共查询到20条相似文献,搜索用时 31 毫秒
1.
矩阵特征值、特征向量的确定 总被引:4,自引:1,他引:3
首先对由 A的特征值、特征向量求 A- 1 ,AT,A* ( A的伴随矩阵 )、P- 1 AP以及 A的多项式φ( A)的特征值和特征向量的结论作了个归纳 ;对相反的情形 ,我们给出了部分已有的结果 ,并通过四道例题着重讨论了如何由 φ( A)的特征值来求 A的特征值 . 相似文献
2.
This paper studies the behaviors of the solutions in the vicinity of a givenalmost periodic solution of the autonomous system
x′=f(x), x Rn , (1)
where f C1 (Rn ,Rn ). Since the periodic solutions of the autonomous system are not Liapunov asymptotic stable, we consider the weak orbitally stability.
For the planar autonomous systems (n=2), the classical result of orbitally stability about its periodic solution with period w belongs to Poincare, i.e. 相似文献
3.
V. M. Babich 《Journal of Mathematical Sciences》1996,79(4):1166-1168
The equation for SH-waves is considered for the following parameters μ and ρ: μ=a(x)·b(y), ρ=a(x)b(y)(c(x)+d(y)) (a,b,c,d
are known functions). For such μ and ρ the variables in this equation can be separated. An explicit solution of the problem
of the interaction of a whispering gallery wave with a vertical interface of two media is obtained. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 12–16.
Translated by N. S. Zabavnikova. 相似文献
4.
Let S = {x1, x2,..., xn} be a set of distinct positive integers. The n x n matrix (S) whose i, j-entry is the greatest common divisor (xi, xj) of xi and xj is called the GCD matrix on S. A divisor d of x is said to be a unitary divisor of x if (d, x/d) = 1. The greatest common unitary divisor (GCUD) matrix (S**) is defined analogously. We show that if S is both GCD-closed and GCUD-closed, then det(S**) ≥ det(S), where the equality holds if and Only if (S**) = (S). 相似文献
5.
6.
D. Suryanarayana 《Periodica Mathematica Hungarica》1979,10(4):261-271
LetL(x) denote the number of square full integers ≤x. By a square-full integer, we mean a positive integer all of whose prime factors have multiplicity at least two. It is well known that $$\left. {L(x)} \right| \sim \frac{{\zeta ({3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2})}}{{\zeta (3)}}x^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} + \frac{{\zeta ({2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3})}}{{\zeta (2)}}x^{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}} ,$$ where ζ(s) denotes the Riemann Zeta function. Let Δ(x) denote the error function in the asymptotic formula forL(x). On the basis of the Riemann hypothesis (R.H.), it is known that \(\Delta (x) = O(x^{\tfrac{{13}}{{81}} + \varepsilon } )\) for every ε>0. In this paper, we prove the following results on the assumption of R.H.: (1) $$\frac{1}{x}\int\limits_1^x {\Delta (t)dt} = O(x^{\tfrac{1}{{12}} + \varepsilon } ),$$ (2) $$\int\limits_1^x {\frac{{\Delta (t)}}{t}\log } ^{v - 1} \left( {\frac{x}{t}} \right) = O(x^{\tfrac{1}{{12}} + \varepsilon } )$$ for any integer ν≥1. In fact, we prove some general results and deduce the above from them. On the basis of (1) and (2) above, we conjecture that \(\Delta (x) = O(x^{{1 \mathord{\left/ {\vphantom {1 {12}}} \right. \kern-0em} {12}} + \varepsilon } )\) under the assumption of R.H. 相似文献
7.
设σ(k,n)表示最小的正整数m,使得对于每个n项正可图序列,当其项和至少为m时,有一个实现含k 1个顶点的团作为其子图。Erdos等人猜想:σ(k,n)=(k-1)(2n-k) 2.Li等人证明了这个猜想对于k≥5,n≥(^k2))+3是对的,并且提出如下问题:确定最小的整数N(k),使得这个猜想对于n≥N(k)成立。他们同时指出:当k≥5时,[5k-1/2]≤N(k)≤(^k2) 3.Mubayi猜想:当k≥5时,N(k)=[5k-1/2]。在本文中,我们证明了N(8)=20,即Mubayi猜想对于k=8是成立的。 相似文献
8.
令P=NAM是SU(n+1,1)的极小抛物子群,它可以看作是Heisenberg群Hn上的仿射自同构群.根据[1]中的可允许条件,我们给出了Hn上的带状小波.利用小波变换,我们得到了L2(Un+1,dμl(z,t,ρ))的另一个正交直和分解.进一步还给出了L2(P,dμl(z,t,ρ,u))的正交分解. 相似文献
9.
Pham Tien Dung 《Analysis Mathematica》2009,35(4):289-299
The result of Golubov [5, Theorem 2] on the boundedness of the Hardy-Littlewood operator $$ \mathcal{B}f(x): = \frac{1} {x}\int_0^x {f(t)} dt $$ in the space BMO(?) is well known. The author of the present paper solves the analogous problem in the weighted space BMO on the semi-axis ?+ for the operator $$ T_w f(x): = \frac{1} {{W(x)}}\int_0^x {f(t)w(t)} dt $$ and also in the classical space BMO(?+) for a class of integral operators involving, for example, the Riemann-Liouville fractional integral. 相似文献
10.
Exact estimates are presented for the solutions of the problem $\ddot y + \lambda ^2 p(t)y = 0, y(0) = 0, \dot y(0) = 1$ withp(t) satisfying one of the following conditions: $$(i) |p(t)| \leqslant M< \infty ; (ii) 0< \omega _1 \leqslant p(t) \leqslant \omega _2< \infty ; (iii) \mathop {sup}\limits_x \int_x^{x + T} {p(t)dt = P_T /T.} $$ The extremal solutions are found. 相似文献
11.
本文讨论了连续Domain D的极大点Max(D)的紧子集Com(Max(D))与凸幂Domain CD的极大点Max(CD)一一对应的条件以及Max(CD)上拓扑的性质, 证明了当X为局部紧Hausdorff空间时,X的上空间UX的凸幂Domain C(UX)的极大点Max(C(UX))与Com(Max(UX))(即X的紧子集)一一对应.X的上空间UX上的Lawson拓扑与X紧子集上的Vietoris拓扑相同,并且与Max(C(UX))带有C(UX)上的相对Scott拓扑同胚. 相似文献
12.
《Mathematical and Computer Modelling》2006,43(1-2):1-8
The Maximum Entropy Principle (MEP) maximises the entropy subject to the constraint that the effort remains constant. The Principle of Least Effort (PLE) minimises the effort subject to the constraint that the entropy remains constant. The paper investigates the relation between these two principles. It is shown that (MEP) is equivalent with the principle “(PLE) or (PME)” where (PME) is (introduced in this paper) the Principle of Most Effort, meaning that the effort is maximised subject to the constraint that the entropy remains constant. 相似文献
13.
Ye Maodong 《数学年刊B辑(英文版)》1990,11(3):359-362
Let f (x) ∈ C [-1, 1], p_n~* (x) be the best approximation polynomial of degree n tof (x). G. Iorentz conjectured that if for all n, p_(2n)~* (x) = p_(2n+1)~* (x), then f is even; and ifp_(2n+1)~* (x) = p_(2n+2)~* (x), p_o~* (z) = 0, then f is odd. In this paper, it is proved that, under the L_1-norm, the Lorentz conjecture is validconditionally, i. e. if (i) (1-x~2) f (x) can be extended to an absolutely convergentTehebyshev sories; (ii) for every n, f (x) - p_(2n+1)~* (x) has exactly 2n + 2 zeros (or, in thearcond situation, f (x) - p_(2n+2)~* (x) has exaetly 2n+3 zeros), then Lorentz conjecture isvalid. 相似文献
14.
For a continuous domain D, some characterization that the convex powerdomain CD is a domain hull of Max(CD) is given in terms of compact subsets of D. And in this case, it is proved that the set of the maximal points Max(CD) of CD with the relative Scott topology is homeomorphic to the set of all Scott compact subsets of Max(.D) with the topology induced by the Hausdorff metric derived from a metric on Max(D) when Max(D) is metrizable. 相似文献
15.
Horst R. Thieme 《manuscripta mathematica》1980,31(4):379-412
We study the Volterra-Hammerstein integral equation $$U(t,x) = U_O (t,x) + \mathop \smallint \limits_O^t \mathop \smallint \limits_D f(y, U (t - s,y)) h (x,y,s)dsdy,$$ t≥0, x∈D. We derive sufficient conditions for the boundedness of all non-negative solutions U. We show that, for bounded non-negative solutions U, U(t,.) is positive on D for sufficiently large t>0, if we impose appropriate positivity assumptions on f and h. If we additionally assume that, for y∈D, rf(y,r) strictly monotone increases and f(y,r)/r strictly monotone decreases as r>0 increases, the following alternative holds for any bounded non-negative solution U: Either U(t,.) converges toward zero for t→∞, pointwise on D, or U(t,.) converges, for t→∞, toward the unique bounded positive solution of the corresponding Hammerstein integral equation, uniformly on D. We indicate conditions for the occurrence of each of the two cases. 相似文献
16.
Let H n ( F ) be the space of n -square symmetric matrices over the field F . We generalize the main result of [M.H. Lim (1979). A note on the relation between the determinant and the permanent. Linear and Multilinear Algebra , 7 , 145-147], proving that the determinant is not convertible into the permanent on H n ( F ), provided that n ? 3, F has at least n elements and the characteristic of F is not 2. The case n = 2 is also studied. 相似文献
17.
Fernando Szechtman 《Semigroup Forum》2005,70(2):238-242
Let $e$ be an idempotent in the monoid $T(X)$ of all functions
from a set $X$ into itself. Let $C(e)$ be the centralizer of $e$
in $T(X)$. It has recently been shown that the unit and
automorphism groups of $C(e)$ are canonically isomorphic. Our goal
is to furnish an alternative proof of this fact and make the
observation that automorphism group of $C(e)$ is isomorphic to the
direct product ${\Pi}_{i\in I}( \Sym(A_i)\wr
\Sym(B_i))$ of wreath products of symmetric groups, where
the sets $I$, $A_i$, $B_i$ are defined in terms of $e$. 相似文献
18.
丢番图方程与实二次域类数的可除性 总被引:3,自引:3,他引:0
设d无平方因子,h(d)是二次域的类数。本文证明了:在方程U ̄2-dV ̄2=4,(U,V)=1有整数解时,丢番图方程4x ̄(2n)-dy ̄2=-1,n>2无|y|>1的整数解;如果正整数a,k,n满足,k>1,n>2且而是Pell方程x ̄2-dy ̄2=-1的基本解,则h(d)≡0(modn)。 相似文献
19.
We prove that the admissibility of any pair of vector-valued Schäffer function spaces (satisfying a very general technical condition) implies the existence of a “no past” exponential dichotomy for an exponentially bounded, strongly continuous cocycle (over a semiflow). Roughly speaking the class of Schäffer function spaces consists in all function spaces which are invariant under the right-shift and therefore our approach addresses most of the possible pairs of admissible spaces. Complete characterizations for the exponential dichotomy of cocycles are also obtained. Moreover, we involve a concept of a “no past” exponential dichotomy for cocycles weaker than the classical concept defined by Sacker and Sell (1994) in [23]. Our definition of exponential dichotomy follows partially the definition given by Chow and Leiva (1996) in [4] in the sense that we allow the unstable subspace to have infinite dimension. The main difference is that we do not assume a priori that the cocycle is invertible on the unstable space (actually we do not even assume that the unstable space is invariant under the cocycle). Thus we generalize some known results due to O. Perron (1930) [14], J. Daleckij and M. Krein (1974) [7], J.L. Massera and J.J. Schäffer (1966) [11], N. van Minh, F. Räbiger and R. Schnaubelt (1998) [26]. 相似文献
20.
拟就以下内容进行了探讨 .(i)该课程究竟应该讲什么内容、怎样讲 ,才能使学生在较短的时间内 ,掌握数学建模的基本知识和基本方法 ;(ii)该课程怎样与数学实验更好地结合起来 ,以培养学生的动手能力 ;(iii)该课程应采用什么样的教学手段和教学方法 ,才能加大课堂信息量 ,加强直观性和趣味性等 .我们的解决方法是 :(i)以介绍建立数学模型为主 ,按数学知识内容的不同来选取数学模型的典型案例 ,通过案例介绍 ,使学生学会怎样建立模型 .(ii)适当介绍数学软件包 ,让学生掌握运用软件包来求解模型能力 .(iii)做大作业 ,教员给出题目 ,学生自己收集资料、讨论、上机求解 ,最后写出报告 .(iv)开展多媒体教学 ,对主要的教学内容进行模块化教学 ,将建模分成 1 4个专题 ,做成 1 4个多媒体课件 相似文献