in this paper we illustrate recent results about factorizations of finite groups into conjugate subgroups. the illustrated results are joint works with john cannon, dan levy, attila mar'oti and iulian i. simion.

We tested predictions derived from the gaze cascade model of preference decision making (Shimojo, Simion, Shimojo, & Scheier, 2003; Simion & Shimojo, 2006, 2007). In each trial, participants' eye movements were monitored while they performed an eight-alternative decision task in which four of the items in the array were preexposed prior to the trial. Replicating previous findings, we found a ga...

We propose two iterative procedures for the computation of the stabilizing solution of coupled generalized algebraic Riccati equations with indefinite quadratic term such equations appear in the solution of stochastic H∞ control problems. The method used in this paper is a generalization of the defect correction method introduced in [17] and extends to this framework the algorithm derived in [1...

Simion had a unimodality conjecture concerning the number of lattice paths in a rectangular grid with the Ferrers diagram of a partition removed. Hildebrand recently showed the stronger result that these numbers are log concave. Here we present a simple proof of Hildebrand’s result.

We show how lattice paths and the re ection principle can be used to give easy proofs of unimodality results. In particular, we give a \one-line" combinatorial proof of the unimodality of the binomial coe cients. Other examples include products of binomial coe cients, polynomials related to the Legendre polynomials, and a result connected to a conjecture of Simion.

This paper describes some computer-based activities to bring the study of charged particle optics to undergraduate students, to be performed as a part of a one-semester accelerator-based experimental course. The computational simulations were carried out using the commercially available SIMION program. The performance parameters, such as the focal length and P–Q curves are obtained. The three-e...