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

Characterizing Width Uniformity by Wave Propagation

This work describes a novel image analysis approach to characterize the uniformity of objects in agglomerates by using the propagation of normal wavefronts. The problem of width uniformity is discussed and its importance for the characterization of composite structures normally found in physics and biology highlighted. The methodology involves identifying each cluster (i.e. connected component) of interest, which can correspond to objects or voids, and estimating the respective medial axes by using a recently proposed wavefront propagation approach, which is briefly reviewed. The distance values along such axes are identified and their mean and standard deviation values obtained. As illustrated with respect to synthetic and real objects (in vitro cultures of neuronal cells), the combined use of these two features provide a powerful description of the uniformity of the separation between the objects, presenting potential for several applications in material sciences and biology.Comment: 14 pages, 23 figures, 1 table, 1 referenc

The role of emotion, values, and beliefs in the construction of innovative work realities

Traditional approaches to requirements elicitation stress systematic and rational analysis and representation of organizational context and system requirements. This paper argues that (1) for an organization, a software system implements a shared vision of a future work reality and that (2) understanding the emotions, feelings, values, beliefs, and interests that drive organizational human action is needed in order to invent the requirements of such a software system. This paper debunks some myths about how organizations transform themselves through the adoption of Information and Communication Technology; describes the concepts of emotion, feeling, value, and belief; and presents some constructionist guidelines for the process of eliciting requirements for a software system that helps an organization to fundamentally change its work patterns.(undefined

Influence of Thermally Induced Chemorheological Changes on the Inflation of Spherical Elastomeric Membranes

When an elastomeric material is deformed and subjected to temperatures above some chemorheological value T cr (near 100°C for natural rubber), its macromolecular structure undergoes time and temperature dependent chemical changes. The process continues until the temperature decreases below T cr . Compared to the virgin material, the new material system has modified properties (often a reduced stiffness) and permanent set on removal of the applied load. A recently proposed constitutive theory is used to study the influence of chemorheological changes on the inflation of an initially isotropic spherical rubber membrane. The membrane is inflated while at a temperature below T cr . We then look at the pressure response assuming the sphere's radius is held fixed while the temperature is increased above T cr for a period of time and then returned to its original value. The inflation pressure during this process is expressed in terms of the temperature, representing entropic stiffening of the elastomer, and a time dependent property that represents the kinetics of the chemorheological change in the elastomer. When the membrane has been returned to its original temperature, it is shown to have a permanent set and a modified pressure-inflated radius relation. Their dependence on the initial inflated radius, material properties and kinetics of chemorheological change is studied when the underlying elastomeric networks are neo-Hookean or Mooney–Rivlin.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42688/1/10659_2005_Article_9020.pd

First measurement of direct f0(980)f_0(980) photoproduction on the proton

We report on the results of the first measurement of exclusive $f_0(980)$ meson photoproduction on protons for $E_\gamma=3.0 - 3.8$ GeV and $-t = 0.4-1.0$ GeV$^2$. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. The resonance was detected via its decay in the $\pi^+ \pi^-$ channel by performing a partial wave analysis of the reaction $\gamma p \to p \pi^+ \pi^-$. Clear evidence of the $f_0(980)$ meson was found in the interference between $P$ and $S$ waves at $M_{\pi^+ \pi^-}\sim 1$ GeV. The $S$-wave differential cross section integrated in the mass range of the $f_0(980)$ was found to be a factor of 50 smaller than the cross section for the $\rho$ meson. This is the first time the $f_0(980)$ meson has been measured in a photoproduction experiment

A Bayesian analysis of pentaquark signals from CLAS data

We examine the results of two measurements by the CLAS collaboration, one of which claimed evidence for a $\Theta^{+}$ pentaquark, whilst the other found no such evidence. The unique feature of these two experiments was that they were performed with the same experimental setup. Using a Bayesian analysis we find that the results of the two experiments are in fact compatible with each other, but that the first measurement did not contain sufficient information to determine unambiguously the existence of a $\Theta^{+}$. Further, we suggest a means by which the existence of a new candidate particle can be tested in a rigorous manner.Comment: 5 pages, 3 figure

Study of the B^0 Semileptonic Decay Spectrum at the Upsilon(4S) Resonance

We have made a first measurement of the lepton momentum spectrum in a sample of events enriched in neutral B's through a partial reconstruction of B0 --> D*- l+ nu. This spectrum, measured with 2.38 fb**-1 of data collected at the Upsilon(4S) resonance by the CLEO II detector, is compared directly to the inclusive lepton spectrum from all Upsilon(4S) events in the same data set. These two spectra are consistent with having the same shape above 1.5 GeV/c. From the two spectra and two other CLEO measurements, we obtain the B0 and B+ semileptonic branching fractions, b0 and b+, their ratio, and the production ratio f+-/f00 of B+ and B0 pairs at the Upsilon(4S). We report b+/b0=0.950 (+0.117-0.080) +- 0.091, b0 = (10.78 +- 0.60 +- 0.69)%, and b+ = (10.25 +- 0.57 +- 0.65)%. b+/b0 is equivalent to the ratio of charged to neutral B lifetimes, tau+/tau0.Comment: 14 page, postscript file also available at http://w4.lns.cornell.edu/public/CLN

Observation of the Ξc+\Xi_c^+ Charmed Baryon Decays to Σ+K−π+\Sigma^+ K^-\pi^+, Σ+Kˉ∗0\Sigma^+ \bar{K}^{*0}, and ΛK−π+π+\Lambda K^-\pi^+\pi^+

We have observed two new decay modes of the charmed baryon $\Xi_c^+$ into $\Sigma^+ K^-\pi^+$ and $\Sigma^+ \bar{K}^{*0}$ using data collected with the CLEO II detector. We also present the first measurement of the branching fraction for the previously observed decay mode $\Xi_c^+\to\Lambda K^-\pi^+\pi^+$. The branching fractions for these three modes relative to $\Xi_c^+\to\Xi^-\pi^+\pi^+$ are measured to be $1.18 \pm 0.26 \pm 0.17$, $0.92 \pm 0.27 \pm 0.14$, and $0.58 \pm 0.16 \pm 0.07$, respectively.Comment: 12 page uuencoded postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Radiative Decay Modes of the D0D^{0} Meson

Using data recorded by the CLEO-II detector at CESR we have searched for four radiative decay modes of the $D^0$ meson: $D^0\to\phi\gamma$, $D^0\to\omega\gamma$, $D^0\to\bar{K}^{*}\gamma$, and $D^0\to\rho^0\gamma$. We obtain 90% CL upper limits on the branching ratios of these modes of $1.9\times 10^{-4}$, $2.4\times 10^{-4}$, $7.6\times 10^{-4}$ and $2.4\times 10^{-4}$ respectively.Comment: 15 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Measurement of the Mass Splittings between the bbˉχb,J(1P)b\bar{b}\chi_{b,J}(1P) States

We present new measurements of photon energies and branching fractions for the radiative transitions: Upsilon(2S)->gamma+chi_b(J=0,1,2). The masses of the chi_b states are determined from the measured radiative photon energies. The ratio of mass splittings between the chi_b substates, r==(M[J=2]-M[J=1])/(M[J=1]-M[J=0]) with M the chi_b mass, provides information on the nature of the bbbar confining potential. We find r(1P)=0.54+/-0.02+/-0.02. This value is in conflict with the previous world average, but more consistent with the theoretical expectation that r(1P)<r(2P); i.e., that this mass splittings ratio is smaller for the chi_b(1P) triplet than for the chi_b(2P) triplet.Comment: 11 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN