Related papers: A note on the Zassenhaus product formula

We prove new interaction Morawetz type (correlation) estimates in one and two dimensions. In dimension two the estimate corresponds to the nonlinear diagonal analogue of Bourgain's bilinear refinement of Strichartz. For the 2d case we…

For a $p$-permutation equivalence between two block algebras of finite groups, we introduce new square diagrams that link the $p$-permutation equivalence via the Brauer construction to local equivalences between stabilizers of corresponding…

Higher order terms in the effective action of noncommutative gauge theories exhibit generalizations of the *-product (e.g. *' and *-3). These terms do not manifestly respect the noncommutative gauge invariance of the tree level action. In…

We review some of our results from the theory of product systems of Hilbert modules. We explain that the product systems obtained from a CP-semigroup in a paper by Bhat and Skeide and in a paper by Muhly and Solel are commutants of each…

One-instanton predictions for the prepotential are obtained from the Seiberg-Witten curve for the Coulomb branch of N=2 supersymmetric gauge theory for the product group \prod_{n=1}^{m} SU(N_n) with a massless matter hypermultiplet in the…

We compute the number of ways a given permutation can be written as a product of exactly $k$ transpositions. We express this number as a linear combination of explicit geometric sequences, with coefficients which can be computed in many…

We give a short proof of the inner product conjecture for the symmetric Macdonald polynomials of type $A_{n-1}$. As a special case, the corresponding constant term conjecture is also proved.

We prove that, for all positive integers $n_1, \ldots, n_m$, $n_{m+1}=n_1$, and non-negative integers $j$ and $r$ with $j\leqslant m$, the following two expressions \begin{align*} &\frac{1}{[n_1+n_m+1]}{n_1+n_{m}\brack…

We give a simple proof for the reciprocity formulas of character Dedekind sums associated with two primitive characters, whose modulus need not to be same, by utilizing the character analogue of the Euler-MacLaurin summation formula.…

Let $G$ be a multiplicative finite group and $S=a_1\cdot\ldots\cdot a_k$ a sequence over $G$. We call $S$ a product-one sequence if $1=\prod_{i=1}^ka_{\tau(i)}$ holds for some permutation $\tau$ of $\{1,\ldots,k\}$. The small Davenport…

The Lie-Trotter formula $e^{\hat{A}+\hat{B}} = \lim_{N\to \infty} (e^{\hat{A}/N} e^{\hat{B}/N})^N$ is of great utility in a variety of quantum problems ranging from the theory of path integrals and Monte Carlo methods in theoretical…

A product state of a composite quantum system AB is customarily interpreted physically to mean subsystem A has property A1 and subsystem B has property B1. But this interpretation contradicts both the theory and observed outcomes of…

A detailed proof of a recent result on explicit formulae for the product moments $E \left \{ X_1^{a_1} X_2^{a_2} \cdots X_n^{a_n}\right \}$ of multivariate Gaussian random variables is provided in this note.

A simple application of the semipositivity.

Given two sets of positive integers $A$ and $B$, let $AB := \{ab : a \in A,\, b \in B\}$ be their product set and put $A^k := A \cdots A$ ($k$ times $A$) for any positive integer $k$. Moreover, for every positive integer $n$ and every…

Given n quaternions we investigate the extent of non-commutativity of their multiple products, commutators and exponential products.

Let $D$ be an open disk of radius $\le 1$ in $\mathbb C$, and let $(\epsilon_n)$ be a sequence of $\pm 1$. We prove that for every analytic function $f: D \to \mathbb C$ without zeros in $D$, there exists a unique sequence $(\alpha_n)$ of…

Let $\mathbb{Z}_n$ be the ring of residue classes modulo $n$, and let $\mathbb{Z}_n^{\ast}$ be the group of its units. 90 years ago, Brauer obtained a formula for the number of representations of $c\in \mathbb{Z}_n$ as the sum of $k$ units.…

Let $A$ and $B$ be finite subsets of $\mathbb{C}$ such that $|B|=C|A|$. We show the following variant of the sum product phenomenon: If $|AB|<\alpha|A|$ and $\alpha \ll \log |A|$, then $|kA+lB|\gg |A|^k|B|^l$. This is an application of a…

We consider a sequence of composite bivariate Bernstein operators and the cubature formula associated with them. The upper bounds for the remainder term of the cubature formula are described in terms of moduli of continuity of order two.…