Affine completeness of Kleene algebras

An algebra is called affine complete if all its compatible (i.e. congruence-preserving) functions are polynomial functions. In this paper we characterize affine complete members in the variety of Kleene algebras. We also characterize local polynomial functions of Kleene algebras and use this result to describe locally affine complete Kleene algebras. Received December 20, 1996; accepted in final form March 24, 1997.     

Extendability of Cyclic Orders

A cyclic order is a ternary relation that satisfies ternary transitivity and asymmetry conditions. Such a ternary relation is extendable if it is included in a complete cyclic order on the same ground set. Unlike the case of linear extensions of partial orders, a cyclic order need not be extendable. The extension problem for cyclic orders is to determine if a cyclic order is extendable. This problem is known to be NP-complete. We introduce a class of cyclic orders in which the extension problem can be solved in polynomial time. The class provides many explicit examples of nonextendable cyclic orders that were not previously known, including a nonextendable cyclic order on seven points. Let μ be the maximum cardinality of a ground set on which all cyclic orders are extendable. It has been shown that μ≤9. We prove that μ=6. This answers a question of Novák. In addition, we characterize the nonextendable cyclic orders on seven and eight points. Our results are intimately related to irreducible partially ordered set of order dimension three, and to fractional vertices of generalized transitive tournament polytopes. As by-products, we obtain a characterization of cyclically ordered sets of dimension two, and a new proof of a theorem of Dridi on small linear ordering polytopes. This revised version was published online in June 2006 with corrections to the Cover Date.     

非线性不适定问题的正则化方法

本文考虑非线性不适定问题Tx=y的近似求解,利用Тихоноь正则化方法来逼近问题的x-极小模解,当算子和右端都近似已知时,给出一种决定正则化参数的方法,并给出正则解的收效性和渐近收敛阶估计。     

A characterization of total reflection orders

Let be a Coxeter system with set of reflections . It is known that if is a total reflection order for , then, for each , and its complement are stable under conjugation by . Moreover the upper and lower -conjugates of are still total reflection orders. For any total order on , say that is stable if is stable under conjugation by for each . We prove that if and all orders obtained from by successive lower or upper -conjugations are stable, then is a total reflection order.

     

On fundamental domains of arithmetic Fuchsian groups

Let be a totally real algebraic number field and an order in a quaternion algebra over . Assume that the group of units in with reduced norm equal to is embedded into as an arithmetic Fuchsian group. It is shown how Ford's algorithm can be effectively applied in order to determine a fundamental domain of as well as a complete system of generators of .

     

中药配伍系统(CSCMM)的复杂网络拓扑特征分析

通过构建表征中药配伍系统(CSCMM)的复杂网络,按照整体论、系统论的思想,运用复杂网络的理论,借助整体网络的分析技术和计算机可视化算法对CSCMM进行了宏观综合的量化分析和定性阐释,揭示了该网络诸如小世界和近似无标度等网络拓扑特征,以期为中药配伍的现代化研究提供一定的思考和启发.     

A New Characterization of A 22 by Its Spectrum

It is proved that a finite group whose element order set is the same as that of an alternating group A ₂₂ of degree 22 is isomorphic to A ₂₂.     

On Groups with the Second Largest Value of the Sum of Element Orders

For a finite group G, let ψ(G) denote the sum of element orders of G. It is known that the maximum value of ψ on the set of groups of order n, where n is a positive integer, will occur at the cyclic group ? _n . In this paper, we investigate groups with the second largest value of ψ on the set of groups of the same order.