An application of the generalized alternating polynomials to the numerical solution of Fredholm integral equations

Generalized alternating polynomials have been introduced by the author earlier. In the present paper their indirect analogue is constructed for numerical solution of the Fredholm linear integral equations. Although the proposed method is a particular case of the general projection scheme, its valuable feature is the presence of a sequence of parameters, which, for sufficiently smooth kernels and inhomogeneous terms, serves as an indicator of the quality of approximation.     

Diffusion in Lorentz lattice gas automata with backscattering

The probability of first return to the initial intervalx and the diffusion tensorD _x are calculated exactly for a ballistic Lorentz gas on a Bethe lattice or Cayley tree. It consists of a moving particle and a fixed array of scatterers, located at the nodes, and the lengths of the intervals between scatterers are determined by a geometric distribution. The same values forx andD _x apply also to a regular space lattice with a fraction of sites occupied by a scatterer in the limit of a small concentration of scatterers. If backscattering occurs, the results are very different from the Boltzmann approximation. The theory is applied to different types of lattices and different types of scatterers having rotational or mirror symmetries.     

Die Berechnung von Einelektronen-Integralen in der SCF-Xα-SW-Methode: I. Die Normierung

A normalization of the wave functions by means of the theoretical exact Multiple-Scattering-(MS)-formalism is discussed within the framework of the SCF-X-SW-method. For the atomic and extramolecular regions the integrals of normalization can be easily determined and the results can be described by the corresponding electronic charges. The calculation of the integral of the interatomic region is problematic. The needful volume integration is only necessary to theGreen's functions of the wave functions and can be solved by means of the residual theory. The further analytical calculation of the surface integrals leads to a complicated formalism which can be numerically evaluated.

     

一种新型的表面声波阻抗传感器及其在液相体系中的应用

一种新型的表面声波阻抗传感器及其在液相体系中的应用姚守拙，陈康，刘德忠，聂利华（湖南大学化学化工系，长沙，４１００８２）关键词表面声波，阻抗传感器，液相应用表面声波传感器（ＳＡＷＳ）具有较高的灵敏度和检测精度，已广泛应用于气体微量组分分析、色谱检测和...     

Characterization of cyclodextrin-modified infrared chemical sensors: Part I. Modeling the mechanisms of interaction

To explore the properties of cyclodextrins (CDs) as an optical sensing phase, the behavior of immobilized CD in interaction with analytes was studied in this work. CDs having different cavity sizes were immobilized onto the surface of infrared (IR) internal reflection-sensing element (IRE) to kinetically monitor the behavior of CD in interaction with analytes. Several aromatic compounds having various molecular sizes and functional groups were used to characterize the interaction mechanism. A two-layer modification method was proposed in this work, which utilized a thin hydrophobic film (polyvinyl benzyl chloride) to stick on the IRE and to covalently bond to the CDs through an ethylene diamine linker. The synthesized CD phases exhibited high stability in aqueous solution. To analyze the behavior during the formation of complexes between the guest molecules and the CD phases, we modeled the interaction behavior and treated the kinetic data with the theoretical equations developed in this work. The results indicate that the behavior of the interaction between guest molecules and CDs was explained by considering the formation of two types of complexes: adsorbed complexes and inclusion complexes. The formation of the inclusion complexes was relatively fast, the time required to reach equilibrium could be shorter than a few minutes. The adsorbed complexes were also observed, but their rate of formation was relatively slow; equilibrium could be reached at times greater than 60 min. Based on the signals observed under equilibrium conditions, the concentration of inclusion complexes was approximately three times than that of the adsorbed complexes.     

On solving a D.C. programming problem by a sequence of linear programs

We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in ⁿ . This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.Parts of this research were accomplished while the third author was visiting the University of Trier, Germany, as a fellow of the Alexander von Humboldt foundation.     

Generalizations of Slater's constraint qualification for infinite convex programs

In this paper we study constraint qualifications and duality results for infinite convex programs (P) = inf{f(x): g(x) – S, x C}, whereg = (g ₁,g ₂) andS = S ₁ ×S ₂,S _i are convex cones,i = 1, 2,C is a convex subset of a vector spaceX, andf andg _i are, respectively, convex andS _i -convex,i = 1, 2. In particular, we consider the special case whenS ₂ is in afinite dimensional space,g ₂ is affine andS ₂ is polyhedral. We show that a recently introduced simple constraint qualification, and the so-called quasi relative interior constraint qualification both extend to (P), from the special case thatg = g ₂ is affine andS = S ₂ is polyhedral in a finite dimensional space (the so-called partially finite program). This provides generalized Slater type conditions for (P) which are much weaker than the standard Slater condition. We exhibit the relationship between these two constraint qualifications and show how to replace the affine assumption ong ₂ and the finite dimensionality assumption onS ₂, by a local compactness assumption. We then introduce the notion of strong quasi relative interior to get parallel results for more general infinite dimensional programs without the local compactness assumption. Our basic tool reduces to guaranteeing the closure of the sum of two closed convex cones.     

On laplace continued fraction for the normal integral

The Laplace continued fraction is derived through a power series. It provides both upper bounds and lower bounds of the normal tail probability % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqbfA6agzaaraaaaa!3DC0!\[\bar \Phi\](x), it is simple, it converges for x>0, and it is by far the best approximation for x3. The Laplace continued fraction is rederived as an extreme case of admissible bounds of the Mills' ratio, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqbfA6agzaaraaaaa!3DC0!\[\bar \Phi\](x)/(x), in the family of ratios of two polynomials subject to a monotone decreasing absolute error. However, it is not optimal at any finite x. Convergence at the origin and local optimality of a subclass of admissible bounds are investigated. A modified continued fraction is proposed. It is the sharpest tail bound of the Mills' ratio, it has a satisfactory convergence rate for x1 and it is recommended for the entire range of x if a maximum absolute error of 10^-4 is required.The efforts of the author were supported by the NSERC of Canada.     

Capture by stabilized continuum: Classical and quantum aspects

We review here the results of our investigations concerning chaotic atomic scattering in the presence of a laser field. Particular emphasis is put on the existence of classical stable resonance structures, induced by the intense laser field, which are embedded in the field-free continuum. We show that phase space structures in the vicinity of a resonance island play an important role in the chaotic scattering behavior and form the basis for a mechanism to enhance the lifetimes of the collisional partners. Quantum calculations, based on a wave packet propagation method, show that quantum solutions are strongly influenced by the classical phase space structures. More specifically, a wave packet is found to spread differently in the regular and chaotic regions; in the latter case it spreads exponentially with time until saturation occurs, defining the saturation time. We also investigate the dependence of the spreading rates in both the regular and chaotic regimes. Calculations with an ensemble of classical trajectories are also presented to further illustrate the smoothing effects of varying.     

Quarter wave plates for submillimeter wavelengths

A review is given of different types of quarter wave plates as presently used in the optical and microwave spectral range, with a view to their application in the sub-mm wave-length range. Two types of quarter wave plates have been constructed and results of measurements at 640m are given.