On totally *-paranormal operators

In this paper we study some properties of a totally *-paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally *-paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally *-paranormal operators through the local spectral theory. Finally, we show that every totally *-paranormal operator satisfies an analogue of the single valued extension property for W ²(D, H) and some of totally *-paranormal operators have scalar extensions.     

Linear combinations of heuristics for examination timetabling

Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic to measure the difficulty of a vertex. Relatively less attention has been paid to select an appropriate colour for the selected vertex. Some recent work has demonstrated the superiority of combining a number of different heuristics for vertex and colour selection. In this paper, we explore this direction and introduce a new strategy of using linear combinations of heuristics for weighted graphs which model the timetabling problems under consideration. The weights of the heuristic combinations define specific roles that each simple heuristic contributes to the process of ordering vertices. We include specific explanations for the design of our strategy and present the experimental results on a set of benchmark real world examination timetabling problem instances. New best results for several instances have been obtained using this method when compared with other constructive methods applied to this benchmark dataset.     

The hit problem for the Dickson algebra

Let the mod 2 Steenrod algebra, , and the general linear group, , act on with in the usual manner. We prove the conjecture of the first-named author in Spherical classes and the algebraic transfer, (Trans. Amer. Math Soc. 349 (1997), 3893-3910) stating that every element of positive degree in the Dickson algebra is -decomposable in for arbitrary 2$">. This conjecture was shown to be equivalent to a weak algebraic version of the classical conjecture on spherical classes, which states that the only spherical classes in are the elements of Hopf invariant one and those of Kervaire invariant one.

     

Students' Retention of Mathematical Knowledge and Skills in Differential Equations

This study investigates students' retention of mathematical knowledge and skills in two differential equations classes. Posttests and delayed posttests after 1 year were administered to students in inquiry‐oriented and traditional classes. The results show that students in the inquiry‐oriented class retained conceptual knowledge, as seen by their performance on modeling problems, and retained equal proficiency in procedural problems, when compared with students in the traditionally taught classes. The results of this study add additional support to the claim that teaching for conceptual understanding can lead to longer retention of mathematical knowledge.     

Variational analysis of extended generalized equations via coderivative calculus in Asplund spaces

This paper is devoted to the development of variational analysis and generalized differentiation in the framework of Asplund spaces. We mainly concern the study of a special class of set-valued mapping given in the form

where both F and Q are set-valued mappings between Asplund spaces. Models of this type are associated with solutions maps to the so-called (extended) generalized equations and play a significant role in many aspects of variational analysis and its applications to optimization, stability, control theory, etc. In this paper we conduct a local variational analysis of such extended solution maps S and their remarkable specifications based on dual-space generalized differential constructions of the coderivative type. The major part of our analysis revolves around coderivative calculus largely developed and implemented in this paper and then applied to establishing verifiable conditions for robust Lipschitzian stability of extended generalized equations and related objects.     

A Multisensor Deconvolution Problem

Meisters and Peterson gave an equivalent condition under which the multisensor deconvolution problem has a solution when there are two convolvers, each the characteristic function of an interval. In this article we find additional conditions under which the deconvolution problem for multiple characteristic functions is solvable. We extend the result to the space of Gevrey distributions and prove that every linear operator S, fromthe space of Gevrey functions with compact support onto itself, which commutes with translations can be represented as convolution with a unique Gevrey distribution T of compact support. Finally, we find explicit formula for deconvolvers when the convolvers satisfy weaker conditions than the equivalence conditions using nonperiodic sampling method.     

Spectral Analysis for HSS Preconditioners

In this paper,we are interested in HSS preconditioners for saddle point lin- ear systems with a nonzero(2,2)-th block.We study an approximation of the spectra of HSS preconditioned matrices and use these results to illustrate and explain the spectra obtained from numerical examples,where the previous spectral analysis of HSS precon- ditioned matrices does not cover.     

$$I_0$$ and combinatorics at $$\lambda ^+$$λ+

We investigate the compatibility of \(I_0\) with various combinatorial principles at \(\lambda ^+\), which include the existence of \(\lambda ^+\)-Aronszajn trees, square principles at \(\lambda \), the existence of good scales at \(\lambda \), stationary reflections for subsets of \(\lambda ^{+}\), diamond principles at \(\lambda \) and the singular cardinal hypothesis at \(\lambda \). We also discuss whether these principles can hold in \(L(V_{\lambda +1})\).