Lefschetz–Verdier Trace Formula and a Generalization of a Theorem of Fujiwara

The goal of this paper is to generalize a theorem of Fujiwara (Deligne’s conjecture) to the situation appearing in a joint work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our proof is more elementary than the original one and stays in the realm of ordinary algebraic geometry, that is, does not use rigid geometry. We also give a proof of the Lefschetz–Verdier trace formula and of the additivity of filtered trace maps, thus making the paper essentially self-contained. The work was supported by the Israel Science Foundation (Grant No. 555/04) Received: May 2005 Accepted: August 2005     

Analysis of heterojunction resonant cavity-enhanced Schottky photodiodes by using two-valley transport model

The article concerns heterojunction resonant cavity-enhanced (RCE) Schottky photodiodes with GaAs in the absorption layer. The quantum efficiency and linear pulse response have thoroughly been analysed. For the first time, the response of a heterojunction photodiode has been modelled by the phenomenological model for a two-valley semiconductor. The results obtained have shown that the satellite valleys, as well as the parasitic time constant, significantly influence the response and, accordingly, have to be taken into account when analysing and optimizing RCE photodetectors.     

Study of local lattice relaxation of substitutional impurities in silicon and germanium

Local lattice relaxation of substitutional donors in silicon investigated using self‐consistent multiple scattering Xα (MSXα) method within the framework of the standard muffin‐tin potential approximation is extended to substitutional donors in germanium and substitutional acceptors in both silicon and germanium. Incorporating the effect of lattice relaxation surrounding the impurity makes the model suitable for both shallow and deep levels. Chemical trends of some aspects of impurity states, such as local lattice relaxation and charge transfer, of the impurities both in silicon and germanium are inferred. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Nondispersive two-electron wave packets in driven helium

We provide a detailed quantum treatment of the spectral characteristics and of the dynamics of nondispersive two-electron wave packets along the periodically driven, collinear frozen planet configuration of helium. These highly correlated, long-lived wave packets arise as a quantum manifestation of regular islands in a mixed classical phase space, which are induced by nonlinear resonances between the external driving and the unperturbed dynamics of the frozen-planet configuration. Particular emphasis is given to the dependence of the ionization rates of the wave packet states on the driving field parameters and on the quantum mechanical phase space resolution, preceded by a comparison of 1D and 3D life times of the unperturbed frozen planet. Furthermore, we study the effect of a superimposed static electric field component, which, on the grounds of classical considerations, is expected to stabilize the real 3D dynamics against large (and possibly ionizing) deviations from collinearity. Received 7 November 2002 / Received in final form 2 December 2002 Published online 28 January 2003     

POROSITY CALCULATION OFMIXTURES OF FIBROUS PARTICLES

The initial forming of fiber blend to high green density, i.e. the packing of fibrous particles, is important to the reinforcement of composite materials. It is very useful to develop a general predictive method for the optimum selection of particle mixtures for the property control of ceramic or composite products. This paper presents such a mathematical model developed on the basis of the similarity analysis between the spherical and non-spherical particle packings and assesses its applicability to the packing of fibrous particles with discrete and/or continuous length distributions. The results indicate that the model can predict this packing system well and hence provide an effective way to solve various packing problems in the composite materials processing.     

聚能射流的断裂时间

从描述聚能射流失稳的一维近似方程出发，导出了聚能射流断裂时间的近似公式。这个近似公式定量显示了屈服应力、本构关系、粘度和径向收缩效应等对射流断裂时间的影响，在４个不同的特殊近似下，可以自然演化为近１０年来所发表的几个半经验解析公式，并且在合理的参数范围内，公式给出的断裂时间曲线覆盖了射流断裂时间的全部实验点。     

Theoretical study of cyclization of 2′-hydroxychalcone

The isomerization mechanism of 2′(OH)chalcone (1) in flavanone (2) was studied. The calculations were performed with the semiempirical method AM1, using totally optimized molecular geometries. A 6-step mechanism including several equilibrium states was proposed. It was concluded that: (a) At the conformational equilibrium of 1 there could be 43.9% of s-cis conformer; (b) The acid dissociation of 1 trans-s-trans is considerable; (c) The E_E, ΔH_f and net charges show that the rotation of ring A of 1 and the formation of ring C of 2 occurs without greater impairments; (d) Although the keto structure is the most stable one, the enolate of 2 is present in the reaction medium; (e) The conversion of enol of 2 in the keto form would be the limiting step of the analyzed isomerization rate.     

On the phase space approach to complexity

We elaborate in some detail on a new phase space approach to complexity, due to Y.-C. Zhang. We show in particular that the connection between maximal complexity and power law noise or correlations can be derived from a simple variational principle. For a 1D signal we find 1/f noise, in accordance with Zhang.     

Classical limit of relativistic quantal system with attractive Coulomb interaction

Using the appropriate harmonic oscillator states and reasonable approximations, we construct coherent wavepackets corresponding to the solutions of the Klein-Gordon equation for the attractive potentialV(r)=−k/r, k>0, in two and three space dimensions. We deduce the corresponding classical limit in two dimension by requiring that the expectation value 〈r〉 of the radial variable is large. In the case of three dimensions, besides the condition of large 〈r〉, we make the uncertainty Δr=[〈r ²〉 − 〈r〉²]^1/2 a minimum with respect to certain parameter of the wavepacket. We then investigate the trajectory traversed by the wavepacket in the classical limit. We find that the classical limit of this relativistic quantal problem gives, in the leading order, the same expression for the rate of motion of the perihelion as that given by the solution of the corresponding special relativistic classical dynamical problem. We also briefly discuss some of the subtle aspects of the classical limit of the relativistic quantal system, in general.     

THE SOLUTION OF _b－EQUATION OF （P，Q）－FORMS AND IT＇S L~P＆HOLDER ESTIMATES ON A STEIN MANIFOLD

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