Colpitts电路中的双涡卷混沌寄生振荡分析

通过在Colpitts振荡器中引入二次反馈项,观察到了新奇的双涡卷吸引子.这个具有反馈项的混沌系统具有3个平衡点,产生不同于Lorenz和Colpitts系统的复杂吸引子.对系统的一些基本特性,如平衡点、稳定性、Lyapunov指数谱、分岔图、相轨与庞加莱截面等进行了详细的分析.     

On a discretization process of fractional-order Logistic differential equation

In this work we introduce a discretization process to discretize fractional-order differential equations. First of all, we consider the fractional-order Logistic differential equation then, we consider the corresponding fractional-order Logistic differential equation with piecewise constant arguments and we apply the proposed discretization on it. The stability of the fixed points of the resultant dynamical system and the Lyapunov exponent are investigated. Finally, we study some dynamic behavior of the resultant systems such as bifurcation and chaos.     

算术函数ep(n)和无3次因子数列的性质

设p为素数,ep(n)表示n中包含素数p的最大指数,研究了ep(n)作用在无3次因子数列上的均值性质,并给出一个有趣的渐近公式.     

Chaotic motion of the dynamical system under both additive and multiplicative noise excitations

With both additive and multiplicative noise excitations, the effect on the chaotic behaviour of the dynamical system is investigated in this paper. The random Melnikov theorem with the mean-square criterion that applies to a type of dynamical systems is analysed in order to obtain the conditions for the possible occurrence of chaos. As an example, for the Duffing system, we deduce its concrete expression for the threshold of multiplicative noise amplitude for the rising of chaos, and by combining figures, we discuss the influences of the amplitude, intensity and frequency of both bounded noises on the dynamical behaviour of the Duffing system separately. Finally, numerical simulations are illustrated to verify the theoretical analysis according to the largest Lyapunov exponent and Poincaré map.     

含对称非零元的奇数阶本原矩阵的指标集

本文证明了:当n为奇数时,含对称非零元的n阶本原矩阵类B的指标集E_B的上确界为3n-4;并且E_B={1, 2, …, 3n-4},不存在缺数段;又设N(A)是A中含正元的个数,则A是含最少正元的n阶本原矩阵的充要条件是A同构于定理6中的A.     

南极瑞穗站大气光学特征研究

本文利用南极瑞穗站１９７９年太阳可见光波段直接辐射的分光测量和微气象观测资料＾［１－２］。分别计算了整层大气、分子大气、臭氧和气溶胶的散射和吸收所构成的光学厚度τｔ（λ）、τＲ（λ）、τ０３（λ）和τａ（λ）及埃斯屈朗浑浊度系数β和波长指数ａ，并与北京和拉萨的相应值进行了比较＾［３－５］。文中对波长指数和埃斯屈朗浑浊度系数及整层大气垂直光学厚度与大气稳定度参数、湍流热通量的关系也进行了讨论。     

疲劳指数值对起重机金属结构件疲劳许用应力的影响

本文定量化分析了疲劳指数对起重机载荷谱系数、工作级别和结构疲劳许用应力的影响。根据分析和计算结果，作者认为疲劳指数值对起重机工作级别划分和结构疲劳许用应力值的影响很大，《起重机设计规范》中取疲劳指数为３是不太合理的，建议在该规范修订时重视疲劳指数值的研究     

关于猜想γ（A）≤（m－1）~2＋1

设Ａ是一个非负矩阵，若存在正整数ｋ，使得Ａ~ｋ＞０，则称Ａ为本原矩阵，而上述ｋ的最小者称为Ａ的本原指数，记作γ（Ａ）．设ｍ为Ａ的最小多项式的次数，ｇ为Ａ的伴随有向图的围长，当ｇ≤ｍ－１时，猜想γ（Ａ）≤（ｍ－１）~２＋１成立。     

Stable Exponents in Discrete Groups

It is known that in a word hyperbolic group the stable exponent of every nontorsion element is an integer. We prove that this is also true in finitely generated nilpotent groups. On the other hand, we show that for any rational number 1 there exists a torsionfree CAT(0) group containing an element whose stable exponent is equal to .     

The independence of initial vectors in the subdivision schemes

Starting with an initial vector λ = (λ(κ))κ∈z ∈ ep(Z), the subdivision scheme generates asequence (Snaλ)∞n=1 of vectors by the subdivision operator Saλ(κ) = ∑λ(j)a(k - 2j), k ∈ Z. j∈zSubdivision schemes play an important role in computer graphics and wavelet analysis. It is very interesting tounderstand under what conditions the sequence (Snaλ)∞n=1 converges to an Lp-function in an appropriate sense.This problem has been studied extensively. In this paper we show that the subdivision scheme converges forany initial vector in ep(Z) provided that it does for one nonzero vector in that space. Moreover, if the integertranslates of the refinable function are stable, the smoothness of the limit function corresponding to the vectorλ is also independent of λ.