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161.
David Yang Gao 《Journal of Global Optimization》2006,35(1):131-143
This paper presents a set of complete solutions to a class of polynomial optimization problems. By using the so-called sequential canonical dual transformation developed in the author’s recent book [Gao, D.Y. (2000), Duality Principles in Nonconvex Systems: Theory, Method and Applications,
Kluwer Academic Publishers, Dordrecht/Boston/London, xviii + 454 pp], the nonconvex polynomials in
can be converted into an one-dimensional canonical dual optimization problem, which can be solved completely. Therefore,
a set of complete solutions to the original problem is obtained. Both global minimizer and local extrema of certain special
polynomials can be indentified by Gao-Strang’s gap function and triality theory. For general nonconvex polynomial minimization
problems, a sufficient condition is proposed to identify global minimizer. Applications are illustrated by several examples. 相似文献
162.
也谈厄米多项式的递推关系 总被引:1,自引:1,他引:1
由厄米多项式的母函数出发,推导出厄米多项式的递推关系以及厄米多项式中系数的递推关系. 相似文献
163.
V. N. Dubinin 《Mathematical Notes》2006,80(1-2):31-35
It is shown that if P(z) = z n + ? is a polynomial with connected lemniscate E(P) = {z: ¦P(z)¦ ≤ 1} and m critical points, then, for any n? m+1 points on the lemniscate E(P), there exists a continuum γ ? E(P) of logarithmic capacity cap γ ≤ 2?1/n which contains these points and all zeros and critical points of the polynomial. As corollaries, estimates for continua of minimum capacity containing given points are obtained. 相似文献
164.
For matrices whose eigenvalues are real (such as Hermitian or real symmetric matrices), we derive simple explicit estimates for the maximal (λmax) and the minimal (λmin) eigenvalues in terms of determinants of order less than 3. For 3 × 3 matrices, we derive sharper estimates, which use det A but do not require to solve cubic equations. 相似文献
165.
许多非线性动力系统都有某种对称性,在不同情形下可有不同的表现形式,但始终保持其对称的特点.不同对称形式间的转变导致对称破缺分岔或激变.关于非线性动力系统中相空间运动轨道的对称破缺分岔,已有大量研究工作,但绝大多数是指周期或拟周期相轨的对称破缺,偶尔提到对称系统中的混沌相轨也存在“对偶性”.最近,在简谐外激Duffing系统周期轨道对称破缺引发鞍-结分岔的研究中,得到了分岔后由Poincaré映射点间断流构成的图像,其中包括两个稳定周期结点、一个周期鞍点,及其稳定流形与不稳定流形,均较规则.本工作研究了正弦
关键词:
对称破缺
混沌
激变
分形吸引域 相似文献
166.
We present a fully polynomial time approximation scheme (FPTAS) for a capacitated economic lot-sizing problem with a monotone
cost structure. An FPTAS delivers a solution with a given relative error ɛ in time polynomial in the problem size and in 1/ɛ. Such a scheme was developed by van Hoesel and Wagelmans [8] for a capacitated economic lot-sizing problem with monotone
concave (convex) production and backlogging cost functions. We omit concavity and convexity restrictions. Furthermore, we
take advantage of a straightforward dynamic programming algorithm applied to a rounded problem. 相似文献
167.
Summary For P∈ F2[z] with P(0)=1 and deg(P)≧ 1, let A =A(P) be the unique subset of N (cf. [9]) such that Σn≧0 p(A,n)zn ≡ P(z) mod 2, where p(A,n) is the number of partitions of n with parts in A. To determine the elements of the set A, it is important to consider the sequence σ(A,n) = Σ d|n, d∈A d, namely, the periodicity of the sequences (σ(A,2kn) mod 2k+1)n≧1 for all k ≧ 0 which was proved in [3]. In this paper, the values of such sequences will be given in terms of orbits. Moreover, a formula
to σ(A,2kn) mod 2k+1 will be established, from which it will be shown that the weight σ(A1,2kzi) mod 2k+1 on the orbit <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>z_i$
is moved on some other orbit zj when A1 is replaced by A2 with A1= A(P1) and A2= A(P2) P1 and P2 being irreducible in F2[z] of the same odd order. 相似文献
168.
Pairwise linear discriminant analysis can be regarded as a process to generate rankings of the populations. But in general, not all rankings are generated. We give a characterization of generated rankings. We also derive some basic properties of this model. 相似文献
169.
Yuan Yuan LIU Zhen Ting HOU 《数学学报(英文版)》2007,23(7):1289-1296
This paper investigates the explicit convergence rates to the stationary distribution π of the embedded M/G/1 queue; specifically, for suitable rate functions r(n) which may be polynomial with r(n) = n^l, l 〉 0 or geometric with r(n) = α^n, a 〉 1 and "moments" f ≥ 1, we find the conditions under which Σ∞n=0 r(n)||P^n(i,·) - π(·)||f ≤ M(i) for all i ∈ E. For the polynomial case, the explicit bounds on M(i) are given in terms of both "drift functions" and behavior of the first hitting time on the state O; and for the geometric case, the largest geometric convergence rate α* is obtained. 相似文献
170.
The E-characteristic polynomial of an even order supersymmetric tensor is a useful tool in determining the positive definiteness of an even degree multivariate form. In this paper, for an even order tensor, we first establish the formula of its E-characteristic polynomial by using the classical Macaulay formula of resultants, then give an upper bound for the degree of that E-characteristic polynomial. Examples illustrate that this bound is attainable in some low order and dimensional cases. 相似文献