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1.
We prove that any linear multi-step method G1^T of the form ∑k=0^mαkZk = T∑k=0^mβkJ^-1↓ΔH(Zk) with odd order u (u≥ 3) cannot be conjugate to a symplectic method G2^T of order w (w 〉 u) via any generalized linear multi-step method G3^T of the form ∑k=0^mαkZk = T∑k=0^mβkJ^-1↓ΔH(∑l=0^mγklZl). We also give a necessary condition for this kind of generalized linear multi-step methods to be conjugate-symplectic. We also demonstrate that these results can be easily extended to the case when G3^T is a more general operator.  相似文献   

2.
This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0 (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.  相似文献   

3.
This paper deals with the steady state bifurcation of the K-S equation in two spatial dimensions with periodic boundary value condition and of zero mean. With the increase of parameter a, the steady state bifurcation behaviour can be very complicated. For convenience, only the cases a=2 and a=5 witl be discussed. The asymptotic expressions of the steady state solutions bifurcated from the trivial solution near a=2 and a=5 are given. And the stability of thenontriviat sotutions bifurcated from a=2 is studied. Of course, the cases a=n^2 m^2,n,m∈N(a≠2,5) can be similarly discussed by the same method which is used to discussing the cases a=2 and a= 5.  相似文献   

4.
The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3) Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*,B). Then the functional dimension of (B*,σ(B*,B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.  相似文献   

5.
All parabolic subgroups and Borel subgroups of PΩ(2m 1, F) over a linear-able field F of characteristic 0 are shown to be complete groups, provided m > 3.  相似文献   

6.
This paper is concerned with the stability of theoretical solution and numerical solutionof a class of nonlinear differential equations with piecewise delays.At first,a sufficientcondition for the stability of theoretical solution of these problems is given,then numericalstability and asymptotical stability are discussed for a class of multistep methods whenapplied to these problems.  相似文献   

7.
In this paper, a class of higher order linear differential equation is investigated. The order and the hyper-order of the solutions of the equation are exactly estimated under some certain conditions.  相似文献   

8.
The solutions of linear system of elliptic type equations with first order isdiscussed by using the method of several complex analysis and, a series of newextended results of the solutions for the system of elliptic type are obtained.  相似文献   

9.
This paper is devoted to the homogenization of a semilinear parabolic equation with rapidly oscillating coefficients in a domain periodically perforated byε-periodic holes of size ε. A Neumann condition is prescribed on the boundary of the holes.The presence of the holes does not allow to prove a compactness of the solutions in L2. To overcome this difficulty, the authors introduce a suitable auxiliary linear problem to which a corrector result is applied. Then, the asymptotic behaviour of the semilinear problem as ε→ 0 is described, and the limit equation is given.  相似文献   

10.
Oscillation of solutions for a class of nth-order linear differential equation with impulses are considered and some sufficient conditions for oscillation of solutions are obtained, which improve and popularize some results in parts of the relative references.  相似文献   

11.
《代数通讯》2013,41(9):4267-4275
Abstract

In Fortes (2001), we introduced a notion of order for associative pairs and we obtained a Goldie-like characterization of left orders in a semiprime pair coinciding with its socle. In this paper, we take up again that notion of order to establish a Faith-Utumi theorem, which studies left orders in a prime pair coinciding with its socle.  相似文献   

12.
《Quaestiones Mathematicae》2013,36(4):451-466
Abstract

Let d be a positive integer, and F be a field of characteristic zero. Suppose that for each positive integer n, I n, is a GL n,(F)- invariant of forms of degree d in x1, …, x n, over F. We call {I n} an additive family of invariants if I p+q (fg) = I p(f).I q(g) whenever f; g are forms of degree d over F in x l, …, x p; …, x q respectively, and where (fg)(x l, …, x p+q) = f(x 1, …, x p,) + g (x p+1, …, x p+q). It is well-known that the family of discriminants of the quadratic forms is additive. We prove that in odd degree d each invariant in an additive family must be a constant. We also give an example in each even degree d of a nontrivial family of invariants of the forms of degree d. The proofs depend on the symbolic method for representing invariants of a form, which we review.  相似文献   

13.
一类微分方程组的非允许解   总被引:1,自引:0,他引:1  
张文腾 《数学杂志》2004,24(4):381-384
利用亚纯函数Nevanlinna的值分布理论,我们研究了一类代数微分方程组非允许解的存在性问题。并通过亏量δ(a,w)改进了非允许解的估计.  相似文献   

14.
关于抑制物对肿瘤生长直接效果模型的数学分析   总被引:7,自引:0,他引:7  
本文研究一个用于描述抑制物对肿瘤生长直接作用效果的数学模型,该模型是对Byrne和chaplain相应模型的一个改进.我们分别在c_1=c_2=0和c_1>0,c_2>o但很小两种情况下研究了该模型解的存在性和解在t→∞时的渐近状况,证明了未血管化的肿瘤在某些情况下趋于消失,而在另一些情况下趋于一个休眠态,且抑制物总能减小肿瘤的半径.  相似文献   

15.
《代数通讯》2013,41(8):2705-2711
Let A be a strong independence algebra of finite rank with at most one constant, and let G he the group of automorphisms of A. Let α be a singular endomorphism of αG = 〈{α} U G〉. We describe the elements of αG and give additional characterisations when A is a proper independence algebra and G is a periodic group.  相似文献   

16.
本文研究了两个幂等矩阵P与Q的组合aP+bQ-cPQ-dQP-ePQP (其中a,b,c,d,e∈(C),a≠0,b≠0)的可逆性. 利用P-Q的可逆性及幂等矩阵的性质,得到了aP+bQ-cPQ-dQP-ePQP可逆的一些充要条件. 推广了J. J.Koliha 和 V.RakoA(c)eviA(c)[1]及Zuo Kezheng[2]的结论.  相似文献   

17.
近几年,国内在研究小康水平的定量指标分析中,应用较多的有综合评分法、层次分析法和模糊识别法。这几种方法比单项指标更全面、灵活,但在权数的确定上都难以克服人为因素的影响。当指标之间存在两个或两个以上的高度相关时,对问题的研究总存在一定的局限性。为了科学地研究小康问题,本文基于判别分析,建立城市小康的判别系数,来综合评价出我国城市小康水平的定量标准。  相似文献   

18.
邓国泰  刘春苔 《数学杂志》2011,31(5):847-852
本文研究了Cantor集和其并的自相似性.利用Cantor展式的方法,得到了关于Cantor集和迭代函数系的一个基本关系:T∪(T+α)为自相似的当且仅当存在一个非负整数n使得α=±(k2-k1)dn.进一步,若T∪(T+α)是自相似的,则它满足开集条件.  相似文献   

19.
江秀海  高凌云 《数学杂志》2006,26(4):361-365
本文讨论了一类复微分方程组的亚纯解的分量的Nevanlinna特征估计,利用亚纯函数Nevanlinna值分布理论,得到了一个有关方程组亚纯解的分量的Nevanlinna特征估计定理.该结果推广了高凌云等人的一些结果.  相似文献   

20.
Barnsley-Elton-Hardin的一个定理的修正   总被引:1,自引:0,他引:1  
Barnsley等在关联矩阵不可约的条件下,得到了递归FIF的分形维数公式。本文首先指出该九公式是错误的,然后给出新的维数公式,并且新维数公式没有关联矩阵为不可约的限制条件。  相似文献   

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