Canonical symbolic dynamics for one-dimensional generalized solenoids

We define canonical subshift of finite type covers for Williams' one-dimensional generalized solenoids, and use resulting invariants to distinguish some closely related solenoids.

     

Homology and AH conjecture for groupoids on one-dimensional solenoids

We show that Matui’s AH conjecture holds for groupoids of the Bratteli–Vershik systems embedded in the unstable equivalence relation on one-dimensional solenoids.     

Nowhere-zero 3-flows in Cayley graphs on generalized dihedral group and generalized quaternion group

Tutte conjectured that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we show that this conjecture is true for Cayley graph on generalized dihedral groups and generalized quaternion groups, which generalizes the result of F. Yang and X. Li [Inform. Process. Lett., 2011, 111: 416–419]. We also generalizes an early result of M. Nánásiová and M. ?koviera [J. Algebraic Combin., 2009, 30: 103–110].     

Generalized cover facet inequalities for the generalized assignment problem

The generalized assignment problem is that of finding an optimal assignment of agents to tasks, where each agent may be assigned multiple tasks and each task is performed exactly once. This is an NP-complete problem. Algorithms that employ information about the polyhedral structure of the associated polytope are typically more effective for large instances than those that ignore the structure. A class of generalized cover facet-defining inequalities for the generalized assignment problem is derived. These inequalities are based upon multiple knapsack constraints and are derived from generalized cover inequalities.     

Generalized Cardinal Properties of Lattices and Lattice Ordered Groups

We denote by K the class of all cardinals; put K = K {}. Let be a class of algebraic systems. A generalized cardinal property f on is defined to be a rule which assings to each A an element fA of K such that, whenever A₁, A₂ and A₁ A₂, then fA ₁ = fA ₂. In this paper we are interested mainly in the cases when (i) is the class of all bounded lattices B having more than one element, or (ii) is a class of lattice ordered groups.     

Projective characters of the infinite generalized symmetric group

We consider the infinite generalized symmetric group S(∞)?? _m ^∞ , introduce its covering $\tilde B_m $ , and describe all indecomposable characters on the group $\tilde B_m $ .     

Subdirect decompositions and the radical of a generalized Boolean algebra extension of a lattice ordered group

The extension of a lattice ordered group A by a generalized Boolean algebra B will be denoted by A _B . In this paper we apply subdirect decompositions of A _B for dealing with a question proposed by Conrad and Darnel. Further, in the case when A is linearly ordered we investigate (i) the completely subdirect decompositions of A _B and those of B, and (ii) the values of elements of A _B and the radical R(A _B ).     

On Some Interpolation Rules for Lattice Ordered Groups

Let be an infinite cardinal. In this paper we define an interpolation rule IR() for lattice ordered groups. We denote by C() the class of all lattice ordered groups satisfying IR(), and prove that C() is a radical class.     

On quotients of generalized Euclidean group rings

Let R = ?[C] be the integral group ring of a finite cyclic group C. Dennis et al. [4 Dennis, K., Magurn, B., Vaserstein, L. (1984). Generalized Euclidean group rings. J. Reine Angew. Math. 351:113–128.[Web of Science ®] , [Google Scholar]] proved that R is a generalized Euclidean ring in the sense of Cohn [3 Cohn, P. M. (1966). On the structure of the GL₂ of a ring. Inst. Hautes Études Sci. Publ. Math. 30:5–53.[Crossref] , [Google Scholar]], i.e., SL_n(R) is generated by the elementary matrices for all n. We prove that every proper quotient of R is also a generalized Euclidean ring.     

An Algorithm for the Generalized Assignment Problem with Special Ordered Sets

The generalized assignment problem (GAP), the 0–1 integer programming (IP) problem of assigning a set of n items to a set of m knapsacks, where each item must be assigned to exactly one knapsack and there are constraints on the availability of resources for item assignment, has been further generalized recently to include cases where items may be shared by a pair of adjacent knapsacks. This problem is termed the generalized assignment problem with special ordered sets of type 2 (GAPS2). For reasonably large values of m and n the NP-hard combinatorial problem GAPS2 becomes intractable for standard IP software, hence there is a need for the development of heuristic algorithms to solve such problems. It will be shown how a heuristic algorithm developed previously for the GAP problem can be modified and extended to solve GAPS2. Encouraging results, in terms of speed and accuracy, have been achieved.     

A hierarchy of generalized invariants for linear partial differential operators

We study invariants of linear partial differential operators in two variables under gauge transformations. Using the Beals-Kartashova factorization, we construct a hierarchy of generalized invariants for operators of an arbitrary order. We study the properties of these invariants and give some examples. We also show that the classic Laplace invariants correspond to some particular cases of generalized invariants. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 3, pp. 470–478, June, 2006.     

On generalized m-S-permutable subgroups of a finite group

In this paper, we give some new conditions under which a normal subgroup E of a finite group G is hypercyclically embedded in G, that is, every chief factor of G below E is cyclic.     

序线性空间中向量极值问题的最优性条件

本文在序线性空间中建立了广义次似凸映射下的择一定理,运用此定理,得出一类向量极值问题的最优性条件.     

Derivation algebra and automorphism group of generalized topological N = 2 superconformal algebra

We determine the derivation algebra and the automorphism group of the generalized topological N = 2 superconformal algebra.     

Banaschewski’s theorem for generalized <Emphasis Type="Italic">MV</Emphasis>-algebras

A generalized MV-algebra A is called representable if it is a subdirect product of linearly ordered generalized MV-algebras. Let S be the system of all congruence relations ϱ on A such that the quotient algebra A/ϱ is representable. In the present paper we prove that the system S has a least element. This work was supported by Science and Technology Assistance Agency under Contract No AVPT-51-032002. The work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information (grant I/2/2005).     

双重广义线性模型的经验似然推断

基于截面经验似然方法,将双重广义线性模型的拟似然估计方程作为截面经验似然比函数的约束条件,构造了均值模型和散度模型未知参数的置信区间.最后通过数据模拟,将该方法与正态逼近方法比较,说明了该方法是有效和可行的.     

Double centralizing theorem for wreath products of the alternating group

The double centralizing theorem between the action of the symmetric group S_n and the action of the general linear group on the tensor space T_n(W) was obtained by Schur. Here we obtain a double centralizing theorem when S_n is replaced by the wreath product of a finite group G and the alternating group A_n.     

Quantum double constructions for compact quantum group

For a non-degenerate pair of compact quantum groups, we first construct the quantum double as an algebraic compact quantum group in an algebraic framework. Then by adopting some completion procedure, we give the universal and reduced quantum double constructions in the correspondence C＊-algebraic settings, which generalize Drinfeld＇s quantum double construction and yield new C＊-algebraic compact quantum groups.     

Direct summands and retract mappings of generalized <Emphasis Type="Italic">MV</Emphasis>-algebras

In the present paper we deal with generalized MV-algebras (GMV-algebras, in short) in the sense of Galatos and Tsinakis. According to a result of the mentioned authors, GMV-algebras can be obtained by a truncation construction from lattice ordered groups. We investigate direct summands and retract mappings of GMV-algebras. The relations between GMV-algebras and lattice ordered groups are essential for this investigation. Supported by VEGA Agency grant 1/2002/05. 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.