Distributions of class Lα

L_α (0 α 1) is a class of infinitely divisible distributions defined by restricting the measure in the Levy-Khinchin formula to a special form. When α = 1, L_α is just the classical class L. Several properties for L_α classes, which are similar to the most important properties for the class L, are established. Also, a conjecture of Wolfe about unimodality of some L_α distributions is disproved by giving a counterexample.     

On finite groups whose every proper normal subgroup is a union of a given number of conjugacy classes

Let G be a finite group andA be a normal subgroup ofG. We denote by ncc(A) the number ofG-conjugacy classes ofA andA is calledn-decomposable, if ncc(A)= n. SetK _G = {ncc(A)|A ⊲ G}. LetX be a non-empty subset of positive integers. A groupG is calledX-decomposable, ifK _G =X. Ashrafi and his co-authors [1-5] have characterized theX-decomposable non-perfect finite groups forX = {1, n} andn ≤ 10. In this paper, we continue this problem and investigate the structure ofX-decomposable non-perfect finite groups, forX = {1, 2, 3}. We prove that such a group is isomorphic to Z₆, D₈, Q₈, S₄, SmallGroup(20, 3), SmallGroup(24, 3), where SmallGroup(m, n) denotes the mth group of ordern in the small group library of GAP [11].     

Conditions Implying Self-adjointness of Operators

In this paper, we show that if is a quasi-class A operator and S is an arbitrary operator for which and ST = T*S, then T is self-adjoint, and we also show that quasisimilar quasi-class A operators have equal spectra and essential spectra. This work of the second author was supported by the University of Incheon Research Grant in 2008.     

Fuzzy subgroups of nilpotent groups

In 1991, Asaad has suggested the following question: What can be said about the structure of a group G when information is known about the structure of a fuzzy subgroup A of G and vice-versa? This question has been partially investigated in Fuzzy Sets and Systems39 (1991) 323–328. The purpose of this paper is to continue more investigations for the above mentioned question.     

Commuting involutions with fixed point set of constant codimension

Special generators of the unoriented cobordism ringMO _* are constructed to determine the groupsJ _n,κ ^r ofn-dimensional cobordism classes inMO _n containing a representativeM ⁿ admitting a (Z ₂) ^k -action with fixed point set of constant codimension. This work is supported by HNSF     

On Some Extremal Properties of Lagrange Interpolatory Polynomials

In this paper, we will show that Lagrange interpolatory polynomials are optimal for solving some approximation theory problems concerning the finding of linear widths.In particular, we will show that

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, where _n is a set of the linear operators with finite rank n+1 defined on −1,1], and where _n+1 denotes the set of polynomials p=∑_i=0ⁿ⁺¹a_ixⁱ of degreen+1 such that a_n+11. The infimum is achieved for Lagrange interpolatory polynomial for nodes .     

The Selmer Groups of Elliptic Curves

Let E/K be an elliptic curve with K-rational p-torsion points.The p-Selmer group of E is described by the image of a map λk and hence an upper bound of its order is given in terms of the class numbers of the S-ideal class group of K and the p-division field of E.     

On automorphisms of A-groups

Let G be an A-group (i.e. a group in which xx ^α  = x ^α x for all and let denote the subgroup of Aut(G) consisting of all automorphisms that leave invariant the centralizer of each element of G. The quotient is an elementary abelian 2-group and natural analogies exist to suggest that it might always be trivial. It is shown that, in fact, for any odd prime p and any positive integer r, there exist infinitely many finite pA-groups G for which has rank r. Received: 23 March 2008, Revised: 20 May 2008     

Nondurable K-Theory Equivalence and Bousfield Localization*

In this paper we consider what happens when Adams self maps are modified by adding certain unstable maps. The unstable maps which are added are trivial after a single suspension. We can choose the modification so that the maps are still K-theory equivalences but the loops on the map are no longer K-theory equivalences. As a corollary we note that the maps are K-theory equivalences but not v ₁-periodic equivalences. Another consequence is the behavior of the cobar spectral sequences for generalized homology theories. Tamaki shows that in certain cases a cobar-type spectral sequence for generalized homology theories is well behaved. The maps we construct give an example where despite the connectivity of the spaces the cobar spectral sequence is still poorly behaved. Finally we use our maps to construct spaces whose Bousfield class is distinct from the cofiber of the Adams map but which becomes the same after one suspension.     

Commuting Involutions with Fixed Point Set of Variable Codimension

Special generators of the unoriented cobordism ring MO _* are constructed to determine some groups of cobordism classes in MO _n containing a representative M ⁿ admitting a (Z ₂) ^k -action with the fixed point set of (n−l _i )-dimensional submanifolds of M ⁿ . This work is supported by HNSF and BSHJJ     

Exact Convergence Rate for the Distributions of GI/M/c/K Queue as K Tends to Infinity

We obtain the exact convergence rate of the stationary distribution ^(K) of the embedded Markov chain in GI/M/c/K queue to the stationary distribution of the embedded Markov chain in GI/M/c queue as K. Similar result for the time-stationary distributions of queue size is also included. These generalize Choi and Kim's results of the case c=1 by nontrivial ways. Our results also strengthen the Simonot's results [5].     

Normal <Emphasis Type="Italic">π</Emphasis>-complements for finite groups

Let G be a finite group. For a finite p-group P the subgroup generated by all elements of order p is denoted by Ω₁(p). Zhang [5] proved that if P is a Sylow p-subgroup of G, Ω₁(P) ≦ Z(P) and N _G (Z(P)) has a normal p-complement, then G has a normal p-complement. The object of this paper is to generalize this result. This paper was partly supported by Hungarian National Foundation for Scientific Research Grant # T049841 and T038059.     

<Emphasis Type="Italic">K</Emphasis>-Radical classes and product radical classes of <Emphasis Type="Italic">MV</Emphasis>-algebras

For an MV-algebra let J ₀( ) be the system of all closed ideals of ; this system is partially ordered by the set-theoretical inclusion. A radical class X of MV-algebras will be called a K-radical class iff, whenever ∈ X and is an MV-algebra with J ₀( ) ≅ J ₀( ), then ∈ X. An analogous notation for lattice ordered groups was introduced and studied by Conrad. In the present paper we show that there is a one-to-one correspondence between K-radical classes of MV-algebras and K-radical classes of abelian lattice ordered groups. We also prove an analogous result for product radical classes of MV-algebras; product radical classes of lattice ordered groups were studied by Ton. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information, Grant I/2/2005.     

δ- and θ-modifications of generalized topologies

It is shown that the theory of δ-and θ-modifications of topological spaces (see [3]) can be generalized for the case when the topology is replaced by a generalized topology in the sense of [1]. Research supported by Hungarian Foundation for Scientific Research, grant No. T 49786.     

Analysis of customers’ impatience in queues with server vacations

Many models for customers impatience in queueing systems have been studied in the past; the source of impatience has always been taken to be either a long wait already experienced at a queue, or a long wait anticipated by a customer upon arrival. In this paper we consider systems with servers vacations where customers’ impatience is due to an absentee of servers upon arrival. Such a model, representing frequent behavior by waiting customers in service systems, has never been treated before in the literature. We present a comprehensive analysis of the single-server, M/M/1 and M/G/1 queues, as well as of the multi-server M/M/c queue, for both the multiple and the single-vacation cases, and obtain various closed-form results. In particular, we show that the proportion of customer abandonments under the single-vacation regime is smaller than that under the multiple-vacation discipline. This work was supported by the Euro-Ngi network of excellence.     

Varieties and Torsion Classes of m-Groups

We prove that every variety of m-groups is a torsion class; find basis of identities for a product variety of m-groups; and show that the product of every finitely based variety of m-groups and a variety of Abelian m-groups is a finitely based variety.     

Radical classes and weak radical mappings of GMV-algebras

We use the concept of generalized MV-algebra (GMV-algebra, in short) in the sense of Galatos and Tsinakis; the main tool in their investigation was a truncation construction. The relations between radical classes of GMV-algebras and radical classes of lattice ordered groups are investigated in the present paper. Further, we apply the truncation construction for dealing with weak retract mappings of GMV-algebras. This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence — Physics of Information (Grant I/2/2005).     

Modular Lattice for C 0-Operators

We prove modularity of the lattice Lat (T) of closed invariant subspaces for a C ₀-operator T with property (P). To my parents     

Some greedyt-intersecting families of finite sequences

Letn, s ₁,s ₂, ... ands _n be positive integers. Assume is an integer for eachi}. For , , and , denotes _p (a)={j|1jn,a _j p}, , and . is called anI _t ^p -intersecting family if, for any a,b ,a _i b _i =min(a _i ,b _i )p for at leastt i's. is called a greedyI _t ^P -intersecting family if is anI _t ^p -intersecting family andW _p (A)W _p (B+A ^c ) for anyAS _p ( ) and any with |B|=t–1.In this paper, we obtain a sharp upper bound of | | for greedyI _t ^p -intersecting families in for the case 2ps _i (1in) ands ₁>s ₂>...>s _n .This project is partially supported by the National Natural Science Foundation of China (No.19401008) and by Postdoctoral Science Foundation of China.     

Congruences for the class numbers of real cyclic sextic number fields

LetK ₆ be a real cyclic sextic number field, andK ₂,K ₃ its quadratic and cubic subfield. Leth(L) denote the ideal class number of fieldL. Seven congruences forh ^- =h (K ₆)/(h(K ₂)h(K ₃)) are obtained. In particular, when the conductorf ₆ ofK ₆ is a primep, , whereC is an explicitly given constant, andB _n is the Bernoulli number. These results on real cyclic sextic fields are an extension of the results on quadratic and cyclic quartic fields. Project supported by the National Natural Science Foundation of China (Grant No. 19771052).