Self-consistent Sources and Conservation Laws for Sup er-Geng Equation Hierarchy

Based on the matrix Lie super algebra and supertrace identity, the integrable super-Geng hierarchy with self-consistent is established. Furthermore, we establish the in-finitely many conservation laws for the integrable super-Geng hierarchy. The methods de-rived by us can be generalized to other nonlinear equation hierarchies.     

Accuracy of approximation in the Poisson theorem in terms of the χ<Superscript>2</Superscript>-distance

We study the limit behavior of the χ²-distance between the distributions of the nth partial sum of independent not necessarily identically distributed Bernoulli random variables and the accompanying Poisson law. As a consequence in the i.i.d. case we make the multiplicative constant preciser in the available upper bound for the rate of convergence in the Poisson limit theorem.     

Identities on Clifford algebras

We obtain some estimates of the codimensions and PI-exponent of identities on the Clifford algebras associated to a quadratic form of a given rank, find a hook where the cocharacters of Clifford algebras lie, exhibit an identity that holds on the Clifford algebras of a given rank, and describe the multilinear identities of minimal degree for the Clifford algebras of rank 1.     

Characterizations and construction of Poisson/symplectic and symmetric multi-revolution implicit Runge–Kutta methods of high order

This paper deals with the characterizations and construction of Poisson/symplectic and (φ⁻¹)-symmetric implicit high-order multi-revolution Runge–Kutta methods (MRRKMs). The basic tool is a modified W-transformation based on quadrature formulas and orthogonal polynomials. Two sufficient conditions can be obtained under which MRRKMs are Poisson/symplectic or (φ⁻¹)-symmetric. We construct two classes of high order implicit MRRKMs by using these sufficient conditions. Our results can be considered as an extension of related results of the standard Runge–Kutta methods in some references.     

Bounds for tail probabilities of martingales using skewness and kurtosis

Let M _n = X ₁ + ⋯ + X _n be a sum of independent random variables such that X _k ⩽ 1, and EX _k ² = σ _k ² for all k. Hoeffding [15, Theorem 3] proved that

Biorthogonal exponential sequences with weight function on the real line and an orthogonal sequence of trigonometric functions

Some orthogonal functions can be mapped onto other orthogonal functions by the Fourier transform. In this paper, by using the Fourier transform of Stieltjes-Wigert polynomials, we derive a sequence of exponential functions that are biorthogonal with respect to a complex weight function like on . Then we restrict these introduced biorthogonal functions to a special case to obtain a sequence of trigonometric functions orthogonal with respect to the real weight function on .

     

Normalized binomial mid-coefficients and power means

Let

     

电容近炸引信目标定向探测技术研究

为电容引信实现定向起爆控制提供理论技术基础。方法 利用３个等方位分布的电极阵列探测器获取目标方位信息,依据它对铸铁板的目标特性建立目标方位信号识别准则,信号处理采用ＤＳＰ技术。     

一类包含Bernoulli多项式与广义Fibonacci,Lucas序列的恒等式

本文从Bernoulli多项式的定义出发,利用其余幅角定理,给出了一类包含Bernoulli多项式与广义Fibonacci,Lucas序列的恒等式．