A NEW ALGORITHM OF RELAXATION METHOD FOR PARTICLE ANALYSIS FROM FORWARD SCATTERED LIGHT

1. Introduction In many cases, particle dimension and size distribution play an important role in application. The analysis of parti- cle size is therefore necessary for research and develop- ment and also for process quality control in powder tech- nology and for many particle systems (Wang et al., 2000). Many instruments have been developed and constructed for this purpose. With the rapid development and availabil- ity of laser techniques, optoelectronics and microcomputer science, light sc…     

NaCl interaction with interfacially polymerized polyamide films of reverse osmosis membranes: A solid-state Na NMR study

²³Na nuclear magnetic resonance (NMR) spectroscopy of NaCl-exchanged polyamide (PA) films comparable to those of the active skin layer of many reverse osmosis (RO) membranes provides novel insight into the structural environments and dynamical behavior of Na⁺ in such films. Unsupported PA films were synthesized via interfacial polymerization of trimesoyl chloride in hexane and m-phenylenediamine in aqueous solution, and SEM, FT-IR, and ¹³C NMR data demonstrate successful thin film polymerization. Compositional data confirm this conclusion and demonstrate equal Na and Cl incorporation during NaCl exchange from aqueous solution. The ²³Na NMR spectra for freshly made polymer samples exchanged in 1 M NaCl solution show significant relative humidity (RH) dependence. At near 0% RH, there are resonances for crystalline NaCl and rigidly held Na⁺ in the PA. With increasing RH, a resonance for solution-like dynamically averaged Na⁺ appears and above 51% RH is the only signal observed. The slightly negative chemical shift of this resonance suggests a dominantly hydrous environment with some atomic-scale coordination by atoms of the polymer. The greatly reduced ²³Na T₁ relaxation rates for this resonance relative to bulk solution and crystalline NaCl confirm close association with the polymer. Variable temperature ²³Na NMR spectra for a sample equilibrated at 97% RH obtained from −80 to 20 °C show the presence of rigidly held Na⁺ in a hydrated environment at low temperatures and replacement of this resonance by the dynamically averaged signal at temperatures above about −20 °C. The results provide support for the solution–diffusion model for RO membranes transport and demonstrate the capabilities of multi-nuclear NMR methods to investigate molecular-scale structure and dynamics of the interactions between dissolved species and RO membranes.     

General Theory of Acoustic Wave Propagation in Liquids and Gases

We study the propagation of small-amplitude acoustic waves in liquids and gases and use the hydrodynamic equations to obtain an exact dispersion equation. This equation in dimensionless variables contains only two material constants p and q. We solve the dispersion equation, obtaining an exact solution that holds for all values of the parameters and all frequencies up to hypersonic, and thus analytically establish exactly how the speed of sound c, the wave vector k, and the damping factor x depend on the frequency ω and the dimensionless material constants p and q. Studying the behavior of the solution in the sonic and ultrasonic frequency bands for ω < 10⁷ sec^-1 results in an expression for the damping factor, which differs from the Kirchhoff formula. The speed of sound c and the wave vector k are shown to have finite nonzero values for all hypersonic frequencies. At the same time, there exists a certain maximum frequency value, ω_max ≈ 10¹¹-10¹² sec^-1, at which the damping factor x is zero. This frequency determines the boundary of the applicability domain for the hydrodynamic equations. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 2, pp. 340–352, February, 2006.     

Asymptotic results in robust quasi-bayesian estimation

Let Θ be a real random variable with a known (a priori) distribution. Let the observations given Θ be iid with a common distributionF₀(·)=F(·−0)F is known to belong to some family of distributions on the real line. We find estimators of Θ which are asymptotically minimax for two types of loss functions.     

A Class of Linear Biased Estimators of Regression ParameterMatrix in the Growth Curve Model

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Rapidly progressing photophysical and photochemical relaxation processes in complex organic molecules

Using methods of high-speed kinetic laser spectroscopy, we investigated the dynamics and mechanisms of rapidly progressing relaxation processes in multiatomic molecules. We separated intra- and intermolecular channels of relaxation of the vibrational energy of excitation by the rate of transformation of nonstationary absorption spectra in a picosecond range of times. The role of highly excited electronic states in the process of electronic-vibrational relaxation in molecules of the class of phenazines was ascertained. Applying femtosecond light pulses in a real time scale, we recorded the dynamics of the decay of optically induced anisotropy in rarefied vapors of organic compounds. Several mechanisms of transfer of a hydrogen atom in the process of formation of free radicals in photoreduction of ketones were established. The dynamics of formation of inter- and intramolecular exciplexes in binary gas-phase systems was investigated. We determined the mechanisms of intramolecular dissociation of a C–O chemical bond in spiropyrans and xanthene dyes. Photodissociation of S–S bonds in molecules of disulfides was studied. The possibility of the existence of states with intramolecular charge transport with a twisted configuration for organic free radicals is shown. To whom correspondence should be addressed. Institute of Molecular and Atomic Physics of the National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 5, pp. 635–661, September–October, 1998.     

On the equivalence of the parallel channel and the correlated cluster relaxation models

The question of the origins of nonexponential relaxation is addressed in terms of the probabilistic approach to relaxation. The interconnection between two differently rooted probabilistic models, i.e., between the parallel channel and the correlated cluster models, is presented. We show that clearly different probabilistic origins yield in both approaches a well-defined class of universally valid two-power-law responses with the stretched-exponential and exponential decay laws as special cases. The equivalence of both models indicates that variations in the local environment of the relaxing configurational units (parallel channel relaxation) can provide a basis for self-similar relaxation dynamics without the need for hierarchically constrained dynamics (correlated clusters relaxation).     

Zero temperature phase transitions in spin-ladders: Phase diagram and dynamical studies of Cu2(C5H12N2)2Cl4>

In a magnetic field, spin-ladders undergo two zero-temperature phase transitions at the critical fields H_c1 and H_c2. An experimental review of static and dynamical properties of spin-ladders close to these critical points is presented. The scaling functions, universal to all quantum critical points in one-dimension, are extracted from (a) the thermodynamic quantities (magnetization) and (b) the dynamical functions (NMR relaxation). A simple mapping of strongly coupled spin ladders in a magnetic field on the exactly solvable XXZ model enables to make detailed fits and gives an overall understanding of a broad class of quantum magnets in their gapless phase (between H_c1 and H_c2). In this phase, the low temperature divergence of the NMR relaxation demonstrates its Luttinger liquid nature as well as the novel quantum critical regime at higher temperature. The general behavior close these quantum critical points can be tied to known models of quantum magnetism. Received: 13 March 1998 / Received in final form and Accepted: 21 July 1998     

Influences of tissue composition and structural features of biological media on the ultrasonic nonlinearity parameter

The Acoustic nonlinearity parameter is an important parameter innonlinear acoustics.In this article,the nonlinearity parameter B/A of normaland eight kinds of pathological porcine liver tissues were measured by finiteamplitude insert-substitution method.The mixture law for nonlinearityparameter is used to analyze and predict the volume fractions of the compo-nents in a given tissue.It was found that the nonlinearity parameter is sensitiveto the pathological forms of biological tissues and the values of B/A dependon the tissue composition and structural features.     

Quantitative cerebral magnetic resonance imaging during ACTH treatment of multiple sclerosis

Serial MR scans were performed with the 2DFT imaging method and the filtered backprojection imaging method on 12 patients with multiple sclerosis in acute phase, 4 in a relapsing/remitting form, and 8 in a progressive form, before, during and after ACTH treatment. Both T₁ and T_2mono relaxation times, obtained by fitting transverse magnetization decay curves with a monoexponential function within the apparently normal white matter and the areas of increased signal, were measured. With the backprojection method it was possible to fit the transverse magnetization decay curve with a biexponential function and obtain T_2long and T_2short relaxation times. The T_2mono and T₁ relaxation times of the apparently normal white matter were significantly different from those obtained for volunteers, but no significant differences were found before, during, or after treatment. The transverse magnetization decay curves of the areas of increased signal were better fitted by a biexponential function. No significant changes in these relaxation times were observed after ACTH treatment. These results argue against an anti-oedematous action of ACTH and may suggest that it has an immunosuppressant effect.