Intersection multiplicities over Gorenstein rings

We construct a complex of free-modules over a Gorenstein ring R of dimension five, for which the Euler characteristic and Dutta multiplicity are different. This complex is the resolution of an R-module of finite length and finite projective dimension. As a consequence, the ring R has a nonzero Todd class tau_3(R) and a bounded free complex whose local Chern character does not vanish on this class. In the course of our work, we construct a module N of finite length and finite projective dimension over the hypersurface A=K[u,v,w,x,y,z]/(ux+vy+wz), such that the Serre intersection multiplicity of the modules N and A/(u,v,w)A is -2

Electronic structure of S-C6H5 self-assembled monolayers on Cu(111) and Au(111) substrates

We use first principles density functional theory to calculate the electronic structure of the phenylthiolate (S-C$_6$H$_5$) self-assembled monolayer (SAM) on Cu(111) and Au(111) substrates. We find significant lateral dispersion of the SAM molecular states and discuss its implications for transport properties of the molecular wire array. We calculate the two photon photoemission spectra and the work function of the SAM on Cu(111) and compare them with the available experimental data. Our results are used to discuss assignments of the observed spectral data and yield predictions for new electronic states due to the monolayer not yet accessed experimentally.Comment: 7 pages, 7 figure

A first-order differential double subordination with applications

Let $q_1$ and $q_2$ belong to a certain class of normalized analytic univalent functions in the open unit disk of the complex plane. Sufficient conditions are obtained for normalized analytic functions $p$ to satisfy the double subordination chain $q_1(z)\prec p(z)\prec q_2(z)$. The differential sandwich-type result obtained is applied to normalized univalent functions and to $\Phi$-like functions

Specific heat study of the Na(0.3)CoO(2).1.3H(2)O superconductor: influence of the complex chemistry

We report results of specific heat measurements on polycrystalline samples of the layered superconductor, Na(0.3)CoO(2).1.3H(2)O. The electronic contribution to the specific heat, gamma, is found to be 12.2 mJ/mol-K2. The feature at the superconducting transition is rather sharp, becoming broad and strongly suppressed in an applied magnetic field. The data indicate a residual normal state electronic specific heat at low temperatures, implying that there is a sizable population of normal state electrons in the samples even below Tc. Inhomogeneity in the Na content, to which the superconducting state is exquisitely sensitive, appears to be the most likely explanation for these results. These results further indicate that special sample handling is required for an accurate characterization of the superconducting state in this material.Comment: publication information adde

Phase transitions of barotropic flow coupled to a massive rotating sphere - derivation of a fixed point equation by the Bragg method

The kinetic energy of barotropic flow coupled to an infnitely massive rotating sphere by an unresolved complex torque mechanism is approximated by a discrete spin-lattice model of fluid vorticity on a rotating sphere, analogous to a one-step renormalized Ising model on a sphere with global interactions. The constrained energy functional is a function of spin-spin coupling and spin coupling with the rotation of the sphere. A mean field approximation similar to the Curie-Weiss theory, modeled after that used by Bragg and Williams to treat a two dimensional Ising model of ferromagnetism, is used to find the barotropic vorticity states at thermal equilibrium for given temperature and rotational frequency of the sphere. A fixed point equation for the most probable barotropic flow state is one of the main results.Comment: 31 pages, 6 figure