On (p, q) − equations with concave terms

We consider a (p, q)− equation (1 < q < p, p ≥ 2) with a parametric concave term and a (p − 1)− linear perturbation. We show that the problem have five nontrivial smooth solutions: four of constant sign and the fifth nodal. When q = 2 (i.e., (p, 2) equation) we show that the problem has six nontrivial smooth solutions, but we do not specify the sign of the sixth solution. Our approach uses variational methods, together with truncation and comparison techniques and Morse theory.

The equivalence principle revisited

A precise fomulation of the strong Equivalence Principle is essential to the understanding of the relationship between gravitation and quantum mechanics. The relevant aspects are reviewed in a context including General Relativity but allowing for the presence of torsion. For the sake of brevity, a concise statement is proposed for the Principle: An ideal observer immersed in a gravitational field can choose a reference frame in which gravitation goes unnoticed. This statement is given a clear mathematical meaning through an accurate discussion of its terms. It holds for ideal observers (time-like smooth non-intersecting curves), but not for real, spatially extended observers. Analogous results hold for gauge fields. The difference between gravitation and the other fundamental interactions comes from their distinct roles in the equation of force.

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form

2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50

Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zeros

Using a combination of several methods, such as variational methods. the sub and supersolutions method, comparison principles and a priori estimates. we study existence, multiplicity, and the behavior with respect to lambda of positive solutions of p-Laplace equations of the form -Delta(p)u = lambda h(x, u), where the nonlinear term has p-superlinear growth at infinity, is nonnegative, and satisfies h(x, a(x)) = 0 for a suitable positive function a. In order to manage the asymptotic behavior of the solutions we extend a result due to Redheffer and we establish a new Liouville-type theorem for the p-Laplacian operator, where the nonlinearity involved is superlinear, nonnegative, and has positive zeros. (C) 2009 Elsevier Inc. All rights reserved.

Torsion and the gravitational interaction

By using a nonholonomous-frame formulation of the general covariance principle, seen as an active version of the strong equivalence principle, an analysis of the gravitational coupling prescription in the presence of curvature and torsion is made. The Coupling prescription implied by this principle is found to be always equivalent to that of general relativity, a result that reinforces the completeness of this theory, as well as the teleparallel point of view according to which torsion does not represent additional degrees of freedom for gravity, but simply an alternative way of representing the gravitational field.

Torsion gravity: A reappraisal

The role played by torsion in gravitation is critically reviewed. After a description of the problems and controversies involving the physics of torsion, a comprehensive presentation of the teleparallel equivalent of general relativity is made. According to this theory, curvature and torsion are alternative ways of describing the gravitational field, and consequently related to the same degrees of freedom of gravity. However, more general gravity theories, like for example Einstein-Cartan and gauge theories for the Poincare and the affine groups, consider curvature and torsion as representing independent degrees of freedom. By using an active version of the strong equivalence principle, a possible solution to this conceptual question is reviewed. This solution ultimately favors the teleparallel point of view, and consequently the completeness of general relativity. A discussion of the consequences for gravitation is presented.

Gravity and the quantum: Are they reconcilable?

General relativity and quantum mechanics are not consistent with each other. This conflict stems from the very fundamental principles on which these theories are grounded. General relativity, on one hand, is based on the equivalence principle, whose strong version establishes the local equivalence between gravitation and inertia. Quantum mechanics, on the other hand, is fundamentally based on the uncertainty principle, which is essentially nonlocal. This difference precludes the existence of a quantum version of the strong equivalence principle, and consequently of a quantum version of general relativity. Furthermore, there are compelling experimental evidences that a quantum object in the presence of a gravitational field violates the weak equivalence principle. Now it so happens that, in addition to general relativity, gravitation has an alternative, though equivalent, description, given by teleparallel gravity, a gauge theory for the translation group. In this theory torsion, instead of curvature, is assumed to represent the gravitational field. These two descriptions lead to the same classical results, but are conceptually different. In general relativity, curvature geometrizes the interaction while torsion, in teleparallel gravity, acts as a force, similar to the Lorentz force of electrodynamics. Because of this peculiar property, teleparallel gravity describes the gravitational interaction without requiring any of the equivalence principle versions. The replacement of general relativity by teleparallel gravity may, in consequence, lead to a conceptual reconciliation of gravitation with quantum mechanics. © 2006 American Institute of Physics.

Strong impact of smoking on multimorbidity and cardiovascular risk among human immunodeficiency virus-infected individuals in comparison with the general population.

Background.  Although acquired immune deficiency syndrome-associated morbidity has diminished due to excellent viral control, multimorbidity may be increasing among human immunodeficiency virus (HIV)-infected persons compared with the general population. Methods.  We assessed the prevalence of comorbidities and multimorbidity in participants of the Swiss HIV Cohort Study (SHCS) compared with the population-based CoLaus study and the primary care-based FIRE (Family Medicine ICPC-Research using Electronic Medical Records) records. The incidence of the respective endpoints were assessed among SHCS and CoLaus participants. Poisson regression models were adjusted for age, sex, body mass index, and smoking. Results.  Overall, 74 291 participants contributed data to prevalence analyses (3230 HIV-infected; 71 061 controls). In CoLaus, FIRE, and SHCS, multimorbidity was present among 26%, 13%, and 27% of participants. Compared with nonsmoking individuals from CoLaus, the incidence of cardiovascular disease was elevated among smoking individuals but independent of HIV status (HIV-negative smoking: incidence rate ratio [IRR] = 1.7, 95% confidence interval [CI] = 1.2-2.5; HIV-positive smoking: IRR = 1.7, 95% CI = 1.1-2.6; HIV-positive nonsmoking: IRR = 0.79, 95% CI = 0.44-1.4). Compared with nonsmoking HIV-negative persons, multivariable Poisson regression identified associations of HIV infection with hypertension (nonsmoking: IRR = 1.9, 95% CI = 1.5-2.4; smoking: IRR = 2.0, 95% CI = 1.6-2.4), kidney (nonsmoking: IRR = 2.7, 95% CI = 1.9-3.8; smoking: IRR = 2.6, 95% CI = 1.9-3.6), and liver disease (nonsmoking: IRR = 1.8, 95% CI = 1.4-2.4; smoking: IRR = 1.7, 95% CI = 1.4-2.2). No evidence was found for an association of HIV-infection or smoking with diabetes mellitus. Conclusions.  Multimorbidity is more prevalent and incident in HIV-positive compared with HIV-negative individuals. Smoking, but not HIV status, has a strong impact on cardiovascular risk and multimorbidity.

Relativistic LCAO with Minimax Principle and New Balanced Basis Sets

Relativistic density functional theory is widely applied in molecular calculations with heavy atoms, where relativistic and correlation effects are on the same footing. Variational stability of the Dirac Hamiltonian is a very important field of research from the beginning of relativistic molecular calculations on, among efforts for accuracy, efficiency, and density functional formulation, etc. Approximations of one- or two-component methods and searching for suitable basis sets are two major means for good projection power against the negative continuum. The minimax two-component spinor linear combination of atomic orbitals (LCAO) is applied in the present work for both light and super-heavy one-electron systems, providing good approximations in the whole energy spectrum, being close to the benchmark minimax finite element method (FEM) values and without spurious and contaminated states, in contrast to the presence of these artifacts in the traditional four-component spinor LCAO. The variational stability assures that minimax LCAO is bounded from below. New balanced basis sets, kinetic and potential defect balanced (TVDB), following the minimax idea, are applied with the Dirac Hamiltonian. Its performance in the same super-heavy one-electron quasi-molecules shows also very good projection capability against variational collapse, as the minimax LCAO is taken as the best projection to compare with. The TVDB method has twice as many basis coefficients as four-component spinor LCAO, which becomes now linear and overcomes the disadvantage of great time-consumption in the minimax method. The calculation with both the TVDB method and the traditional LCAO method for the dimers with elements in group 11 of the periodic table investigates their difference. New bigger basis sets are constructed than in previous research, achieving high accuracy within the functionals involved. Their difference in total energy is much smaller than the basis incompleteness error, showing that the traditional four-spinor LCAO keeps enough projection power from the numerical atomic orbitals and is suitable in research on relativistic quantum chemistry. In scattering investigations for the same comparison purpose, the failure of the traditional LCAO method of providing a stable spectrum with increasing size of basis sets is contrasted to the TVDB method, which contains no spurious states already without pre-orthogonalization of basis sets. Keeping the same conditions including the accuracy of matrix elements shows that the variational instability prevails over the linear dependence of the basis sets. The success of the TVDB method manifests its capability not only in relativistic quantum chemistry but also for scattering and under the influence of strong external electronic and magnetic fields. The good accuracy in total energy with large basis sets and the good projection property encourage wider research on different molecules, with better functionals, and on small effects.

Strong Impact of Smoking on Multimorbidity and Cardiovascular Risk Among Human Immunodeficiency Virus-Infected Individuals in Comparison With the General Population.

Background.  Although acquired immune deficiency syndrome-associated morbidity has diminished due to excellent viral control, multimorbidity may be increasing among human immunodeficiency virus (HIV)-infected persons compared with the general population. Methods.  We assessed the prevalence of comorbidities and multimorbidity in participants of the Swiss HIV Cohort Study (SHCS) compared with the population-based CoLaus study and the primary care-based FIRE (Family Medicine ICPC-Research using Electronic Medical Records) records. The incidence of the respective endpoints were assessed among SHCS and CoLaus participants. Poisson regression models were adjusted for age, sex, body mass index, and smoking. Results.  Overall, 74 291 participants contributed data to prevalence analyses (3230 HIV-infected; 71 061 controls). In CoLaus, FIRE, and SHCS, multimorbidity was present among 26%, 13%, and 27% of participants. Compared with nonsmoking individuals from CoLaus, the incidence of cardiovascular disease was elevated among smoking individuals but independent of HIV status (HIV-negative smoking: incidence rate ratio [IRR] = 1.7, 95% confidence interval [CI] = 1.2-2.5; HIV-positive smoking: IRR = 1.7, 95% CI = 1.1-2.6; HIV-positive nonsmoking: IRR = 0.79, 95% CI = 0.44-1.4). Compared with nonsmoking HIV-negative persons, multivariable Poisson regression identified associations of HIV infection with hypertension (nonsmoking: IRR = 1.9, 95% CI = 1.5-2.4; smoking: IRR = 2.0, 95% CI = 1.6-2.4), kidney (nonsmoking: IRR = 2.7, 95% CI = 1.9-3.8; smoking: IRR = 2.6, 95% CI = 1.9-3.6), and liver disease (nonsmoking: IRR = 1.8, 95% CI = 1.4-2.4; smoking: IRR = 1.7, 95% CI = 1.4-2.2). No evidence was found for an association of HIV-infection or smoking with diabetes mellitus. Conclusions.  Multimorbidity is more prevalent and incident in HIV-positive compared with HIV-negative individuals. Smoking, but not HIV status, has a strong impact on cardiovascular risk and multimorbidity.

A comparison of the leaf-litter ant fauna in a secondary atlantic forest with an adjacent pine plantation in southeastern Brazil

We investigated the influence of Pinus afforestation on the structure of leaf-litter ant communities in the southeastern Brazilian Atlantic Forest, studying an old secondary forest and a nearly 30 year-old never managed Pinus elliottii reforested area. A total of 12,826 individual ants distributed among 95 species and 32 genera were obtained from 50 1 m² samples/ habitat. Of these, 60 species were recorded in the pine plantation and 82 in the area of Atlantic forest; almost 50% of the species found in the secondary forest area were also present in the pine plantation. The number of species per sample was significantly higher in the secondary forest than in the pine plantation. Forest-adapted taxa are the most responsible for ant species richness differences between areas, and the pine plantation is richer in species classified as soil or litter omnivorous-dominants. The specialized ant predators registered in the pine plantation, as seven Dacetini, two Basiceros, two Attini and two Discothyrea, belong to widely distributed species. The NMDS (non-metric multidimensional scaling) ordination also suggested strong differences in similarity among samples of the two areas. Furthermore, this analysis indicated higher sample heterogeneity in the secondary forest, with two clusters of species, while in the pine plantation the species belong to a single cluster. We applied the ant mosaic hypothesis to explain the distribution of the leaf-litter fauna and spatial autocorrelation tests among samples. We argue that the results are likely related to differences in quality and distribution of the leaf-litter between the pine plantation and the secondary area.

Endurance in judogi grip strength tests: comparison between elite and non-elite judo players

Background and Study Aim: The ability to develop a strong grip and maintain it during a judo match has become an important element for judo athletes. Therefore, the purpose of this investigation was to examine differences between measurements of maximal isometric time on judogi pull-up, and number of repetitions during dynamic judogi pull-up. Material/Methods: The sample was composed by two groups: 16 high-level judo athletes from the male Brazilian National Team and 12 male state-level judo athletes, with at least one athlete per weight category. The tests were compared through analysis of co-variance (body mass as co-variable), followed by a post-hoc test (Scheffe). Significance level was set at 5%. Results: No difference was found in the isometric test: Brazilian Team: 35 +/- 18s; Regional: 39 +/- 14s. However, the Brazilian Team performed a high number of repetitions (12 +/- 5 rep) compared to regional group (9 +/- 4 rep) during the dynamic grip strength endurance test. Conclusions: Thus, dynamic grip strength endurance seems to be a discriminating variable between judo athletes, probably because judo combat involves many elbow extensions and flexions in order to avoid the opponent`s grip and to subdue them.