相关论文: A New Form of Williamson's Product Theorem

Symplectic eigenvalues are conventionally defined for symmetric positive-definite matrices via Williamson's diagonal form. Many properties of standard eigenvalues, including the trace minimization theorem, are extended to the case of…

In the present paper we prove Liouville-type theorems: non-existence theorems for some complete Riemannian almost product manifolds and special mappings of complete Riemannian manifolds which generalize similar results for compact…

A brief introduction is given to the topic of Smith normal forms of incidence matrices. A general discussion of techniques is illustrated by some classical examples. Some recent advances are described and the limits of our current…

We prove a discretized sum-product theorem for representations of Lie groups whose Jordan-H\"older decomposition does not contain the trivial representation. This expansion result is used to derive a product theorem in perfect Lie groups.

We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.

The notion of the Moore-Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate this theory by producing a few characterizations of different generalized inverses of tensors. A…

The authors continue a series of articles studying certain unitary representations of the Richard Thompson groups $F,T,V$ called Pythagorean. They all extend to the Cuntz algebra $\mathcal{O}$ and conversely all representations of…

It was shown recently that Birkhoff's theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of the Birkhoff theorem for…

Williamson's theorem states that if $A$ is a $2n \times 2n$ real symmetric positive definite matrix then there exists a $2n \times 2n$ real symplectic matrix $M$ such that $M^T A M=D \oplus D$, where $D$ is an $n \times n$ diagonal matrix…

In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…

We introduce sequential warped product submanifolds of Kaehler manifolds, provide examples and establish Chen's inequality for such submanifolds. The equality case is also studied. Moreover, by inspiring Lawson and Simons's integral…

In this paper we prove two inequalities relating the warping function to various curvature terms, for warped products isometrically immersed in Riemannian manifolds. This extends work of B. Y. Chen for the case of immersions into space…

We consider arbitrary splits of field operators into two parts, and use the corresponding definition of normal ordering introduced by Evans and Steer. In this case the normal ordered products and contractions have none of the special…

We investigate the interaction between the product of invariant types and domination-equivalence. We present a theory where the latter is not a congruence with respect to the former, provide sufficient conditions for it to be, and study the…

We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.

In this paper we show how to find a closed form solution for third order difference operators in terms of solutions of second order operators. This work is an extension of previous results on finding closed form solutions of recurrence…

The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor…

We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…

We prove a new T(1) theorem for multiparameter singular integrals

New version, including a variant of Quillen's proof of the Solomon-Tits theorem.