995 resultados para associated graded Lie algebra


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Inspired in recent works of Biedenham [1, 2] on the realization of the q-algebra su(q)(2), We show in this note that the condition [2j + 1](q) = N-q(j) = integer, implies the discretization of the deformation parameter alpha, where q = e(alpha). This discretization replaces the continuum associated to ct by an infinite sequence alpha(1), alpha(2), alpha(3),..., obtained for the values of j, which label the irreps of su(q)(2). The algebraic properties of N-q(j) are discussed in some detail, including its role as a trace, which conducts to the Clebsch-Gordan series for the direct product of irreps. The consequences of this process of discretization are discussed and its possible applications are pointed out. Although not a necessary one, the present prescription is valuable due to its algebraic simplicity especially in the regime of appreciable values of alpha.

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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.

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We obtain the exact classical algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, now containing a calculable correction of order one unit lower. The relation with Yangians and the role of the results in the context of Lie-Poisson algebras are also discussed.

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We show that the 2-matrix string model corresponds to a coupled system of 2 + 1-dimensional KP and modified KP ((m)KP2+1) integrable equations subject to a specific symmetry constraint. The latter together with the Miura-Konopelchenko map for (m)KP2+1 are the continuum incarnation of the matrix string equation. The (m)KP2+1 Miura and Backhand transformations are natural consequences of the underlying lattice structure. The constrained (m)KP2+1 system is equivalent to a 1 + 1-dimensional generalized KP-KdV hierarchy related to graded SL(3,1). We provide an explicit representation of this hierarchy, including the associated W(2,1)-algebra of the second Hamiltonian structure, in terms of free currents.

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In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure. © 2013 World Scientific Publishing Company.

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Background: COX-2 is one of the most important prostaglandin involved in urologic cancer and seems to be associated with tumor progression, invasion, and metastasis. In addition, several effects have been reported for VEGF, including inducing angiogenesis, promoting cell migration, and inhibiting apoptosis. COX2 and VEGF up-regulation have been reported in human prostate cancer. Due to the importance of canine natural model for prostate cancer, the aim of this study was to evaluate COX-2 and VEGF protein expression in canine carcinogenic process. Material and Methods: Seventy-four prostatic tissues from dogs were selected to be evaluated for protein expression by immunohistochemistry (IHC), including: 10 normal prostatic tissues, 20 benign prostatic hyperplasias (BPH), 25 proliferative inflammatory atrophies (PIA) and 20 prostatic carcinomas (PCa). COX-2 and VEGF were detected using the monoclonal antibody CX-294 (1:50 dilution, Dako Cytomation and sc-53463 (1:100 dilution, Santa Cruz), respectively. The immunolabelling was performed by a polymer method (Histofine, Nichirei Biosciences). All reaction included negative controls by omitting the primary antibody. The percentage of C-MYC, E-cadherin, and p63- positive cells per lesion was evaluated according to Prowatke et al. (2007). The samples were scored separately according to staining intensity and graded semi-quantitatively as negative, weakly positive (1), moderately positive, and strongly positive. The score was done in one 400 magnification field, considering only the lesion, since this was done in a TMA core of 1 mm. For statistical analyses, the immunostaining classifications were reduced to two categories: negative and positive. The negative category included negative and weakly positive staining. Chi-square or Fisher exact test was used to determine the association between the categorical variables. Results: The COX-2 protein expression was elevated in the cytoplasm of the canine PCa and PIA compared to normal prostate (p=0.002). VEGF protein expression was increased in 94.75% of the PCa and 100% of the PIA compared with to normal prostate (p = 0.001). No difference was found when compared normal prostate with BPH. Conclusions: This study has demonstrated that the carcinogenesis of canine prostatic tissue may be related to gain of COX-2 and VEGF protein expression.

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We show that the partition function of the super eigenvalue model satisfies, for finite N (non-perturbatively), an infinite set of constraints with even spins s = 4, 6, . . . , ∞. These constraints are associated with half of the bosonic generators of the super (W∞/2 ⊕ W1+∞/2) algebra. The simplest constraint (s = 4) is shown to be reducible to the super Virasoro constraints, previously used to construct the model.

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Pós-graduação em Física - IFT

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OBJECTIVE: The purpose of this study was to evaluate the following: 1) the effects of continuous exercise training and interval exercise training on the end-tidal carbon dioxide pressure (PETCO2) response during a graded exercise test in patients with coronary artery disease; and 2) the effects of exercise training modalities on the association between PETCO2 at the ventilatory anaerobic threshold (VAT) and indicators of ventilatory efficiency and cardiorespiratory fitness in patients with coronary artery disease. METHODS: Thirty-seven patients (59.7 +/- 1.7 years) with coronary artery disease were randomly divided into two groups: continuous exercise training (n = 20) and interval exercise training (n = 17). All patients performed a graded exercise test with respiratory gas analysis before and after three months of the exercise training program to determine the VAT, respiratory compensation point (RCP) and peak oxygen consumption. RESULTS: After the interventions, both groups exhibited increased cardiorespiratory fitness. Indeed, the continuous exercise and interval exercise training groups demonstrated increases in both ventilatory efficiency and PETCO2 values at VAT, RCP, and peak of exercise. Significant associations were observed in both groups: 1) continuous exercise training (PETCO(2)VAT and cardiorespiratory fitness r = 0.49; PETCO(2)VAT and ventilatory efficiency r = -0.80) and 2) interval exercise training (PETCO(2)VAT and cardiorespiratory fitness r = 0.39; PETCO(2)VAT and ventilatory efficiency r = -0.45). CONCLUSIONS: Both exercise training modalities showed similar increases in PETCO2 levels during a graded exercise test in patients with coronary artery disease, which may be associated with an improvement in ventilatory efficiency and cardiorespiratory fitness.

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The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

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The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

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Tesi in algebra che propone uno studio parallelo di risolubilità e nilpotenza nei gruppi e nelle algebre di Lie. Vengono descritte dapprima le algebre di Lie in modo da fornire una conoscenza preliminare riguardo a questa struttura algebrica. In seguito esse vengono messe a confronto con i gruppi sotto l'aspetto appunto di risolubilità e nilpotenza.

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A lumped parameter model of the cardiovascular system has been developed and optimized using experimental data obtained from 13 healthy subjects during graded head-up tilt (HUT) from the supine position to [Formula: see text]. The model includes descriptions of the left and right heart, direct ventricular interaction through the septum and pericardium, the systemic and pulmonary circulations, nonlinear pressure volume relationship of the lower body compartment, arterial and cardiopulmonary baroreceptors, as well as autoregulatory mechanisms. A number of important features, including the separate effects of arterial and cardiopulmonary baroreflexes, and autoregulation in the lower body, as well as diastolic ventricular interaction through the pericardium have been included and tested for their significance. Furthermore, the individual effect of parameter associated with heart failure, including LV and RV contractility, baseline systemic vascular resistance, pulmonary vascular resistance, total blood volume, LV diastolic stiffness and reflex gain on HUT response have also been investigated. Our fitted model compares favorably with our experimental measurements and published literature at a range of tilt angles, in terms of both global and regional hemodynamic variables. Compared to the normal condition, a simulated congestive heart failure condition produced a blunted response to HUT with regards to the percentage changes in cardiac output, stroke volume, end diastolic volume and effector response (i.e., heart contractility, venous unstressed volume, systemic vascular resistance and heart rate) with progressive tilting.

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OBJECTIVE The aim of this study was to elucidate the relationship between the echogenicity of carotid artery plaques and the following risk factors: circulating oxLDL, hsCRP, the metabolic syndrome (MetS), and several of the traditional cardiovascular (CV) risk factors. MATERIAL AND METHODS A cross-sectional population-based study of 513 sixty-one-year-old men. The levels of circulating oxLDL were determined in plasma samples by sandwich ELISA utilizing a specific murine monoclonal antibody (mAb-4E6). High-sensitivity CRP was measured in plasma by ELISA. Plaque occurrence, size and echogenicity were evaluated from B-mode ultrasound registrations in the carotid arteries. Plaque echogenicity was assessed based on a four-graded classification scale. RESULTS A higher frequency of echolucent carotid plaques was observed with increasing levels of oxLDL and systolic blood pressure (p = 0.008 and p = 0.041, respectively). Subjects with the MetS had a significantly higher frequency of echogenic plaques than subjects without the MetS (p = 0.009). In a multiple logistic regression analysis, oxLDL turned out to be independently associated with echolucent carotid plaques. CONCLUSIONS The occurrence of echolucent carotid plaques was associated with oxLDL and systolic blood pressure, and oxLDL was associated with echolucent carotid plaques independently of systolic blood pressure.