Polynomially solvable cases for the maximum stable set problem

We describe two classes of graphs for which the stability number can be computed in polynomial time. The first approach is based on an iterative procedure which, at each step, builds from a graph G a new graph G′ which has fewer vertices and has the property that (G′) = (G) − 1. For the second class, it can be decided in polynomial time whether there exists a stable set of given size k.     

Polynomial Time Uniform Word Problems

We have two polynomial time results for the uniform word problem for a quasivariety Q: (a) The uniform word problem for Q can be solved in polynomial time iff one can find a certain congruence on finite partial algebras in polynomial time. (b) Let Q* be the relational class determined by Q. If any universal Horn class between the universal closure S(Q*) and the weak embedding closure S?(Q*) of Q* is finitely axiomatizable then the uniform word problem for Q is solvable in polynomial time. This covers Skolem's 1920 solution to the uniform word problem for lattices and Evans' 1953 applications of the weak embeddability property for finite partial V algebras.     

Bezier曲线的矩阵形式及其应用

本文给出了Ｂｅｚｉｅｒ曲线的矩阵形式及其某些应用     

Polynomial sequential continuity on C(K,E) spaces

We show that, for bounded sequences in C(K,E), the polynomial sequential convergence is not equivalent to the pointwise polynomial sequential convergence. We introduce several conditions on E under which different versions of the result are true when K is a scattered compact space. These conditions are related with some others appeared in the literature and they seem to be of independent interest.     

Factorization properties of birational mappings

We analyse birational mappings generated by transformations on q × q matrices which correspond respectively to two kinds of transformations: the matrix inversion and a permutation of the entries of the q × q matrix. Remarkable factorization properties emerge for quite general involutive permutations.

It is shown that factorization properties do exist, even for birational transformations associated with noninvolutive permutations of entries of q × q matrices, and even for more general transformation which are rational transformations but no longer birational. The existence of factorization relations independent of q, the size of the matrices, is underlined.

The relations between the polynomial growth of the complexity of the iterations, the existence of recursions in a single variable and the integrability of the mappings, are sketched for the permutations yielding these properties.

All these results show that permutations of the entries of the matrix yielding factorization properties are not so rare. In contrast, the occurrence of recursions in a single variable, or of the polynomial growth of the complexity are, of course, less frequent but not completely exceptional.     

Machines Over the Reals and Non-Uniformity

We survey the research performed in the last few years on a specific topic: the power of real machines over binary inputs. This research attempts to characterize the classes of decision problems over a finite alphabet - say {0,1} - which can be decided by real machines working under several resource restrictions. Non-uniformity appears here in a natural way. However, since this is a technical concept which is not widely known, we summarize in Section 2 some of the intuitive notions, as well as a few basic theorems related to it. In Section 3 we do this for the subject of real machines and then, in Section 4 we present the state of the art of the surveyed topic. We devote Section 1 to introduce the main concepts of complexity theory. Proofs in this article are quite sketchy and are included more to convey intuitive ideas than to completely prove the claimed statements. Bibliographical references to the original literature are supplied for the latter purpose.     

Robust Stability of Polynomials: New Approach

The problem of the robust stability of a Hurwitz polynomial which is the characteristic polynomial of a discrete-time linear time-invariant system is investigated. A new approach based on the Rouché theorem of classical complex analysis is adopted. An interesting sufficient condition for robust stability is derived. Three examples are included to support the theoretical result.     

On Measures Induced by Extremal Signatures in Best Real Polynomial Approximation

We consider the limit distribution of measures μ _n , that appear in extremal signatures in the best polynomial approximation of a real-valued function . Relations between structural properties of the function f and weak-star limit points of (μ _n ) _n are proved. April 4, 1996. Date revised: October 25, 1996.     

Witness sets of projections

Elimination is a basic algebraic operation which geometrically corresponds to projections. This article describes using the numerical algebraic geometric concept of witness sets to compute the projection of an algebraic set. The ideas described in this article apply to computing the image of an algebraic set under any linear map.     

The near-best solution of a polynomial minimization problem by the Carathéodory-Fejér method

For a compact set C, 1, we consider the Chebyshev problem