Index theorems on manifolds with straight ends

We study Fredholm properties and index formulas for Dirac operators over complete Riemannian manifolds with straight ends. An important class of examples of such manifolds are complete Riemannian manifolds with pinched negative sectional curvature and finite volume

On the discrete spectrum of spin-orbit Hamiltonians with singular interactions

We give a variational proof of the existence of infinitely many bound states below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba and Dresselhaus cases) perturbed by measure potentials thus extending the results of J.Bruening, V.Geyler, K.Pankrashkin: J. Phys. A 40 (2007) F113--F117.Comment: 10 pages; to appear in Russian Journal of Mathematical Physics (memorial volume in honor of Vladimir Geyler). Results improved in this versio

2-Aminoterephthalic acid dimethyl ester

Single crystals of the title compound, C10H11NO4, an inter­mediate in the industrial synthesis of yellow azo pigments, were obtained from the industrial production. The mol­ecules crystallize as centrosymmetic dimers connected by two symmetry-related N—H⋯O=C hydrogen bonds. Each mol­ecule also contains an intra­molecular N—H⋯O=C hydrogen bond. The dimers form stacks along the a-axis direction. Neighbouring stacks are arranged into a herringbone structure

Summary Report of Session VI

This report gives a brief review of the presentations in Session VI of the Ecloud'02 Workshop and summarizes the major points during the discussions. Some points (e.g., the critical mass phenomenon) are not conclusive and even controversial. But it has been agreed that further investigations are warranted. The topic of Session VI in the Ecloud'02 workshop is ''Discussions of future studies, collaborations and possible solutions.'' Half of the session is devoted to presentations, another half to discussions. This report will focus on the latter. There are six presentations: (1) R. Macek, Possible cures to the e-cloud problem; (2) G. Rumolo, Driving the electron-cloud instability by an electron cooler; (3) U. Iriso Ariz, RF test benches for electron-cloud studies; (4) F. Caspers, Stealth clearing electrodes; (5) F. Ruggiero, Future electron-cloud studies at CERN; and (6) E. Perevedentsev, Beam-beam and transverse impedance model

Two-dimensional semiconducting nanostructures based on single graphene sheets with lines of adsorbed hydrogen atoms

It is shown that lines of adsorbed hydrogen pair atoms divide the graphene sheet into strips and form hydrogen-based superlattice structures (2HG-SL). We show that the forming of 2HG-SL drastically changes the electronic properties of graphene from semimetal to semiconductor. The electronic spectra of "zigzag" (n,0) 2HG-SL is similar to that of (n,0) carbon nanotubes and have a similar oscillation of band gap with number n, but with non-zero minimal values. The composite dual-periodic (n,0)+(m,0) 2HG-SLs of "zigzag" strips are analyzed, with the conclusion that they may be treated as quasi-two-dimensional heterostructures. We also suggest an experimental way of fabricating hydrogen superlattices.Comment: 12 pages, 3 figure

Heat kernels on curved cones

A functorial derivation is presented of a heat-kernel expansion coefficient on a manifold with a singular fixed point set of codimension two. The existence of an extrinsic curvature term is pointed out.Comment: 4p.,sign errors corrected and a small addition,uses JyTeX,MUTP/94/0

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years