Construção de gráficos de funções polinomiais de grau 3

Pós-graduação em Matemática em Rede Nacional - IBILCE

Class Notes for Math 921/922: Real Analysis, Instructor Mikil Foss

Topics include: Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon- Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration, Semicontinuity, equicontinuity, absolute continuity, metric spaces, compact spaces, Ascoli’s theorem, Stone Weierstrass theorem, Borel and Lebesque measures, measurable functions, Lebesque integration, convergence theorems, Lp spaces, general measure and integration theory, Radon-Nikodyn theorem, Fubini theorem, Lebesque-Stieltjes integration.

Reduced serum levels of adiponectin in elderly patients with major depression

Recent studies have implicated adiponectin and other adipocytokines in brain function, particularly in processes related to memory and cognition. Blood levels of adiponectin are reduced in patients with primary cognitive disorders, such as Alzheimer's disease and mild cognitive impairment, and in adult patients with major depression. The aim of the present study is to determine serum levels of adiponectin in a sample of elderly patients with major depressive disorder (MOD) as compared to healthy older adults, and to examine the correlations between adiponectin levels and parameters indicative of mood and cognitive state. We recruited fifty-one unmedicated outpatients with late-life depression (LLD) and 47 age-matched controls in this study. The diagnosis of MDD was made according to the DSM-IV criteria, and the severity of depressive episode was determined with the 21-item Hamilton Depression Scale (HORS). Cognitive state was ascertained with the Cambridge Cognitive Test (CAMCOG) and the Mini-Mental State Examination (MMSE). Serum concentrations of adiponectin were determined using a sandwich ELISA method. Serum levels of adiponectin were significantly reduced in individuals with LLD (F = p < 0.001). Adiponectin level remained significantly reduced in after controlling for BMI index, scores on the CAMCOG, MMSE and HDRS and educational level (p < 0.001). Adiponectin levels showed a negative correlation with HORS scores (r = -0.59, p < 0.001) and BMI index (r = -0.42, p < 0.001); and showed a positive correlation with CAMCOG (r = 0.34, p < 0.01) and MMSE scores (r = 0.20, p = 0.05). The availability of circulating adiponectin is reduced in older adults with major depression, with likely implications on cognitive and mood state. Additional studies are required to determine whether this abnormality pertains to the pathophysiology of geriatric depression per se, or is a consequence of the morbid state. (C) 2012 Elsevier Ltd. All rights reserved.

Differential calculus and integration of generalized functions over membranes

In this paper we continue the development of the differential calculus started in Aragona et al. (Monatsh. Math. 144: 13-29, 2005). Guided by the so-called sharp topology and the interpretation of Colombeau generalized functions as point functions on generalized point sets, we introduce the notion of membranes and extend the definition of integrals, given in Aragona et al. (Monatsh. Math. 144: 13-29, 2005), to integrals defined on membranes. We use this to prove a generalized version of the Cauchy formula and to obtain the Goursat Theorem for generalized holomorphic functions. A number of results from classical differential and integral calculus, like the inverse and implicit function theorems and Green's theorem, are transferred to the generalized setting. Further, we indicate that solution formulas for transport and wave equations with generalized initial data can be obtained as well.

On scale-mixture Birnbaum-Saunders distributions

We present for the first time a justification on the basis of central limit theorems for the family of life distributions generated from scale-mixture of normals. This family was proposed by Balakrishnan et al. (2009) and can be used to accommodate unexpected observations for the usual Birnbaum-Saunders distribution generated from the normal one. The class of scale-mixture of normals includes normal, slash, Student-t, logistic, double-exponential, exponential power and many other distributions. We present a model for the crack extensions where the limiting distribution of total crack extensions is in the class of scale-mixture of normals. (C) 2012 Elsevier B.V. All rights reserved.

On the Hilbert transform in the framework of generalized functions

In this paper, a definition of the Hilbert transform operating on Colombeau's temperated generalized functions is given. Similar results to some theorems that hold in the classical theory, or in certain subspaces of Schwartz distributions, have been obtained in this framework.

New characterizations for hyperbolic cylinders in anti-de Sitter spaces

In this paper we study complete maximal spacelike hypersurfaces in anti-de Sitter space H-1(n+1) with either constant scalar curvature or constant non-zero Gauss-Kronecker curvature. We characterize the hyperbolic cylinders H-m(c(1)) x Hn-m(c(2)), 1 <= m <= n - 1, as the only such hypersurfaces with (n - 1) principal curvatures with the same sign everywhere. In particular we prove that a complete maximal spacelike hypersurface in H-1(5) with negative constant Gauss-Kronecker curvature is isometric to H-1(c(1)) x H-3(c(2)). (C) 2012 Elsevier Inc. All rights reserved.

Circulating Glial-derived neurotrophic factor is reduced in late-life depression

Background: The Glial Cell-line derived neurotrophic factor (GDNF) is part of the TGF-beta superfamily and is abundantly expressed in the central nervous system. Changes in GDNF homeostasis have been reported in affective disorders. Aim: To assess serum GDNF concentration in elderly subjects with late-life depression, before antidepressant treatment, as compared to healthy elderly controls. Methods: Thirty-four elderly subjects with major depression and 37 age and gender-matched healthy elderly controls were included in this study. Diagnosis of major depression was ascertained by the SCID interview for DSM-IV and the severity of depressive symptoms was assessed by the Hamilton Depression Rating Scale (HDRS-21). Serum GDNF concentration were determined by sandwich ELISA. Results: Patients with major depression showed a significant reduction in GDNF levels as compared to healthy elderly controls (p < 0.001). Also, GDNF level was negatively correlated with HDRS-21 scores (r = -0.343, p = 0.003). Discussion: Our data provide evidence that GDNF may be a state marker of depressive episode in older adults. Changes in the homeostatic control of GDNF production may be a target to development of new antidepressant strategies. (C) 2011 Elsevier Ltd. All rights reserved.

Gauge and integrable theories in loop spaces

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1 + 1) dimensions, Chern-Simons theories in (2 + 1) dimensions, and non-abelian gauge theories in (2 + 1) and (3 + 1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3 + 1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations. (C) 2012 Elsevier B.V. All rights reserved.

Monocyte Chemoattractant-1 as a Urinary Biomarker for the Diagnosis of Activity of Lupus Nephritis in Brazilian Patients

Objective. Monocyte chemotactic protein (MCP-1), involved in the pathogenesis of lupus nephritis (LN), has recently been indicated as a new biomarker of kidney activity in systemic lupus erythematosus (SLE). Our aim was to assess urinary MCP-1 (uMCP-1) as a biomarker of renal activity in patients with SLE and to compare it to other disease activity markers, using the ELISA. Methods. Seventy-five female Brazilian patients with SLE and a control group participated in our study. Patients with SLE were distributed among 3 groups according to kidney involvement and classified according to disease activity based on clinical and laboratory measures such as urinary sediment, proteinuria, kidney function, C3, C4, anti-dsDNA, disease activity index, and renal SLE disease activity index. The serum and uMCP-1 concentrations were measured by sandwich ELISA. Results. In the A-LN group (active lupus nephritis: SLE with kidney involvement), the concentration of uMCP-1 was significantly higher than in other groups. A cutoff point was established using the results of the control group to apply this test in the detection of LN. A-LN had a higher frequency of positive results for uMCP-1 in comparison to the other groups (p < 0.001). To detect disease activity in patients with LN, a new cutoff was determined based on the results of patients with SLE with kidney involvement. Setting specificity at 90%, the sensitivity of the test was 50%. Conclusion. The high specificity makes uMCP-1 a useful test as a predictor of kidney activity in SLE, especially when associated to other measures used in clinical practice. (First Release Sept 1 2012; J Rheumatol 2012;39:1948-54; doi :10.3899/jrheum.110201)

Hypergraphs with many Kneser colorings

For fixed positive integers r, k and E with 1 <= l < r and an r-uniform hypergraph H, let kappa(H, k, l) denote the number of k-colorings of the set of hyperedges of H for which any two hyperedges in the same color class intersect in at least l elements. Consider the function KC(n, r, k, l) = max(H epsilon Hn) kappa(H, k, l), where the maximum runs over the family H-n of all r-uniform hypergraphs on n vertices. In this paper, we determine the asymptotic behavior of the function KC(n, r, k, l) for every fixed r, k and l and describe the extremal hypergraphs. This variant of a problem of Erdos and Rothschild, who considered edge colorings of graphs without a monochromatic triangle, is related to the Erdos-Ko-Rado Theorem (Erdos et al., 1961 [8]) on intersecting systems of sets. (C) 2011 Elsevier Ltd. All rights reserved.

Experimental analyses of the poly(vinyl chloride) foams' mechanical anisotropic behavior

Assessing a full set of mechanical properties is a rather complicate task in the case of foams, especially if material models must be calibrated with these results. Many issues, for example anisotropy and heterogeneity, influence the mechanical behavior. This article shows through experimental analyses how the microstructure affects different experimental setups and it also quantifies the degree of anisotropy of a poly(vinyl chloride) foam. Monotonic and cyclic experimental tests were carried out using standard compression specimens and non-standard tensile specimens. Results are complemented and compared with the aid of a digital image correlation technique and scanning electron microscopy analyses. Mechanical properties (e.g., elastic and plastic Poisson's ratios) are evaluated for compression and tensile tests, for two different material directions (normal and in-plane). The material is found to be transversely isotropic. Differences in the results of the mechanical properties can be as high as 100%, or even more depending on the technique used and the loading direction. Also, the experimental analyses show how the material's microstructure behavior, like the evolution of the herein identified yield fronts and a spring back phenomenon, can influence the phenomenological response and the failure mechanisms as well as the hardening curves. POLYM. ENG. SCI., 52:2654-2663, 2012. (C) 2012 Society of Plastics Engineers

Relating network rigidity, time scale hierarchies, and expression noise in gene networks

Fluctuation-dissipation theorems can be used to predict characteristics of noise from characteristics of the macroscopic response of a system. In the case of gene networks, feedback control determines the "network rigidity," defined as resistance to slow external changes. We propose an effective Fokker-Planck equation that relates gene expression noise to topology and to time scales of the gene network. We distinguish between two situations referred to as normal and inverted time hierarchies. The noise can be buffered by network feedback in the first situation, whereas it can be topology independent in the latter.

ENERGY AND VOLUME OF VECTOR FIELDS ON SPHERICAL DOMAINS

We present a "boundary version" for theorems about minimality of volume and energy functionals on a spherical domain of an odd-dimensional Euclidean sphere.

How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.