On abstract differential equations with nonlocal conditions involving the temporal derivative of the solution

In this paper we discuss the existence of solutions for a class of abstract differential equations with nonlocal conditions for which the nonlocal term involves the temporal derivative of the solution. Some concrete applications to parabolic differential equations with nonlocal conditions are considered. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

On bifurcation of solutions of the Yamabe problem in product manifolds

We study local rigidity and multiplicity of constant scalar curvature metrics in arbitrary products of compact manifolds. Using (equivariant) bifurcation theory we determine the existence of infinitely many metrics that are accumulation points of pairwise non-homothetic solutions of the Yamabe problem. Using local rigidity and some compactness results for solutions of the Yamabe problem, we also exhibit new examples of conformal classes (with positive Yamabe constant) for which uniqueness holds. (C) 2011 Elsevier Masson SAS. All rights reserved.

Bourgin-Yang version of the Borsuk-Ulam theorem for Z(pk)-equivariant maps

Let G = Z(pk) be a cyclic group of prime power order and let V and W be orthogonal representations of G with V-G = W-G = W-G = {0}. Let S(V) be the sphere of V and suppose f: S(V) -> W is a G-equivariant mapping. We give an estimate for the dimension of the set f(-1){0} in terms of V and W. This extends the Bourgin-Yang version of the Borsuk-Ulam theorem to this class of groups. Using this estimate, we also estimate the size of the G-coincidences set of a continuous map from S(V) into a real vector space W'.

A new analysis of the GJ581 extrasolar planetary system

We have done a new analysis of the available observations of the GJ581 exoplanetary system. Today this system is controversial due to choices that can be done in the orbital determination. The main ones are the occurrence of aliases and the additional bodies-the planets f and g-announced in Vogt et al. (Astrophys J 723:954-965, 2010). Any dynamical study of exoplanets requires the good knowledge of the orbital elements and the investigations involving the planet g are particularly interesting, since this body would lie in the habitable zone (HZ) of the star GJ581. This region, for this system, is very attractive of the dynamical point of view due to several resonances of two and three bodies present there. In this work, we investigate the conditions under which the planet g may exist. We stress the fact that the planet g is intimately related with the orbital elements of the planet d; more precisely, we conclude that it is not possible to disconnect its existence from the determination of the eccentricity of the planet d. Concerning the planet f, we have found one solution with period a parts per thousand 450 days, but we are judicious about any affirmation concerning this body because its signal is in the threshold of detection and the high period is in a spectral region where the occurrence of aliases is very common. Besides, we outline some dynamical features of the HZ with the dynamical map and point out the role played by some resonances laying there.

Isatin-Schiff base copper(II) complexes-A DFT study of the metal-ligand bonding situation

Herein, we report results of calculations based on density functional theory (BP86/TZVP) of a set of isatin-Schiff base copper(II) and related complexes, 1-12, that have shown significant pro-apoptotic activity toward diverse tumor cells. The interaction of the copper(II) cation with different ligands has been investigated at the same level of theory. The strength and character of the Cu(II)-L bonding was characterized by metal-ligand bond lengths, vibrational frequencies, binding energies, ligand deformation energies, and natural population analysis. The metal-ligand bonding situation was also characterized by using two complementary topological approaches, the quantum theory of atoms-in-molecules (QTAIM) and the electron localization function (ELF). The calculated electronic g-tensor and hyperfine coupling constants present significant agreement with the EPR experimental data. The calculated parameters pointed to complex 10 as the most stable among the isatin-Schiff base copper(II) species, in good agreement with experimental data that indicate this complex as the most reactive in the series. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

TRANSITIVITY AND ROTATION SETS WITH NONEMPTY INTERIOR FOR HOMEOMORPHISMS OF THE 2-TORUS

We show that if f is a homeomorphism of the 2-torus isotopic to the identity and its lift (f) over tilde is transitive, or even if it is transitive outside the lift of the elliptic islands, then (0,0) is in the interior of the rotation set of (f) over tilde. This proves a particular case of Boyland's conjecture.

On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier Inc. All rights reserved.

Describing some of the Dimensions that comprise the Profile of the Faculty Staff of Statistics Departments in Brazil

Statistics is a required course in virtually all undergraduate programs in Brazilian universities. In addition, undergraduate programs in Statistics are offered in many public universities. However, despite the importance of this science, there are no systematic studies in the national literature regarding the characterization of the faculty staff, which is responsible for the teaching of statistics in the country. In this context, this paper presents a description of the faculty members of undergraduate courses in Statistics. This description was based on a descriptive sample, related to aspects of their education and scientific production. A prediction of future demand for PhDs in Statistics to fill the vacancies is also provided based on the retirement of faculty members in undergraduate courses in Statistics in the country.

Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.

Impacts of Trade in Non-timber Forest Products on Cooperation among Caboclo Households of the Brazilian Amazon

Trade in non-timber forest products (NTFPs) has been touted as promoting forest conservation and enhancing the well-being of local residents through increased cash income, which is considered a positive outcome. However, research on cooperation has demonstrated that increased market access and income may strengthen or weaken cooperation. Because cooperation is essential for community resilience in small-scale societies, negative effects on people's well-being can be expected if increased NTFP trade reduces cooperation. To evaluate whether NTFP trade affected cooperation, we used household data (survey and systematic observations) to compare the frequency of cooperation in two communities of Brazilian Amazon Caboclos, one of which engaged in NTFP trade, while the other did not. Cooperation was less frequent in the community trading NTFPs, but neither household cash income nor household participation in NTFP exploitation was associated with cooperative behavior. Decreased frequency most likely derived from indirect effects of NTFP trade, such as less time to fish or socialize, or other outcomes observable only at the community level, such as income inequality, the influx of new residents and consequent population growth. Our results indicate that conservation and development projects based on NTFP trade may negatively impact social and economic well-being of local communities.

An in-depth analysis of the HIV-1/AIDS dynamics by comprehensive mathematical modeling

This work presents major results from a novel dynamic model intended to deterministically represent the complex relation between HIV-1 and the human immune system. The novel structure of the model extends previous work by representing different host anatomic compartments under a more in-depth cellular and molecular immunological phenomenology. Recently identified mechanisms related to HIV-1 infection as well as other well known relevant mechanisms typically ignored in mathematical models of HIV-1 pathogenesis and immunology, such as cell-cell transmission, are also addressed. (C) 2011 Elsevier Ltd. All rights reserved.

Influence of the initial condition in equilibrium last-passage percolation models

In this paper we consider an equilibrium last-passage percolation model on an environment given by a compound two-dimensional Poisson process. We prove an L-2-formula relating the initial measure with the last-passage percolation time. This formula turns out to be a useful tool to analyze the fluctuations of the last-passage times along non-characteristic directions.

The local power of the gradient test

The asymptotic expansion of the distribution of the gradient test statistic is derived for a composite hypothesis under a sequence of Pitman alternative hypotheses converging to the null hypothesis at rate n(-1/2), n being the sample size. Comparisons of the local powers of the gradient, likelihood ratio, Wald and score tests reveal no uniform superiority property. The power performance of all four criteria in one-parameter exponential family is examined.