Integral closure of rings of integer-valued polynomials on algebras

Let $D$ be an integrally closed domain with quotient field $K$. Let $A$ be a torsion-free $D$-algebra that is finitely generated as a $D$-module. For every $a$ in $A$ we consider its minimal polynomial $\mu_a(X)\in D[X]$, i.e. the monic polynomial of least degree such that $\mu_a(a)=0$. The ring ${\rm Int}_K(A)$ consists of polynomials in $K[X]$ that send elements of $A$ back to $A$ under evaluation. If $D$ has finite residue rings, we show that the integral closure of ${\rm Int}_K(A)$ is the ring of polynomials in $K[X]$ which map the roots in an algebraic closure of $K$ of all the $\mu_a(X)$, $a\in A$, into elements that are integral over $D$. The result is obtained by identifying $A$ with a $D$-subalgebra of the matrix algebra $M_n(K)$ for some $n$ and then considering polynomials which map a matrix to a matrix integral over $D$. We also obtain information about polynomially dense subsets of these rings of polynomials.Comment: Keywords: Integer-valued polynomial, matrix, triangular matrix, integral closure, pullback, polynomially dense set. accepted for publication in the volume "Commutative rings, integer-valued polynomials and polynomial functions", M. Fontana, S. Frisch and S. Glaz (editors), Springer 201

Effects of QCD Resummation on Distributions of Leptons from the Decay of Electroweak Vector Bosons

We study the distributions of leptons from the decay of electroweak vector bosons produced in hadron collisions. The effects of the initial state multiple soft-gluon emission, using the Collins--Soper resummation formalism, are included. The resummed results are compared with the next-to-leading-order results for the distributions of the transverse momentum, rapidity asymmetry, and azimuthal angle of the decay leptons.Comment: 12 pages, 3 figures uuencoded, LaTeX, uses epsf.tex for figures. (Was replaced on 5/2/95 because of mailer problems.

How Ontologies Can Help in an eMarketplace

Recently, ontologies have been developed in various business domains with the recent maturing of the Semantic Web technologies. However, ontology-related researches have largely focused on the facilitation of successful matchmaking but not much on traders’ requirement elicitation and potential negotiations in e-marketplaces. Because ontology provides the key knowledge about the inter-relationships among the issues and alternatives of the traders’ requirements, we show how to elicit trade requirements, alternatives, and tradeoff from an agreed ontology. This facilitates the whole business process of the e-marketplace, from matchmaking, recommendation, to negotiation. We further propose a novel methodology for the elicitation of dependencies among traders’ requirements for the formulation of an effective decision plan. As a result, traders can have a better cognition of their requirements and the overall operations of the e-marketplace can be streamlined

Report on an all-sky LIGO search for periodic gravitational waves in the S4 data

We report on an all-sky search with the LIGO detectors for periodic gravitational waves in the frequency range 50-1000 Hz and having a negative frequency time derivative with magnitude between zero and $10^{-8}$ Hz/s. Data from the fourth LIGO science run have been used in this search. Three different semi-coherent methods of summing strain power were applied. Observing no evidence for periodic gravitational radiation, we report upper limits on strain amplitude and interpret these limits to constrain radiation from rotating neutron stars.Comment: 5 pages, 1 figure, presented at Amaldi7, Sydney (July 2007

Searching for stochastic gravitational-wave background with the co-located LIGO interferometers

This paper presents techniques developed by the LIGO Scientific Collaboration to search for the stochastic gravitational-wave background using the co-located pair of LIGO interferometers at Hanford, WA. We use correlations between interferometers and environment monitoring instruments, as well as time-shifts between two interferometers (described here for the first time) to identify correlated noise from non-gravitational sources. We veto particularly noisy frequency bands and assess the level of residual non-gravitational coupling that exists in the surviving data.Comment: Proceedings paper from the 7th Edoardo Amaldi Conference on Gravitational Waves, held in Sydney, Australia from 8-14 July 2007. Accepted to J. Phys.: Conf. Se

IP3R-driven increases in mitochondrial Ca2+ promote neuronal death in NPC disease

Ca2+ is the most ubiquitous second messenger in neurons whose spatial and temporal elevations are tightly controlled to initiate and orchestrate diverse intracellular signaling cascades. Numerous neuropathologies result from mutations or alterations in Ca2+ handling proteins; thus, elucidating molecular pathways that shape Ca2+ signaling is imperative. Here, we report that loss-of-function, knockout, or neurodegenerative disease-causing mutations in the lysosomal cholesterol transporter, Niemann-Pick Type C1 (NPC1), initiate a damaging signaling cascade that alters the expression and nanoscale distribution of IP3R type 1 (IP3R1) in endoplasmic reticulum membranes. These alterations detrimentally increase Gq-protein coupled receptor-stimulated Ca2+ release and spontaneous IP3R1 Ca2+ activity, leading to mitochondrial Ca2+ cytotoxicity. Mechanistically, we find that SREBP-dependent increases in Presenilin 1 (PS1) underlie functional and expressional changes in IP3R1. Accordingly, expression of PS1 mutants recapitulate, while PS1 knockout abrogates Ca2+ phenotypes. These data present a signaling axis that links the NPC1 lysosomal cholesterol transporter to the damaging redistribution and activity of IP3R1 that precipitates cell death in NPC1 disease and suggests that NPC1 is a nanostructural disease

Recollements of Module Categories

We establish a correspondence between recollements of abelian categories up to equivalence and certain TTF-triples. For a module category we show, moreover, a correspondence with idempotent ideals, recovering a theorem of Jans. Furthermore, we show that a recollement whose terms are module categories is equivalent to one induced by an idempotent element, thus answering a question by Kuhn.Comment: Comments are welcom

A p-adic analogue of Siegel's Theorem on sums of squares

Siegel proved that every totally positive element of a number field K is the sum of four squares, so in particular the Pythagoras number is uniformly bounded across number fields. The p ‐adic Kochen operator provides a p ‐adic analogue of squaring, and a certain localisation of the ring generated by this operator consists of precisely the totally p ‐integral elements of K . We use this to formulate and prove a p ‐adic analogue of Siegel's theorem, by introducing the p ‐Pythagoras number of a general field, and showing that this number is uniformly bounded across number fields. We also generally study fields with finite p ‐Pythagoras number and show that the growth of the p ‐Pythagoras number in finite extensions is bounded

An integrative study of motivation and goal regulation processes in subclinical anxiety, depression and hypomania

Research has implicated motivation and goal regulation in susceptibility to mood disorders. We studied for the first time key facets of motivation and goal regulation concurrently in relation to affective symptoms. The cross-national sample comprised 510 university students from the United States (n = 279) and United Kingdom (n = 231). Participants completed self-report measures of motivation, conditional goal setting, urgency, depression, anxiety, and mania risk. Structural Equation Modeling results found that behavioral activation system scores correlated negatively with depression and positively with mania risk, but were unrelated to anxiety. High conditional goal setting correlated uniquely with higher depression but not to anxiety or mania risk. Urgency correlated with higher anxiety, depression, and mania risk. Behavioral inhibition system scores correlated negatively with mania risk but unexpectedly did not correlate with anxiety in the multivariate model. The behavioral activation, behavioral inhibition, conditional goal setting, and urgency results showed shared and distinct patterns of relationships with depression, anxiety and mania risk. Our findings indicate unique and common risk vulnerabilities in depressive, anxious, and manic syndromes and extend an integrative knowledge of these syndromes in relation to goal regulation