Multigraded Hilbert Series of noncommutative modules

In this paper, we propose methods for computing the Hilbert series of multigraded right modules over the free associative algebra. In particular, we compute such series for noncommutative multigraded algebras. Using results from the theory of regular languages, we provide conditions when the methods are effective and hence the sum of the Hilbert series is a rational function. Moreover, a characterization of finite-dimensional algebras is obtained in terms of the nilpotency of a key matrix involved in the computations. Using this result, efficient variants of the methods are also developed for the computation of Hilbert series of truncated infinite-dimensional algebras whose (non-truncated) Hilbert series may not be rational functions. We consider some applications of the computation of multigraded Hilbert series to algebras that are invariant under the action of the general linear group. In fact, in this case such series are symmetric functions which can be decomposed in terms of Schur functions. Finally, we present an efficient and complete implementation of (standard) graded and multigraded Hilbert series that has been developed in the kernel of the computer algebra system Singular. A large set of tests provides a comprehensive experimentation for the proposed algorithms and their implementations.Comment: 28 pages, to appear in Journal of Algebr

Kinetics of Competing Reactions of N-aryl-4-chloro-1,8-naphthalimides with Primary Amines

Color poster with text, diagrams, tables, and graphs.This study presented the mechanistic implications of the kinetics of competing reactions of N-aryl-4-chloro-1,8-naphthalimides with primary amines.University of Wisconsin--Eau Claire Office of Research and Sponsored Programs; Petroleum Research Fund

Coronavirus mRNA synthesis: identification of novel transcription initiation signals which are differentially regulated by different leader sequences.

The mRNA synthesis of mouse hepatitis virus (MHV) has been proposed to be the result of interaction between the leader RNA and the intergenic sites. Previously, we have identified a transcription initiation site (for mRNA 2-1), which is more efficiently transcribed by viruses containing two copies of UCUAA sequence in the leader RNA than by those with three copies. In this study, we have identified several sites which are regulated in the opposite way, namely, they are efficiently transcribed by the leader RNA with three UCUAA copies but not by those with two copies. These sites were characterized by primer extension and amplification by polymerase chain reaction. One of these sites is in the gene 3 region of a recombinant virus between A59 and JHM strains of MHV. Another is in the gene 2 region of MHV-1 strain. Both of these sites have a sequence similar to but different from the consensus transcription initiation signal (UCUAAUCUAUC and UUUAAUCUU, as opposed to UCUAAAC). These two novel intergenic sequences are not present in the genome of the JHM strain, consistent with the absence of these mRNAs in the JHM-infected cells. The discovery of this type of transcription initiation site provides additional evidence for the importance of the leader RNA in the transcription initiation of MHV mRNAs

Introduction

The costs and benefits of European Imperialism from the conquest of Ceuta, 1415, to the Treaty of Lusaka, 1974.Twelfth International Economic History Congress. Madrid, 1998.Patrick K. O'Brien and Leandro Prados de la Escosura (eds.)Editada en la Fundación Empresa PúblicaPatrick K. O'Brien and Leandro Prados de la Escosura. The Costs and Benefits for Europeans from their Empires Overseas.Publicad

Electronic structure of the ferromagnetic superconductor UCoGe from first principles

The superconductor UCoGe is analyzed with electronic structure calculations using Linearized Augmented Plane Wave method based on Density Functional Theory. Ferromagnetic and antiferromagnetic calculations with and without correlations (via LDA+U) were done. In this compound the Fermi level is situated in a region where the main contribution to DOS comes from the U-5f orbital. The magnetic moment is mainly due to the Co-3d orbital with a small contribution from the U-5f orbital. The possibility of fully non-collinear magnetism in this compound seems to be ruled out. These results are compared with the isostructural compound URhGe, in this case the magnetism comes mostly from the U-5f orbital

Independence in constraint logic programs

Studying independence of literals, variables, and substitutions has proven very useful in the context of logic programming (LP). Here we study independence in the broader context of constraint logic programming (CLP). We show that a naive extrapolation of the LP definitions of independence to CLP is unsatisfactory (in fact, wrong) for two reasons. First, because interaction between variables through constraints is more complex than in the case of logic programming. Second, in order to ensure the efUciency of several optimizations not only must independence of the search space be considered, but also an orthogonal issue - "independence of constraint solving." We clarify these issues by proposing various types of search independence and constraint solver independence, and show how they can be combined to allow different independence-related optimizations, from parallelism to intelligent backtracking. Sufficient conditions for independence which can be evaluated "a-priori" at run-time are also proposed. Our results suggest that independence, provided a suitable definition is chosen, is even more useful in CLP than in LP

Analyzing logic programs with dynamic scheduling

Traditional logic programming languages, such as Prolog, use a fixed left-to-right atom scheduling rule. Recent logic programming languages, however, usually provide more flexible scheduling in which computation generally proceeds leftto- right but in which some calis are dynamically "delayed" until their arguments are sufRciently instantiated to allow the cali to run efficiently. Such dynamic scheduling has a significant cost. We give a framework for the global analysis of logic programming languages with dynamic scheduling and show that program analysis based on this framework supports optimizations which remove much of the overhead of dynamic scheduling