1-forms over the moduli space of irreducible connections defined by the spectrum of Dirac operators

Let (P) be the moduli space of irreducible connections of a G-principal bundle P over a closed Riemannian spin manifold M. Let D_A be the Dirac operator of M coupled to a connection A of P and f a smooth function on M. We consider a smooth variation A(u) of A with tangent vector ω and denote T_ω:= (D_A(u)−f) (u=0. The coefficients of the asymptotic expansion of trace (T_ω · e^-t(D_A−f)2) near t=0 define 1-forms a^(k)_f, K=0, 1, 2, … on (P). In this paper we calculate aa⁽⁰⁾_f, a⁽¹⁾_f, a⁽²⁾_f and study some of their properties. For instance using the 1-form a⁽²⁾_f for suitable functions f we obtain a foliation of codimension 5 of the space of G-instantons of S⁴.     

Sensitivity of depolarized lidar signals to cloud and aerosol particle properties

Measurements from depolarized lidars provide a promising method to retrieve both cloud and aerosol properties and a versatile complement to passive satellite-based sensors. For lidar observations of clouds and aerosols, multiple scattering plays an important role in the scattering process. Monte Carlo simulations are carried out to investigate the sensitivity of lidar backscattering depolarization to cloud and aerosol properties. Lidar parameters are chosen to be similar to those of the upcoming space-based CALIPSO lidar. Cases are considered that consist of a single cloud or aerosol layer, as well as a case in which cirrus clouds overlay different types of aerosols. It is demonstrated that besides thermodynamic cloud phase, the depolarized lidar signal may provide additional information on ice or aerosol particle shapes. However, our results show little sensitivity to ice or aerosol particle sizes. Additionally, for the case of multiple but overlapping layers involving both clouds and aerosols, the depolarized lidar contains information that can help identify the particle properties of each layer.     

Eye tissue structure and refraction alterations upon nondestructive laser action

A new approach to alterations in eye refraction upon nondestructive laser action on the sclera and cornea is studied. It is demonstrated in in vivo experiments on rabbit eyes that sequential laser irradiation of the sclera and cornea yields a significant alteration in the eye refraction. The collagen structure of the sclera and cornea is studied after the nondestructive laser action with noninvasive polarization-sensitive optical coherence tomography. It is demonstrated that collagen fibers that provide for the cornea tension and applanation partially survive in the zone of the local denaturation of sclera. An irradiation mode that corresponds to an increase in the cornea’s plasticity and does not cause visible structural changes is chosen. The simplest theoretical model for alterations in the eye refraction upon the nonablative laser action on sclera is analyzed. The alteration in the cornea curvature upon stretching resulting from the local sclera coagulation and the corresponding decrease in its volume is calculated. The model makes it possible to approximately estimate the laser irradiation modes that provide the desired alterations in eye refraction.     

Existence theorems for lagrange control problems with unbounded time domain

Existence theorems are proved for usual Lagrange control systems, in which the time domain is unbounded. As usual in Lagrange problems, the cost functional is an improper integral, the state equation is a system of ordinary differential equations, with assigned boundary conditions, and constraints may be imposed on the values of the state and control variables. It is shown that the boundary conditions at infinity require a particular analysis. Problems of this form can be found in econometrics (e.g., infinite-horizon economic models) and operations research (e.g., search problems).The author wishes to thank Professor L. Cesari for his many helpful comments and assistance in the preparation of this paper. This work was sponsored by the United States Air Force under Grants Nos. AF-AFOSR-69-1767-A and AFOSR-69-1662.     

The impact of ice particle roughness on the scattering phase matrix

The goal of this study is to explore the influence of ice particle habit (or shape) and surface roughness on the scattering phase matrix. As an example, reported here are the results for two wavelengths: 0.67 and 1.61 μm. For this effort, a database of single-scattering properties has been computed for a set of habits including hexagonal plates, hollow and solid columns, hollow and solid 3D bullet rosettes, droxtals, aggregates of solid columns, and aggregates of plates. The database provides properties for each of the habits at 101 wavelengths between 0.45 and 2.24 μm for smooth, moderately roughened, and severely roughened particles. At each wavelength, the scattering properties are provided at 233 discrete particle diameters ranging from 2 to 10,000 μm. A single particle size distribution from a very cold ice cloud sampled during the CRYSTAL-FACE field campaign (T_cld=–76 °C) is used to illustrate the influence of habit and roughness on the phase matrix. In all, four different habit mixtures are evaluated. The nonzero elements of the phase matrix are shown to be quite sensitive to the assumed habit, particularly in the case of ?P₁₂/P₁₁ that is associated with the degree of linear polarization of scattered radiation. Surface roughness is shown to smooth out maxima in the scattering phase function and in the other elements of the phase matrix, consistent with other studies. To compare with the theoretical simulations of the phase matrix for smooth and roughened particles, a full year of cloud-aerosol lidar with orthogonal polarization (CALIOP) data from 2008 is analyzed to provide global statistics on the values of P₁₁ and P₂₂/P₁₁ in the backscattering direction. In a comparison of two of the habit mixtures (one used for MODIS Collection 5 and another that incorporates new habits including hollow bullet rosettes and aggregates of plates) with the CALIOP data, the values for P₁₁ are higher regardless of the degree of particle surface roughness, and the values for P₂₂/P₁₁ are lower than those for CALIOP. Further investigation is warranted to better understand this discrepancy.     

Phase-locked ultrashort pulse trains at separate and independently tunable wavelengths

The generation and characterization of femtosecond pulses at three independently tunable visible wavelengths is reported. Selected spectral portions of a common continuum generated in sapphire are amplified in noncollinear optical parametric amplifiers. The phase relation of the pulse trains is analyzed with a nonlinear interferometer based on coherent anti-Stokes Raman scattering and is found to be locked to better than 250 mrad rms. Small spectral shifts of the pulses lead to interference behavior that is consistent with 1 kHz frequency combs.     

Highly Tin‐Selective Stille Coupling: Synthesis of a Polymer Containing a Stannole in the Main Chain

The incorporation of heavier Group 14 element heteroles into semiconducting polymers leads to unusual optoelectronic properties. However, polymers containing stannoles have not been accessible to date. We report a synthetic route to a well‐defined, stannole‐containing polymer, the first example of this class of π‐conjugated polymers. This route was made possible by developing difunctionalized stannole monomers and highly tin‐selective Stille coupling reactions that leave the tin in the stannole untouched. Compared to poly(3‐n‐hexylthiophene), the resulting polymer displays a remarkable bathochromic shift in its absorption.     

Beitrag zur Züchtung von ZnSiP2 unter nichtstöchiometrischen Bedingungen aus der Gasphase in Auswertung mikroanalytischer Untersuchungen

Röntgenographically identified single-phase ZnSiP₂ of stoichiometric composition which has been grown in gas phase has a specific resistance of > 10³ Ωcm and locally limited luminescence spectra. The presence of foreign phases and inhomogeneities as well as stoichiometric deviations in the ZnSiP₂ are possible causes of these physical properties. An attempt was made to grow, in the gas phase, ZnSiP₂ containing foreign phases. For this purpose, synthesis and crystallization of ZnSiP₂ were carried out using non-stoichiometric proportions of silicon. The phase composition of the crystals was investigated by means of light microscopy and electron-beam microanalysis. In the case of hypostoichiometric silicon amounts (–50 mole% Si) the ZnSiP₂ matrix contains the binary phases ZnP₂ and Zn₃P₂. Under hyperstoichiometric conditions (> 100 mole% Si) ZnS₁₃P₂ layers are deposited on the ZnSiP₂. Distinct differences between the physical properties of stoichiometric single-phase ZnSiP₂ and ZnSiP₂ containing foreign phases could not be detected.