Blocking probability for a multistage clos connecting network

The blocking probability is computed by assuming a thermodynamic limit when the number of stages increases above a certain value. In this limit we exhibit a set of two algebraic equations which gives the blocking probability as a function of the traffic demand. A comparison with a computer simulation of the system gives an excellent agreement.     

A Closure for Isotropic Turbulence Based on Extended Scale Similarity Theory in Physical Space

The closure of a turbulence field is a longstanding fundamental problem, while most closure models are introduced in spectral space. Inspired by Chou's quasi-normal closure method in spectral space, we propose an analytical closure model for isotropic turbulence based on the extended scale similarity theory of the velocity structure function in physical space. The assumptions and certain approximations are justified with direct numerical simulation. The asymptotic scaling properties are reproduced by this new closure method, in comparison to the classical Batchelor model.     

Bayesian and E-Bayesian Estimations of Bathtub-Shaped Distribution under Generalized Type-I Hybrid Censoring

For the purpose of improving the statistical efficiency of estimators in life-testing experiments, generalized Type-I hybrid censoring has lately been implemented by guaranteeing that experiments only terminate after a certain number of failures appear. With the wide applications of bathtub-shaped distribution in engineering areas and the recently introduced generalized Type-I hybrid censoring scheme, considering that there is no work coalescing this certain type of censoring model with a bathtub-shaped distribution, we consider the parameter inference under generalized Type-I hybrid censoring. First, estimations of the unknown scale parameter and the reliability function are obtained under the Bayesian method based on LINEX and squared error loss functions with a conjugate gamma prior. The comparison of estimations under the E-Bayesian method for different prior distributions and loss functions is analyzed. Additionally, Bayesian and E-Bayesian estimations with two unknown parameters are introduced. Furthermore, to verify the robustness of the estimations above, the Monte Carlo method is introduced for the simulation study. Finally, the application of the discussed inference in practice is illustrated by analyzing a real data set.     

A new generalization of the Bernoulli and related polynomials

In this paper, we introduce and investigate a generalization of the Bernoulli polynomials by means of a suitable generating function. We establish several interesting properties of these general polynomials. Furthermore, we give explicit series representations for these general polynomials in terms of a certain generalized Hurwitz-Lerch zeta function and the familiar Gauss hypergeometric function.     

同轴法射线相衬成像的数值模拟计算与分析

对同轴法射线相衬成像进行数值模拟计算,可用于特定对象检测方法的可行性分析或检测参数优化。为此,分析了同轴法射线相衬成像系统数值模拟计算的原理及其实现方法,并针对圆形物体、长条形物体进行了相衬成像实验的数值模拟计算。对照计算结果进行分析可知:对物体平面进行离散化的尺寸很大程度上影响到数值模拟计算结果的准确程度,究其原因在于对物体平面进行离散化时决定了成像系统光学传递函数离散化的准确程度;为保证数值模拟结果的准确性,应使数值计算中光学传递函数取值点连续、不存在明显的失真;保证数值模拟结果准确所需的光学传递函数的离散化尺寸不是固定的,而是应与检测对象的大小相匹配。     

On the coherence length of a monochromator for use with a michelson stellar interferometer

The drop in visibility due to path difference errors in a Michelson stellar interferometer is normally controlled by a monochromator in the system. It is shown that the effect of this monochromator on the visibility is governed by a product of two factors, one geometrical and the other a function of the resolving power of the monochromator. The second factor causes the visibility to vanish identically for path differences exceeding a certain value. A comparison of prisms and gratings shows that in general a prism train is preferable as a dispersing device.     

Adaptive synchronization of weighted complex dynamical networks through pinning

This paper considers the problem of controlling weighted complex dynamical networks by applying adaptive control to a fraction of network nodes. We investigate the local and global synchronization of the controlled dynamical network through the construction of a master stability function and a Lyapunov function. Analytical results show that a certain number of nodes can be controlled by using adaptive pinning to ensure the synchronization of the entire network. We present numerical simulations to verify the effectiveness of the proposed scheme. In comparison with feedback pinning, the proposed pinning control scheme is robust when tested by noise, different weighting and coupling structures, and time delays.     

Emergence of classical orbits in few-cycle above-threshold ionization of atomic hydrogen

The time-dependent Schr?dinger equation for atomic hydrogen in few-cycle laser pulses is solved numerically. Introducing a positive definite quantum distribution function in energy-position space, a straightforward comparison of the numerical ab initio results with classical orbit theory is facilitated. Integration over position space yields directly the photoelectron spectra so that the various pathways contributing to a certain energy in the photoelectron spectra can be established in an unprecedented direct and transparent way.     

Leader channel models for long air positive electrical discharges

The models proposed for the positive long air gap electrical discharge can be considered to be either engineering or physical in their approach. In this work, we make a general review of the available models and use two of them for a comparison with experimental data. Common underlying assumptions were found in most of the models analyzed. The comparison with the experimental data revealed that the results obtained from the models were a good representation of the physical situation when the leader potential distribution and the leader-corona region evolution were described with certain physical assumptions.     

杂化能带与电子-声子耦合的本征上限

本文用角动量分波表象的能带论方法研究了杂化导带的一般性质。得出了电子态密度和分波含量的一般关系式。发现引用一个径向波函数φ_l的“相位函数”y_l,可以方便地对球对称势场造成的相移和φ_l的对数微商作解析近似处理。在此基础上研究了电子-声子耦合中的系数η的性质。论证了η有一个“本征上限”,并估计了它的量级。讨论了影响η强弱的一般规律,与实验现象作了比较。指出提高导带角动量杂化程度,特别是提高d导带中的f分波含量,以至试图实现似f导带,可能是强化电子-声子耦合潜力较大的探索方向。 关键词：     

Towards a Nonperturbative Renormalization Group Analysis

We prove that a certain class of convex gradient models in high dimensional spaces without the presence of a small parameter renormalizes to a free field. As a consequence we establish a certain asymptotic formula for the partition function. In some ways, this is a realization of Gawedzki and Kupiainen’s idea to use correlation inequalities to augment the rigorous renormalization group methods. We use the more particular suggestion of Spencer to use certain inequalities of Brascamp and Lieb and also the formulation of the correlation functions in terms of the solutions to some partial differential equations given by Helffer and Sjöstrand.     

UPS and EELS study of zirconium oxidation

The electronic structures of metallic zirconium, zirconium oxide, and zirconium surfaces with intermediate degrees of oxidation have been studied by photoemission spectroscopy using synchrotron radiation and by electron energy loss spectroscopy. Both methods are used to analyze the same samples in one experimental cycle. Some specific features of the electronic structures that had not been detected earlier are revealed. The experimental data obtained are explained using the first-principles calculations of the electronic states of hcp metallic zirconium and cubic or monoclinic zirconia. The dielectric function and the electron-energy-loss function are calculated for comparison with the experimental data. Despite certain quantitative differences, the experimental and calculated data on the electronic structures of zirconium and its oxide are in good qualitative agreement.     

Surface wave propagation at the interface between lossy metamaterials medium and nonlinear media with arbitrary nonlinearity

The dispersion relation in a system that consists of a lossy metamaterials (MTMs) film surrounded by a linear substrate and a nonlinear cladding with an arbitrary nonlinearity is derived. The surface plasmonic (SP) wave at the interfaces between metamaterials (MTMs) and the nonlinear cover is recovered by taking certain limits. Lossy MTMs have simultaneously complex-negative permeability μ and complex-negative permittivity ε. Results are presented by plotting the SP frequency as a function of the nonlinearity at chosen damping factors. Both the real and imaginary parts are studied. Results also display the wave frequency as a function of plasma frequency. For comparison, the imaginary part is set to zero and curves are reproduced.     

ON FINITE NORMAL SERIES SOLUTIONS OF RELATIVISTIC WAVE EQUATIONS

We present a method for finding exact solutions of relativistic wave equations (RWE) that are given by finite normal series (FNS). Using a certain factorization method we rewrite the most general potential for which the RWE is solved by a FNS function in a canonical form such that FNS solutions for rational potentials can be obtained by solving simple algebraic equations.     

Designer gravity and field theory effective potentials

Motivated by the anti-de Sitter conformal field theory correspondence, we show that there is remarkable agreement between static supergravity solutions and extrema of a field theory potential. For essentially any function V(alpha) there are boundary conditions in anti-de Sitter space so that gravitational solitons exist precisely at the extrema of V and have masses given by the value of V at these extrema. Based on this, we propose new positive energy conjectures. On the field theory side, each function V can be interpreted as the effective potential for a certain operator in the dual field theory.     

Size distribution in quantum-dot heterostructures

The size distribution functions for nanoclusters in quantum-dot heterostructures are calculated within the LSW theory. The most common numerical characteristics are calculated for these distributions. The corresponding size distribution functions are selected by means of comparison of the calculated dispersion and mean square deviation with the experimental values obtained for real quantum-dot heterostructures. The regularities of variations of certain numerical characteristics as a function of growth mechanism are shown for different distributions, from the well-known modified Wagner and Lifshitz-Slezov distributions to the distributions proposed in this work. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 59–66, April, 2006.     

A new approach to Catalan numbers using differential equations

In this paper, we introduce two differential equations arising from the generating function of the Catalan numbers which are ‘inverses’ to each other in a certain sense. From these differential equations, we obtain some new and explicit identities for Catalan and higher-order Catalan numbers. In addition, by other means than differential equations, we also derive some interesting identities involving Catalan numbers which are of arithmetic and combinatorial nature.     

Public-key encryption based on generalized synchronization of coupled map lattices

Currently used public-key cryptosystems are based on difficulties in solving certain numeric theoretic problems, in which the way to predict the private key from the knowledge of the public key is computationally infeasible. Here we propose a method of constructing public-key cryptosystems by generalized synchronization of coupled map lattices, in which the difficulty in predicting the synchronous function is used as the trap-door function to deduce the private key from the public key. In specific, we implement this idea on the method of "Merkle's puzzles," and find that, incorporated with the chaotic dynamics, this traditional method is equipped with some new features and can be practical in certain situations.     

Simulating Entangling Unitary Operator Using Non-maximally Entangled States

We use non-maximally entangled states （NMESs） to simulate an entangling unitary operator （EUO） with a certain probability. Given entanglement resources, the probability of the success we achieve is a decreasing function of the parameters of the EUO. Given an EUO, for certain entanglement resources the result is optimal, i.e., the probability obtains a maximal vaiue, and for optimal result higher parameters of the EUO match more amount of entanglement resources. The probability of the success we achieve is higher than the known results under some condition.