The differential systems satisfied by orthogonal polynomials with arbitrary semiclassical measures supported on contours in the complex plane are derived, as well as the compatible systems of deformation equations obtained from varying such measures. These are shown to preserve the generalized monodromy of the associated rank-2 rational covariant derivative operators. The corresponding matrix m...

In this note we study generalizations in many directions of the contraction procedure for Lie algebras introduced by Saletan [Sa]. We consider products of arbitrary nature, not necessarily Lie brackets, and we generalize to infinite dimension, considering a modification of the approach by Nijenhuis tensors to bilinear operations on sections of finite-dimensional vector bundles. We apply our gen...

In this paper we show that a (non-abelian) free pro-p group cannot be obtained as a closed subgroup of GLn(F ), where F is a nonarchimedean local field and n is arbitrary. Using a theorem of E. I. Zel’manov we deduce some group theoretic properties of linear pro-p groups over a local field. Our main tool is a recent theorem by Pink characterizing compact subgroups of GLn(F ). ∗Partially support...

Multiwavelet is attracting more and more attention for its good properties such as orthogonality, symmetry, compactly supported, high vanishing moment and balance contrast with the traditional wavelet. These properties, along with optimum time-frequency resolution (OPTFR) are all very important in image processing. Multifilter banks having all properties of symmetry, balancing, optimum time-fre...

We enumerate the edges in the Hasse diagram of several lattices arising in the combinatorial context of lattice paths. Specifically, we consider the case of Dyck, Grand Dyck, Motzkin, Grand Motzkin, Schröder and Grand Schröder lattices. Finally, we give a general formula for the number of edges in an arbitrary Young lattice (which can be interpreted in a natural way as a lattice of paths). 1 Pa...

We explore the gravitational influence of pressure supported stellar systems on the internal density distribution of a gaseous environment. We conclude that compact massive star clusters with masses & 10 M⊙ act as cloud condensation nuclei and are able to accrete gas recurrently from a warm interstellar medium which may cause further star formation events and account for multiple stellar popula...

We calculate the spin density matrix of top quark pairs for the reaction e+e− → tt̄X to order αs. As an application we show next-to-leading order results for a variety of spin observables for the tt̄ system. These include the top quark and antiquark polarizations and tt̄ spin-spin correlations as a function of the center-of-mass energy and of the top quark scattering angle for arbitrary longitudin...

We consider the following activation process in undirected graphs: a vertex is active either if it belongs to a set of initially activated vertices or if at some point it has at least 2 active neighbors. A contagious set is a set whose activation results with the entire graph being active. Given a graph G, let m(G, 2) be the minimal size of a contagious set. We consider the binomial random grap...

We provide a computationally efficient black-box reduction from mechanism design to algorithm design in very general settings. Specifically, we give an approximation-preserving reduction from truthfully maximizing any objective under arbitrary feasibility constraints with arbitrary bidder types to (not necessarily truthfully) maximizing the same objective plus virtual welfare (under the same fe...