Integrality of hook ratios

We study integral ratios of hook products of quotient partitions. This question is motivated by an analogous question in number theory concerning integral factorial ratios. We prove an analogue of a theorem of Landau that already applied in the factorial case. Under the additional condition that the ratio has one more factor on the denominator than the numerator, we provide a complete classification. Ultimately this relies on Kneser's theorem in additive combinatorics.Comment: 13 pages, 3 figures Keywords: partitions, hook products, Kneser's theorem, McKay numbers, Beurling-Nyman criterio

A note on moments of derivatives of characteristic polynomials

We present a simple technique to compute moments of derivatives of unitary characteristic polynomials. The first part of the technique relies on an idea of Bump and Gamburd: it uses orthonormality of Schur functions over unitary groups to compute matrix averages of characteristic polynomials. In order to consider derivatives of those polynomials, we here need the added strength of the Generalized Binomial Theorem of Okounkov and Olshanski. This result is very natural as it provides coefficients for the Taylor expansions of Schur functions, in terms of shifted Schur functions. The answer is finally given as a sum over partitions of functions of the contents. One can also obtain alternative expressions involving hypergeometric functions of matrix arguments.Comment: 12 page

Application of Hierarchical Matrix Techniques To The Homogenization of Composite Materials

In this paper, we study numerical homogenization methods based on integral equations. Our work is motivated by materials such as concrete, modeled as composites structured as randomly distributed inclusions imbedded in a matrix. We investigate two integral reformulations of the corrector problem to be solved, namely the equivalent inclusion method based on the Lippmann-Schwinger equation, and a method based on boundary integral equations. The fully populated matrices obtained by the discretization of the integral operators are successfully dealt with using the H-matrix format

An invariance principle for weakly dependent stationary general models

The aim of this article is to refine a weak invariance principle for stationary sequences given by Doukhan & Louhichi (1999). Since our conditions are not causal our assumptions need to be stronger than the mixing and causal $\theta$-weak dependence assumptions used in Dedecker & Doukhan (2003). Here, if moments of order $>2$ exist, a weak invariance principle and convergence rates in the CLT are obtained; Doukhan & Louhichi (1999) assumed the existence of moments with order $>4$. Besides the previously used $\eta$- and $\kappa$-weak dependence conditions, we introduce a weaker one, $\lambda$, which fits the Bernoulli shifts with dependent inputs.Comment: 30 page

Electrocarboxylation of chloroacetonitrile mediated by electrogenerated cobalt(I) phenanthroline

The electrocarboxylation of chloroacetonitrilemediated by [Co(II)(phen)3]2+ has been investigated. Cyclic voltammetry studies of [Co(II)(phen)3]2+ have shown that [Co(I)(phen)3]+, an 18 electron complex, activates chloroacetonitrile by an oxidative addition through the loss of a phenanthroline ligand to give [RCo(III)(phen)2Cl]+. The unstable one-electron-reduced complex underwent Co–C bond cleavage. In carbon dioxide saturated solution, CO2 insertion proceeds after reduction of the alkylcobalt complex. A catalytic current is observed which corresponds to the electrocarboxylation of chloroacetonitrile into cyanoacetic acid. Electrolyses confirmed the process and gave faradic yield of 62% in cyanoacetic acid at potentials that are about 0.3 V less cathodic than the one required for Ni(salen)