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91.
Popularized by Zassenhaus in the seventies, several algorithms for factoring polynomials use a so-called lifting and recombination scheme. Concerning bivariate polynomials, we present a new algorithm for the recombination stage that requires a lifting up to precision twice the total degree of the polynomial to be factored. Its cost is dominated by the computation of reduced echelon solution bases of linear systems. We show that our bound on precision is asymptotically optimal.
92.
Yuanqiu Huang 《Discrete Applied Mathematics》2007,155(3):405-409
A stable set of a graph is a vertex set in which any two vertices are not adjacent. It was proven in [A. Brandstädt, V.B. Le, T. Szymczak, The complexity of some problems related to graph 3-colorability, Discrete Appl. Math. 89 (1998) 59-73] that the following problem is NP-complete: Given a bipartite graph G, check whether G has a stable set S such thatG-Sis a tree. In this paper we prove the following problem is polynomially solvable: Given a graph G with maximum degree 3 and containing no vertices of degree 2, check whether G has a stable set S such thatG-Sis a tree. Thus we partly answer a question posed by the authors in the above paper. Moreover, we give some structural characterizations for a graph G with maximum degree 3 that has a stable set S such that G-S is a tree. 相似文献
93.
M.Z. Arslanov 《Operations Research Letters》2007,35(5):636-644
We consider the problem of guillotine cutting a rectangular sheet into two rectangular pieces without rotations. The question is whether there exists a cutting pattern with given numbers of occurrences of both rectangular pieces. A polynomial time algorithm is described to construct the convex hull of solutions to this problem. 相似文献
94.
Josef Obermaier 《Journal of Approximation Theory》2003,125(2):303-312
Let
be compact with #S=∞ and let C(S) be the set of all real continuous functions on S. We ask for an algebraic polynomial sequence (Pn)n=0∞ with deg Pn=n such that every fC(S) has a unique representation f=∑i=0∞ αiPi and call such a basis Faber basis. In the special case of
, 0<q<1, we prove the existence of such a basis. A special orthonormal Faber basis is given by the so-called little q-Legendre polynomials. Moreover, these polynomials state an example with A(Sq)≠U(Sq)=C(Sq), where A(Sq) is the so-called Wiener algebra and U(Sq) is the set of all fC(Sq) which are uniquely represented by its Fourier series. 相似文献
95.
本文对一类具有对称轴的图A_n(n≥0),得到了它的特征多项式及匹配多项式的精确表达式;同时还得到A_(?)的完美匹配数。 相似文献
96.
We give a polynomial time controlled version of a theorem of M. Hall: every real number can be written as the sum of two irrational numbers whose developments into a continued fraction contain only 1, 2, 3 or 4. Mathematics Subject Classification: 03D15, 03F60, 11A55, 68Q25. 相似文献
97.
综合国力的数学建模 总被引:2,自引:0,他引:2
王树禾 《高校应用数学学报(A辑)》1997,(1):29-36
本文考虑社会文明与社会导恶现象的制约机制,建立一个综合国力的非线性数学模型,从数学上讨论了相应的二次微分系统的Hopf分叉,中心与细焦点的判定,极限环的存在唯一性等问题,并对数学结论予以合理解释,把社会相平面划成社发展区域,社会动荡区域和社会崩溃区域,研讨社会走向,确定纳入社会发展区域的途径。 相似文献
98.
我们发现可以把二元多项式盾成系数为一元多项式的一元多项式来进行分解,据此,本文建立了二元整系数多项式因式分解的一种理论,提出了一个完整的分解二元整系数多项式的算法。这个算法还能很自然地推广成分解多元整系数多项式的算法。 相似文献
99.
In this paper we introduce and study polynomial spline collocation methods for systems of Volterra integral equations with unknown lower integral limit arising in mathematical economics. Their discretization leads to implicit Runge-Kutta-type methods. The global convergence and local superconvergence properties of these methods are proved, and the theory is illustrated by a numerical example arising in the application of such equations in certain mathematical models of liquidation. 相似文献
100.