The analytic torsion of a cone over an odd dimensional manifold

We study the analytic torsion of a cone over an orientable odd dimensional compact connected Riemannian manifold W. We prove that the logarithm of the analytic torsion of the cone decomposes as the sum of the logarithm of the root of the analytic torsion of the boundary of the cone, plus a topological term, plus a further term that is a rational linear combination of local Riemannian invariants of the boundary. We show that this last term coincides with the anomaly boundary term appearing in the Cheeger Muller theorem [3, 2] for a manifold with boundary, according to Bruning and Ma (2006) [5]. We also prove Poincare duality for the analytic torsion of a cone. (C) 2010 Elsevier B.V. All rights reserved.

On the manifold structure of the set of unparameterized embeddings with low regularity

Given manifolds M and N, with M compact, we study the geometrical structure of the space of embeddings of M into N, having less regularity than C(infinity) quotiented by the group of diffeomorphisms of M.

On the Multiplicity of Orthogonal Geodesics in Riemannian Manifold With Concave Boundary. Applications to Brake Orbits and Homoclinics

Let (M, g) be a complete Riemannian Manifold, Omega subset of M an open subset whose closure is diffeomorphic to an annulus. If partial derivative Omega is smooth and it satisfies a strong concavity assumption, then it is possible to prove that there are at least two geometrically distinct geodesics in (Omega) over bar = Omega boolean OR partial derivative Omega starting orthogonally to one connected component of partial derivative Omega and arriving orthogonally onto the other one. The results given in [6] allow to obtain a proof of the existence of two distinct homoclinic orbits for an autonomous Lagrangian system emanating from a nondegenerate maximum point of the potential energy, and a proof of the existence of two distinct brake orbits for a. class of Hamiltonian systems. Under a further symmetry assumption, it is possible to show the existence of at least dim(M) pairs of geometrically distinct geodesics as above, brake orbits and homoclinics.

Can physical exercise during gestation attenuate the effects of a maternal perinatal low-protein diet on oxygen consumption in rats?

A protocol of physical exercise, based on maximal oxygen uptake ((V) over dot(O2max)), for female rats before and during pregnancy was developed to evaluate the impact of a low-protein diet on oxygen consumption during gestation and growth rate of the offspring. Virgin female Wistar rats were divided into four groups as follows: untrained (NT, n = 5); trained (T, n = 5); untrained with low-protein diet (NT+LP, n = 5); and trained with low-protein diet (T+LP, n = 5). Trained rats were submitted to a protocol of moderate physical training on a treadmill over a period of 4 weeks (5 days week(-1) and 60 min day(-1), at 65% of (V) over dot(O2max)). At confirmation of pregnancy, the intensity and duration of the exercise was reduced. Low-protein groups received an 8% casein diet, and their peers received a 17% casein diet. The birthweight and growth rate of the pups up to the 90th day were recorded. Oxygen consumption ((V) over dot(O2)), CO(2) production and respiratory exchange ratio (RER) were determined using an indirect open-circuit calorimeter. Exercise training increased. (V) over dot(O2max) by about 20% when compared with the initial values (45.6 +/- 1.0 ml kg(-1) min(-1)). During gestation, all groups showed a progressive reduction in the resting (V) over dot(O2) values. Dams in the NT+LP group showed lower values of resting (V) over dot(O2) than those in the NT group. The growth rate of pups from low-protein-fed mothers was around 50% lower than that of their respective controls. The T group showed an increase in body weight from the 60th day onwards, while the NT+LP group presented a reduced body weight from weaning onwards. In conclusion, physical training attenuated the impact of the low- protein

Augmentation of insulin secretion by leucine supplementation in malnourished rats: possible involvement of the phosphatidylinositol 3-phosphate kinase/mammalian target protein of rapamycin pathway

A regimen of low-protein diet induces a reduction of pancreatic islet function that is associated with development of metabolic disorders including diabetes and obesity afterward. In the present study, the influence of leucine supplementation on metabolic parameters, insulin secretion to glucose and to amino acids, as well as the levels of proteins that participate in the phosphatidylinositol 3-phosphate kinase (PI3K) pathway was investigated in malnourished rats. Four groups were fed with different diets for 12 weeks: a normal protein diet (17%) without (NP) or with leucine supplementation (NPL) or a low (6%)-protein diet without (LP) or with leucine supplementation (LPL). Leucine was given in the drinking water during the last 4 weeks. As indicated by the intraperitoneal glucose tolerance test, LPL rats exhibited increased glucose tolerance as compared with NPL group. Both NPL and LPL rats had higher circulating insulin levels than controls. The LPL rats also showed increased insulin secretion by pancreatic islets in response to glucose or arginine compared with those observed in islets from LP animals. Glucose oxidation was significantly reduced in NPL, LP, and LPL isolated islets as compared with NP; but no alteration was observed for leucine and glutamate oxidation among the 4 groups. Western blotting analysis demonstrated increased PI3K and mammalian target protein of rapamycin protein contents in LPL compared with LP islets. A significant increase in insulin-induced insulin receptor substrate I associated PI3K activation was also observed in LPL compared with LP islets. These findings indicate that leucine supplementation can augment islet function in malnourished rats and that activation of the PI3K/maminalian target protein of rapamycin pathway may play a role in this process. (C) 2010 Elsevier Inc. All rights reserved.

Preliminary report: Leucine supplementation enhances glutamate dehydrogenase expression and restores glucose-induced insulin secretion in protein-malnourished rats

Low-protein diet impairs insulin secretion in response to nutrients and may induce several metabolic disorders including diabetes, obesity, and cardiovascular disease. In the present study, the influence of leucine supplementation on glutamate dehydrogenase (GDH) expression and glucose-induced insulin secretion (GIIS) was investigated in malnourished rats. Four groups were fed with different diets for 12 weeks: a normal-protein diet (17%) without or with leucine supplementation or a low (6%)-protein diet without (LP) or with leucine supplementation (LPL). Leucine (1.5%) was supplied in the drinking water. Western blotting analysis revealed reduced GIN! expression in LP, whereas LPL displayed improved GDH expression, similar to control. The GHS and leucinc-induced insulin release were also enhanced in LPL compared with LP and similar to those observed in rats fed a normal-protein diet without leucine supplementation. In addition, GDH allosteric activators produced an increased insulin secretion in LPL. These findings indicate that leucine supplementation was able to increase GDH expression leading to Cl IS restoration, probably by improved leucine metabolic pathways. (C) 2010 Elsevier Inc. All rights reserved.

COMPARISON BETWEEN LINEAR AND DAILY UNDULATING PERIODIZED RESISTANCE TRAINING TO INCREASE STRENGTH

Prestes, J, Frollini, AB, De Lima, C, Donatto, FF, Foschini, D, de Marqueti, RC, Figueira Jr, A, and Fleck, SJ. Comparison between linear and daily undulating periodized resistance training to increase strength. J Strength Cond Res 23(9): 2437-2442, 2009-To determine the most effective periodization model for strength and hypertrophy is an important step for strength and conditioning professionals. The aim of this study was to compare the effects of linear (LP) and daily undulating periodized (DUP) resistance training on body composition and maximal strength levels. Forty men aged 21.5 +/- 8.3 and with a minimum 1-year strength training experience were assigned to an LP (n = 20) or DUP group (n = 20). Subjects were tested for maximal strength in bench press, leg press 45 degrees, and arm curl (1 repetition maximum [RM]) at baseline (T1), after 8 weeks (T2), and after 12 weeks of training (T3). Increases of 18.2 and 25.08% in bench press 1 RM were observed for LP and DUP groups in T3 compared with T1, respectively (p <= 0.05). In leg press 45 degrees, LP group exhibited an increase of 24.71% and DUP of 40.61% at T3 compared with T1. Additionally, DUP showed an increase of 12.23% at T2 compared with T1 and 25.48% at T3 compared with T2. For the arm curl exercise, LP group increased 14.15% and DUP 23.53% at T3 when compared with T1. An increase of 20% was also found at T2 when compared with T1, for DUP. Although the DUP group increased strength the most in all exercises, no statistical differences were found between groups. In conclusion, undulating periodized strength training induced higher increases in maximal strength than the linear model in strength-trained men. For maximizing strength increases, daily intensity and volume variations were more effective than weekly variations.

ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n).

Transitivity of codimension-one Anosov actions of R(k) on closed manifolds

We consider Anosov actions of R(k), k >= 2, on a closed connected orientable manifold M, of codimension one, i.e. such that the unstable foliation associated to some element of R(k) has dimension one. We prove that if the ambient manifold has dimension greater than k + 2, then the action is topologically transitive. This generalizes a result of Verjovsky for codimension-one Anosov flows.

UNIVERSAL COVERING OF DRIFTLESS CONTROL SYSTEMS

Let M be a finite-dimensional manifold and Sigma be a driftless control system on M of full rank. We prove that for a given initial state x epsilon M, the covering space Gamma(Sigma, x) for a monotonic homotopy of trajectories of Sigma which is recently constructed in [1] coincides with the simply connected universal covering manifold of M and that the terminal projection epsilon(x) : Gamma(Sigma, x) -> M given by epsilon(x) ([alpha]) = alpha(1) is a covering mapping.

Global analytic regularity for structures of co-rank one

We consider real analytic involutive structures V, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of V. We prove that analytic regularity propagates along them. With a further assumption on the level sets of V we characterize the global analytic hypoellipticity of a differential operator naturally associated to V. As an application we study a case of tube structures.

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.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Blowout bifurcation and spatial mode excitation in the bubbling transition to turbulence

The transition to turbulence (spatio-temporal chaos) in a wide class of spatially extended dynamical system is due to the loss of transversal stability of a chaotic attractor lying on a homogeneous manifold (in the Fourier phase space of the system) causing spatial mode excitation Since the latter manifests as intermittent spikes this has been called a bubbling transition We present numerical evidences that this transition occurs due to the so called blowout bifurcation whereby the attractor as a whole loses transversal stability and becomes a chaotic saddle We used a nonlinear three-wave interacting model with spatial diffusion as an example of this transition (C) 2010 Elsevier B V All rights reserved

Tokamak magnetic field lines described by simple maps

The magnetic field line structure in a tokamak can be obtained by direct numerical integration of the field line equations. However, this is a lengthy procedure and the analysis of the solution may be very time-consuming. Otherwise we can use simple two-dimensional, area-preserving maps, obtained either by approximations of the magnetic field line equations, or from dynamical considerations. These maps can be quickly iterated, furnishing solutions that mirror the ones obtained from direct numerical integration, and which are useful when long-term studies of field line behavior are necessary (e.g. in diffusion calculations). In this work we focus on a set of simple tokamak maps for which these advantages are specially pronounced.