We present a short analytic proof of the equality between the analytic and combinatorial torsion. We use the same approach as in the proof given by Burghelea, Friedlander and Kappeler, but avoid using the difficult Mayer-Vietoris type formula for the determinants of elliptic operators. Instead, we provide a direct way of analyzing the behaviour of the determinant of the Witten deformation of th...

To manage information overload users segment their information resources into smaller and smaller partitions. Yet, these partitions are often orthogonal to the expression of an underlying phenomenon. Our objective is to enable a user to identify new phenomena by developing automated methods that synthesize typically unused evidence from existing scientific articles. To demonstrate our approach,...

Effects of the Dirac sea on the excitation energy of the giant monopole states are investigated in an analytic way within the σ − ω model. The excitation energy is determined by the relativistic Landau-Migdal parameters, F0 and F1. Their analytic expressions are derived in the relativistic random phase approximation(RRPA) without the Dirac sea, with the Pauli blocking terms and with the full Di...

This paper describes a method of matrix decomposition which retains the ability of factor analytic techniques to summarize data in terms of a relatively low number of coordinates; but at the same time, does not sacrifice the useful analysis of variance heuristic of partitioning data matrices into independent sources of variation which are relatively simple to interpret. The basic model is essen...

The goal of this paper is to express simply the number of photons impinging on a target in the framework of accelerator-based Compton X-ray sources. From the basic kinematics of Compton sources, analytic formulas for the angular and the spectral fluxes are established as functions of the energy spread or/and the angular divergence of the electron and the laser beams. Their detailed predictions ...

There are the notes of rather informal lectures given by the first co-author in UPMC, Paris, in January 2017. Practical goal is to explain how to compute or estimate the Morse index of the second variation. Symplectic geometry allows to effectively do it even for very degenerate problems with complicated constraints. Main geometric and analytic tool is the appropriately rearranged Maslov index....

Several methods for the computation of the discrete Wigner Distribution (DWD) through the use of two-dimensional (2-D) analytic signals have been proposed, depending of the direction of the phase shift. Most of the methods cope the problem of aliasing of the DWD by lowpass prefiltering the spectrum but reducing spatial frequency support. In this correspondence, a new method for 2-D DWD free of ...

Movement classification or activity analysis is one of the most important areas in video surveillance. However, manually detecting, classifying and analyzing interesting moving objects by humans does not guarantee absolute correctness. When considering thereal environment and trying to relate the way objects interact in a surveillance covered area, it is not so easy interpreting every activity ...

We used multiconfiguration quasidegenerate perturbation theory and the fourfold-way direct diabatization scheme to calculate ab initio potential-energy surfaces at 3600 nuclear geometries of NH3. The calculations yield the adiabatic and diabatic potential-energy surfaces for the ground and first electronically excited singlet states and also the diabatic coupling surfaces. The diabatic surfaces...

An extensively revised heuristic-analytic theory of reasoning is presented incorporating three principles of hypothetical thinking. The theory assumes that reasoning and judgment are facilitated by the formation of epistemic mental models that are generated one at a time (singularity principle) by preconscious heuristic processes that contextualize problems in such a way as to maximize relevanc...