Uniqueness of meromorphic functions and differential polynomials

In this paper, we study the uniqueness theorem of meromorphic functions concerning differential polynomials, and obtain two theorems, which improve and generalize the related results of Fang, S.S. Bhoosnurmath and R.S. Dyavanal and Xiao-Yu Zhang and Wei-Chuan Lin.     

Uniqueness of entire functions that share one value

Using Nevanlinna’s value distribution theory, we study the uniqueness of entire functions that share only one value and prove some theorems which are related to one famous problem of Hayman [W.K. Hayman, Research Problems in Functions Theory, Athlone Press, London, 1967].     

Uniqueness theorems on meromorphic functions sharing one value

In this paper, we study with a weighted sharing method the uniqueness problem of [fⁿ(z)]^(k) and [gⁿ(z)]^(k) sharing one value and obtain some results which extend the theorems given by M. Fang, S. Bhoosnurmath and S. Dyavanal et al.     

Certain classes of meromorphic multivalent functions

In this paper, we introduce and investigate two new classes of meromorphic multivalent functions. Such results as subordination properties, coefficient inequalities, convolution properties and integral representations are proved. Several sufficient conditions for meromorphic multivalent starlikeness and convexity are also derived.     

布尔函数和伪布尔函数多项式表示的快速实现算法

布尔函数和伪布尔函数在不同的领域有着广泛的应用,利用多项式表示有利于刻划它们的一些特征属性。论文首先在已知输入都能得到输出的条件下给出了布尔函数多项式表示的快速实现算法,该算法仅用到模2加运算,运算次数少,具有简洁、易于编程实现、准确而快速的特点,而且该算法很易推广为伪布尔函数多项式表示的快速实现算法,只需把模2加运算换成实数加运算即可。接着通过比较说明了伪布尔函数多项式表示的快速实现算法,同时指出任何伪布尔函数都能通过多项式形式表示出来。最后通过实例进一步验证了算法的正确性。     

求解非线性方程组的BFGS差分进化算法

针对差分进化算法进化后期收敛缓慢和稳定性不强的缺陷,将BFGS算法插入差分进化算法当中,提出了一种BFGS差分进化算法,用来求解非线性方程组。通过5个非线性方程组和一个工程实例的实验,说明：算法收敛精度较高、收敛速度较快、鲁棒性强、收敛成功率高,是一种较好的解决非线性方程组的方法。     

A unified presentation of some classes of meromorphically multivalent functions

The authors introduce and investigate various properties of a general class

U_k[p,a,β,A,B]

p, k ε N {1, 2, 3,…,}; 0 α < p; β 0

;

−1 A < B 1; 0 < B 1)

,which unifies and extends several (known or new) subclasses of meromorphically multivalent functions. The properties and characteristics of this general class, which are presented here, include growth and distortion theorems; they also involve Hadamard products (or convolution) of functions belonging to the class U_k[p,α,β,A,B].     

Delay-dependent exponential stability of stochastic delay differential system whose coefficients obey the polynomial growth condition

This article discusses the exponential stability of nonlinear stochastic delay differential systems (SDDSs) whose coefficients obey the polynomial growth condition. Delay-dependent criteria on almost sure exponential stability and pth moment exponential stability of such SDDSs have been established. By applying some novel techniques, our criteria work for many SDDSs including some cases in which the ?V operator has a complicated form, which seemingly prevents the existing results from being directly used. The range of order of moment exponential stability and the decay rate can be estimated through the coefficients of the system.     

Complexity of boolean functions in a class of canonical polarized polynomials

Relationships for the maximum of a minimal number of summands among all canonical polarized polynomials of a Boolean function are obtained. Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 179–183, May–June, 2000.     

Numerical solution of system of first-order delay differential equations using polynomial spline functions

The use of two constructed polynomial spline functions to approximate the solution of a system of first-order delay differential equations is described. The first spline function is a polynomial with an undetermined constant coefficient in the last term. The other has a polynomial spline form. The error analysis and stability of the second function are theoretically investigated and a test example is given. A comparison of the two forms is carried out to illustrate the pertinent features of the proposed techniques.     

一类多项式光滑函数的逼近精度

针对一类支持向量机的多项式光滑函数,采用二分法求解它们尚未解决的逼近精度问题。为克服二分法可能会漏根的缺点,首先把多项式光滑函数的逼近精度问题表示为一个求逼近函数的最大值问题,把这个逼近函数分成4 段,分别求出每段的最大值,然后得到逼近函数在整个x轴上的最大值。并以1阶和2阶多项式光滑函数为例,用二分法解决了它们的逼近精度问题。研究表明,二分法是求解这类多项式光滑函数逼近精度的有效方法。     

The use of polynomial spline functions for the solution of system of second order delay differential equations

This paper presents the use of spline functions of polynomial form to approximate the solution of system of second order delay differential equations. The error analysis and stability of the method are theoretically investigated. A numerical example is given to illustrate the applicability, accuracy and stability of the proposed method.     

Robust control design of a class of nonlinear systems in polynomial lower-triangular form

This paper investigates the problem of global robust stabilization for a wide class of nonlinear systems, called polynomial lower-triangular form (pLTF), which expands LTF to a more general case. The aim is explicitly constructing the smooth controller for the class of systems with static uncertainties, by adding and modifying a power integrator in a recursive manner. The pLTF relaxes the restrictions on the structure of the normal LTF and enlarges the family of systems that are stabilizable. Examples are also provided to show the practical usage of this class of systems and the effectiveness of the design method. Recommended by Editorial Board member Hyungbo Shim under the direction of Editor Jae Weon Choi. Bing Wang received the B.S. degree from the Huazhong University of Science and Technology, and the Ph.D. degree from the University of Science and Technology of China, in 1998 and 2006, respectively. He is currently working in College of Electrical Engineering, Hohai University. His research interests include robust control, nonlinear control and power systems. Haibo Ji received the B.S. and Ph.D. degrees in Mechanical Engineering from ZheJiang University and Beijing University in 1984 and 1990 respectively. He is currently a Professor in the Dept. of Automation, USTC. His research interests include nonlinear control and adaptive control. Jin Zhu received the B.S. and Ph.D. degrees in Control Science and Engineering from University of Science & Technology of Chinain 2001 and 2006 respectively. He is currently a Post-doc in Han-Yang University, Korea. His research interests include Markovian jump systems and nonlinear control.     

A class of meromorphic multivalent functions with negative coefficients defined by a differential operator

For 0≤μ≤λ, 0<α≤1, 1/(p+1)<τ≤1, m∈N₀=N∪{0} and p∈N, a new class of meromorphic p-valent functions defined by means of the differential operator is introduced and systematically studied. Membership in this class is characterized through coefficient estimates. Distortion, radii of starlikeness and convexity of order , Hadamard convolution product, an integral operator, convex combinations and neighborhoods are also investigated.     

The generalized center problem of resonant infinity for a polynomial differential system

This paper explores the problems of generalized center conditions and integrability of resonant infinity for a complex polynomial differential system. The method is based on converting resonant infinity into an elementary singular point by a homeomorphic transformation. The calculation of generalized singular point quantities is an effective way of finding necessary conditions for integrable systems. A new recursive algorithm for computing generalized singular point quantities at the origin of the transformed system is derived. At the same time, a necessary and sufficient condition for resonant infinity to be a generalized complex center is presented. As an application of the new recursive algorithm, the generalized center conditions for resonant infinity for a class of cubic systems are discussed. To the best of our knowledge, this is the first time that the generalized center problem has been considered for p:−q resonant infinity.     

The almost sure asymptotic stability and pth moment asymptotic stability of nonlinear stochastic delay differential systems with polynomial growth

In this paper, we discuss the asymptotic stability of nonlinear stochastic delay differential systems (SDDSs) whose coefficients obey the polynomial growth condition. By applying some novel techniques, we establish some easily verifiable conditions under which such SDDSs are almost surely asymptotically stable and pth moment asymptotically stable. A nontrivial example is provided to illustrate the effectiveness of our results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Adaptive stabilization of a class of uncertain nonlinear systems: A differential inclusion approach

Within the framework of controlled differential inclusions, a stabilizing strategy is developed for a class of uncertain nonlinear dynamical systems. The strategy has a linear plus discontinuous output feedback structure with bounded adaptive scalar gain.     

Construction of a polynomial invariant annihilation attack of degree 7 for T-310

Abstract

Cryptographic attacks are typically constructed by black-box methods and combinations of simpler properties, for example in [Generalised] Linear Cryptanalysis. In this article, we work with a more recent white-box algebraic-constructive methodology. Polynomial invariant attacks on a block cipher are constructed explicitly through the study of the space of Boolean polynomials which does not have a unique factorisation and solving the so-called Fundamental Equation (FE). Some recent invariant attacks are quite symmetric and exhibit some sort of clear structure, or work only when the Boolean function is degenerate. As a proof of concept, we construct an attack where a highly irregular product of seven polynomials is an invariant for any number of rounds for T-310 under certain conditions on the long term key and for any key and any IV. A key feature of our attack is that it works for any Boolean function which satisfies a specific annihilation property. We evaluate very precisely the probability that our attack works when the Boolean function is chosen uniformly at random.     

Chebyshev approximation of functions by the sum of a polynomial and an expression with a nonlinear parameter and endpoint interpolation

Sufficient existence conditions are established for the uniform Chebyshev (minimax) approximation of a function by the sum of a polynomial and an expression with a nonlinear parameter with the minimum absolute error and interpolation at the interval endpoints. An algorithm for determining the parameters of such an approximation using the Remez algorithm is proposed. The application of the iterative method to calculating the nonlinear parameter is substantiated. Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 64–75, January–February 2009.