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 Edcarlos D. da Silva Abstract and Applied Analysis , 2010, DOI: 10.1155/2010/237826 Abstract: We establish existence and multiplicity of solutions for an elliptic system which presents resonance at infinity of Landesman-Lazer type. In order to describe the resonance, we use an eigenvalue problem with indefinite weights. In all results, we use Variational Methods, Morse Theory and Critical Groups. 1. Introduction In this paper, we discuss results on existence and multiplicity of solutions for the system where is bounded smooth domain in , with and . We assume that the system (1.1) is of gradient type, that is, there is some function such that . Throughout this paper, denotes the gradient in the variables and for each fixed. From a variational standard point of view, to find weak solutions of (1.1) in is equivalent to find critical points of the functional given by where denotes the Dirichlet norm We observe that the problem (1.1) represents a steady state case of reaction-diffusion systems of interest in Biology, Chemistry, Physics, and Ecology; see [1, 2]. In order to define the resonance conditions, we need to consider eigenvalue problems for functions , where denotes the set of all matrices of order 2. Let us denote by the set of all continuous, cooperative, and symmetric functions of order 2 written as satisfying the following hypotheses. is cooperative, that is, for all Moreover, we assume that has zero Lebesgue measure. There is such that or In this way, given , we consider the eigenvalue problem with weights as follows: Using the conditions and above and applying the Spectral Theory for compact operators, we get a sequence of eigenvalues such that as . Here, each eigenvalue ; see [3–5]. We point out that the Problem (1.1) presents a resonance phenomenon depending on the behavior of the functions and at infinity. We assume all along this paper the following basic hypothesis. There is such that Under these hypotheses, system (1.1) is asymptotically quadratic at infinity due to the presence of a linear part given by the function . In addition, when for some the problem (1.1) becomes resonant. In this case, in order to obtain existence and multiplicity of solutions for (1.1), we will assume conditions of the Landesman-Lazer type introduced in the scalar case in [6]. These famous conditions are well known in the scalar case. However for gradient systems, to the best our knowledge, these conditions have not been explored in our case. In order to introduce our Landesman-Lazer conditions for system (1.1), we need the following auxiliary assumptions. There are functions such that Moreover, there are functions such that where the limits in (1.9) and
 Journal of the Brazilian Society of Mechanical Sciences and Engineering , 2011, DOI: 10.1590/S1678-58782011000300002 Abstract: a mathematical model is developed for a liquid flow on solid particles in a trickle bed reactor. a mathematical formulation is followed based on the liquid-solid model approach where the liquid phase with the (kcl) tracer is treated as a continuum. the physical modeling is discussed, including the formulation of initial and boundary conditions and the description of the solution methodology. results of mathematical model are presented and validated. the model is validated through comparison using three experimental cases. the optimized values of the axial dispersion (dax), liquid-solid mass transfer (kls), and partial wetting efficiency (fm) coefficients are obtained simultaneously using the objective function. the behavior of dax, kls, and fm is analyzed by the empirical correlations.
 Aisthesis , 2009, DOI: 10.4067/S0718-71812009000100012 Abstract: the article focuses on the analysis of the new cultural places raised within contemporary society, which affects musical expressions attached to aboriginal cultures in chile. the article claims that, next to the socio-aesthetical diasporas of indigenous musical performance, a parallel shift is being produced, from ritualistic places to spaces where no artistic expressions had been before hypermodernity. this reconfiguration of space is a new challenge to ethnomusicology because nowadays, not only the study of new forms of ethnic art in an intercultural context is required, but also the inclusion of the anthropological place. this modifies the aspects (and specters) of oral art and relocates the researcher in a new coordinate, the ？non-place？.
 Icy D’Silva International Journal of Engineering and Technology , 2011, Abstract: Recombinant technology has led the way to monumental advances in the development of useful molecules, including the development of safe probiotics. The development of novel approaches using recombinant technology and probiotics that allow accurate targeting of therapeutics to the mucosa is an interesting area of research. The creation and use of recombinant probiotics expressing recombinantovalbumin, recombinant ovalbumin mutants and yet-to-be-designed recombinant hypo/non-allergenic molecules offer the opportunity to further investigate their effects for food, nutrition, environment andhealth. This review highlights advances in native probiotics and recombinant probiotics expressing native and recombinant molecules for food, nutrition, environment and health.