Differential Operators and Finite-Dimensional Algebras

AbstractLet R be a Dedekind domain that is finitely generated over k, an algebraically closed field of characteristic zero. Let M be a torsionfree module of rank one over a subalgebra of R with integral closure R. This paper investigates the structure of D(M), the ring of differential operators on M. It is shown that D(M) has a unique minimal non-zero ideal, J(M), and that the factor, D(M)/J(M), is a finite-dimensional k-algebra. This factor is realised as the algebra of all endomorphisms of an associated vector space that preserve certain subspaces. The main result is that given any finite-dimensional k-algebra A there exists such an M with A ≅ D(M)/J(M)

Further restrictions on the topology of stationary black holes in five dimensions

We place further restriction on the possible topology of stationary asymptotically flat vacuum black holes in 5 spacetime dimensions. We prove that the horizon manifold can be either a connected sum of Lens spaces and "handles" $S^1 \times S^2$, or the quotient of $S^3$ by certain finite groups of isometries (with no "handles"). The resulting horizon topologies include Prism manifolds and quotients of the Poincare homology sphere. We also show that the topology of the domain of outer communication is a cartesian product of the time direction with a finite connected sum of $\mathbb R^4,S^2 \times S^2$'s and $CP^2$'s, minus the black hole itself. We do not assume the existence of any Killing vector beside the asymptotically timelike one required by definition for stationarity.Comment: LaTex, 22 pages, 9 figure

Methane Flux in Cropland and Adjacent Riparian Buff ers with Different Vegetation Covers

While water quality functions of conservation buffers established adjacent to cropped fields have been widely documented, the relative contribution of these re-established perennial plant systems to greenhouse gases has not been completely documented. In the case of methane (CH(4)), these systems have the potential to serve as sinks of CH(4) or may provide favorable conditions for CH(4) production. This study quantifies CH(4) flux from soils of riparian buffer systems comprised of three vegetation types and compares these fluxes with those of adjacent crop fields. We measured soil properties and diel and seasonal variations of CH(4) flux in 7 to 17 yr-old re-established riparian forest buffers, warm-season and cool-season grass filters, and an adjacent crop field located in the Bear Creek watershed in central Iowa. Forest buffer and grass filter soils had significantly lower bulk density (P \u3c 0.01); and higher pH (P \u3c 0.01), total carbon (TC) (P \u3c 0.01), and total nitrogen (TN) (P \u3c 0.01) than crop field soils. There was no significant relationship between CH(4) flux and soil moisture or soil temperature among sites within the range of conditions observed. Cumulative CH(4) flux was -0.80 kg CH(4)-C ha(-1) yr(-1) in the cropped field, -0.46 kg CH(4)-C ha(-1) yr(-1) within the forest buffers, and 0.04 kg CH(4)-C ha(-1) yr(-1) within grass filters, but difference among vegetation covers was not significant. Results suggest that CH(4) flux was not changed after establishment of perennial vegetation on cropped soils, despite significant changes in soil properties

An experimental and theoretical study of the valence shell photoelectron spectra of 2-chloropyridine and 3-chloropyridine

The valence shell photoelectron spectra of 2-chloropyridine and 3-chloropyridine have been studied both experimentally and theoretically. Synchrotron radiation has been employed to record angle resolved photoelectron spectra in the photon energy range 20–100 eV, and these have enabled anisotropy parameters and branching ratios to be derived. The experimental results have been compared with theoretical predictions obtained using the continuum multiple scattering Xα approach. This comparison shows that the anisotropy parameter associated with the nominally chlorine lone-pair orbital lying in the molecular plane is strongly affected by the atomic Cooper minimum. In contrast, the photoionization dynamics of the second lone-pair orbital, orientated perpendicular to the molecular plane, seem relatively unaffected by this atomic phenomenon. The outer valence ionization has been studied theoretically using the third-order algebraic-diagrammatic construction (ADC(3)) approximation scheme for the one-particle Green’s function, the outer valence Green’s function method, and the equation-of-motion (EOM) coupled cluster (CC) theory at the level of the EOM-IP-CCSD and EOM-EE-CC3 models. The convergence of the results to the complete basis set limit has been investigated. The ADC(3) method has been employed to compute the complete valence shell ionization spectra of 2-chloropyridine and 3-chloropyridine. The relaxation mechanism for ionization of the nitrogen σ-type lone-pair orbital (σN LP) has been found to be different to that for the corresponding chlorine lone-pair (σCl LP). For the σN LP orbital, π-π* excitations play the main role in the screening of the lone-pair hole. In contrast, excitations localized at the chlorine site involving the chlorine πCl LP lone-pair and the Cl 4p Rydberg orbital are the most important for the σCl LP orbital. The calculated photoelectron spectra have allowed assignments to be proposed for most of the structure observed in the experimental spectra. The theoretical work also highlights the formation of satellite states, due to the breakdown of the single particle model of ionization, in the inner valence region

Facts, Values and Quanta

Quantum mechanics is a fundamentally probabilistic theory (at least so far as the empirical predictions are concerned). It follows that, if one wants to properly understand quantum mechanics, it is essential to clearly understand the meaning of probability statements. The interpretation of probability has excited nearly as much philosophical controversy as the interpretation of quantum mechanics. 20th century physicists have mostly adopted a frequentist conception. In this paper it is argued that we ought, instead, to adopt a logical or Bayesian conception. The paper includes a comparison of the orthodox and Bayesian theories of statistical inference. It concludes with a few remarks concerning the implications for the concept of physical reality.Comment: 30 pages, AMS Late

Emissive spin-0 triplet-pairs are a direct product of triplet–triplet annihilation in pentacene single crystals and anthradithiophene films

Singlet fission and triplet–triplet annihilation represent two highly promising ways of increasing the efficiency of photovoltaic devices. Both processes are believed to be mediated by a biexcitonic triplet-pair state, 1(TT). Recently however, there has been debate over the role of 1(TT) in triplet–triplet annihilation. Here we use intensity-dependent, low-temperature photoluminescence measurements, combined with kinetic modelling, to show that distinct 1(TT) emission arises directly from triplet–triplet annihilation in high-quality pentacene single crystals and anthradithiophene (diF-TES-ADT) thin films. This work demonstrates that a real, emissive triplet-pair state acts as an intermediate in both singlet fission and triplet–triplet annihilation and that this is true for both endo- and exothermic singlet fission materials

Reading related white matter structures in adolescents are influenced more by dysregulation of emotion than behavior

Mood disorders and behavioral are broad psychiatric diagnostic categories that have different symptoms and neurobiological mechanisms, but share some neurocognitive similarities, one of which is an elevated risk for reading deficit. Our aim was to determine the influence of mood versus behavioral dysregulation on reading ability and neural correlates supporting these skills in youth, using diffusion tensor imaging in 11- to 17-year-old children and youths with mood disorders or behavioral disorders and age-matched healthy controls. The three groups differed only in phonological processing and passage comprehension. Youth with mood disorders scored higher on the phonological test but had lower comprehension scores than children with behavioral disorders and controls; control participants scored the highest. Correlations between fractional anisotropy and phonological processing in the left Arcuate Fasciculus showed a significant difference between groups and were strongest in behavioral disorders, intermediate in mood disorders, and lowest in controls. Correlations between these measures in the left Inferior Longitudinal Fasciculus were significantly greater than in controls for mood but not for behavioral disorders. Youth with mood disorders share a deficit in the executive-limbic pathway (Arcuate Fasciculus) with behavioral-disordered youth, suggesting reduced capacity for engaging frontal regions for phonological processing or passage comprehension tasks and increased reliance on the ventral tract (e.g., the Inferior Longitudinal Fasciculus). The low passage comprehension scores in mood disorder may result from engaging the left hemisphere. Neural pathways for reading differ mainly in executive-limbic circuitry. This new insight may aid clinicians in providing appropriate intervention for each disorder

Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops

We discuss how to extract renormalized from bare Polyakov loops in SU(N) lattice gauge theories at nonzero temperature in four spacetime dimensions. Single loops in an irreducible representation are multiplicatively renormalized without mixing, through a renormalization constant which depends upon both representation and temperature. The values of renormalized loops in the four lowest representations of SU(3) were measured numerically on small, coarse lattices. We find that in magnitude, condensates for the sextet and octet loops are approximately the square of the triplet loop. This agrees with a large $N$ expansion, where factorization implies that the expectation values of loops in adjoint and higher representations are just powers of fundamental and anti-fundamental loops. For three colors, numerically the corrections to the large $N$ relations are greatest for the sextet loop, $\leq 25$; these represent corrections of $\sim 1/N$ for N=3. The values of the renormalized triplet loop can be described by an SU(3) matrix model, with an effective action dominated by the triplet loop. In several ways, the deconfining phase transition for N=3 appears to be like that in the $N=\infty$ matrix model of Gross and Witten.Comment: 24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion for clarity, results unchange

SPACA3gene variants in a New Zealand cohort of infertile and fertile couples

SPRASA (also referred to as SLLP1) is a protein identified in the acrosome of human sperm and encoded by the gene SPACA3. SPRASA is associated with sperm-oocyte recognition and binding, and may play a role in fertility. In order to determine whether variants in the SPACA3 gene are associated with human infertility, we undertook a genetic analysis of 102 infertile and 104 fertile couples. Three gene variants were identified using PCR-based DNA sequencing; 1) an insertion of TGC within a quadruple tri-nucleotide (TGC) repeat region in the 5’ untranslated region (UTR) (g.–22TGC(4_5), 2) a guanine to adenosine transition at position 239 (c.239G> A) resulting in a non-synonymous amino acid substitution from cysteine to tyrosine (p.C80Y) at position 80 in the putative transmembrane region, and 3) a novel nucleotide variant (c.691G> C) located in the 3’UTR. A functional effect of the g.–22TGC (4_5) was confirmed by a luciferase expression assay, while the effects of the variants c.239G> A and c.691G> C were predicted using in silico analysis. Although the frequencies of these variants were not significantly different between the infertile and fertile populations, we present evidence that the variants could affect the expression levels or function of SPRASA, thereby affecting a couple's fertility. Larger populations, especially individuals/couples with unexplained infertility, need to be screened for these variants to validate a relationship with fertility