Algebras in the Positive Cone of po-Groups

We systemize a number of algebras that are especially known in the field of quantum structures and that in particular arise from the positive cones of partially ordered groups. Generalized effect algebras, generalized difference posets, cone algebras, commutative BCK-algebras with the relative cancellation property, and positive minimal clans are included in the text.All these structures are conveniently characterizable as special cases of generalized pseudoeffect algebras, which we introduced in a previous paper. We establish the exact relations between all mentioned structures, thereby adding new structures whenever necessary to make the scheme of order complete.Generalized pseudoeffect algebras were under certain conditions proved to be representable by means of a po-group. From this fact, we will easily establish representation theorems for all of the structures included in discussion.     

“Minimal Surfaces in ℍ<Superscript>2</Superscript> × ℝ”

In ² × ℝ one has catenoids, helicoids and Scherk-type surfaces. A Jenkins-Serrin type theorem holds here. Moreover there exist complete minimal graphs in ² with arbitrary continuous asymptotic values. Finally, a graph on a domain of ² cannot have an isolated singularity. Received: 20 June 2002     

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.     

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.

     

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。     

Distinguishing a SM-like MSSM Higgs boson from SM Higgs boson at muon collider

We explore the possibility of distinguishing the SM-like MSSM Higgs boson from the SM Higgs boson via Higgs boson pair production at future muon collider. We study the behavior of the production cross-section in SM and MSSM with Higgs boson mass for various MSSM parameters tan β and m _A . We observe that at fixed CM energy, in the SM, the total cross-section increases with the increase in Higgs boson mass whereas this trend is reversed for the MSSM. The changes that occur for the MSSM in comparison to the SM predictions are quantified in terms of the relative percentage deviation in cross-section. The observed deviations in cross-section for different choices of Higgs boson masses suggest that the measurements of the cross-section could possibly distinguish the SM-like MSSM Higgs boson from the SM Higgs boson.      

A Loopless Algorithm for Generation of Basic Minimal Interval Orders

Erhlich introduced the concept of generating combinatorial structures in constant time per generated item. Such algorithms are called loopless and have been described for many objects. Myers introduced the idea of a basic minimal interval order. This paper presents a loopless algorithm for generating basic minimal interval orders.     

Minimal Fine Limits for a Class of Potentials

We consider potentials G _k associated with the Weinstein equation with parameter k in , _j=1 ⁿ (² u/ x ² _j ) + (k/x _n ) ( u/ x _n ) = 0, on the upper half space in ⁿ . We show that if the representing measure satisfies the growth condition y _n /(1+|y|) ^n-k < , where max(k, 2 – n) < 1, then G _k has a minimal fine limit of 0 at every boundary point except for a subset of vanishing (n – 2 + ) dimensional Hausdorff measure. We also prove this exceptional set is best possible.     

The Congruence Lattice of Bruck–Reilly Extensions

We study the lattice. C(S) of congruences of a monoid S which is the Bruck-Reilly extension of a monoid T by a homomorphism . The inclusion, meet and join of congruences are described in terms of congruences and ideals of T. We show that C(S) can be naturally decomposed into three sublattices, corresponding (roughly speaking) to the three different types of congruences on such semigroups.1991 Mathematics Subject Classification: 20M10