Toeplitz operators and the full asymptotic torsion forms

We present a new proof, as well as a C/Q extension (and also certain C/Z extension), of the Riemann–Roch–Grothendieck theorem of Bismut–Lott for flat vector bundles. The main techniques used are the computations of the adiabatic limits of η-invariants associated to the so-called sub-signature operators. We further show that the Bismut–Lott analytic torsion form can be derived naturally from transgressions of η-forms appearing in the adiabatic limit computations.

We report on the construction of secondary invariants in connection with the Atiyah-Singer index theorem for families, and the Theorem of Riemann-Roch-Grothendieck. The local families index theorem plays an important role in the construction. In complex geometry, the corresponding objects are the analytic torsion forms and the analytic torsion currents. These objects exhibit natural functorial properties with respect to composition of maps. Gillet and Soulé have used these objects to prove a Riemann-Roch theorem in Arakelov geometry. Also we state a Riemann-Roch theorem for flat vector bundles, and report on the construction of corresponding higher analytic torsion forms.

In this note we prove a vanishing theorem for the analytic torsion of a locally symmetric space.

We prove the smoothness of the L^2-analytic torsion form on some fiber bundles with non-compact fibers of positive Novikov-Shubin invariant. We do so by generalizing the arguments of Azzali-Goette-Schick to an appropriate Sobolev space, and proving that the Novikov-Shubin invariant remains positive in the Sobolev settings, using an argument of Alvarez Lopez-Kordyukov.

The purpose of this paper is to explain how Toeplitz operators can be used in studying asymptotic torsion, and also in the theory of the hypoelliptic Laplacian. The role of the hypoelliptic Laplacian in the explicit computation of orbital integrals will be described. The geodesic flow will be viewed as implementing a dynamical version of Fourier transform.

The purpose of this paper is to give an explicit local formula for the difference of two natural versions of equivariant analytic torsion in de Rham theory. This difference is the sum of the integral of a Chern-Simons current and of a new invariant, the V -invariant of an odd dimensional manifold equipped with an action of a compact Lie group. The V -invariant localizes on the critical manifolds of invariant Morse-Bott functions. The results in this paper are shown to be compatible with results of Bunke, and also our with previous results on analytic torsion forms.

In this paper we extend first the Bismut-Lott's analytic torsion form for flat vector bundles to the boundary case, then we establish its gluing formula on a smooth fibration under the assumption that a fiberwise Morse function exists. We assume that the metrics have product structures near the cutting hypersurface.

This paper is a continuation of an earlier work (arXiv:1210.7928) which computed analytically the tree-level annihilation rates of a collection of non-relativistic neutralino and chargino two-particle states in the general MSSM. Here we extend the results by providing the next-to-next-to-leading order corrections to the rates in the non-relativistic expansion in momenta and mass differences, which include leading P-wave effects, in analytic form. The results are a necessary input for the calculation of the Sommerfeld-enhanced dark matter annihilation rates including short-distance corrections at next-to-next-to-leading order in the non-relativistic expansion in the general MSSM with neutralino LSP.

Algeria’s energy needs are actually satisfied mainly through the use of hydrocarbons. Demand for energy is growing exponentially because the population is growing massively and the building sector is in full expansion in order to address and solve the problems of housing, health and education. In 2011, Algeria initiated a dynamic green energy program by launching an ambitious development project aims at developing a renewable energy power source of 22000 MW and to save more than 60 Million TOE in energy efficiency by the year 2030. Our research topic is linked to the energy efficiency program initiated in Algeria. The objective of this article in to present a study carried out on the thermal performance of Phase Change Materials (PCMs) and their integration in buildings in order to achieve thermal comfort and to reduce the energy consumption. Then, an investigation on the capacity of using (PCMs) in Algeria is presented for a sustainable development and rational energy consumption.

Regulators and cycle maps in higher-dimensional differential algebraic K-theory

Finite volume based asymptotic homogenization theory for periodic materials under anti-plane shear

In this work, we present a new solution representation for the Helmholtz transmission problem in a bounded domain in ℝ2with a thin and periodic layer of finite length. The layer may consists of a periodic pertubation of the material coefficients or it is a wall modelled by boundary conditions with an periodic array of small perforations. We consider the periodicity in the layer as the small variableδand the thickness of the layer to be at the same order. Moreover we assume the thin layer to terminate at re-entrant corners leading to a singular behaviour in the asymptotic expansion of the solution representation. This singular behaviour becomes visible in the asymptotic expansion in powers ofδwhere the powers depend on the opening angle. We construct the asymptotic expansion order by order. It consists of a macroscopic representation away from the layer, a boundary layer corrector in the vicinity of the layer, and a near field corrector in the vicinity of the end-points. The boundary layer correctors and the near field correctors are obtained by the solution of canonical problems based, respectively, on the method of periodic surface homogenization and on the method of matched asymptotic expansions. This will lead to transmission conditions for the macroscopic part of the solution on an infinitely thin interface and corner conditions to fix the unbounded singular behaviour at its end-points. Finally, theoretical justifications of the second order expansion are given and illustrated by numerical experiments. The solution representation introduced in this article can be used to compute a highly accurate approximation of the solution with a computational effort independent of the small periodicityδ.

An explicit formula for analytic torsion forms for fibrations by projective curves is given. In particular one obtains a formula for direct images in Arakelov geometry in the corresponding setting. The main tool is a new description of Bismut’s equivariant Bott–Chern current in the case of isolated fixed points.

An algorithm for the numerical evaluation of the associated Legendre functions that runs in time independent of degree and order

The historical data on the consumption of spares are usually available in the form that the renewal function of the item could not easily be obtained by the process described by Cox/sup 1/. In this paper, a technique is discussed as to how such data be used for the renewal functions through Bayesian approach. A Beta alpha priori density for the parameter of Poisson demand is assumed that the Predictive demand distribution for such items is obtained. The renewal function in its analytical and asymptotic forms are also obtained.