The Atiyah class, Hochschild cohomology and the Riemann-Roch theorem

We develop a formalism involving Atiyah classes of sheaves on a smooth manifold, Hochschild chain and cochain complexes. As an application we prove a version of the Riemann--Roch theorem.Comment: 16 pages; added references, corrected typos and removed irrelevant passage

A Lower Bound for Chaos on the Elliptical Stadium

The elliptical stadium is a plane region bounded by a curve constructed by joining two half-ellipses by two parallel segments of equal length. The billiard inside it, as a map, generates a two parameters family of dynamical systems. It is known that the system is ergodic for a certain region of the parameter space. In this work we study the stability of a particular family of periodic orbits obtaining good bounds for the chaotic zone.Comment: 13 pages, LaTeX. 7 postscript low resolution figures included. High resolution figures avaiable under request to [email protected]

Spectroscopy of Stellar-Like Objects Contained in the Second Byurakan Survey. I

The results of spectroscopic observations of 363 star-like objects from the Second Byurakan Survey (SBS) are reported. This SBS's subsample has proven to be a rich source of newly identified quasars, Seyfert type galaxies, degenerate stars and hot subdwarfs. In the subsample here studied, we identified 35 new QSOs, 142 White Dwarfs (WDs) the majority of which, 114 are of DA type, 55 subdwarfs (29 of which are sdB-type stars), 10 HBB, 16 NHB, 54 G-type and 25 F-type stars, two objects with composite spectra, four Cataclismic Variables (CV), two peculiar emission line stars, 17 objects with continuous spectra, as well as one planetary nebula. Among the 35 QSOs we have found two Broad Absorption Line (BAL) QSOs, namely SBS 1423+500 and SBS 1435+500A. Magnitudes, redshifts, and slit spectra for all QSOs, also some typical spectra of the peculiar stars are presented. We estimate the minimum surface density of bright QSOs in redshift range 0.3<z<2.2 to be 0.05 per sq. deg. for B<17.0 and 0.10 per sq. deg. for B<17.5.Comment: 22 pages, 3 tables, 4 figures, PASP in pres

A local ergodic theorem for non-uniformly hyperbolic symplectic maps with singularities

In this paper, we prove a criterion for the local ergodicity of non-uniformly hyperbolic symplectic maps with singularities. Our result is an extension of a theorem of Liverani and Wojtkowski.Comment: 35 page

Alien Registration- Markarian, Vartan (Lewiston, Androscoggin County)

https://digitalmaine.com/alien_docs/22326/thumbnail.jp

Low temperature dielectric relaxation study of aqueous solutions of diethylsulfoxide

In the present work, dielectric spectra of mixtures of diethylsulfoxide (DESO) and water are presented, covering a concentration range of 0.2 - 0.3 molar fraction of DESO. The measurements were performed at frequencies between 1 Hz and 10 MHz and for temperatures between 150 and 300 K. It is shown that DESO/water mixtures have strong glass-forming abilities. The permittivity spectra in these mixtures reveal a single relaxation process. It can be described by the Havriliak-Negami relaxation function and its relaxation times follow the Vogel-Fulcher-Tammann law, thus showing the typical signatures of glassy dynamics. The concentration dependence of the relaxation parameters, like fragility, broadening, and glass temperature, are discussed in detail.Comment: 20 pages, 5 figure

A note on the symplectic structure on the space of G-monopoles

Let $G$ be a semisimple complex Lie group with a Borel subgroup $B$. Let $X=G/B$ be the flag manifold of $G$. Let $C=P^1\ni\infty$ be the projective line. Let $\alpha\in H_2(X,{\Bbb Z})$. The moduli space of $G$-monopoles of topological charge $\alpha$ (see e.g. [Jarvis]) is naturally identified with the space $M_b(X,\alpha)$ of based maps from $(C,\infty)$ to $(X,B)$ of degree $\alpha$. The moduli space of $G$-monopoles carries a natural hyperk\"ahler structure, and hence a holomorphic symplectic structure. We propose a simple explicit formula for the symplectic structure on $M_b(X,\alpha)$. It generalizes the well known formula for $G=SL_2$ (see e.g. [Atiyah-Hitchin]). Let $P\supset B$ be a parabolic subgroup. The construction of the Poisson structure on $M_b(X,\alpha)$ generalizes verbatim to the space of based maps $M=M_b(G/P,\beta)$. In most cases the corresponding map $T^*M\to TM$ is not an isomorphism, i.e. $M$ splits into nontrivial symplectic leaves. These leaves are explicilty described.Comment: v2: List of authors updated; v3: The formula for the symplectic form corrected; v4: Notations changed; v5: A few more corrections: final versio