Hulls for Various Kinds of α-Completeness in Archimedean Lattice-Ordered Groups

Within Archimedean -groups, and with an infinite cardinal or , we consider X-hulls where X stands for any of the following classes of -groups: -projectable; laterally -complete; boundedly laterally -complete; conditionally -complete; combinations of the preceding, together with divisibility and/or relative uniform completeness. All these hulls exist, and may be obtained by iterated adjunction of the required extra elements, within the essential hull. When the -groups is relatively -complemented one step in the iteration suffices for several crucial properties. We derive from the above a considerable number of equations involving combinations of these hull operators.     

Splittings of Mapping Tori of Free Group Automorphisms

We present necessary and sufficient conditions for the existence of a splitting over of the mapping torus of a free group automorphism .     

On Generalizations of Ostrowski Inequality and Some Related Results

Some generalizations of the Ostrowski inequality, the Milovanovi-Peari-Fink inequality, the Dragomir-Agarwal inequality and the Hadamard inequality are given.     

Some Properties of Isologism of Groups and Baer-Invariants

Let be a variety of groups defined by the set of laws V. In this paper we study the concept of -isologism of groups in terms of -extensions and their connections with the Baer-invariant of groups are also discussed.AMS Subject Classification (2000): primary 20F14, 20F19, secondary 20E10     

(φ,ξ,η,λ)‐Structures of Parabolic Type

We consider (,,,)structures of parabolic type on hypersurfaces of dual spaces and study the rank of the affinor . We consider almost contact metric structures of parabolic type of the first kind on hypersurfaces of 4dimensional dual metric space. We study the properties of these structures and give examples of normal, integrable, and Sasakian parabolic structures.     

On θ-Principal Extension and H-Closedness

A type of extensions called the -extention of topological spaces and their -equivalence and -trace systems are introduced, which ultimately characterize H-closed -extensions of a Hausdorff topological space. Also, the notion of -principal extensions is defined. A typical -principal extension consisting of certain grills on a Hausdorff space is constructed, and finally, some characterizations of H-closedness of a Hausdorff space are obtained.AMS Subject Classification (2000) 54D30 54D99     

Topological existence and stability for stackelberg problems

The aim of this paper is to study, in a topological framework, existence and stability for the solutions to a parametrized Stackelberg problem. To this end, approximate solutions are used, more precisely, -solutions and strict -solutions. The results given are of minimal character and the standard types of constraints are considered, that is, constant constraints, constraints defined by a finite number of inequalities, and more generally constraints defined by an arbitrary multifunction.     

Σ-Subsets of Natural Numbers

It is shown that the class of all possible families of -subsets of finite ordinals in admissible sets coincides with a class of all non-empty families closed under e-reducibility and . The construction presented has the property of being minimal under effective definability. Also, we describe the smallest (w.r.t. inclusion) classes of families of subsets of natural numbers, computable in hereditarily finite superstructures. A new series of examples is constructed in which admissible sets lack in universal -function. Furthermore, we show that some principles of classical computability theory (such as the existence of an infinite non-trivial enumerable subset, existence of an infinite computable subset, reduction principle, uniformization principle) are always satisfied for the classes of all -subsets of finite ordinals in admissible sets.     

On the Algebraic Structure of Quasi-cyclic Codes II: Chain Rings

The ring decomposition technique of part I is extended to the case when the factors in the direct product decomposition are no longer fields but arbitrary chain rings. This includes not only the case of quasi-cyclic codes over rings but also the case of quasi-cyclic codes over fields whose co-index is no longer prime to the characteristic of the field. A new quaternary construction of the Leech lattice is derived.     

The lower algebraicK-theory of virtually infinite cyclic groups

This paper gives a proof of a conjecture of W.-C. Hsiang for the negativeK-theory of integral grouprings , when the group is a subgroup of a uniform lattice in a Lie group. The authors' earlier paper reduced this result to the very special cases where either is finite or is virtually infinite cyclic. The finite case was done much earlier by Carter extending results of Bass and Murthy. The major work of the present paper consists of proving the conjecture when is virtually infinite cyclic.Both authors were supported in part by the National Science Foundation.     

Finiteness Result for the Simplicial Branch-and-Bound Algorithm Based on ω-Subdivisions

The question of the finiteness of simplicial branch-and-bound algorithms employing only -subdivisions is considered. In Ref. 1, it was shown that this algorithm is convergent; here, it is proved that the algorithm is also finite if two assumptions are fulfilled. The first assumption requires the function values at vertices of the initial simplex to be lower than the optimal value of the problem. The second assumption requires each vertex of the initial simplex to violate at most one of the constraints defining the feasible polytope. The first assumption is mild from a theoretical point of view; the second assumption is strong, but holds always for instance when the feasible region is a hypercube.     

The Nonexistence of Some Optimal Ternary Codes of Dimension Five

We prove the nonexistence of codes with parameters [143,5,94]₃ and [147,5,97]₃. This determines the exact value of n₃(5,d) for d=94,95,96,97,98,99. These were the only d's for which the exact value of n₃(5,d) was not known.     

Piecewise Constant Roughly Convex Functions

This paper investigates some kinds of roughly convex functions, namely functions having one of the following properties: -convexity (in the sense of Klötzler and Hartwig), -convexity and midpoint -convexity (in the sense of Hu, Klee, and Larman), -convexity and midpoint -convexity (in the sense of Phu). Some weaker but equivalent conditions for these kinds of roughly convex functions are stated. In particular, piecewise constant functions satisfying f(x) = f([x]) are considered, where [x] denotes the integer part of the real number x. These functions appear in numerical calculation, when an original function g is replaced by f(x):=g([x]) because of discretization. In the present paper, we answer the question of when and in what sense such a function f is roughly convex.     

Explicit Formulas for Green’s Functions on the Annulus and on the Möbius Strip

Given a fixed point free antianalytic involution k of a domain G in thecomplex plane, bounded by a finite number of analytic curves, k-invariant Greensfunctions are defined on G. The Lindelöfs principle is extended to k-invariantGreens functions. When G is the annulus, k-invariant Greens functions areobtained in the explicit form. Since the factorization of the annulus by the group kgenerated by k produces a Möbius strip, the respective result helped us to obtain explicitforms for Greens functions on the Möbius strip.     

Uniform and universal Glivenko-Cantelli classes

A class of measurable functions on a probability space is called a Glivenko-Cantelli class if the empirical measuresP _n converge to the trueP uniformly over almost surely. is a universal Glivenko-Cantelli class if it is a Glivenko-Cantelli Cantelli class for all lawsP on a measurable space, and a uniform Glivenko-Cantelli class if the convergence is also uniform inP. We give general sufficient conditions for the Glivenko-Cantelli and universal Glivenko-Cantelli properties and examples to show that some stronger conditions are not necessary. The uniform Glivenko-Cantelli property is characterized, under measurability assumptions, by an entropy condition.     

Start‐up class models in multiple‐class queues with N‐policy

In this paper, we consider multipleclass queueing systems with Npolicy in which the idle server starts service as soon as the number of customers in the startup class reaches threshold N. We consider the cases of FCFS and nonpreemptive priority. We obtain the Laplace–Stieltjes transform of the waiting times of each class of customers. We also show some results for the general behavior of such systems.     

Inequality of Petrović and Giaccardi for Convex Function of Higher Order

In this paper we use Lidstone polynomials to prove further generalization of Giaccardi generalization of the well-known Petrovis inequality.     

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.     

Study of Noetherian Γ-Semirings via Operator Semirings

In this paper we study Noetherian -semirings and obtain Cohens theorem for a special class of -semirings. Weak primary decomposition theorem for a particular type of -semirings is also obtained.Presently Lecturer in Mathematics, University of Burdwan, GOLAPBAG, W.B. INDIA.     

Connections between Interval and Unit Circle for Sobolev Orthogonal Polynomials. Strong Asymptotics on the Real Line

In this paper we show the connection between Sobolev orthogonal Laurent polynomials on the unit circle and Sobolev orthogonal polynomials on a bounded interval of the real line. As a consequence we deduce the strong outer asymptotics for Sobolev orthogonal polynomials with respect to the inner product