-Penrose inverse. A necessary and…
The purpose of this short article is to prove a product formula relating the log Gromov-Witten invariants of $V \times W$ with those of $V$ and $W$ in the case the log structure on $V$ is trivial.
We provide conditions under which an isometric immersion of a (warped) product of manifolds into a space form must be a (warped) product of isometric immersions.
We introduce the operation of forming the tensor product in the theory of analytic Frobenius manifolds. Building on the results for formal Frobenius manifolds which we extend to the additional structures of Euler fields and flat identities,…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
We make use of product integrals to provide an unambiguous mathematical representation of Wilson line and Wilson loop operators. Then, drawing upon various properties of product integrals, we discuss such properties of these operators as…
We show that there are four possibilities for the product of all elements in the multiplicative group of a quotient of the ring of integers in a number field, and give precise conditions for each of the possibilities to occur. This…
Two results on product of compact filters are shown to be the common principle behind a surprisingly large number of theorems.
I provide an alternate and self-contained proof of Botha's theorem on products of idempotent and square-zero matrices where the product contains two square-zero factors, and provide a conclusive characterisation of products of singular…
We show that two tensor permutation matrices permutate tensor product of rectangle matrices. Some examples, in the particular case of tensor commutation matrices, for studying some linear matrix equations are given.
We present a simple proof of the factorization of (complex) symmetric matrices into a product of a square matrix and its transpose, and discuss its application in establishing a uniqueness property of certain antilinear operators.
We study Virasoro constraints for Gromov-Witten theory of a product variety when one factor has semi-simple quantum cohomology.