Cyclic Cohomology and Higher Indexes for Noncompact Complete Manifolds

AbstractThe indices of generalized Dirac operators on noncompact complete Riemannian manifolds live in the K theory of (uniform) Roe algebras. In this paper we shall compute the cyclic cohomology of (uniform) Roe algebras associated to noncompact manifolds. The cyclic cohomology of the (uniform) Roe algebras is identified with (uniform) simplical cohomology with infinite support of the Rips′ polyhedrons associated to a net of the Riemannian manifold. We also compute the Chern character of the K theoretic indices of generalized Dirac operators. We apply such a computation to the analysis and geometry of noncompact complete Riemannian manifolds. In particular we show that a uniformly contractible Riemnannian manifold with bounded geometry cannot have uniform positive scalar curvature outside a compact set if the volume and contractibility radius have certain subexponential growth

Bioequivalence of Oral Products and the Biopharmaceutics Classification System: Science, Regulation, and Public Policy

The demonstration of bioequivalence (BE) is an essential requirement for ensuring that patients receive a product that performs as indicated by the label. The BE standard for a particular product is set by its innovator, and this standard must subsequently be matched by generic drug products. The Biopharmaceutics Classification System (BCS) sets a scientific basis for an improved BE standard for immediate-release solid oral dosage forms. In this paper, we discuss BE and the BCS, as well as the issues that are currently relevant to BE as a pharmaceutical product standard

Effective nonlinear optical properties of composite media of graded spherical particles

We have developed a nonlinear differential effective dipole approximation (NDEDA), in an attempt to investigate the effective linear and third-order nonlinear susceptibility of composite media in which graded spherical inclusions with weak nonlinearity are randomly embedded in a linear host medium. Alternatively, based on a first-principles approach, we derived exactly the linear local field inside the graded particles having power-law dielectric gradation profiles. As a result, we obtain also the effective linear dielectric constant and third-order nonlinear susceptibility. Excellent agreement between the two methods is numerically demonstrated. As an application, we apply the NDEDA to investigate the surface plasma resonant effect on the optical absorption, optical nonlinearity enhancement, and figure of merit of metal-dielectric composites. It is found that the presence of gradation in metal particles yields a broad resonant band in the optical region, and further enhances the figure of merit.Comment: 20 pages, 5 figure

Teleparallel Versions of Friedmann and Lewis-Papapetrou Spacetimes

This paper is devoted to investigate the teleparallel versions of the Friedmann models as well as the Lewis-Papapetrou solution. We obtain the tetrad and the torsion fields for both the spacetimes. It is shown that the axial-vector vanishes for the Friedmann models. We discuss the different possibilities of the axial-vector depending on the arbitrary functions $\omega$ and $\psi$ in the Lewis-Papapetrou metric. The vector related with spin has also been evaluated.Comment: 13 pages, accepted for publication in GR

Review and Comparison of Computational Approaches for Joint Longitudinal and Time‐to‐Event Models

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/1/insr12322.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/2/insr12322_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151312/3/Supplement_ReviewComputationalJointModels_final.pd

Stochastic Quantization of the Chern-Simons Theory

We discuss Stochastic Quantization of $d$=3 dimensional non-Abelian Chern-Simons theory. We demonstrate that the introduction of an appropriate regulator in the Langevin equation yields a well-defined equilibrium limit, thus leading to the correct propagator. We also analyze the connection between $d$=3 Chern-Simons and $d$=4 Topological Yang-Mills theories showing the equivalence between the corresponding regularized partition functions. We study the construction of topological invariants and the introduction of a non-trivial kernel as an alternative regularization.Comment: 30 page

Spin-Polarized Electron Transport at Ferromagnet/Semiconductor Schottky Contacts

We theoretically investigate electron spin injection and spin-polarization sensitive current detection at Schottky contacts between a ferromagnetic metal and an n-type or p-type semiconductor. We use spin-dependent continuity equations and transport equations at the drift-diffusion level of approximation. Spin-polarized electron current and density in the semiconductor are described for four scenarios corresponding to the injection or the collection of spin polarized electrons at Schottky contacts to n-type or p-type semiconductors. The transport properties of the interface are described by a spin-dependent interface resistance, resulting from an interfacial tunneling region. The spin-dependent interface resistance is crucial for achieving spin injection or spin polarization sensitivity in these configurations. We find that the depletion region resulting from Schottky barrier formation at a metal/semiconductor interface is detrimental to both spin injection and spin detection. However, the depletion region can be tailored using a doping density profile to minimize these deleterious effects. For example, a heavily doped region near the interface, such as a delta-doped layer, can be used to form a sharp potential profile through which electrons tunnel to reduce the effective Schottky energy barrier that determines the magnitude of the depletion region. The model results indicate that efficient spin-injection and spin-polarization detection can be achieved in properly designed structures and can serve as a guide for the structure design.Comment: RevTex

Global Analysis with SNO: Toward the Solution of the Solar Neutrino Problem

We perform a global analysis of the latest solar neutrino data including the SNO result on the CC-event rate. This result further favors the LMA solution of the solar neutrino problem. The best fit values of parameters we find are: \Delta m^2 = (4.8 - 5.0)10^{-5} eV^2, tan^2 \theta = 0.35 - 0.38, f_B = 1.08 - 1.12, and f_{hep} = 1 - 4. With respect to this best fit the LOW solution is accepted at 90% C.L.. The Vacuum oscillation solution with \Delta m^2 = 1.4 10^{-10} eV^2, gives good fit of the data provided that the boron neutrino flux is substantially smaller than the SSM flux (f_B \sim 0.5). The SMA solution is accepted only at 3\sigma level. We find that vacuum oscillations to sterile neutrino, VAC(sterile), with f_B \sim 0.5 also give rather good global fit of the data. All other sterile solutions are strongly disfavored. We check the quality of the fit by constructing the pull-off diagrams of observables. Predictions for the day-night asymmetry, spectrum distortion and NC/CC ratio at SNO are calculated. In the best fit points of the global solutions we find: A_{DN}^{CC} \approx (7 - 8)% for LMA, \sim 3% for LOW, and (2 - 3)% for SMA. It will be difficult to see the distortion of the spectrum expected for LMA as well as LOW solutions. However, future SNO spectral data can significantly affect the VAC and SMA solutions. We also calculate expectations for the BOREXINO rate.Comment: 35 pages, latex, 9 figures; results of analysis slightly changed due to different treatment of the hep neutrino flux; predictions for NC/CC ratio and Borexino rate adde

Electron Spin Relaxation in a Semiconductor Quantum Well

A fully microscopic theory of electron spin relaxation by the D'yakonov-Perel' type spin-orbit coupling is developed for a semiconductor quantum well with a magnetic field applied in the growth direction of the well. We derive the Bloch equations for an electron spin in the well and define microscopic expressions for the spin relaxation times. The dependencies of the electron spin relaxation rate on the lowest quantum well subband energy, magnetic field and temperature are analyzed.Comment: Revised version as will appear in Physical Review

Calculation of the anomalous exponents in the rapid-change model of passive scalar advection to order ε3\varepsilon^{3}

The field theoretic renormalization group and operator product expansion are applied to the model of a passive scalar advected by the Gaussian velocity field with zero mean and correlation function \propto\delta(t-t')/k^{d+\eps}. Inertial-range anomalous exponents, identified with the critical dimensions of various scalar and tensor composite operators constructed of the scalar gradients, are calculated within the $\varepsilon$ expansion to order $\varepsilon^{3}$ (three-loop approximation), including the exponents in anisotropic sectors. The main goal of the paper is to give the complete derivation of this third-order result, and to present and explain in detail the corresponding calculational techniques. The character and convergence properties of the $\varepsilon$ expansion are discussed; the improved ``inverse'' $\varepsilon$ expansion is proposed and the comparison with the existing nonperturbative results is given.Comment: 34 pages, 5 figures, REVTe