Analyzing electrochemical noise with Chebyshev’s discrete polynomials

The principles underlying a novel method intended for analyzing experimental data obtained when studying fluctuation processes are considered. The method in question is Chebyshev’s spectroscopy. The application of this method allows one to determine statistic characteristics of steady-state electrochemical noise against the background of severe deterministic interference without invoking the procedure of the fitting of the initial data. The potentialities of this novel method, which is intended for treating noise experiment, are demonstrated by examining model examples and analyzing the electrochemical noise generated by a lithium electrode placed in an aprotic organic electrolyte.     

Closed‐form rectangular atomic wave functions of an N‐dimensional atom

A closed‐form expression has been derived to obtain the N‐dimensional rectangular atomic wave functions. The wave functions can be obtained straightforwardly with the knowledge of the angular momentum quantum numbers and the dimension and there is no need to employ recursive methods as in previous works. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem 88: 263–274, 2002     

第一类双变量Chebyshev多项式的最小零偏差性质研究

利用Rivlin和Shapiro提出的符号理论,证明了文献[10]中提出的第一类双变量Chebyshev多项式恰为所谓的Steiner区域上具有特殊首项的最小零偏差多项式,并由此导出了几类具有一定代数精度的数值积分公式.     

Information Shift Dynamics Described by Tsallis q = 3 Entropy on a Compact Phase Space

Recent mathematical investigations have shown that under very general conditions, exponential mixing implies the Bernoulli property. As a concrete example of statistical mechanics that are exponentially mixing we consider the Bernoulli shift dynamics by Chebyshev maps of arbitrary order N≥2, which maximizes Tsallis q=3 entropy rather than the ordinary q=1 Boltzmann-Gibbs entropy. Such an information shift dynamics may be relevant in a pre-universe before ordinary space-time is created. We discuss symmetry properties of the coupled Chebyshev systems, which are different for even and odd N. We show that the value of the fine structure constant αel=1/137 is distinguished as a coupling constant in this context, leading to uncorrelated behaviour in the spatial direction of the corresponding coupled map lattice for N=3.     

Rényi Entropies of Multidimensional Oscillator and Hydrogenic Systems with Applications to Highly Excited Rydberg States

The various facets of the internal disorder of quantum systems can be described by means of the Rényi entropies of their single-particle probability density according to modern density functional theory and quantum information techniques. In this work, we first show the lower and upper bounds for the Rényi entropies of general and central-potential quantum systems, as well as the associated entropic uncertainty relations. Then, the Rényi entropies of multidimensional oscillator and hydrogenic-like systems are reviewed and explicitly determined for all bound stationary position and momentum states from first principles (i.e., in terms of the potential strength, the space dimensionality and the states’s hyperquantum numbers). This is possible because the associated wavefunctions can be expressed by means of hypergeometric orthogonal polynomials. Emphasis is placed on the most extreme, non-trivial cases corresponding to the highly excited Rydberg states, where the Rényi entropies can be amazingly obtained in a simple, compact, and transparent form. Powerful asymptotic approaches of approximation theory have been used when the polynomial’s degree or the weight-function parameter(s) of the Hermite, Laguerre, and Gegenbauer polynomials have large values. At present, these special states are being shown of increasing potential interest in quantum information and the associated quantum technologies, such as e.g., quantum key distribution, quantum computation, and quantum metrology.     

Ka波段8路径向波导空间功率分配（合成）器

通过理论研究以及高频仿真相结合的方法分析设计了一款新型Ka波段8路径向波导空间功率分配（合成）器。研发的新结构输入输出段为标准矩形波导结构,代替了传统功率分配（合成）器输入输出段的同轴结构,这种新型全金属结构更加简单紧凑,更易于加工。仿真结果表明：功率分配（合成）器工作带宽达到了34%（12 GHz）,基本覆盖整个Ka波段;全频带内反射系数S11低于-20 dB,各支路的相位差均小于5。通过在同轴波导渐变段引入切比雪夫渐变结构,在减小了器件尺寸的同时,在整个频带内的网络S参数也不错。这款新型Ka波段8路径向波导功率分配（合成）器将应用于前级固态功率放大器,推动回旋行波管项目研发。     

A formula for the powers of fractional order operators

We derive none some explicit formula for the power of fractional order (differential and integral) operators.     

The a posteriori error estimates of Chebyshev–Petrov–Galerkin methods for second-order equations

In this paper, the a posteriori error estimates of Chebyshev–Petrov–Galerkin approximations are investigated. For simplicity, we choose the Poisson equation with Dirichlet boundary conditions to discuss the a posteriori error estimators, and deduce their efficient and reliable properties. Some numerical experiments are performed to verify the theoretical analysis for the a posteriori error estimators.     

On the rate of convergence for central limit theorems of sojourn times of Gaussian fields

The aim of this paper is to control the rate of convergence for central limit theorems of sojourn times of Gaussian fields in both cases: the fixed and the moving level. Our main tools are the Malliavin calculus and the Stein method, developed by Nualart, Peccati and Nourdin. We also extend some results of Berman to the multidimensional case.