Mixed multiplicities and the minimal number of generator of modules

Let (R, m) be a d-dimensional Noetherian local ring. In this work we prove that the mixed Buchsbaum-Rim multiplicity for a finite family of R-submodules of R(p) of finite colength coincides with the Buchsbaum-Rim multiplicity of the module generated by a suitable superficial sequence, that is, we generalize for modules the well-known Risler-Teissier theorem. As a consequence, we give a new proof of a generalization for modules of the fundamental Rees` mixed Multiplicity theorem, which was first proved by Kirby and Rees in (1994, [8]). We use the above result to give an upper bound for the minimal number of generators of a finite colength R-submodule of R(p) in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, [5]) for m-primary ideals. (C) 2009 Elsevier B.V. All rights reserved.

A new proposal for the picture changing operators in the minimal pure spinor formalism

Using a new proposal for the ""picture lowering"" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the. Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the. Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green`s function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.

Phototransformation of hematoporphyrin in aqueous solution: Anomalous behavior at low oxygen concentration

The photoactivation of a photosensitizer is the initial step in photodynamic therapy (PDT) where photochemical reactions result in the production of reactive oxygen species and eventually cell death. In addition to oxidizing biomolecules, some of these photochemical reactions lead to photosensitizer degradation at a rate dependent on the oxygen concentration among other factors. We investigated photodegradation of Photogem A (R) (28 mu M), a hematoporphyrin derivative, at different oxygen concentrations (9.4 to 625.0 mu M) in aqueous solution. The degradation was monitored by fluorescence spectroscopy. The degradation rate (M/s) increases as the oxygen concentration increases when the molar ratio of oxygen to PhotogemA (R) is greater than 1. At lower oxygen concentrations (< 25 mu M) an inversion of this behavior was observed. The data do not fit a simple kinetic model of first-order dependence on oxygen concentration. This inversion of the degradation rate at low oxygen concentration has not previously been demonstrated and highlights the relationship between photosensitizer and oxygen concentrations in determining the photobleaching mechanism(s). The findings demonstrate that current models for photobleaching are insufficient to explain completely the effects at low oxygen concentration.

Estimating losses in an entanglement concentration scheme using the phenomenological operator approach to dissipation in cavity quantum electrodynamics

In a previous paper, we developed a phenomenological-operator technique aiming to simplify the estimate of losses due to dissipation in cavity quantum electrodynamics. In this paper, we apply that technique to estimate losses during an entanglement concentration process in the context of dissipative cavities. In addition, some results, previously used without proof to justify our phenomenological-operator approach, are now formally derived, including an equivalent way to formulate the Wigner-Weisskopf approximation.

Susceptibility of Staphylococcus aureus to porphyrin-mediated photodynamic antimicrobial chemotherapy: an in vitro study

The ability of Staphylococcus aureus to develop multidrug resistance is well documented, and the antibiotic resistance showed by an increasing number of bacteria has shown the need for alternative therapies to treat infections, photodynamic therapy (PDT) being a potential candidate. The aim of this study was to determine the effect of photodynamic therapy as a light-based bactericidal modality to eliminate Staphylococcus aureus. The study investigated a technique based on a combination of light and a photosensitizer that is capable of producing oxidative species to induce a cytotoxic effect. A Staphylococcus aureus suspension was exposed to a light emitting diode (LED) emitting at 628 nm, 14.6 mW/cm(2), and energy density of 20J/cm(2), 40J/cm(2), or 60 J/cm(2) in the presence of different porphyrin concentrations (PhotogemA (R)). Three drug concentrations were employed: 12 mu l/ml, 25 mu l/ml, and 50 mu l/ml. The treatment response was evaluated by the number of bacterial colony forming units (CFU) after light exposure. The results indicated that exposure to 60 J/cm(2) eliminated 100% (10 log(10) scales) of bacteria, on average. The best PDT response rate to eliminate Staphylococcus aureus was achieved with exposure to LED light in combination with the photosensitizer at concentrations ranging from 25 mu l/ml to 50 mu l/ml. These data suggest that PDT has the potential to eliminate Staphylococcus aureus in suspension and indicates the necessary drug concentration and light fluency.

Influence of chromium concentration on the optical-electronic properties of ruby microstructures

Films of amorphous aluminium nitride (AlN) were prepared by conventional radio frequency sputtering of an Al + Cr target in a plasma of pure nitrogen. The Cr-to-Al relative area determines the Cr content, which remained in the similar to 0-3.5 at% concentration range in this study. Film deposition was followed by thermal annealing of the samples up to 1050 degrees C in an atmosphere of oxygen and by spectroscopic characterization through energy dispersive x-ray spectrometry, photoluminescence and optical transmission measurements. According to the experimental results, the optical-electronic properties of the Cr-containing AlN films are highly influenced by both the Cr concentration and the temperature of the thermal treatments. In fact, thermal annealing at 1050 degrees C induces the development of structures that, because of their typical size and distinctive spectral characteristics, were designated by ruby microstructures (RbMSs). These RbMSs are surrounded by a N-rich environment in which Cr(3+) ions exhibit luminescent features not present in other Cr(3+)-containing systems such as ruby, emerald or alexandrite. The light emissions shown by the RbMSs and surroundings were investigated according to the Cr concentration and temperature of measurement, allowing the identification of several Cr(3+)-related luminescent lines. The main characteristics of these luminescent lines and corresponding excitation-recombination processes are presented and discussed in view of a detailed spectroscopic analysis.

SBTX, a new toxic protein distinct from soyatoxin and other toxic soybean [Glycine max] proteins, and its inhibitory effect on Cercospora sojina growth

SBTX, a novel toxin from soybean, was purified by ammonium sulfate fractionation followed by chromatographic steps DEAE-Cellulose, CM-Sepharose and Superdex 200 HR fast-protein liquid chromatography (FPLC). Lethality of SBTX to mice (LD50 5.6 mg/kg) was used as parameter in the purification steps. SBTX is a 44-kDa basic glycoprotein composed of two polypeptide chains (27 and 17 kDa) linked by a disulfide bond. The N-terminal sequences of the 44 and 27 kDa chains were identical (ADPTFGFTPLGLSEKANLQIMKAYD), differing from that of 17 kDa (PNPKVFFDMTIGGQSAGRIVMEEYA). SBTX contains high levels of Glx, Ala, Asx, Gly and Lys and showed maximum absorption at 280 nm, epsilon(1 cm) (1%) of 6.3, and fluorescence emission in the 290-450nm range upon excitation at 280nm. The secondary structure content was 35% alpha-helix, 13% beta-strand and beta-sheet, 27% beta-turn, 25% unordered, and 1% aromatic residues. Immunological assays showed that SBTX was related to other toxic proteins, such as soyatoxin and canatoxin, and cross-reacted weekly with soybean trypsin inhibitor and agglutinin, but it was devoid of protease-inhibitory and hemagglutinating activities. The inhibitory effect of SBTX on growth of Cercospora sojina, fungus causing frogeye leaf spot in soybeans, was observed at 50 mu g/ml, concentration 112 times lesser than that found to be lethal to mice. This effect on phytopathogenic fungus is a potential attribute for the development of transgenic plants with enhanced resistance to pathogens. (c) 2007 Elsevier Ltd. All rights reserved.

Isolation and characterization of four type 2 ribosome inactivating pulchellin isoforms from Abrus pulchellus seeds

Abrus pulchellus seeds contain at least seven closely related and highly toxic type 2 ribosome-inactivating pulchellins, each consisting of a toxic A-chain linked to a sugar binding B-chain. In the present study, four pulchellin isoforms (termed P I, P II, P III and P IV) were isolated by affinity, ion exchange and chromatofocusing chromatographies, and investigated with respect to toxicity and sugar binding specificity. Half maximal inhibitory concentration and median lethal dose values indicate that P I and P II have similar toxicities and that both are more toxic to cultured HeLa cells and mice than P III and P IV. Interestingly, the secondary structural characteristics and sugar binding properties of the respective pairs of isoforms correlate well with the two toxicity levels, in that P I/P II and P III/P IV form two specific subgroups. From the deduced amino acids sequences of the four isoforms, it is clear that the highest similarity within each subgroup is found to occur within domain 2 of the B-chains, suggesting that the disparity in toxicity levels might be attributed to subtle differences in B-chain-mediated cell surface interactions that precede and determine toxin uptake pathways.

Structured minimal-memory inexact quasi-Newton method and secant preconditioners for augmented Lagrangian optimization

Augmented Lagrangian methods for large-scale optimization usually require efficient algorithms for minimization with box constraints. On the other hand, active-set box-constraint methods employ unconstrained optimization algorithms for minimization inside the faces of the box. Several approaches may be employed for computing internal search directions in the large-scale case. In this paper a minimal-memory quasi-Newton approach with secant preconditioners is proposed, taking into account the structure of Augmented Lagrangians that come from the popular Powell-Hestenes-Rockafellar scheme. A combined algorithm, that uses the quasi-Newton formula or a truncated-Newton procedure, depending on the presence of active constraints in the penalty-Lagrangian function, is also suggested. Numerical experiments using the Cute collection are presented.

Generalized Birnbaum-Saunders distributions applied to air pollutant concentration

The generalized Birnbaum-Saunders (GBS) distribution is a new class of positively skewed models with lighter and heavier tails than the traditional Birnbaum-Saunders (BS) distribution, which is largely applied to study lifetimes. However, the theoretical argument and the interesting properties of the GBS model have made its application possible beyond the lifetime analysis. The aim of this paper is to present the GBS distribution as a useful model for describing pollution data and deriving its positive and negative moments. Based on these moments, we develop estimation and goodness-of-fit methods. Also, some properties of the proposed estimators useful for developing asymptotic inference are presented. Finally, an application with real data from Environmental Sciences is given to illustrate the methodology developed. This example shows that the empirical fit of the GBS distribution to the data is very good. Thus, the GBS model is appropriate for describing air pollutant concentration data, which produces better results than the lognormal model when the administrative target is determined for abating air pollution. Copyright (c) 2007 John Wiley & Sons, Ltd.

Minimal surfaces in S(3) with constant contact angle

We provide a characterization of the Clifford Torus in S(3) via moving frames and contact structure equations. More precisely, we prove that minimal surfaces in S(3) with constant contact angle must be the Clifford Torus. Some applications of this result are then given, and some examples are discussed.

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers` program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size K I into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. (c) 2009 Elsevier Inc. All fights reserved.

The Gauss-Kronecker curvature of minimal hypersurfaces in four-dimensional space forms

LetQ(4)( c) be a four-dimensional space form of constant curvature c. In this paper we show that the infimum of the absolute value of the Gauss-Kronecker curvature of a complete minimal hypersurface in Q(4)(c), c <= 0, whose Ricci curvature is bounded from below, is equal to zero. Further, we study the connected minimal hypersurfaces M(3) of a space form Q(4)( c) with constant Gauss-Kronecker curvature K. For the case c <= 0, we prove, by a local argument, that if K is constant, then K must be equal to zero. We also present a classification of complete minimal hypersurfaces of Q(4)( c) with K constant.

Minimal Lagrangian surfaces in the tangent bundle of a Riemannian surface

Given an oriented Riemannian surface (Sigma, g), its tangent bundle T Sigma enjoys a natural pseudo-Kahler structure, that is the combination of a complex structure 2, a pseudo-metric G with neutral signature and a symplectic structure Omega. We give a local classification of those surfaces of T Sigma which are both Lagrangian with respect to Omega and minimal with respect to G. We first show that if g is non-flat, the only such surfaces are affine normal bundles over geodesics. In the flat case there is, in contrast, a large set of Lagrangian minimal surfaces, which is described explicitly. As an application, we show that motions of surfaces in R(3) or R(1)(3) induce Hamiltonian motions of their normal congruences, which are Lagrangian surfaces in TS(2) or TH(2) respectively. We relate the area of the congruence to a second-order functional F = f root H(2) - K dA on the original surface. (C) 2010 Elsevier B.V. All rights reserved.

Triply periodic minimal surfaces which converge to the Hoffman-Wohlgemuth example

We get a continuous one-parameter new family of embedded minimal surfaces, of which the period problems are two-dimensional. Moreover, one proves that it has Scherk`s second surface and Hoffman-Wohlgemuth`s example as limit-members.