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31.
Qifan Zhang 《Journal of Number Theory》2004,105(1):192-202
We extend some classical results on polynomial functions . We prove all results in algebraic methods avoiding any combinatorial calculation. As applications of our methods, we obtain some interesting new results on permutation polynomials in several variables over some finite commutative rings. 相似文献
32.
Dimitar K. Dimitrov 《Journal of Mathematical Analysis and Applications》2004,299(1):127-132
We prove that the zeros of the polynomials Pm(a) of degree m, defined by Boros and Moll via
33.
The stable set problem is to find in a simple graph a maximum subset of pairwise non-adjacent vertices. The problem is known to be NP-hard in general and can be solved in polynomial time on some special classes, like cographs or claw-free graphs. Usually, efficient algorithms assume membership of a given graph in a special class. Robust algorithms apply to any graph G and either solve the problem for G or find in it special forbidden configurations. In the present paper we describe several efficient robust algorithms, extending some known results. 相似文献
34.
We make a conjecture that the number of isolated local minimum points of a 2n-degree or (2n+1)-degree r-variable polynomial is not greater than n
r when n 2. We show that this conjecture is the minimal estimate, and is true in several cases. In particular, we show that a cubic polynomial of r variables may have at most one local minimum point though it may have 2r critical points. We then study the global minimization problem of an even-degree multivariate polynomial whose leading order coefficient tensor is positive definite. We call such a multivariate polynomial a normal multivariate polynomial. By giving a one-variable polynomial majored below a normal multivariate polynomial, we show the existence of a global minimum of a normal multivariate polynomial, and give an upper bound of the norm of the global minimum and a lower bound of the global minimization value. We show that the quartic multivariate polynomial arising from broad-band antenna array signal processing, is a normal polynomial, and give a computable upper bound of the norm of the global minimum and a computable lower bound of the global minimization value of this normal quartic multivariate polynomial. We give some sufficient and necessary conditions for an even order tensor to be positive definite. Several challenging questions remain open. 相似文献
35.
Zbigniew Jelonek 《Proceedings of the American Mathematical Society》2003,131(5):1361-1367
Let be a polynomial of degree . Assume that the set there is a sequence s.t. and is finite. We prove that the set of generalized critical values of (hence in particular the set of bifurcation points of ) has at most points. Moreover, We also compute the set effectively.
36.
Melvyn B. Nathanson 《Journal of Number Theory》2003,103(2):214-233
For the quantum integer [n]q=1+q+q2+?+qn−1 there is a natural polynomial multiplication such that [m]q⊗q[n]q=[mn]q. This multiplication leads to the functional equation fm(q)fn(qm)=fmn(q), defined on a given sequence of polynomials. This paper contains various results concerning the construction and classification of polynomial sequences that satisfy the functional equation, as well open problems that arise from the functional equation. 相似文献
37.
In this paper we present a new limit relation for the equidistant Lagrange interpolation polynomials to |x|, (0, 1] on the internal [–1, 1]. The result extends a well-known result of D. L. Berman and S. M. Losinskii. Furthermore, we briefly discuss on a possible connection of the limit relation to another prominent constant in best uniform polynomial approximation for |x| - the so-called Bernstein constant. 相似文献
38.
Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model whose machines do not distinguish between isomorphic structures and compute exactly PTime properties? This question can be recast as follows: Does there exist a logic that captures polynomial time (without presuming the presence of a linear order)? Earlier, one of us conjectured a negative answer. The problem motivated a quest for stronger and stronger PTime logics. All these logics avoid arbitrary choice. Here we attempt to capture the choiceless fragment of PTime. Our computation model is a version of abstract state machines (formerly called evolving algebras). The idea is to replace arbitrary choice with parallel execution. The resulting logic expresses all properties expressible in any other PTime logic in the literature. A more difficult theorem shows that the logic does not capture all of PTime. 相似文献
39.
Mao-Cheng Cai C.W. Duin Xiaoguang Yang Jianzhong Zhang 《European Journal of Operational Research》2008
In a partial inverse optimization problem there is an underlying optimization problem with a partially given solution. The objective is to find a minimal perturbation of some of the problem’s parameter values, in such a way that the partial solution becomes a part of the optimal solution. 相似文献
40.
Sándor Bozóki 《Central European Journal of Operations Research》2008,16(4):345-358
The aim of the paper is to present a new global optimization method for determining all the optima of the Least Squares Method
(LSM) problem of pairwise comparison matrices. Such matrices are used, e.g., in the Analytic Hierarchy Process (AHP). Unlike
some other distance minimizing methods, LSM is usually hard to solve because of the corresponding nonlinear and non-convex
objective function. It is found that the optimization problem can be reduced to solve a system of polynomial equations. Homotopy
method is applied which is an efficient technique for solving nonlinear systems. The paper ends by two numerical example having
multiple global and local minima.
This research was supported in part by the Hungarian Scientific Research Fund, Grant No. OTKA K 60480. 相似文献