Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

Differential geometry of grassmannians and the Plucker map

Using the Plucker map between grassmannians, we study basic aspects of classic grassmannian geometries. For 'hyperbolic' grassmannian geometries, we prove some facts (for instance, that the Plucker map is a minimal isometric embedding) that were previously known in the 'elliptic' case.

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

STRUCTURE AND BIFURCATION OF PULLBACK ATTRACTORS IN A NON-AUTONOMOUS CHAFEE-INFANTE EQUATION

The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, u(t) = u(xx) + lambda(xx) - lambda u beta(t)u(3), and investigate the bifurcations that this attractor undergoes as A is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case.

Stabilization for an ensemble of half-spin systems

Feedback stabilization of an ensemble of non interacting half spins described by the Bloch equations is considered. This system may be seen as an interesting example for infinite dimensional systems with continuous spectra. We propose an explicit feedback law that stabilizes asymptotically the system around a uniform state of spin +1/2 or -1/2. The proof of the convergence is done locally around the equilibrium in the H-1 topology. This local convergence is shown to be a weak asymptotic convergence for the H-1 topology and thus a strong convergence for the C topology. The proof relies on an adaptation of the LaSalle invariance principle to infinite dimensional systems. Numerical simulations illustrate the efficiency of these feedback laws, even for initial conditions far from the equilibrium. (C) 2011 Elsevier Ltd. All rights reserved.

Local symmetries in gauge theories in a finite-dimensional setting

It is shown that the correct mathematical implementation of symmetry in the geometric formulation of classical field theory leads naturally beyond the concept of Lie groups and their actions on manifolds, out into the realm of Lie group bundles and, more generally, of Lie groupoids and their actions on fiber bundles. This applies not only to local symmetries, which lie at the heart of gauge theories, but is already true even for global symmetries when one allows for fields that are sections of bundles with (possibly) non-trivial topology or, even when these are topologically trivial, in the absence of a preferred trivialization. (C) 2012 Elsevier B.V. All rights reserved.

Periodic solutions of abstract neutral functional differential equations

We characterize the existence of periodic solutions of some abstract neutral functional differential equations with finite and infinite delay when the underlying space is a UMD space. (C) 2011 Elsevier Inc. All rights reserved.

An inverse method to estimate the moving heat source in machining process

The present work propounds an inverse method to estimate the heat sources in the transient two-dimensional heat conduction problem in a rectangular domain with convective bounders. The non homogeneous partial differential equation (PDE) is solved using the Integral Transform Method. The test function for the heat generation term is obtained by the chip geometry and thermomechanical cutting. Then the heat generation term is estimated by the conjugated gradient method (CGM) with adjoint problem for parameter estimation. The experimental trials were organized to perform six different conditions to provide heat sources of different intensities. This method was compared with others in the literature and advantages are discussed. (C) 2012 Elsevier Ltd. All rights reserved.

Plasma cortisol in first episode drug-naive mania: Differential levels in euphoric versus irritable mood

Background: Dysregulation of HPA axis has been widely described in subjects with bipolar disorder (BD), including changes in cortisol levels during mood episodes and euthymia. However, most of the studies were done with medicated BD patients with variable length of illness, which was shown to interfere on peripheral cortisol levels. Therefore, the present study aims to evaluate plasma cortisol levels in drug-naive BD subjects during the first manic episode, as well as investigate the relationship between plasma cortisol levels and manic symptomatology. Methods: Twenty-six drug-naive patients were enrolled meeting criteria for a first manic episode in bipolar I disorder. Severity of mania was assessed using the Young Mania Rating Scale (YMRS). The control group included 27 healthy subjects matched by age and gender. Cortisol was quantified using a direct radioimmunoassay. Results: Plasma cortisol levels were decreased during first manic episode compared to healthy controls. Higher cortisol levels were positively associated with the presence of irritability (dysphoria), while elated mania showed lower cortisol levels compared to controls. Limitation: Data including larger samples are lacking. Conclusion: Higher cortisol in dysphoric mania compared to predominantly elated/euphoric mania may indicate a clinical and neurobiological polymorphic phenomenon, potentially involving a higher biological sensitivity to stress in the presence of irritable mood. The present findings highlight the importance to add a dimensional approach to the traditional categorical diagnosis for future neurobiological studies in BD. (C) 2011 Elsevier B.V. All rights reserved.

Differential Proteomic Analysis of Noncardia Gastric Cancer from Individuals of Northern Brazil

Gastric cancer is the second leading cause of cancer-related death worldwide. The identification of new cancer biomarkers is necessary to reduce the mortality rates through the development of new screening assays and early diagnosis, as well as new target therapies. In this study, we performed a proteomic analysis of noncardia gastric neoplasias of individuals from Northern Brazil. The proteins were analyzed by two-dimensional electrophoresis and mass spectrometry. For the identification of differentially expressed proteins, we used statistical tests with bootstrapping resampling to control the type I error in the multiple comparison analyses. We identified 111 proteins involved in gastric carcinogenesis. The computational analysis revealed several proteins involved in the energy production processes and reinforced the Warburg effect in gastric cancer. ENO1 and HSPB1 expression were further evaluated. ENO1 was selected due to its role in aerobic glycolysis that may contribute to the Warburg effect. Although we observed two up-regulated spots of ENO1 in the proteomic analysis, the mean expression of ENO1 was reduced in gastric tumors by western blot. However, mean ENO1 expression seems to increase in more invasive tumors. This lack of correlation between proteomic and western blot analyses may be due to the presence of other ENO1 spots that present a slightly reduced expression, but with a high impact in the mean protein expression. In neoplasias, HSPB1 is induced by cellular stress to protect cells against apoptosis. In the present study, HSPB1 presented an elevated protein and mRNA expression in a subset of gastric cancer samples. However, no association was observed between HSPB1 expression and clinicopathological characteristics. Here, we identified several possible biomarkers of gastric cancer in individuals from Northern Brazil. These biomarkers may be useful for the assessment of prognosis and stratification for therapy if validated in larger clinical study sets.

Existence of Solutions for Abstract Non-Autonomous Neutral Differential Equations

In this paper we discuss the existence of mild and classical solutions for a class of abstract non-autonomous neutral functional differential equations. An application to partial neutral differential equations is considered.

EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.