Topology Change in (2+1)-Dimensional Gravity

In (2+1)-dimensional general relativity, the path integral for a manifold $M$ can be expressed in terms of a topological invariant, the Ray-Singer torsion of a flat bundle over $M$. For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, we evaluate the amplitude for a simple topology-changing process. We show that certain amplitudes for spatial topology change are nonvanishing---in fact, they can be infrared divergent---but that they are infinitely suppressed relative to similar topology-preserving amplitudes.Comment: 19 pages of text plus 4 pages of figures, LaTeX (using epsf), UCD-11-9

Fluid balance and sodium losses during indoor tennis match play

This study assessed fluid balance, sodium losses, and effort intensity during indoor tennis match play (17 ±2 °C, 42% ± 9% relative humidity) over a mean match duration of 68.1 ± 12.8 min in 16 male tennis players. Ad libitum fluid intake was recorded throughout the match. Sweat loss from change in nude body mass; sweat electrolyte content from patches applied to the forearm, calf, and thigh, and back of each player; and electrolyte balance derived from sweat, urine, and daily food-intake analysis were measured. Effort intensity was assessed from on-court heart rate compared with data obtained during a maximal treadmill test. Sweat rate (M ± SD) was 1.1 ± 0.4 L/hr, and fluid-ingestion rate was 1.0 ± 0.6 L/hr (replacing 93% ± 47% of fluid lost), resulting in only a small mean loss in body mass of 0.15% ± 0.74%. Large interindividual variabilities in sweat rate (range 0.3-2.0 L/hr) and fluid intake (range 0.31-2.52 L/hr) were noted. Whole-body sweat sodium concentration was 38 ± 12 mmol/L, and total sodium losses during match play were 1.1 ± 0.4 g (range 0.5-1.8 g). Daily sodium intake was 2.8 ± 1.1 g. Indoor match play largely consisted of low-intensity exercise below ventilatory threshold (mean match heart rate was 138 ± 24 beats/min). This study shows that in moderate indoor temperature conditions players ingest sufficient fluid to replace sweat losses. However, the wide range in data obtained highlights the need for individualized fluid-replacement guidance

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study of the relations between the Hopf-Lax semigroup and Hamilton-Jacobi equation in metric spaces (X,d). - The equivalence of the heat flow in L^2(X,m) generated by a suitable Dirichlet energy and the Wasserstein gradient flow of the relative entropy functional in the space of probability measures P(X). - The proof of density in energy of Lipschitz functions in the Sobolev space W^{1,2}(X,d,m). - A fine and very general analysis of the differentiability properties of a large class of Kantorovich potentials, in connection with the optimal transport problem. Our results apply in particular to spaces satisfying Ricci curvature bounds in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been propose

An adaptive-binning method for generating constant-uncertainty/constant-significance light curves with Fermi-LAT data

We present a method enabling the creation of constant-uncertainty/constant-significance light curves with the data of the Fermi-Large Area Telescope (LAT). The adaptive-binning method enables more information to be encapsulated within the light curve than with the fixed-binning method. Although primarily developed for blazar studies, it can be applied to any sources. This method allows the starting and ending times of each interval to be calculated in a simple and quick way during a first step. The reported mean flux and spectral index (assuming the spectrum is a power-law distribution) in the interval are calculated via the standard LAT analysis during a second step. The absence of major caveats associated with this method has been established by means of Monte-Carlo simulations. We present the performance of this method in determining duty cycles as well as power-density spectra relative to the traditional fixed-binning method.Comment: 17 pages, 13 figures, 5 tables. Submitted to A&

Upper bounds on the first eigenvalue for a diffusion operator via Bakry-\'{E}mery Ricci curvature II

Let $L=\Delta-\nabla\varphi\cdot\nabla$ be a symmetric diffusion operator with an invariant measure $d\mu=e^{-\varphi}dx$ on a complete Riemannian manifold. In this paper we prove Li-Yau gradient estimates for weighted elliptic equations on the complete manifold with $|\nabla \varphi|\leq\theta$ and $\infty$-dimensional Bakry-\'{E}mery Ricci curvature bounded below by some negative constant. Based on this, we give an upper bound on the first eigenvalue of the diffusion operator $L$ on this kind manifold, and thereby generalize a Cheng's result on the Laplacian case (Math. Z., 143 (1975) 289-297).Comment: Final version. The original proof of Theorem 2.1 using Li-Yau gradient estimate method has been moved to the appendix. The new proof is simple and direc

Preexercise Carbohydrate Feeding and High-Intensity Exercise Capacity: Effects of Timing of Intake and Carbohydrate Concentration

The present study aimed to investigate the influence of timing of pre-exercise carbohydrate feeding (Part A), and carbohydrate concentration (Part B), on short-duration high-intensity exercise capacity. In Part A, seventeen males, and in Part B ten males, performed a peak power output (PPO) test, two familiarisation trials at 90% of PPO, and 4 (for Part A) or 3 (for Part B) experimental trials involving exercise capacity tests at 90% PPO. In Part A, the 4 trials were conducted following ingestion of a 6.4% carbohydrate/electrolyte sports drink ingested 30 (C30) or 120 (C120) minutes before exercise, or a flavour-matched placebo administered either 30 (P30) or 120 (P120) minutes before exercise. In Part B, the 3 trials were performed 30 minutes after ingestion of 0%, 2% or 12% carbohydrate solutions. All trials were performed in a double blind cross-over design following and overnight fast. Dietary intake and activity in the two days before trials was recorded and replicated on each visit. Glucose, lactate, heart rate and mood/arousal were recorded at intervals during the trials. In Part A, C30 produced the greatest exercise capacity (mean±SD; 9.0±1.9 min, P<0.01) compared with all other trials (7.7±1.5 min P30, 8.0±1.7 min P120, 7.9±1.9 min C120). In Part B, exercise capacity (min) following ingestion of the 2% solution (9.2±2.1) compared with 0% (8.2±0.7) and 12% (8.0±1.3) solutions approached significance (p=0.09). This study provides new evidence to suggest that timing of carbohydrate intake is important in short duration high-intensity exercise tasks, but a concentration effect requires further exploration

L^2 torsion without the determinant class condition and extended L^2 cohomology

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L^2 cohomology. Under the determinant class assumption the L^2 torsions of this paper specialize to the invariants studied in our previous work. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler we obtain a Cheeger - Muller type theorem stating the equality between the combinatorial and the analytic L^2 torsions.Comment: 39 page

Semirigid Geometry

We provide an intrinsic description of $N$-super \RS s and $TN$-\SR\ surfaces. Semirigid surfaces occur naturally in the description of topological gravity as well as topological supergravity. We show that such surfaces are obtained by an integrable reduction of the structure group of a complex supermanifold. We also discuss the \s moduli spaces of $TN$-\SR\ surfaces and their relation to the moduli spaces of $N$-\s\ \RS s.Comment: 29p

On Alternative Supermatrix Reduction

We consider a nonstandard odd reduction of supermatrices (as compared with the standard even one) which arises in connection with possible extension of manifold structure group reductions. The study was initiated by consideration of the generalized noninvertible superconformal-like transformations. The features of even- and odd-reduced supermatrices are investigated on a par. They can be unified into some kind of "sandwich" semigroups. Also we define a special module over even- and odd-reduced supermatrix sets, and the generalized Cayley-Hamilton theorem is proved for them. It is shown that the odd-reduced supermatrices represent semigroup bands and Rees matrix semigroups over a unit group.Comment: 22 pages, Standard LaTeX with AmS font