Some refinements of Dade's projective conjecture

In this paper a further refinement of Dade's projective conjecture, due to Boltje, is presented. This new statement includes ideas first published by Isaacs and Navarro as well as the recent contractibility version of Alperin's conjecture introduced by Boltje. Leaning heavily on the work of Robinson, weaker forms of the conjecture are proved in the case of p-solvable groups.     

Group algebras of Kleinian type and groups of units

The algebras of Kleinian type are finite-dimensional semisimple rational algebras A such that the group of units of an order in A is commensurable with a direct product of Kleinian groups. We classify the Schur algebras of Kleinian type and the group algebras of Kleinian type. As an application, we characterize the group rings RG, with R an order in a number field and G a finite group, such that the group of units of RG is virtually a direct product of free-by-free groups.     

Reformulation of the support set selection problem in the logical analysis of data

The paper is concerned with the problem of binary classification of data records, given an already classified training set of records. Among the various approaches to the problem, the methodology of the logical analysis of data (LAD) is considered. Such approach is based on discrete mathematics, with special emphasis on Boolean functions. With respect to the standard LAD procedure, enhancements based on probability considerations are presented. In particular, the problem of the selection of the optimal support set is formulated as a weighted set covering problem. Testable statistical hypothesis are used. Accuracy of the modified LAD procedure is compared to that of the standard LAD procedure on datasets of the UCI repository. Encouraging results are obtained and discussed.     

Assessment of filtered gas–solid momentum transfer models via a linear wave propagation speed test

The propagation speeds of linear waves in gas–solid suspensions depend strongly on the solids volume fraction and the wave frequency. The latter is due to gas–solid momentum transfer and allows a simple test on filtered gas–solid momentum transfer models. Such models may predict linear wave propagation speeds different from those obtained with the non-filtered model at wave frequencies higher than the filter frequency, but not at wave frequencies lower than the filter frequency.     

Commutators of singular integrals on spaces of homogeneous type

In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on L ^p (w) when w belongs to the Muckenhoupt’s class A _p , p > 1. In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature.     

STRONG LAW OF LARGE NUMBERS AND ASYMPTOTIC EQUIPARTITION PROPERTY FOR NONSYMMETRIC MARKOV CHAIN FIELDS ON CAYLEY TREES

Some strong laws of large numbers for the frequcncies of occurrence of states and ordered couples of states for nonsymmetric Markov chain fields(NSMC)on Cayley trees are studied.In the proof,a new technique for the study of strong liinit theorems of Markov chains is extended to the case of Markov chain fields.The asymptotic equiparti- tion properties with almost everywhere(a.e.)convergence for NSMC on Cayley trees are obtained.     

INITIAL VALUE TECHNIQUES FOR THE HELMHOLTZ AND MAXWELL EQUATIONS

We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging.     

Discrete-time GI/Geo/1 queue with multiple working vacations

Consider the discrete time GI/Geo/1 queue with working vacations under EAS and LAS schemes. The server takes the original work at the lower rate rather than completely stopping during the vacation period. Using the matrix-geometric solution method, we obtain the steady-state distribution of the number of customers in the system and present the stochastic decomposition property of the queue length. Furthermore, we find and verify the closed property of conditional probability for negative binomial distributions. Using such property, we obtain the specific expression for the steady-state distribution of the waiting time and explain its two conditional stochastic decomposition structures. Finally, two special models are presented.      

Numerical simulation of critical dependences for symmetric two-layered Josephson junctions

Partial critical dependences of the form current-magnetic field in a two-layered symmetric Josephson junction are modeled. A numerical experiment shows that, for the zero interaction coefficient between the layers of the junction, jumps of the critical currents corresponding to different distributions of the magnetic fluxes in the layers may appear on the critical curves. This fact allows a mathematical interpretation of the results of some recent experimental results for two-layered junctions as a consequence of discontinuities of partial critical curves.     

On the Equivalence of Multiparameter Gaussian Processes

Our purpose is to characterize the multiparameter Gaussian processes, that is Gaussian sheets, that are equivalent in law to the Brownian sheet and to the fractional Brownian sheet. We survey multiparameter analogues of the Hitsuda, Girsanov and Shepp representations. As an application, we study a special type of stochastic equation with linear noise.