Groups with π-Minimal and π-Layer Minimal Conditions. II

For an arbitrary set of prime numbers we study the properties and structure of groups satisfying the -minimal and -layer minimal conditions. In particular, we describe the structure of the almost RN-groups (and thereby that of the locally solvable groups) with these conditions. Under the assumption 2, we describe the structure of locally graded groups (and thereby that of locally finite groups) with these conditions.     

On π-Subpairs of π-Blocks

Alperin and Broug have given the p-subpairs in a finite group, and proved that there is a Sylow theorem for p-subpairs. For a π-separable group with π-Hall subgroup nilpotent, we prove that there is a π-Sylow theorem for π-subpairs. Note that our π-subpairs are different from what Robinson and Staszewski gave.     

Almost π-Lattices

In this paper we establish some conditions for an almost -domain to be a -domain. Next -lattices satisfying the union condition on primes are characterized. Using these results, some new characterizations are given for -rings.     

Weak π-rings

In this paper we establish some characterizations for weak π-rings.     

Generalized Skyrme model for π- and π′-mesons

On the basis of a generalization of the Skyrme model for pseudoscalar -mesons and their radial excitations (-mesons), soliton (skyrmion) solutions are studied. It is shown that taking -mesons into account allows one to solve the problem of the soliton stability. The skyrmion energy, angular moment, and axial coupling constant are computed in this configuration.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 189, pp. 10–14, 1991.The authors would like to thank A. A. Andrianov for discussions and for his constant interest in this work, and V. N. Popov and P. P. Kulish for the possibility of its publishing in these proceedings.     

Morita Contexts, π-Galois Extensions for Hopf π-Coalgebras

Let G = NwrC _n be the wreath product of N by C _n , where N is a finite nilpotent group and C _n is a cyclic group of order n. Then the normalizer property holds for G.     

On π-Solvable and Locally π-Solvable Groups with Factorization

We prove that, in a locally -solvable group G = AB with locally normal subgroups A and B, there exist pairwise-permutable Sylow - and p-subgroups A , A _p and B , B _p , p , of the subgroups A and B, respectively, such that A B is a Sylow -subgroup of the group G and, for an arbitrary nonempty set ,

Hopf π-子模

设H为有限型Hopfπ-代数,研究Hopfπ-代数H上的Hopfπ-模与Hopf π-余代数H *上的Hopfπ-余模之间的对偶关系,得出了Hopfπ-子模与Hopfπ-子 余模之间的充分必要条件,推广了Hopf代数中的相关结论.     

Finite π-Quasisurpersolvable Groups

Ｆｉｎｉｔｅπ－ＱｕａｓｉｓｕｒｐｅｒｓｏｌｖａｂｌｅＧｒｏｕｐｓＹｕＹｕｅｈｕａ（于越华）（ＩｎｓｔｉｔｕｔｅｏｆＩｎｆｏｒｍａｔｉｏｎａｌＥｎｇｉｎｅｅｒｉｎｇ，Ｚｈｅｎｇｚｈｏｕ４５０００２）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｗｅｈａｖｅ...     

On π-Semicommutative Rings

A ring R is said to be π-semicommutative if a, b ∈ R satisfy ab = 0 then there exists a positive integer n such that anRbn= 0. We study the properties of π-semicommutative rings and the relationship between such rings and other related rings. In particular, we answer a question on left GWZI rings negatively.     

Nonlinear Extrapolation Estimates of π

The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in R² and it is well-known that by using linear combinations of these basic estimates,modern extrapolation techniques can greatly speed up the approximation process.Similarly,when n vertices are randomly selected on the circle,the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge t...     

A model for π-selfadjoint operators in π1 and a special linear pencil

The eigenvalue of nonpositive type of a -selfadjoint operator A in a Pontrjagin space of index one is characterized in a model of A. Similar questions are studied for an eigen-value problem G-T in a Hilbert space with a selfadjoint operator T and a special operator G.     

The logic of π1-conservativity

We show that the modal prepositional logicILM (interpretability logic with Montagna's principle), which has been shown sound and complete as the interpretability logic of Peano arithmetic PA (by Berarducci and Savrukov), is sound and complete as the logic of ₁-conservativity over eachbE ₁-sound axiomatized theory containingI ₁ (PA with induction restricted tobE ₁-formulas). Furthermore, we extend this result to a systemILMR obtained fromILM by adding witness comparisons in the style of Guaspari's and Solovay's logicR (this will be done in a separate continuation of the present paper).     

On π-regularity of General Rings

A general ring means an associative ring with or without identity.An idempotent e in a general ring I is called left （right） semicentral if for every x ∈ I,xe=exe （ex=exe）.And I is called semiabelian if every idempotent in I is left or right semicentral.It is proved that a semiabelian general ring I is π-regular if and only if the set N （I） of nilpotent elements in I is an ideal of I and I /N （I） is regular.It follows that if I is a semiabelian general ring and K is an ideal of I,then I is π-regular if and only if both K and I /K are π-regular.Based on this we prove that every semiabelian GVNL-ring is an SGVNL-ring.These generalize several known results on the relevant subject.Furthermore we give a characterization of a semiabelian GVNL-ring.     

Quasi-Normal Spaces and πg-Closed Sets

We introduce the notion of g-closed sets and use it to obtain a characterization and preservation theorems of quasi-normal spaces.     

A Note on π-Engel Conditions

In this paper we show that the weakly -Engel conditions are closely related to the existance of normal -complements; while the -Engel conditions are closely related to the -nilpotent groups.AMS Subject Classification (2000): 20D20     

Hybrid Dynamics of Stochastic π-Calculus

In this paper we describe a method to map stochastic π-calculus processes in chemical ground form into hybrid automata. Hybrid automata are tools widely employed to model systems characterized by both discrete and continuous evolution and their use in the context of Systems Biology allows us to address rather fundamental issues. Specifically, the key ingredient we use in this work is the possibility granted by hybrid automata to implement a separation of control and molecular terms in biochemical systems. The computational counterpart of our analysis turns out to be related to the determination of conservation properties of the system.      

Yetter-Drinfeld π-modules over weak T-coalgebras

InthispaperweintroducethenotionofaweakYetter-Drinfeldgroupmodule over a weak T-coalgebra and give some basic properties. Moreover we also prove that the category of weak Yetter-Drinfeld group modules is isomorphic to the center of the representation category of a weak T-coalgebra H denoted by Z(Rep(H)).