Mutually permutable subgroups and group classes

We consider the product AB of two finite mutually permutable subgroups A, B and find some subnormal subgroups of the product. This leads to local and otherwise generalized statements about products of supersolvable groups.Received: 19 May 2004     

Exchangeable claim sizes in a compound Poisson‐type process

When dealing with risk models the typical assumption of independence among claim size distributions is not always satisfied. Here we consider the case when the claim sizes are exchangeable and study the implications when constructing aggregated claims through compound Poisson‐type processes. In particular, exchangeability is achieved through conditional independence, using parametric and nonparametric measures for the conditioning distribution. Bayes' theorem is employed to ensure an arbitrary but fixed marginal distribution for the claim sizes. A full Bayesian analysis of the proposed model is illustrated with a panel‐type data set coming from a Medical Expenditure Panel Survey (MEPS). Copyright © 2009 John Wiley & Sons, Ltd.     

Pd deposits on Ni(111): a theoretical study

The ASED-MO method has been used to gather electronic and energetic information on Pd deposits on Ni(111) and Pd atom inclusion in the first Ni layer since these model catalysts exhibit a striking catalytic efficiency towards butadiene hydrogenation. The electronic structure of Pd atoms is strongly altered compared with pure Pd. A Pd(4d)→Pd(5s) electronic transfer occurs in the case of the deposit when a slight similar transfer and a charge transfer from Pd to surrounding Ni takes place in the case of the inclusion. Those results are consistent with XPS experimental data. A low density of states, near the Fermi level, is also observed. The optimal geometrical situation for Pd deposits is found to be 2D-aggregates (in pseudoepitaxy or pseudomorphy with the underlying Ni surface, depending on the aggregate size). Small aggregates (part of the first Ni layer) are found to be the most stable in the case of a Pd inclusion in the Ni with a Pd---Pd distance of 2.64 Å, in agreement with available EXAFS experimental data.     

On the imaginary simple roots of the Borcherds algebra II9,1

In a recent paper [O. Bärwald, R.W. Gebert, M. Günaydin and H. Nicolai, preprint KCL-MTH-97-22, IASSNS-HEP-97/20, PSU-TH-178, AEI-029, hep-th/9703084, to appear in Commun. Math. Phys.] it was conjectured that the imaginary simple roots of the Borcherds algebra _II9,1 at level 1 are its only ones. We here propose an independent test of this conjecture, establishing its validity for all roots of norm − 8. However, the conjecture fails for roots of norm −10 and beyond, as we show by computing the simple multiplicities down to norm −24, which turn out to be remarkably small in comparison with the corresponding E₁₀ multiplicities. Our derivation is based on a modified denominator formula combining the denominator formulas for E₁₀ and _II9,1, and provides an efficient method for determining the imaginary simple roots. In addition, we compute the E₁₀ multiplicities of all roots up to height 231, including levels up to l = 6 and norms −42.     

On the well‐posedness of a mathematical model of quorum‐sensing in patchy biofilm communities

We analyze a system of reaction–diffusion equations that models quorum‐sensing in a growing biofilm. The model comprises two nonlinear diffusion effects: a porous medium‐type degeneracy and super diffusion. We prove the well‐posedness of the model. In particular, we present for the first time a uniqueness result for this type of problem. Moreover, we illustrate the behavior of model solutions in numerical simulations. Copyright © 2011 John Wiley & Sons, Ltd.     

Shift-coupling in continuous time

Summary The result linking shift-coupling to time-average total variation convergence and to the invariant -field is extended to continuous time and an analogous result established linking -couplings to smooth total variation convergence and to a smooth tail -field. Shift- and -coupling inequalities are presented.     

Spline collocation methods for nonlinear Volterra integral equations with unknown delay

In this paper we introduce and study polynomial spline collocation methods for systems of Volterra integral equations with unknown lower integral limit arising in mathematical economics. Their discretization leads to implicit Runge-Kutta-type methods. The global convergence and local superconvergence properties of these methods are proved, and the theory is illustrated by a numerical example arising in the application of such equations in certain mathematical models of liquidation.     

Spectral methods for pantograph-type differential and integral equations with multiple delays

We analyze the convergence properties of the spectral method when used to approximate smooth solutions of delay differential or integral equations with two or more vanishing delays. It is shown that for the pantograph-type functional equations the spectral methods yield the familiar exponential order of convergence. Various numerical examples are used to illustrate these results.      

Blow-up behavior of Hammerstein-type delay Volterra integral equations

We consider the blow-up behavior of Hammerstein-type delay Volterra integral equations (DVIEs). Two types of delays, i.e., vanishing delay (pantograph delay) and non-vanishing delay (constant delay), are considered. With the same assumptions of Volterra integral equations (VIEs), in a similar technology to VIEs, the blow-up conditions of the two types of DVIEs are given. The blow-up behaviors of DVIEs with non-vanishing delay vary with different initial functions and the length of the lag, while DVIEs with pantograph delay own the same blow-up behavior of VIEs. Some examples and applications to delay differential equations illustrate this influence.     

Splines (with optimal knots) are better

Let S^M _k be the Polynominal splines of degree n-1, and with K segments. If f∈ C ⁿ [a,b],then the distance in the L^p-norm form(0< p ≦ ∞)of from S ^M _k is boundedby M/K ⁿ , with a much smaller M than in similar estimates for other processes of approximation.