奇异摄动问题在Bakhvalov-Shishkin 网格上的流线扩散有限元逼近

本文采用线性插值的流线扩散有限元在Bakhvalov-Shishkin网格上求解一维对流扩散型的奇异摄动问题. 在ε ≤ N^-1的前提下,可以得到,关于扰动参数ε 是一致收敛的. 在离散的SD范数下,其u-u_I的误差阶提高到N^-2,u-u_h的误差阶达到N^-2（lnN）^0.5. 最后,通过数值算例,验证了理论分析.     

广义Schr(o)dinger扰动耦合系统孤子解

研究了一类广义非线性Schr(o)dinger扰动耦合系统.首先,利用待定系数投射的特殊方法求得了相应的无扰动耦合系统的孤子精确行波解.然后,选定对应的无扰动耦合系统的精确行波解作为扰动系统的初始近似,再用同伦分析方法,构造了一组同伦映射,依次得到原扰动耦合系统的各次近似解.最后通过举例,并参照摄动理论可以看出:由同伦分析方法得到的广义非线性Schr(o)dinger扰动耦合系统的近似解方便而有效.     

广义Schrdinger扰动耦合系统孤子解

研究了一类广义非线性Schrdinger扰动耦合系统.首先,利用待定系数投射的特殊方法求得了相应的无扰动耦合系统的孤子精确行波解.然后,选定对应的无扰动耦合系统的精确行波解作为扰动系统的初始近似,再用同伦分析方法,构造了一组同伦映射,依次得到原扰动耦合系统的各次近似解.最后通过举例,并参照摄动理论可以看出:由同伦分析方法得到的广义非线性Schrdinger扰动耦合系统的近似解方便而有效.     

一个三次等时中心在非光滑扰动下的极限环分支

本文研究了一个三次等时中心在非光滑扰动下的极限环分支问题.利用非光滑系统的一阶平均方法,获得了在任意小的分段三次多项式扰动下,从未扰动系统的周期环域中至多分支出7个极限环,而且此上界可以达到,推广了光滑扰动下的结果.     

一类中立型时滞系统周期运动的近似解

对一类中立型时滞系统在临界状态小扰动下的平衡点进行了稳定性分析,同时讨论了该系统在非线性扰动下的周期运动的近似解及稳定性.     

非线性脉冲扰动下带强迫项的次线性时滞微分系统解的渐近性

讨论了带强迫项的次线性时滞微分系统在非线性脉冲扰动下系统解的渐近性,得到了带强迫项的次线性时滞微分系统在非线性脉冲扰动下系统解渐近吸引的充分性条件.     

一类大型互联非线性系统的鲁棒分散控制

本文对带有界扰动的一类大型互联非线性系统进行了分散状态反馈控制设计,通过子系统状态的线性变换,得到分散状态反馈控制律.当状态反馈控制律作用于该系统时,无扰动的闭环系统是渐近稳定的.当扰动较小时,系统的状态能够收敛到原点的一个小邻域内.     

一类扰动系统的指数稳定性问题

主要讨论了一类扰动系统的指数稳定性问题 .若扰动项的控制函数满足无穷可积、 L2 可积或者 Lp可积时 ,x =0是常系统的指数稳定点 ,则也是扰动系统的指数稳定点 .推广和丰富了 Khalil[1] 的结果     

一类Fermi气体光晶格非线性机制的轨线研究

研究了一类Fermi气体光晶格轨线的非线性扰动模型.首先求得了Fermi气体光晶格在无扰动情形下模型轨线的精确解.然后引入一组广义泛函分析同伦映射,构造一组迭代系统,得到了Fermi气体光晶格非线性扰动模型轨线的任意次渐近解.最后讨论了一个微扰系统.该文在方法上可较方便地得到轨线的渐近表示式.     

平面系统的随机稳定性

本文首先研究了确定性平面系统的双曲极限环在加法噪声扰动下的随机稳定性;其次考察了一类平面"拟Hamilton"系统在随机扰动下的稳定性,并指出结构稳定性系统与非结构稳定性系统的随机稳定性具有显著差异.     

A class of completek-caps inPG(3,q) forq an odd prime

The main problem on caps, posed originally by Segre in the fifties, is to determine the values of k for which there exists a complete k-cap. Very few results on this problem are known. The cardinality of the largest cap(s) and the smallest complete cap(s) are crucial. In this paper it is shown that there exist complete k-caps in PG(3, q), q an odd prime 5 or q = 9, such that k = (q² + q + 6)/3 or k = (q² + 2q + 6)/3. These complete caps are smaller than those currently known for q odd.In memoriam Giuseppe Tallini     

Linear ordinal quasi-symmetry model and decomposition of symmetry for multi-way tables

For multi-way tables with same categories, Bhapkar and Darroch [4] and Agresti [2], p. 440, considered the general order quasi-symmetry model and the ordinal quasi-symmetry model, respectively. Yamamoto, Iwashita and Tomizawa [16] considered the three kinds of linear ordinal quasi-symmetry models, which are special cases of the first and second order quasi-symmetry models. For multi-way tables with same ordinal categories, the present paper proposes the general linear ordinal quasi-symmetry models, which are special cases of the general order quasi-symmetry model, and gives new decomposition of the symmetry model. Moreover it is shown that the likelihood ratio statistic for testing goodness-of-fit of the symmetry model is asymptotically equivalent to the sum of those for testing goodness-of-fit of the decomposed models.     

2-Cohomologies of the groups SL(n, q)

Let G = SL(n, q), where q is odd, V be a natural module over G, and L = S²(V) be its symmetric square. We construct a 2-cohomology group H²(G, L). The group is one-dimensional over F _q if n = 2 and q ≠ 3, and also if (n, q) = (4, 3). In all other cases H²(G, L) = 0. Previously, such groups H²(G, L) were known for the cases where n = 2 or q = p is prime. We state that H²(G, L) are trivial for n ⩾ 3 and q = p^m, m ⩾ 2. In proofs, use is made of rather elementary (noncohomological) methods. __________ Translated from Algebra i Logika, Vol. 47, No. 6, pp. 687–704, November–December, 2008.     

Existence of (q,6,1) Difference Families withq a Prime Power

The existence of a (q,k,1) difference family in GF(q) has been completely solved for k=3, 4, 5. For k=6 fundamental results have been given by Wilson. In this article, we continue the investigation and show that the necessary condition for the existence of a(q,6,1) difference family in GF(q), i.e. q 1 (mod 30) is also sufficient with one exception of q=61. The method of this paper is to lower Wilson's bound by using Weil's theorem on character sums to exploit Wilson's sufficient conditions for the existence of (q,6,1) difference families. The remaining gap is closed by computer searches.     

Surfaces with p g = q = 1, K 2 = 6 and Non-birational Bicanonical Maps

Let S be a smooth minimal projective surface of general type with p_g(S) = q(S) = 1,K_S~2= 6. We prove that the degree of the bicanonical map of S is 1 or 2. So if S has non-birational bicanonical map, then it is a double cover over either a rational surface or a K3 surface.     

稳定性理论中微分方程与微分差分方程的等价性问题

<正> §1.问题的提出任取一最简单的开式控制系统如图1.     

Exact Conditional P Value Calculation for the Quasi-Symmetry Model

Earlier literature introduced a network algorithm for computing an exact test of independence in a two-way contingency table. This article adapts that algorithm to tests of quasi-symmetry in square tables. The algorithm is generally faster than competing Monte Carlo methods, and essentially eliminates the need for asymptotic approximation of P values for assessing goodness-of-fit of the quasi-symmetry model. A macro written for the R computing package is available for implementing the method.     

The p-variation of functions

A formula is derived for the p-variation of functions of the class Vq (1 q < p < ) and it is proved that this formula ceases to hold when 1 相似文献   

Modified Alternating $$\vec{k}$$–generators

This paper deals with a class of pseudorandom bit generators – modified alternating –generators. This class is constructed similarly to the class of alternating step generators. Three subclasses of are distinguished, namely linear, mixed and nonlinear generators. The main attention is devoted to the subclass of linear and mixed generators generating periodic sequences with maximal period lengths. A necessary and sufficient condition for all sequences generated by the linear generators of to be with maximal period lengths is formulated. Such sequences have good statistical properties, such as distribution of zeroes and ones, and large linear complexity. Two methods of cryptanalysis of the proposed generators are given. Finally, three new classes of modified alternating –generators, designed especially to be more secure, are presented.