A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

THE CRYSTAL STRUCTURE OF A MICROLITE-GROUP MINERAL WITH A FORMULA NEAR NaCaTa(2)O(6)F FROM THE MORRO REDONDO MINE, CORONEL MURTA, MINAS GERAIS, BRAZIL

We present electron-microprobe and single-crystal X-ray-diffraction data for a microlite-group mineral with a formula near NaCaTa(2)O(6)F from the Morro Redondo mine, Coronel Murta, Minas Gerais, Brazil. On the basis of these data, the formula is A(Na(0.88)Ca(0.88)Pb(0.02)square(0.22))(Sigma 2.00) (B)(Ta(1.70)Nb(0.14)Si(0.12)As(0.04))(Sigma 2.00) (X)[(O(5.75)(OH)(0.25)](Sigma 6.00) (Y)(F(0.73)square(0.27))(Sigma 1.00). According to the new nomenclature for the pyrochlore-supergroup minerals, it is intermediate between fluornatromicrolite and "" fluorcalciomicrolite"". The crystal structure, F (d3) over barm, a = 10.4396(12) angstrom, has been refined to an R(1) value of 0.0258 (wR(2) = 0.0715) for 107 reflections (MoK alpha radiation). There is a scarcity of crystal-chemical data for pyrochlore-supergroup minerals in the literature. A compilation of these data is presented here.

On a product formula for the Conley-Zelmder index of symplectic paths and its applications

Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley-Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.

On a formula for the spectral flow and its applications

We consider a continuous path of bounded symmetric Fredholm bilinear forms with arbitrary endpoints on a real Hilbert space, and we prove a formula that gives the spectral flow of the path in terms of the spectral flow of the restriction to a finite codimensional closed subspace. We also discuss the case of restrictions to a continuous path of finite codimensional closed subspaces. As an application of the formula, we introduce the notion of spectral flow for a periodic semi-Riemannian geodesic, and we compute its value in terms of the Maslov index. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

A matrix formula for the skewness of maximum likelihood estimators

We give a general matrix formula for computing the second-order skewness of maximum likelihood estimators. The formula was firstly presented in a tensorial version by Bowman and Shenton (1998). Our matrix formulation has numerical advantages, since it requires only simple operations on matrices and vectors. We apply the second-order skewness formula to a normal model with a generalized parametrization and to an ARMA model. (c) 2010 Elsevier B.V. All rights reserved.

Covariance matrix formula for Birnbaum-Saunders regression models

The Birnbaum-Saunders regression model is commonly used in reliability studies. We derive a simple matrix formula for second-order covariances of maximum-likelihood estimators in this class of models. The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors. Some simulation results show that the second-order covariances can be quite pronounced in small to moderate sample sizes. We also present empirical applications.

A Character Formula for the Category (O)over-tilde of Modules for Affine sl(2)

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2) using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realize the irreducible modules with finite-dimensional weight spaces in the category (O) over tilde of Chari. In this work, an expression for the formal character of such a module is derived using the highest weight theory of truncations of the loop algebra.

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.

Innovation and entrepreneurship in scientific research

This research wants to lay emphasis on topics that historicize and rescue concepts, in addition, shows the relation between innovation and socioeconomic development resulted; reviews the legal framework to stimulate new innovation into Brazilian society; considers the definition and the entrepreneur university's new paradigm; and finally, this research highlights the importance of teaching entrepreneur at universities, with straight society benefits. The results suggests that innovation is directly enrolled with a successful development of certain society, as well, is actually the biggest business competitive differential into corporative universe. In one way of getting results of social advancement to inform entrepreneur research practice, it appears that entrepreneurs concepts, necessarily, must be incorporated into the array of Science/Technology/Innovation for the effective development of supported formula. This article develops a thought about actual scientific researches paradigm, the way that is built on today, and if it's sufficient to effectively get the results that society expects from main bodies to create human resource and researches, especially those with innovation aspects, at Brazilian economic improvement.

Validity and reliability of the Structured Clinical Interview for Mood Spectrum: Brazilian version (SCIMOODS-VB)

OBJECTIVE: The aim of this study was to translate the Structured Clinical Interview for Mood Spectrum into Brazilian Portuguese, measuring its reliability, validity, and defining scores for bipolar disorders. METHOD: Questionnaire was translated (into Brazilian Portuguese) and back-translated into English. Sample consisted of 47 subjects with bipolar disorder, 47 with major depressive disorder, 18 with schizophrenia and 22 controls. Inter-rater reliability was tested in 20 subjects with bipolar disorder and MDD. Internal consistency was measured using the Kuder Richardson formula. Forward stepwise discriminant analysis was performed. Scores were compared between groups; manic (M), depressive (D) and total (T) threshold scores were calculated through receiver operating characteristic (ROC) curves. RESULTS: Kuder Richardson coefficients were between 0.86 and 0.94. Intraclass correlation coefficient was 0.96 (CI 95 % 0.93-0.97). Subjects with bipolar disorder had higher M and T, and similar D scores, when compared to major depressive disorder (ANOVA, p < 0.001). The sub-domains that best discriminated unipolar and bipolar subjects were manic energy and manic mood. M had the best area under the curve (0.909), and values of M equal to or greater than 30 yielded 91.5% sensitivity and 74.5% specificity. CONCLUSION: Structured Clinical Interview for Mood Spectrum has good reliability and validity. Cut-off of 30 best differentiates subjects with bipolar disorder vs. unipolar depression. A cutoff score of 30 or higher in the mania sub-domain is appropriate to help make a distinction between subjects with bipolar disorder and those with unipolar depression.

An analytical solution for the critical number of particles for stable bose-einstein condensation under the influence of an anisotropic potential

We have considered a Bose gas in an anisotropic potential. Applying the the Gross-Pitaevskii Equation (GPE) for a confined dilute atomic gas, we have used the methods of optimized perturbation theory and self-similar root approximants, to obtain an analytical formula for the critical number of particles as a function of the anisotropy parameter for the potential. The spectrum of the GPE is also discussed.

T.W. Adorno e a psicologia social

Neste ensaio, ressalta-se a importância da disciplina Psicologia Social na obra de T. W. Adorno e a concepção que formula acerca dessa disciplina. Esse autor defende que há uma nova forma de configuração dos indivíduos, expressada por atitudes e comportamentos individuais padronizados e por um ego frágil, facilmente cooptado por movimentos sociais totalitários. Tais indivíduos surgem em uma sociedade caracterizada por uma forma de dominação calcada na racionalidade administrativa e tecnológica. Para esse autor, a Psicologia Social deveria estudar esse objeto para que, com o esclarecimento produzido e difundido, os indivíduos possam resistir à adesão cega a movimentos sociais irracionais, tal como o fascismo, insistindo que a determinação desses movimentos não é individual, mas social.

New species of the genus Leporinus Agassiz (Characiformes: Anostomidae) from the rio Curuá, rio Xingu basin, Serra do Cachimbo, Brazil, with comments on Leporinus reticulatus

A new species of Leporinus Agassiz is described from the rio Curuá, a tributary of the rio Iriri, rio Xingu basin, Serra do Cachimbo, Pará State, Brazil. The new species is diagnosed by the color pattern, which consists of eight to ten midlateral round dark blotches plus 20 to 40 smaller ones scattered over the body, dental formula 3/4, subinferior to inferior mouth, 37 to 38 lateral line scales, 4/3-4 transversal series of scales, and 12 circumpeduncular scale series. The new species most closely resembles L. octomaculatus and L. reticulatus from the upper Tapajós basin, and L. marcgravii and L. microphthalmus from the rio São Francisco and the rio Paranaíba, respectively. Based on recently collected specimens, L. reticulatus is re-diagnosed as having an allometric elongation of the snout.

Description of a new species of the genus Leporinus Spix (Characiformes: Anostomidae) from the rio Araguaia, Brazil, with comments on the taxonomy and distribution of L. parae and L. lacustris

A new species of the genus Leporinus is described from the rio Araguaia, in Mato Grosso and Goiás states, Brazil. The new species has the dental formula 4/3, a unique feature within the genus; all other species of Leporinus have dental formulae 3/3, 3/4 or 4/4. In addition, the new species can also be distinguished by the following combination of characters: 36 to 37 scales in the lateral line, 4/4.5 or 4/5 series of scales in the transversal line, 16 circumpeduncular scale series, anal fin surpassing base of lower caudal-fin rays and three blotches along the lateral line. The new species shares with L. parae and L. lacustris a rather deep body, terminal mouth, long anal fin, three small dark blotches on the lateral line, the latter two, particularly the last one, usually fading, and preference for lentic habitats. Comments on the taxonomy and distribution of the species L. parae and L. lacustris are provided.