On the variations of the Betti numbers of regular levels of Morse flows

We generalize results in Cruz and de Rezende (1999) [7] by completely describing how the Beth numbers of the boundary of an orientable manifold vary after attaching a handle, when the homology coefficients are in Z, Q, R or Z/pZ with p prime. First we apply this result to the Conley index theory of Lyapunov graphs. Next we consider the Ogasa invariant associated with handle decompositions of manifolds. We make use of the above results in order to obtain upper bounds for the Ogasa invariant of product manifolds. (C) 2011 Elsevier B.V. All rights reserved.

Boutet de Monvel`s calculus and groupoids I

Can Boutet de Monvel`s algebra on a compact manifold with boundary be obtained as the algebra Psi(0)(G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C*-algebra C*(G). While the answer to the above question remains open, we exhibit in this paper a groupoid G such that C*(G) possesses an ideal I isomorphic to G. In fact, we prove first that G similar or equal to Psi circle times K with the C*-algebra Psi generated by the zero order pseudodifferential operators on the boundary and the algebra K of compact operators. As both Psi circle times K and I are extensions of C(S*Y) circle times K by K (S*Y is the co-sphere bundle over the boundary) we infer from a theorem by Voiculescu that both are isomorphic.

NIELSEN COINCIDENCE THEORY OF FIBRE-PRESERVING MAPS AND DOLD`S FIXED POINT INDEX

Let M -> B, N -> B be fibrations and f(1), f(2): M -> N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f(1), f(2) over B to a coincidence free pair of maps. In the special case where the two fibrations axe the same and one of the maps is the identity, a weak version of our omega-invariant turns out to equal Dold`s fixed point index of fibre-preserving maps. The concepts of Reidemeister classes and Nielsen coincidence classes over B are developed. As an illustration we compute e.g. the minimal number of coincidence components for all homotopy classes of maps between S(1)-bundles over S(1) as well as their Nielsen and Reidemeister numbers.

Theoretical investigation of electronic and optical properties of andalusite within density functional theory

The electronic and optical properties of andalusite were studied by using quantum-mechanical calculations based on the density functional theory (DFT). The electronic structure shows that andalusite has a direct band gap of 5.01 eV. The complex dielectric function and optical constants, such as extinction coefficient, refractive index, reflectivity and energy-loss spectrum, are calculated. The optical properties of andalusite are discussed based on the band structure calculations. It is shown that the O-2p states and Al-3s states play a major role in optical transitions as initial and final states, respectively. (C) 2010 Elsevier Ltd. All rights reserved.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

An algebraic theory for generalized Jordan chains and partial signatures in the Lagrangian Grassmannian

We discuss an algebraic theory for generalized Jordan chains and partial signatures, that are invariants associated to sequences of symmetric bilinear forms on a vector space. We introduce an intrinsic notion of partial signatures in the Lagrangian Grassmannian of a symplectic space that does not use local coordinates, and we give a formula for the Maslov index of arbitrary real analytic paths in terms of partial signatures.

Association of polymorphisms at the ADIPOR1 regulatory region with type 2 diabetes and body mass index in a Brazilian population with European or African ancestry

Association studies between ADIPOR1 genetic variants and predisposition to type 2 diabetes (DM2) have provided contradictory results. We determined if two single nucleotide polymorphisms (SNP c.-8503G>A and SNP c.10225C>G) in regulatory regions of ADIPOR1 in 567 Brazilian individuals of European (EA; N = 443) or African (AfA; N = 124) ancestry from rural (quilombo remnants; N = 439) and urban (N = 567) areas. We detected a significant effect of ethnicity on the distribution of the allelic frequencies of both SNPs in these populations (EA: -8503A = 0.27; AfA: -8503A = 0.16; P = 0.001 and EA: 10225G = 0.35; AfA: 10225G = 0.51; P < 0.001). Neither of the polymorphisms were associated with DM2 in the case-control study in EA (SNP c.-8503G>A: DM2 group -8503A = 0.26; control group -8503A = 0.30; P = 0.14/SNP 10225C>G: DM2 group 10225G = 0.37; control group 10225G = 0.32; P = 0.40) and AfA populations (SNP c.-8503G>A: DM2 group -8503A = 0.16; control group -8503A = 0.15; P = 0.34/SNP 10225C>G: DM2 group 10225G = 0.51; control group 10225G = 0.52; P = 0.50). Similarly, none of the polymorphisms were associated with metabolic/anthropometric risk factors for DM2 in any of the three populations, except for HDL cholesterol, which was significantly higher in AfA heterozygotes (GC = 53.75 ± 17.26 mg/dL) than in homozygotes. We conclude that ADIPOR1 polymorphisms are unlikely to be major risk factors for DM2 or for metabolic/anthropometric measurements that represent risk factors for DM2 in populations of European and African ancestries.

Pulsar binary systems in a nonsymmetric theory of gravitation II. Dipole radiation

This paper deals with the emission of gravitational radiation in the context of a previously studied metric nonsymmetric theory of gravitation. The part coming from the symmetric part of the metric coincides with the mass quadrupole moment result of general relativity. The one associated to the antisymmetric part of the metric involves the dipole moment of the fermionic charge of the system. The results are applied to binary star systems and the decrease of the period of the elliptical motion is calculated.

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

Analyzing the n→π* Electronic Transition of Formaldehyde in Water. A Sequential Monte Carlo/Time-Dependent Density Functional Theory

The n→π* absorption transition of formaldehyde in water is analyzed using combined and sequential classical Monte Carlo (MC) simulations and quantum mechanics (QM) calculations. MC simulations generate the liquid solute-solvent structures for subsequent QM calculations. Using time-dependent density functional theory in a localized set of gaussian basis functions (TD-DFT/6-311++G(d,p)) calculations are made on statistically relevant configurations to obtain the average solvatochromic shift. All results presented here use the electrostatic embedding of the solvent. The statistically converged average result obtained of 2300 cm-1 is compared to previous theoretical results available. Analysis is made of the effective dipole moment of the hydrogen-bonded shell and how it could be held responsible for the polarization of the solvent molecules in the outer solvation shells.

Diet quality index adjusted for energy requirements in adults

This study aimed to develop a diet quality index (DQI-a) adjusted for energy requirement. Dietary intake of adults was assessed using 24-hour food recall. The DQI was developed for scores evenly distributed across ten items characterizing different aspects of diet: food groups, nutrients, and variety. The components categorized under the food groups from the Dietary Guide for Brazilians were adjusted according to the estimated energy requirements of the population studied. Index consistency and correlation with nutrients of the diet was analyzed by Cronbach's alpha. A total of 737 individuals were assessed and energy requirements ranged from 1,800 to 2,500kcal among women and 2,500 to 3,400kcal in men. The food group with greatest variation in total portions was cereals and tubers. Cronbach's alpha of the DQI-a was 0.643 and the index correlated with most of the nutrients. The DQI-a can be considered a valuable instrument for assessing diet quality of the Brazilian population.

Body Mass Index, Cigarette Smoking, and Alcohol Consumption and Cancers of the Oral Cavity, Pharynx, and Larynx: Modeling Odds Ratios in Pooled Case-Control Data

study-specific results, their findings should be interpreted with caution

Density functional theory study of Fe(3)Ga

First-principles scalar relativistic calculations in supercells of 16 atoms are used to represent disordered B2 ordering of Fe(3)Ga in order to observe the effect of Ga-Ga pairs on the electronic structure of this alloy. From a comparison with pure bcc Fe it is observed that the energy position and occupation of e(g) and t(2g) states are largely affected by the Ga-Ga pairs and strengthened intraplane interactions takes place. The results show that a larger hybridization of the conduction band is in the source of the magnetostriction enhancement experimentally observed in Galfenol. (C) 2011 American Institute of Physics. [doi:10.1063/1.3525609]

A new constitutive theory extending Hypoplasticity

The purpose of the present theory is to improve Hypoplasticity, especially in relation to reloading processes. This is done by means of two hypoplastic equations (a classical equation along with a new one containing a so-called mnemonic tensor), a cone in stress space and a criterion defining loading, unloading and reloading. (C) 2010 Elsevier Ltd. All rights reserved.