遗传密码的进化稳定性

本评述了遗传密码的进化有关的物理问题。主要讨论了：1）从进化稳定性的观点研究遗传密码的简并规则,证明了现有密码表中多重态的简并规则是突变危险性极小的;2）从进化稳定性的观点研究了遗传密码表中氨基酸和终止密码子的排布,导出了总体突变危险性极小的表,并证明了标准密码表是在某些约束（这些约束反映了密码形成时期的初始条件）下总体突变危险性极小的表;3）密码表中20种氨基酸和终止密码简并度的分布,以及改变简并度条件下密码反常的出现。     

A Characterization of Minimal Legendrian Submanifolds in S2n+1

Let x: L ⁿ S²ⁿ⁺¹ R²ⁿ⁺² be a minimal submanifold in S²ⁿ⁺¹. In this note, we show that L is Legendrian if and only if for any A su(n + 1) the restriction to L of Ax, (–1)x satisfies f = 2(n + 1)f. In this case, 2(n + 1) is an eigenvalue of the Laplacian with multiplicity at least (n(n + 3)). Moreover if the multiplicity equals to ;(n(n + 3)), then L ⁿ is totally geodesic.     

On Ptak's Generalization of Hankel Operators

In 1997 Ptak defined generalized Hankel operators as follows: Given two contractions and , an operator is said to be a generalized Hankel operator if and X satisfies a boundedness condition that depends on the unitary parts of the minimal isometric dilations of T ₁ and T ₂. This approach, call it (P), contrasts with a previous one developed by Ptak and Vrbova in 1988, call it (PV), based on the existence of a previously defined generalized Toeplitz operator. There seemed to be a strong but somewhat hidden connection between the theories (P) and (PV) and we clarify that connection by proving that (P) is more general than (PV), even strictly more general for some T ₁ and T ₂, and by studying when they coincide. Then we characterize the existence of Hankel operators, Hankel symbols and analytic Hankel symbols, solving in this way some open problems proposed by Ptak.     

Bounded and Almost-Periodic Solutions of Nonlocal Perturbations of Nonautonomous Logistic-Type Equations

This paper is concerned with the study of dynamics of nonlinear nonlocal perturbations of nonautonomous logistic-type equations. More specifically, we prove the existence and uniqueness of a bounded solution that is positive, and that does not approach the zero solution in the past and in the future. We also show that this solution is an attractor for all other positive solutions. Since the zero solution is shown to be a repeller for all solutions that remain below the aforementioned one, we obtain an attractor-repeller pair. Almost-periodic attractor is also discussed.     

Mean Curvature and Volume of Extrinsic Spheres in Hypersurfaces of Real Space Forms

Given a hypersurface P^n-1 in a real space form of constantcurvature b, , we have obtained a lower bound for the norm of the mean curvature normal vector field of extrinsicspheres in P^n-1 in terms of the mean curvature of the geodesic spheres in , with the same radius, and the meancurvature of P^n-1, characterizing too the equality.     

A weak Asplund space whose dual is not weak fragmentable

Under the assumption that there exists in the unit interval an uncountable set with the property that every continuous mapping from a Baire metric space into is constant on some non-empty open subset of , we construct a Banach space such that belongs to Stegall's class but is not fragmentable.

     

Pivot rules for linear programming: A survey on recent theoretical developments

The purpose of this paper is to discuss the various pivot rules of the simplex method and its variants that have been developed in the last two decades, starting from the appearance of the minimal index rule of Bland. We are mainly concerned with finiteness properties of simplex type pivot rules. Well known classical results concerning the simplex method are not considered in this survey, but the connection between the new pivot methods and the classical ones, if there is any, is discussed.In this paper we discuss three classes of recently developed pivot rules for linear programming. The first and largest class is the class of essentially combinatorial pivot rules including minimal index type rules and recursive rules. These rules only use labeling and signs of the variables. The second class contains those pivot rules which can actually be considered as variants or generalizations or specializations of Lemke's method, and so they are closely related to parametric programming. The last class has the common feature that the rules all have close connections to certain interior point methods. Finally, we mention some open problems for future research.On leave from the Eötvös University, Budapest, and partially supported by OTKA No. 2115.     

Discs in unbreakable graphs

We show that every vertex in an unbreakable graph is in a disc, where a disc is a chordless cycle, or the complement of a chordless cycle, with at least five vertices. A corollary is that every vertex in a minimal imperfect graph is in a disc.This research was supported by NSERC Operating Grant OGP-0137764.     

Products of regular-closed spaces

Conditions under which a product space will be regular-closed or minimal regular are studied. It is shown that a product of regular-closed spaces need not be regular-closed and that a product of minimal regular spaces need not be minimal regular.     

Note on prime representations of convex polyhedral sets

Consider a convex polyhedral set represented by a system of linear inequalities. A prime representation of the polyhedron is one that contains no redundant constraints. We present a sharp upper bound on the difference between the cardinalities of any two primes.This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant Nos. A8807, A4625, and A7742.