Position-dependent noncommutativity in quantum mechanics

The model of the position-dependent noncommutativity in quantum mechanics is proposed. We start with given commutation relations between the operators of coordinates [(x) over cap (i), (x) over cap (j)] = omega(ij) ((x) over cap), and construct the complete algebra of commutation relations, including the operators of momenta. The constructed algebra is a deformation of a standard Heisenberg algebra and obeys the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativity.

On quantum integrability of the Landau-Lifshitz model

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Finite-size corrections to entanglement in quantum critical systems

We analyze the finite-size corrections to entanglement in quantum critical systems. By using conformal symmetry and density functional theory, we discuss the structure of the finite-size contributions to a general measure of ground state entanglement, which are ruled by the central charge of the underlying conformal field theory. More generally, we show that all conformal towers formed by an infinite number of excited states (as the size of the system L -> infinity) exhibit a unique pattern of entanglement, which differ only at leading order (1/L)(2). In this case, entanglement is also shown to obey a universal structure, given by the anomalous dimensions of the primary operators of the theory. As an illustration, we discuss the behavior of pairwise entanglement for the eigenspectrum of the spin-1/2 XXZ chain with an arbitrary length L for both periodic and twisted boundary conditions.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.

COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

KeaA, a Dictyostelium kelch-domain protein that regulates the response to stress and development

Background: The protein kinase YakA is responsible for the growth arrest and induction of developmental processes that occur upon starvation of Dictyostelium cells. yakA-cells are aggregation deficient, have a faster cell cycle and are hypersensitive to oxidative and nitrosoative stress. With the aim of isolating members of the YakA pathway, suppressors of the death induced by nitrosoative stress in the yakA-cells were identified. One of the suppressor mutations occurred in keaA, a gene identical to DG1106 and similar to Keap1 from mice and the Kelch protein from Drosophila, among others that contain Kelch domains. Results: A mutation in keaA suppresses the hypersensitivity to oxidative and nitrosoative stresses but not the faster growth phenotype of yakA-cells. The growth profile of keaA deficient cells indicates that this gene is necessary for growth. keaA deficient cells are more resistant to nitrosoative and oxidative stress and keaA is necessary for the production and detection of cAMP. A morphological analysis of keaA deficient cells during multicellular development indicated that, although the mutant is not absolutely deficient in aggregation, cells do not efficiently participate in the process. Gene expression analysis using cDNA microarrays of wild-type and keaA deficient cells indicated a role for KeaA in the regulation of the cell cycle and pre-starvation responses. Conclusions: KeaA is required for cAMP signaling following stress. Our studies indicate a role for kelch proteins in the signaling that regulates the cell cycle and development in response to changes in the environmental conditions.

Giant Vesicles under Oxidative Stress Induced by a Membrane-Anchored Photosensitizer

We have synthesized the amphiphile photosensitizer PE-porph consisting of a porphyrin bound to a lipid head-group. We studied by optical microscopy the response to light irradiation of giant unilamellar vesicles of mixtures of unsaturated phosphatidylcholine lipids and PE-porph. In this configuration, singlet oxygen is produced at the bilayer surface by the anchored porphyrin. Under irradiation, the PE-porph decorated giant unilamellar vesicles exhibit a rapid increase in surface area with concomitant morphological changes. We quantify the surface area increase of the bilayers as a function of time and photosensitizer molar fraction. We attribute this expansion to hydroperoxide formation by the reaction of the singlet oxygen with the unsaturated bonds. Considering data from numeric simulations of relative area increase per phospholipid oxidized (15%), we measure the efficiency of the oxidative reactions. We conclude that for every 270 singlet oxygen molecules produced by the layer of anchored porphyrins, one eventually reacts to generate a hydroperoxide species. Remarkably, the integrity of the membrane is preserved in the full experimental range explored here, up to a hydroperoxide content of 60%, inducing an 8% relative area expansion.

Enhancement of hematoporphyrin IX potential for photodynamic therapy by entrapment in silica nanospheres

The entrapment of hematoporphyrin IX (Hp IX) in silica by means of a microemulsion resulted in silica spheres of 33 +/- 6 nm. The small size, narrow size distribution and lack of aggregation maintain Hp IX silica nanospheres stable in aqueous solutions for long periods and permit a detailed study of the entrapped drug by different techniques. Hp IX entrapped in the silica matrix is accessed by oxygen and upon irradiation generates singlet oxygen which diffuses very efficiently to the outside solution. The Hp IX entrapped in the silica matrix is also reached by iron(II) ions, which causes quenching of the porphyrin fluorescence emission. The silica matrix also provides extra protection to the photosensitizer against interaction with BSA and ascorbic acid, which are known to cause suppression of singlet oxygen generation by the Hp IX free in solution. Therefore, the incorporation of Hp IX molecules into silica nanospheres increased the potential of the photosensitizer to perform photodynamic therapy.

Galerkin Solution of Stochastic Beam Bending on Winkler Foundations

In this paper, the Askey-Wiener scheme and the Galerkin method are used to obtain approximate solutions to stochastic beam bending on Winkler foundation. The study addresses Euler-Bernoulli beams with uncertainty in the bending stiffness modulus and in the stiffness of the foundation. Uncertainties are represented by parameterized stochastic processes. The random behavior of beam response is modeled using the Askey-Wiener scheme. One contribution of the paper is a sketch of proof of existence and uniqueness of the solution to problems involving fourth order operators applied to random fields. From the approximate Galerkin solution, expected value and variance of beam displacement responses are derived, and compared with corresponding estimates obtained via Monte Carlo simulation. Results show very fast convergence and excellent accuracies in comparison to Monte Carlo simulation. The Askey-Wiener Galerkin scheme presented herein is shown to be a theoretically solid and numerically efficient method for the solution of stochastic problems in engineering.

A flexible consensus scheme for multicriteria group decision making under linguistic assessments

The present paper proposes a flexible consensus scheme for group decision making, which allows one to obtain a consistent collective opinion, from information provided by each expert in terms of multigranular fuzzy estimates. It is based on a linguistic hierarchical model with multigranular sets of linguistic terms, and the choice of the most suitable set is a prerogative of each expert. From the human viewpoint, using such model is advantageous, since it permits each expert to utilize linguistic terms that reflect more adequately the level of uncertainty intrinsic to his evaluation. From the operational viewpoint, the advantage of using such model lies in the fact that it allows one to express the linguistic information in a unique domain, without losses of information, during the discussion process. The proposed consensus scheme supposes that the moderator can interfere in the discussion process in different ways. The intervention can be a request to any expert to update his opinion or can be the adjustment of the weight of each expert`s opinion. An optimal adjustment can be achieved through the execution of an optimization procedure that searches for the weights that maximize a corresponding soft consensus index. In order to demonstrate the usefulness of the presented consensus scheme, a technique for multicriteria analysis, based on fuzzy preference relation modeling, is utilized for solving a hypothetical enterprise strategy planning problem, generated with the use of the Balanced Scorecard methodology. (C) 2009 Elsevier Inc. All rights reserved.

Reconfiguration of distribution networks to minimize loss and disruption costs using genetic algorithms

In this paper a computational implementation of an evolutionary algorithm (EA) is shown in order to tackle the problem of reconfiguring radial distribution systems. The developed module considers power quality indices such as long duration interruptions and customer process disruptions due to voltage sags, by using the Monte Carlo simulation method. Power quality costs are modeled into the mathematical problem formulation, which are added to the cost of network losses. As for the EA codification proposed, a decimal representation is used. The EA operators, namely selection, recombination and mutation, which are considered for the reconfiguration algorithm, are herein analyzed. A number of selection procedures are analyzed, namely tournament, elitism and a mixed technique using both elitism and tournament. The recombination operator was developed by considering a chromosome structure representation that maps the network branches and system radiality, and another structure that takes into account the network topology and feasibility of network operation to exchange genetic material. The topologies regarding the initial population are randomly produced so as radial configurations are produced through the Prim and Kruskal algorithms that rapidly build minimum spanning trees. (C) 2009 Elsevier B.V. All rights reserved.

Coarse-grid higher order finite-difference time-domain algorithm with low dispersion errors

Higher order (2,4) FDTD schemes used for numerical solutions of Maxwell`s equations are focused on diminishing the truncation errors caused by the Taylor series expansion of the spatial derivatives. These schemes use a larger computational stencil, which generally makes use of the two constant coefficients, C-1 and C-2, for the four-point central-difference operators. In this paper we propose a novel way to diminish these truncation errors, in order to obtain more accurate numerical solutions of Maxwell`s equations. For such purpose, we present a method to individually optimize the pair of coefficients, C-1 and C-2, based on any desired grid size resolution and size of time step. Particularly, we are interested in using coarser grid discretizations to be able to simulate electrically large domains. The results of our optimization algorithm show a significant reduction in dispersion error and numerical anisotropy for all modeled grid size resolutions. Numerical simulations of free-space propagation verifies the very promising theoretical results. The model is also shown to perform well in more complex, realistic scenarios.

Study of copper electrodeposition mechanism from a strike alkaline bath prepared with 1-hydroxyethane-1,1-diphosphonic acid through cyclic voltammetry technique

Copper strike baths are extensively used in metal plating industry as they present the ability to plate adherent copper layers on less-noble metal substrates such as steel and zinc die castings. However, in the last few years, due to environmental controls and safety policies for operators, the plating industry has been interested in replacing the toxic cyanide copper strike baths with environmentally friendly baths. A broad bibliographic review showed that the published papers, referring to the new nontoxic copper strike baths, are patents, having little or no emphasis focused on electrodeposition mechanisms. Therefore, it was decided to study the copper electrodeposition mechanism from a strike alkaline bath prepared with one of the most nontoxic chelating agents cited in many patents which is the 1-hydroxyethane-1,1-diphosphonic acid, known as HEDP. This acid forms very stable water soluble complexes with Cu(2+) ions, thus cupric sulfate was used for preparing the plating bath. The results obtained through a cyclic voltammetry technique showed that Cu(2+) ion reduction to Cu from an HEDP electrodeposition bath occurs via a direct reduction reaction without a formation of Cu(+) intermediates. (C) 2010 Elsevier Ltd. All rights reserved.

Spatial pattern of black spot incidence within citrus trees related to disease severity and pathogen dispersal

Guignardia citricarpa, the causal agent of citrus black spot, forms airborne ascospores on decomposing citrus leaves and water-spread conidia on fruits, leaves and twigs. The spatial pattern of diseased fruit in citrus tree canopies was used to assess the importance of ascospores and conidia in citrus black spot epidemics in Sao Paulo State, Brazil. The aggregation of diseased fruit in the citrus tree canopy was quantified by the binomial dispersion index (D) and the binary form of Taylor`s Power Law for 303 trees in six groves. D was significantly greater than 1 in 251 trees. The intercept of the regression line of Taylor`s Power Law was significantly greater than 0 and the slope was not different from 1, implying that diseased fruit was aggregated in the canopy independent of disease incidence. Disease incidence (p) and severity (S) were assessed in 2875 citrus trees. The incidence-severity relationship was described (R-2 = 88.7%) by the model ln(S) = ln(a) + bCLL(p) where CLL = complementary log-log transformation. The high severity at low incidence observed in many cases is also indicative of low distance spread of G. citricarpa spores. For the same level of disease incidence, some trees had most of the diseased fruit with many lesions and high disease severity, whereas other trees had most of the fruit with few lesions and low disease severity. Aggregation of diseased fruit in the trees suggests that splash-dispersed conidia have an important role in increasing the disease in citrus trees in Brazil.

Potential beneficial properties of bacteriocin-producing lactic acid bacteria isolated from smoked salmon

Aims: To evaluate the probiotic properties of strains isolated from smoked salmon and previously identified as bacteriocin producers. Methods and Results: Strains Lactobacillus curvatus ET06, ET30 and ET31, Lactobacillus fermentum ET35, Lactobacillus delbrueckii ET32, Pediococcus acidilactici ET34 and Enterococcus faecium ET05, ET12 and ET88 survived conditions simulating the gastrointestinal tract (GIT) and produced bacteriocins active against several strains of Listeria monocytogenes, but presented very low activity against other lactic acid bacteria (LAB). Cell-free supernatants containing bacteriocins, added to 3-h-old cultures of L. monocytogenes 603, suppressed growth over 12 h. Auto-aggregation was strain-specific, and values ranged from 7 center dot 2% for ET35 to 12 center dot 1% for ET05. Various degrees of co-aggregation with L. monocytogenes 603, Lactobacillus sakei ATCC 15521 and Enterococcus faecalis ATCC 19443 were observed. Adherence of the bacteriocinogenic strains to Caco-2 cells was within the range reported for Lactobacillus rhamnosus GG, a well-known probiotic. The highest levels of hydrophobicity were recorded for Lact. curvatus (61 center dot 9-64 center dot 6%), Lact. fermentum (78 center dot 9%), Lact. delbrueckii (43 center dot 7%) and Ped. acidilactici (51 center dot 3%), which are higher than the one recorded for Lact. rhamnosus GG (53 center dot 3%). These strains were highly sensitive to several antibiotics and affected by several drugs from different generic groups in a strain-dependent manner. Conclusions: Smoked salmon is a rich source of probiotic LAB. All strains survived conditions simulating the GIT and produced bacteriocins active against various pathogens. Adherence to Caco-2 cells was within the range reported for Lact. rhamnosus GG, a well-known probiotic. In addition, the high hydrophobicity readings recorded define the strains as good probiotics. Significance and Impact of the Study: Smoked salmon contains a number of different probiotic LAB and could be marketed as having a potential beneficial effect.