The spectrum of an open vertex model based on the U(q)[SU(2)] algebra at roots of unity

We study the exact solution of an N-state vertex model based on the representation of the U(q)[SU(2)] algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal K-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables. (C) 2010 Elsevier B.V. All rights reserved.

Noncommutativity due to spin

Using the Berezin-Marinov pseudoclassical formulation of the spin particle we propose a classical model of spin noncommutativity. In the nonrelativistic case, the Poisson brackets between the coordinates are proportional to the spin angular momentum. The quantization of the model leads to the noncommutativity with mixed spatial and spin degrees of freedom. A modified Pauli equation, describing a spin half particle in an external electromagnetic field is obtained. We show that nonlocality caused by the spin noncommutativity depends on the spin of the particle; for spin zero, nonlocality does not appear, for spin half, Delta x Delta y >= theta(2)/2, etc. In the relativistic case the noncommutative Dirac equation was derived. For that we introduce a new star product. The advantage of our model is that in spite of the presence of noncommutativity and nonlocality, it is Lorentz invariant. Also, in the quasiclassical approximation it gives noncommutativity with a nilpotent parameter.

Quantum and pseudoclassical descriptions of nonrelativistic spinning particles in noncommutative space

We construct a nonrelativistic wave equation for spinning particles in the noncommutative space (in a sense, a theta modification of the Pauli equation). To this end, we consider the nonrelativistic limit of the theta-modified Dirac equation. To complete the consideration, we present a pseudoclassical model (a la Berezin-Marinov) for the corresponding nonrelativistic particle in the noncommutative space. To justify the latter model, we demonstrate that its quantization leads to the theta-modified Pauli equation. We extract theta-modified interaction between a nonrelativistic spin and a magnetic field from such a Pauli equation and construct a theta modification of the Heisenberg model for two coupled spins placed in an external magnetic field. In the framework of such a model, we calculate the probability transition between two orthogonal Einstein-Podolsky-Rosen states for a pair of spins in an oscillatory magnetic field and show that some of such transitions, which are forbidden in the commutative space, are possible due to the space noncommutativity. This allows us to estimate an upper bound on the noncommutativity parameter.

Quantum reflection: The invisible quantum barrier

We construct an invisible quantum barrier which represents the phenomenon of quantum reflection using available data on atom-wall and Bose-Einstein-condensate-wall reflection. We use the Abel equation to invert the data. The resulting invisible quantum barrier is double valued in both axes. We study this invisible barrier in the case of atom and Bose-Einstein condensate (BEC) reflection from a solid silicon surface. A time-dependent, one-spatial-dimension Gross-Pitaevskii equation is solved for the BEC case. We found that the BEC behaves very similarly to the single atom except for size effects, which manifest themselves in a maximum in the reflectivity at small distances from the wall. The effect of the atom-atom interaction on the BEC reflection and correspondingly on the invisible barrier is found to be appreciable at low velocities and comparable to the finite-size effect. The trapping of an ultracold atom or BEC between two walls is discussed.

Anisotropic singularities in modified gravity models

We show that the common singularities present in generic modified gravity models governed by actions of the type S = integral d(4)x root-gf(R, phi, X). with X = -1/2 g(ab)partial derivative(a)phi partial derivative(b)phi, are essentially the same anisotropic instabilities associated to the hypersurface F(phi) = 0 in the case of a nonminimal coupling of the type F(phi)R, enlightening the physical origin of such singularities that typically arise in rather complex and cumbersome inhomogeneous perturbation analyses. We show, moreover, that such anisotropic instabilities typically give rise to dynamically unavoidable singularities, precluding completely the possibility of having physically viable models for which the hypersurface partial derivative f/partial derivative R = 0 is attained. Some examples are explicitly discussed.

An extension of the Pitzer equation for the excess Gibbs energy of aqueous electrolyte systems to aqueous polyelectrolyte solutions

Pitzer`s equation for the excess Gibbs energy of aqueous solutions of low-molecular electrolytes is extended to aqueous solutions of polyelectrolytes. The model retains the original form of Pitzer`s model (combining a long-range term, based on the Debye-Huckel equation, with a short-range term similar to the virial equation where the second osmotic virial coefficient depends on the ionic strength). The extension consists of two parts: at first, it is assumed that a constant fraction of the monomer units of the polyelectrolyte is dissociated, i.e., that fraction does not depend on the concentration of the polyelectrolyte, and at second, a modified expression for the ionic strength (wherein each charged monomer group is taken into account individually) is introduced. This modification is to account for the presence of charged polyelectrolyte chains, which cannot be regarded as punctual charges. The resulting equation was used to correlate osmotic coefficient data of aqueous solutions of a single polyelectrolyte as well as of binary mixtures of a single polyelectrolyte and a salt with low-molecular weight. It was additionally applied to correlate liquid-liquid equilibrium data of some aqueous two-phase systems that might form when a polyelectrolyte and another hydrophilic but neutral polymer are simultaneously dissolved in water. A good agreement between the experimental data and the correlation result is observed for all investigated systems. (c) 2008 Elsevier B.V. All rights reserved.

Memory and hypertext: a reflection on relational knowledge

This paper analyzes the changes the ways of organizing memory have undergone since ancient times, turning them into the current artificial memory systems. It aims to draw a parallel between the art of memory (which associates images to specific texts) and the hypertext (which also uses associations, but in a non-linear way). Our methodology consisted of a qualitative approach, involving the collection of texts about the art of memory and hypertext; this enables us to salvage the historical-cultural changes which have modified form and use of the art of memory and allowed the creation of hypertext. It also analyzes the similarities among artificial memory systems created by different cultures in order to prevent loss of knowledge produced by society.

Dirac equation in noncommutative space for hydrogen atom

We consider the energy levels of a hydrogen-like atom in the framework of theta-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S(1/2), 2P(1/2) and 2P(3/2) is lifted completely, such that new transition channels are allowed. (C) 2009 Elsevier B.V. All rights reserved.

Lie algebra methods for the applications to the statistical theory of turbulence

Approximate Lie symmetries of the Navier-Stokes equations are used for the applications to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to involve the Reynolds number dependence into scaling laws. Moreover, the optimal systems of all finite-dimensional Lie subalgebras of the approximate symmetry transformations of the Navier-Stokes are constructed. We show how the scaling groups obtained can be used to introduce the Reynolds number dependence into scaling laws explicitly for stationary parallel turbulent shear flows. This is demonstrated in the framework of a new approach to derive scaling laws based on symmetry analysis [11]-[13].

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

Fluoride release profile of a nanofilled resin-modified glass ionomer cement

The present study aimed to compare the fluoride (F-) release pattern of a nanofilled resin-modified glass ionomer cement (GIC) (Ketac N100 - KN) with available GICs used in dental practice (resin-modified GIC - Vitremer - V; conventional GIC - Ketac Molar - KM) and a nanofilled resin composite (Filtek Supreme - RC). Discs of each material (n=6) were placed into 4 mL of deionized water in sealed polyethylene vials and shaken, for 15 days. F- release (μg F-/cm²) was measured each day using a fluoride-ion specific electrode. Cumulative F- release means were statistically analyzed by linear regression analysis. In order to analyze the differences among materials and the influence of time in the daily F- release, 2-way ANOVA test was performed (α=0.05). The linear fits between the cumulative F- release profiles of RC and KM and time were weak. KN and V presented a strong relationship between cumulative F- release and time. There were significant differences between the daily F- release overtime up to the third day only for GICs materials. The daily F- release means for RC were similar overtime. The results indicate that the F- release profile of the nanofilled resin-modified GIC is comparable to the resin-modified GIC.

Rehabilitation of severely resorbed edentulous mandible using the modified visor osteotomy technique

The prosthetic rehabilitation of an atrophic mandible is usually unsatisfactory due to the lack of support tissues, mainly bone and keratinized mucosa for treatment with osseointegrated implants or even conventional prosthesis. The prosthetic instability leads to social and functional limitations and chronic physical trauma decreasing the patient's quality of life. A 53-year-old female patient sought care at our surgical service complaining of impairment of her masticatory function associated with the instability of the lower total prosthetic denture. The clinical and complementary exams revealed edentulism in both arches, while the mandibular arch presented severe reabsorption resulting in denture instability and chronic trauma to the oral mucosa. The proposed treatment plan consisted in the mandibular rehabilitation with osseointegrated implants and fixed Brånemark's protocol prosthesis after mandibular reconstruction applying the modified visor osteotomy technique. The proposed technique offered predictable results for reconstruction of the severely resorbed edentulous mandible and posterior rehabilitation with osseointegrated implants.

Shelf-life of a 2.5% sodium hypochlorite solution as determined by arrhenius equation

Accelerated stability tests are indicated to assess, within a short time, the degree of chemical degradation that may affect an active substance, either alone or in a formula, under normal storage conditions. This method is based on increased stress conditions to accelerate the rate of chemical degradation. Based on the equation of the straight line obtained as a function of the reaction order (at 50 and 70 ºC) and using Arrhenius equation, the speed of the reaction was calculated for the temperature of 20 ºC (normal storage conditions). This model of accelerated stability test makes it possible to predict the chemical stability of any active substance at any given moment, as long as the method to quantify the chemical substance is available. As an example of the applicability of Arrhenius equation in accelerated stability tests, a 2.5% sodium hypochlorite solution was analyzed due to its chemical instability. Iodometric titration was used to quantify free residual chlorine in the solutions. Based on data obtained keeping this solution at 50 and 70 ºC, using Arrhenius equation and considering 2.0% of free residual chlorine as the minimum acceptable threshold, the shelf-life was equal to 166 days at 20 ºC. This model, however, makes it possible to calculate shelf-life at any other given temperature.

Isotermas de dessorção de filé de bonito (Sarda sarda) desidratado osmoticamente e defumado

O presente trabalho teve como objetivo a obtenção de isotermas de dessorção de filés de bonito (Sarda sarda), previamente salgados a vácuo e defumados com fumaça líquida. As isotermas foram obtidas a quatro temperaturas (5, 25, 40 e 60 ºC) em condições de dessorção, através do método gravimétrico estático, com soluções salinas saturadas. Os dados experimentais foram ajustados a quatro modelos da literatura (BET linearizado, GAB, Henderson e Oswin modificado). Os resultados mostraram que as isotermas tomaram forma sigmoidal de tipo II e que o modelo de Guggenheim-Anderson-deBoer (GAB) foi aceitável para modelar os dados experimentais. O calor isostérico de dessorção, um parâmetro necessário para simular e projetar adequadamente o secador, também foi calculado e pode ser representado através de um modelo matemático simples, em função da umidade de equilíbrio.

Antibacterial modified diketopiperazines from two ascidians of the genus Didemnum

The chemical investigation of the crude extract of an ascidian of the genus Didemnumled to the isolation of the modified diketopiperazine rodriguesines A (1) and (2) as a mixture of homologues, which could be identified by analysis of spectroscopic data including MS/MS experiments. The investigation of a second Didemnumsp. led to the isolation of N-acetyl-rodriguesine A (3) and N-acetyl-rodriguesine B (4). The absolute configuration of compounds 1and 2could be established by hydrolysis and Marfey's analysis and comparison with literature data reported for compound 3, previously obtained as a synthetic product. The mixture of 1and 2displayed moderate antibiotic activity against a clinical isolate of Streptococcus mutansand against S. mutansUA159 and Staphylococcus aureusATCC6538.