Riemannian manifolds in noncommutative geometry

We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c${}^c$ manifolds; and conversely, in the presence of a spin^c${}^c$ structure. We also show how to obtain an analogue of Kasparov’s fundamental class for a Riemannian manifold, and the associated notion of Poincaré duality. Along the way we clarify the bimodule and first-order conditions for spectral triples.     

The maximal process of nonlinear shot noise

In the nonlinear shot noise system-model shots’ statistics are governed by general Poisson processes, and shots’ decay-dynamics are governed by general nonlinear differential equations. In this research we consider a nonlinear shot noise system and explore the process tracking, along time, the system’s maximal shot magnitude. This ‘maximal process’ is a stationary Markov process following a decay-surge evolution; it is highly robust, and it is capable of displaying both a wide spectrum of statistical behaviors and a rich variety of random decay-surge sample-path trajectories. A comprehensive analysis of the maximal process is conducted, including its Markovian structure, its decay-surge structure, and its correlation structure. All results are obtained analytically and in closed-form.     

Quantum Dot Research: Current State and Future Prospects

This article reviews the current state of research involving semiconductor quantum dots, provides a brief review of the theory behind their unique properties, and an introduction explaining the importance of quantum dot research. The characteristic shifting of the band gap energy with quantum dot size, as predicted from the density of states for low-dimensional structures, allows experimental measurements to determine the extent to which quantum confinement effects play a role in the resulting properties. A few of the current techniques used to measure the presence and physical characteristics of quantum dots and their energy levels is reviewed, including transmission electron microscopy, optical transmission, and Raman and photoluminescence spectroscopy. Finally, some of the more exciting applications for quantum dots currently being researched for use in the field of optoelectronics are reviewed, including quantum dot infrared photodetectors, quantum dot lasers, and quantum dot solar cells. Comments are made on the current progress and the future prospects of quantum dot research and device applications.     

Power limitations in fiber-optic frequency-division multiplexed systems

Abstract

Launch power is limited to the milliwatt level by stimulated Brillouin scattering (SBS) in a single-channel, coherent fiber-optic network. Increasing the number of frequency-division multiplexed channels causes the power limit to decrease quickly to submilliwatt levels due to three-wave intermodulation to keep the signal-to-noise ratio from deteriorating significantly. As the number of channels increases, stimulated Raman scattering (SRS) begins to dominate. If a maximum of 0.5–dB depletion in the highest-frequency channel is allowed, SRS dominates when the number of multiplexed channels reaches about 300. Generally, the launch-power-limiting phenomenon is dependent on the number of channels being multiplexed.     

<Emphasis Type="Italic">In situ</Emphasis> Oxidation of phenol and <Emphasis Type="Italic">o</Emphasis>-aminophenol in the channels of 3d-supramolecular coordination polymers

The host attractive properties of supramolecular coordination polymers of the type _￥³ _\infty^3 [(R₃Sn)₃FeIII(CN)₆], where R = methyl (I), n-butyl (II), and phenyl (III), afford the ability to be used as effective oxidizing reagents for phenol and o-aminophenol forming new host-guest supramolecular coordination polymers. Phenol was oxidized to 1,4-benzoquinone while o-aminophenol was oxidized to poly-o-aminophenol by the polymers I and II and to 2-aminophenoxazin-3-one by the polymer III. The oxidation products were investigated by methods of spectroscopy and high-performance liquid chromatography. The redox reactions were characterized by first-order kinetics. Moreover, mechanisms of the oxidation processes of phenol and o-aminophenol have been proposed.     

Coherent Raman and Infrared Studies of Sulfur Trioxide

High-resolution (0.001 cm⁻¹) coherent anti-Stokes Raman scattering (CARS) was used to observe the Q-branch structure of the IR-inactive ν₁ symmetric stretching mode of ³²S¹⁶O₃ and its various ¹⁸O isotopomers. The ν₁ spectrum of ³²S¹⁶O₃ reveals two intense Q-branches in the region 1065–1067 cm⁻¹, with surprisingly complex vibrational–rotational structure not resolved in earlier studies. Efforts to simulate this with a simple Fermi-resonance model involving ν₁ and 2ν₄ states do not reproduce the spectral detail, nor do they yield reasonable spectroscopic parameters. A more subtle combination of Fermi resonance and indirect Coriolis interactions with nearby states, 2ν₄(1=0, ±2), ν₂+ν₄(1=±1), 2ν₂(1=0), is suspected and a determination of the location of these coupled states by high-resolution infrared measurements is under way. At medium resolution (0.125 cm⁻¹), the infrared spectra reveal Q-branch features from which approximate band origins are estimated for the ν₂, ν₃, and ν₄ fundamental modes of ³²S¹⁸O₃, ³²S¹⁸O₂¹⁶O, and ³²S¹⁸O¹⁶O₂. These and literature data for ³²S¹⁶O₃ are used to calculate force constants for SO₃ and a comparison is made with similar values for SO₂ and SO. The frequencies and force constants are in excellent agreement with those obtained by Martin in a recent ab initio calculation.     

Targetted stochastic matrix inversion

The solution of linear systems by stochastic techniques is investigated as an alternative to the widely used elimination and relaxation procedures. The Pan-Reif algorithm is used to allow any non-singular matrix to be stochastically inverted. New algorithms are devised to overcome some of the efficiency problems of the original Von Neumann-Ulam method and its refinements. The method is tested on some simple physical problems to gauge its effectiveness.     

X-Ray Spectra of Iron Phosphonates

The reaction of dialkyl alkylphosphonates with trivalent metal chlorides has recently been reported (1,2). The typical products of these reactions is a solid which is insoluble in most organic solvents and water. A monomeric structure was postulated for the iron phosphonates(1), while polynuclear structure was proposed for titanium, vanadium, and chromium phosphonates(2). Infrared(1) and Mossbauer-effect(3) studies were unable to differentiate between the monomeric or polynuclear structure for the iron phosphonates, In an attempt to further characterize the iron phosphonates, an x-ray diffration study was undertaken. The results of these studies are reported herein.     

Studies on nano suspensions of silver sol and redispersed nanocrystallite silver in aqueous and alcoholic media

Nanocrystallite silver and silver sol were prepared and characterized by UV-visible spectra, XRD, TEM and HRTEM. The crystallite silver is re-dispersed in two different media, namely, water and alcohol and sonicated before ultrasonic investigation. The silver sol was used as such. Three different models for the propagation of ultrasound through two phase media are compared in these three different types of nano suspensions. Effect of particle size and medium on ultrasonic velocity (U), compressibility (κ) impedance (Z) and viscous relaxation time (τ) is studied. The particle concentration range was 0.2-1 v/v. Density and viscosity of the dispersion and sol are measured at different particle volume fractions. Effective density and ultrasonic velocity are computed by Urick, Kuster and Toksöz and Urick and Ament models and compared with experimental velocities. Values of effective density obtained by using Urick and Urick and Ament equations closely agree with experimental results of density while Urick's equation prediction of velocity is in close agreement with the experimental velocities. This comes as a surprise in view of the large density difference between the medium and suspended particle and suggests the possibility of the balancing effect of the inertial and viscous forces operating in the suspension.