ZETA DETERMINANT AND OPERATOR DETERMINANTS

We apply techniques of zeta functions and regularized products theory to study the zeta determinant of a class of abstract operators with compact resolvent, and in particular the relation with other spectral functions.

Numerical investigation of the quantum fluctuations of optical fields transmitted through an atomic medium

We have numerically solved the Heisenberg-Langevin equations describing the propagation of quantized fields through an optically thick sample of atoms. Two orthogonal polarization components are considered for the field, and the complete Zeeman sublevel structure of the atomic transition is taken into account. Quantum fluctuations of atomic operators are included through appropriate Langevin forces. We have considered an incident field in a linearly polarized coherent state (driving field) and vacuum in the perpendicular polarization and calculated the noise spectra of the amplitude and phase quadratures of the output field for two orthogonal polarizations. We analyze different configurations depending on the total angular momentum of the ground and excited atomic states. We examine the generation of squeezing for the driving-field polarization component and vacuum squeezing of the orthogonal polarization. Entanglement of orthogonally polarized modes is predicted. Noise spectral features specific to (Zeeman) multilevel configurations are identified.

On the mixing property for a class of states of relativistic quantum fields

Let omega be a factor state on the quasilocal algebra A of observables generated by a relativistic quantum field, which, in addition, satisfies certain regularity conditions [satisfied by ground states and the recently constructed thermal states of the P(phi)(2) theory]. We prove that there exist space- and time-translation invariant states, some of which are arbitrarily close to omega in the weak * topology, for which the time evolution is weakly asymptotically Abelian. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3372623]

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.

Long life of Gauss-Bonnet corrected black holes

Dictated by the string theory and various higher dimensional scenarios, black holes in D > 4-dimensional space-times must have higher curvature corrections. The first and dominant term is quadratic in curvature, and called the Gauss-Bonnet (GB) term. We shall show that although the Gauss-Bonnet correction changes black hole's geometry only softly, the emission of gravitons is suppressed by many orders even at quite small values of the GB coupling. The huge suppression of the graviton emission is due to the multiplication of the two effects: the quick cooling of the black hole when one turns on the GB coupling and the exponential decreasing of the gray-body factor of the tensor type of gravitons at small and moderate energies. At higher D the tensor gravitons emission is dominant, so that the overall lifetime of black holes with Gauss-Bonnet corrections is many orders larger than was expected. This effect should be relevant for the future experiments at the Large Hadron Collider (LHC).

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.

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.

HYBRID AND INCREMENTAL FUZZY LEARNING FOR HUMAN SKIN DETECTION

In this paper, a framework for detection of human skin in digital images is proposed. This framework is composed of a training phase and a detection phase. A skin class model is learned during the training phase by processing several training images in a hybrid and incremental fuzzy learning scheme. This scheme combines unsupervised-and supervised-learning: unsupervised, by fuzzy clustering, to obtain clusters of color groups from training images; and supervised to select groups that represent skin color. At the end of the training phase, aggregation operators are used to provide combinations of selected groups into a skin model. In the detection phase, the learned skin model is used to detect human skin in an efficient way. Experimental results show robust and accurate human skin detection performed by the proposed framework.

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.

Improved Bioprocess with CHO-hTSH Cells on Higher Microcarrier Concentration Provides Higher Overall Biomass and Productivity for rhTSH

Since the recombinant thyroid-stimulating hormone (rhTSH) is secreted by stably transfected Chinese hamster ovary (CHO-hTSH) cells, a bioprocess consisting of immobilizing the cells on a substrate allowing their multiplication is very suitable for rhTSH recovering from supernatants at relative high degree of purity. In addition, such a system has also the advantage of easily allowing delicate manipulations of culture medium replacement. In the present study, we show the development of a laboratory scale bioprocess protocol of CHO-hTSH cell cultures on cytodex microcarriers (MCs) in a 1 L bioreactor, for the preparation of rhTSH batches in view of structure/function studies. CHO-hTSH cells were cultivated on a fetal bovine serum supplemented medium during cell growth phase. For rhTSH synthesis phase, 75% of supernatant was replaced by animal protein-free medium every 24 h. Cell cultures were monitored for agitation (rpm), temperature (A degrees C), dissolved oxygen (% DO), pH, cell concentration, MCs coverage, glucose consumption, lactate production, and rhTSH expression. The results indicate that the amount of MCs in the culture and the cell concentration at the beginning of rhTSH synthesis phase were crucial parameters for improving the final rhTSH production. By cultivating the CHO-hTSH cells with an initial cell seeding of four cells/MC on 4 g/L of MCs with a repeated fed batch mode of operation at 40 rpm, 37 A degrees C, 20% DO, and pH 7.2 and starting the rhTSH synthesis phase with 3 x 10(6) cells/mL, we were able to supply the cultures with enough glucose, to maintain low levels of lactate, and to provide high percent (similar to 80%) of fully covered MCs for a long period (5 days) and attain a high cell concentration (similar to 9 x 10(5) cells/mL). The novelty of the present study is represented by the establishment of cell culture conditions allowing us to produce similar to 1.6 mg/L of rhTSH in an already suitable degree of purity. Batches of produced rhTSH were purified and showed biological activity.

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.