A comparative study of a direct discretization and an operator-splitting solver for population balance systems

A direct discretization approach and an operator-splitting scheme are applied for the numerical simulation of a population balance system which models the synthesis of urea with a uni-variate population. The problem is formulated in axisymmetric form and the setup is chosen such that a steady state is reached. Both solvers are assessed with respect to the accuracy of the results, where experimental data are used for comparison, and the efficiency of the simulations. Depending on the goal of simulations, to track the evolution of the process accurately or to reach the steady state fast, recommendations for the choice of the solver are given. (C) 2015 Elsevier Ltd. All rights reserved.

Lower bounds on Ricci flow invariant curvatures and geometric applications

We consider Ricci flow invariant cones C in the space of curvature operators lying between the cones ``nonnegative Ricci curvature'' and ``nonnegative curvature operator''. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to the Ricci flow has its curvature operator which satisfies R + epsilon I is an element of C at the initial time, then it satisfies R + epsilon I is an element of C on some time interval depending only on the scalar curvature control. This allows us to link Gromov-Hausdorff convergence and Ricci flow convergence when the limit is smooth and R + I is an element of C along the sequence of initial conditions. Another application is a stability result for manifolds whose curvature operator is almost in C. Finally, we study the case where C is contained in the cone of operators whose sectional curvature is nonnegative. This allows us to weaken the assumptions of the previously mentioned applications. In particular, we construct a Ricci flow for a class of (not too) singular Alexandrov spaces.

Universality of the Stochastic Airy Operator

We introduce a new method for studying universality of random matrices. Let T-n be the Jacobi matrix associated to the Dyson beta ensemble with uniformly convex polynomial potential. We show that after scaling, Tn converges to the stochastic Airy operator. In particular, the top edge of the Dyson beta ensemble and the corresponding eigenvectors are universal. As a byproduct, these ideas lead to conjectured operator limits for the entire family of soft edge distributions. (C) 2015 Wiley Periodicals, Inc.

Isolated singularities of polyharmonic operator in even dimension

We consider the equation Delta(2)u = g(x, u) >= 0 in the sense of distribution in Omega' = Omega\textbackslash {0} where u and -Delta u >= 0. Then it is known that u solves Delta(2)u = g(x, u) + alpha delta(0) - beta Delta delta(0), for some nonnegative constants alpha and beta. In this paper, we study the existence of singular solutions to Delta(2)u = a(x) f (u) + alpha delta(0) - beta Delta delta(0) in a domain Omega subset of R-4, a is a nonnegative measurable function in some Lebesgue space. If Delta(2)u = a(x) f (u) in Omega', then we find the growth of the nonlinearity f that determines alpha and beta to be 0. In case when alpha = beta = 0, we will establish regularity results when f (t) <= Ce-gamma t, for some C, gamma > 0. This paper extends the work of Soranzo (1997) where the author finds the barrier function in higher dimensions (N >= 5) with a specific weight function a(x) = |x|(sigma). Later, we discuss its analogous generalization for the polyharmonic operator.

Trace Formulae in Operator Theory

In this article, we survey several kinds of trace formulas that one encounters in the theory of single and multi-variable operators. We give some sketches of the proofs, often based on the principle of finite-dimensional approximations to the objects at hand in the formulas.

Action of Hopf on the twisted modular Hecke operator

Let Gamma subset of SL2(Z) be a principal congruence subgroup. For each sigma is an element of SL2(Z), we introduce the collection A(sigma)(Gamma) of modular Hecke operators twisted by sigma. Then, A(sigma)(Gamma) is a right A(Gamma)-module, where A(Gamma) is the modular Hecke algebra introduced by Connes and Moscovici. Using the action of a Hopf algebra h(0) on A(sigma)(Gamma), we define reduced Rankin-Cohen brackets on A(sigma)(Gamma). Moreover A(sigma)(Gamma) carries an action of H 1, where H 1 is the Hopf algebra of foliations of codimension 1. Finally, we consider operators between the levels A(sigma)(Gamma), sigma is an element of SL2(Z). We show that the action of these operators can be expressed in terms of a Hopf algebra h(Z).

p Dissipative operator

In this paper the authors prove that the generalized positive p selfadjoint (GPpS) operators in Banach space satisfy the generalized Schwarz inequality, solve the maximal dissipative extension representation of p dissipative operators in Banach space by using the inequality and introducing the generalized indefinite inner product (GIIP) space, and apply the result to a certain type of Schrodinger operator.

Joan Robinson Was Almost Right: Output under Third-Degree Price Discrimination

In this paper, we show that in order for third-degree price discrimination to increase total output, the demands of the strong markets should be, as conjectured by Robinson (1933), more concave than the demands of the weak markets. By making the distinction between adjusted concavity of the inverse demand and adjusted concavity of the direct demand, we are able to state necessary conditions and sufficient conditions for third-degree price discrimination to increase total output.

La arqueología comercial en España: ¿un sistema sectorial de innovación?

[ES] La publicación de la Ley de Patrimonio Histórico Español en 1985 y el desarrollo de la construcción, especialmente de grandes infraestructuras, en la primera década del siglo XXI han sido los factores desencadenantes de la arqueología comercial en España.

Cooperación interempresarial sectorial y en la cadena de suministro

Presentación para impartir docencia en el curso de comercio interior 2011 (Programa de becarios del Gobierno Vasco) Sesión completa (4horas y 15 minutos)

Fault-tolerant almost exact state transmission

We show that a category of one-dimensional XY-type models may enable high-fidelity quantum state transmissions, regardless of details of coupling configurations. This observation leads to a fault-tolerant design of a state transmission setup. The setup is fault-tolerant, with specified thresholds, against engineering failures of coupling configurations, fabrication imperfections or defects, and even time-dependent noises. We propose an experimental implementation of the fault-tolerant scheme using hard-core bosons in one-dimensional optical lattices.

On reconstruction theorems in noncommutative Riemannian geometry

We present a novel account of the theory of commutative spectral triples and their two closest noncommutative generalisations, almost-commutative spectral triples and toric noncommutative manifolds, with a focus on reconstruction theorems, viz, abstract, functional-analytic characterisations of global-analytically defined classes of spectral triples. We begin by reinterpreting Connes's reconstruction theorem for commutative spectral triples as a complete noncommutative-geometric characterisation of Dirac-type operators on compact oriented Riemannian manifolds, and in the process clarify folklore concerning stability of properties of spectral triples under suitable perturbation of the Dirac operator. Next, we apply this reinterpretation of the commutative reconstruction theorem to obtain a reconstruction theorem for almost-commutative spectral triples. In particular, we propose a revised, manifestly global-analytic definition of almost-commutative spectral triple, and, as an application of this global-analytic perspective, obtain a general result relating the spectral action on the total space of a finite normal compact oriented Riemannian cover to that on the base space. Throughout, we discuss the relevant refinements of these definitions and results to the case of real commutative and almost-commutative spectral triples. Finally, we outline progess towards a reconstruction theorem for toric noncommutative manifolds.

Studies in nuclear reactor dynamics : I. The accuracy of point kinetics. II. The effect of delayed neutrons on the spectrum of the group-diffusion operator

This thesis is a theoretical work on the space-time dynamic behavior of a nuclear reactor without feedback. Diffusion theory with G-energy groups is used.

In the first part the accuracy of the point kinetics (lumped-parameter description) model is examined. The fundamental approximation of this model is the splitting of the neutron density into a product of a known function of space and an unknown function of time; then the properties of the system can be averaged in space through the use of appropriate weighting functions; as a result a set of ordinary differential equations is obtained for the description of time behavior. It is clear that changes of the shape of the neutron-density distribution due to space-dependent perturbations are neglected. This results to an error in the eigenvalues and it is to this error that bounds are derived. This is done by using the method of weighted residuals to reduce the original eigenvalue problem to that of a real asymmetric matrix. Then Gershgorin-type theorems .are used to find discs in the complex plane in which the eigenvalues are contained. The radii of the discs depend on the perturbation in a simple manner.

In the second part the effect of delayed neutrons on the eigenvalues of the group-diffusion operator is examined. The delayed neutrons cause a shifting of the prompt-neutron eigenvalue s and the appearance of the delayed eigenvalues. Using a simple perturbation method this shifting is calculated and the delayed eigenvalues are predicted with good accuracy.

O acesso aos exames de alta complexidade nos planos de saúde privados na perspectiva dos usuários

A dissertação trata do acesso aos serviços de alta complexidade, particularmente os exames diagnósticos e complementares, estudado entre usuários de planos de saúde privados que buscam atendimento e diagnóstico especializado. Desde a década de 80 o usuário do sistema público de saúde vem procurando a saúde suplementar. Contudo, afirmar que o acesso é garantido no domínio privado, através da contratação dos planos de saúde, é uma incerteza que rodeia a inspiração para esta pesquisa, que se justifica pela relevância de ações que possibilitem a melhora da qualidade regulatória dos planos de saúde, a partir do controle social de seus usuários. O objetivo geral é analisar as percepções do acesso aos exames de alta complexidade nos serviços de saúde privados entre usuários de planos de saúde. Os objetivos específicos são descrever as percepções dos usuários de planos de saúde acerca do acesso aos exames de alta complexidade; analisar as motivações dos usuários de planos de saúde privados para a realização de exames de alta complexidade através da rede privada de assistência; e analisar o nível de satisfação dos usuários de planos de saúde quanto ao acesso aos exames de alta complexidade. A metodologia é qualitativa-descritiva, onde a amostra foi de trinta usuários de planos de saúde, acima de 18 anos, selecionados no campo de estudo no ano de 2010. O cenário de estudo foi um laboratório privado de medicina diagnóstica no Rio de Janeiro. As técnicas de coleta de dados utilizadas foram formulário e entrevista individual estruturada. A análise do formulário foi realizada através de estatística descritiva, e as entrevistas através da análise de conteúdo temática-categorial. Os usuários de plano de saúde declararam que o acesso é garantido com facilidade para os exames de alta complexidade. Suas principais motivações para a realização desses exames na rede privada de assistência foram caracterizadas pela rapidez de atendimento, flexibilidade e facilidade de marcação pela internet, telefone ou pessoalmente no laboratório estudado, pronta entrega dos resultados, dificuldade e morosidade do atendimento do SUS, localização do prestador credenciado próxima de bairros residenciais ou do trabalho, resolutividade diagnóstica de imagem de excelência, possibilidade de escolha pelo usuário entre as modalidades aberta e fechada de ressonância magnética e tomografia computadorizada, além da densitometria óssea que foram facilmente acessíveis a todos os sujeitos da pesquisa. O nível de satisfação foi correspondido com a rapidez na realização dos exames em caráter eletivo e de urgência quase equiparados na escala de tempo de acordo com os usuários. Contudo, embora as notas de avaliação dos usuários quanto aos seus planos de saúde tenham sido altas, foram abordadas algumas dificuldades, tais como: prazos de validade dos pedidos médicos com datação prévia; solicitações de senhas de autorização pela operadora; burocracia nos procedimentos de agendamento; dificuldades de acesso para tratamentos como implantes, fisioterapia, RPG, pilates, home care, consultas de check up; negação de reembolsos; restrição de materiais cirúrgicos, em especial as próteses e órteses; e restrições específicas de grau para cirurgias de miopia. Conclui-se que o atendimento rápido dos exames de imagem de alto custo na amostra foi descrito como satisfatório, embora a percepção de rapidez possa variar em função do tipo de produto do plano de saúde privado contratado, com necessidade de melhoria regulatória em alguns aspectos pontuais da saúde suplementar.