Łukasiewicz Tribes are Absolutely Sequentially Closed Bold Algebras

We show that each sequentially continuous (with respect to the pointwise convergence) normed measure on a bold algebra of fuzzy sets (Archimedean MV-algebra) can be uniquely extended to a sequentially continuous measure on the generated ukasiewicz tribe and, in a natural way, the extension is maximal. We prove that for normed measures on ukasiewicz tribes monotone (sequential) continuity implies sequential continuity, hence the assumption of sequential continuity is not restrictive. This yields a characterization of the ukasiewicz tribes as bold algebras absolutely sequentially closed with respect to the extension of probabilities. The result generalizes the relationship between fields of sets and the generated -fields discovered by J. Novák. We introduce the category of bold algebras and sequentially continuous homomorphisms and prove that ukasiewicz tribes form an epireflective subcategory. The restriction to fields of sets yields the epireflective subcategory of -fields of sets.     

Implementation and Test of Auction Methods for Solving Generalized Network Flow Problems with Separable Convex Cost

We describe the implementation and testing of two methods, based on the auction approach, for solving the problem of minimizing a separable convex cost subject to generalized network flow conservation constraints. The first method is the -relaxation method of Ref. 1; the second is an extension of the auction sequential/shortest path algorithm for ordinary network flow to generalized network flow. We report test results on a large set of randomly generated problems with varying topology, arc gains, and cost function. Comparison with the commercial code CPLEX on linear/quadratic cost problems and with the public-domain code PPRN on nonlinear cost ordinary network problems are also made. The test results show that the auction sequential/shortest path algorithm is generally fastest for solving quadratic cost problems and mixed linear/nonlinear cost problems with arc gain range near 1. The -relaxation method is generally fastest for solving nonlinear cost ordinary network problems and mixed linear/nonlinear cost problems with arc gain range away from 1. CPLEX is generally fastest for solving linear cost and mixed linear/quadratic cost problems with arc gain range near 1.     

Rings of maps: sequential convergence and completion

The ring B(R) of all real-valued measurable functions, carrying the pointwise convergence, is a sequential ring completion of the subring C(R) of all continuous functions and, similarly, the ring of all Borel measurable subsets of R is a sequential ring completion of the subring of all finite unions of half-open intervals; the two completions are not categorical. We study -rings of maps and develop a completion theory covering the two examples. In particular, the -fields of sets form an epireflective subcategory of the category of fields of sets and, for each field of sets , the generated -field yields its epireflection. Via zero-rings the theory can be applied to completions of special commutative -groups.     

Asymptotic Expansions for the Congestion Period for the M/M/∞ Queue

We consider the M/M/ queue with arrival rate , service rate and traffic intensity =/. We analyze the first passage distribution of the time the number of customers N(t) reaches the level c, starting from N(0)=m>c. If m=c+1 we refer to this time period as the congestion period above the level c. We give detailed asymptotic expansions for the distribution of this first passage time for , various ranges of m and c, and several different time scales. Numerical studies back up the asymptotic results.     

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.     

CR-Admissible $$\mathbb{{Z}}_{2}$$-gradations and CR-symmetries

Complementing the results of (Lotta and Nacinovich, Adv. Math. 191(1): 114–146, 2005), we show that the minimal orbit M of a real form G of a semisimple complex Lie group in a flag manifold is CR-symmetric (see (Kaup and Zaitsev Adv. Math. 149(2):145–181, 2000)) if and only if the corresponding CR algebra admits a gradation compatible with the CR structure.      

Tanaka Formulae for (α, d, β)-Superprocesses

We establish Tanaka like formulae for the local time of (, d, )-superprocess in the dimensions where the local time exists. The result generalizes the result of Adler, Lewin who proved existence of Tanaka formulae for a class of super-processes with finite variance. The fact that we abandon the finite variance assumption, requires using an L ¹⁺ convergence argument (with 0<<1) rather than L ² convergence, for the derivation of the Tanaka formulae.     

Some Asymptotic Results for the M/M/∞ Queue with Ranked Servers

We consider an M/M/ model with m primary servers and infinitely many secondary ones. An arriving customer takes a primary server, if one is available. We derive integral representations for the joint steady state distribution of the number of occupied primary and secondary servers. Letting =/ be the ratio of arrival and service rates (all servers work at rate ), we study the joint distribution asymptotically for . We consider both m=O(1) and m scaled to be of the same order as . We also give results for the marginal distribution of the number of secondary servers that are occupied.     

Some remarks on the product of two C α-compact subsets

For a cardinal , we say that a subset B of a space X is C -compact in X if for every continuous function is a compact subset of . If B is a C-compact subset of a space X, then (B, X) denotes the degree of C -compactness of B in X. A space X is called -pseudocompact if X is C -compact into itself. For each cardinal , we give an example of an -pseudocompact space X such that X × X is not pseudocompact: this answers a question posed by T. Retta in Some cardinal generalizations of pseudocompactness Czechoslovak Math. J. 43 (1993), 385–390. The boundedness of the product of two bounded subsets is studied in some particular cases. A version of the classical Glicksberg's Theorem on the pseudocompactness of the product of two spaces is given in the context of boundedness. This theorem is applied to several particular cases.     

A Conjecture of Hirschhorn on the 4-Dissection of Ramanujan's Continued Fraction

We show that two recently published conjectures by Hirschhorn concerning the 4-dissection of Ramanujan's continued fraction are correct.     

A Product Formula for Jackson Integral Associated with the Root System F 4

A multiple summation formula for the root system F ₄ originated from Bailey's very-well-poised ₆₆ summation theorem is studied. The multiple sum in this paper is included in a classification list (M. Ito, Compositio Math., 129 (2001), 325–340) of Jackson integral associated with irreducible reduced root system which contains sums investigated by Gustafson, Macdonald, Aomoto, and the author.     

Application of the Superposition of Renewal Processes to the Study of Batch Arrival Queues

The G /G/1-type batch arrival system is considered. We deal with non-steady-state characteristics of the system like the first busy period and the first idle time, the number of customers served on the first busy period. The study is based on a generalization of Korolyuk's method which he developed for semi-Markov random walks.     

Bayesian inference in Markovian queues

This paper is concerned with the Bayesian analysis of general queues with Poisson input and exponential service times. Joint posterior distribution of the arrival rate and the individual service rate is obtained from a sample consisting inn observations of the interarrival process andm complete service times. Posterior distribution of traffic intensity inM/M/c is also obtained and the statistical analysis of the ergodic condition from a decision point of view is discussed.     

A reader-writer queue with reader preference

This paper considers a reader-writer queue with reader preference. The system can process an unlimited number of readers simultaneously. However, writers have to be processed one at a time. Readers are given non-preemptive priority over writers. Both readers and writers arrive according to Poisson processes (PP) and have general independent service times. There is infinite waiting room for both. This system is analyzed to produce stability conditions. The analysis uses anM/G/ queue busy period to model readers, followed by a modifiedM/G/1 queue to model the entire system. Finally, results are presented for the expected wait-in-queue times for the readers and writers. The paper ends with an example.This work was done while the author was visiting the IBM Corporation, Networking Systems, RTP, NC 27709, USA.     

Representable K-Theory for σ-C*-algebras

We define a version of K-theory on the category of -C ^*-algebras (countable inverse limits of C ^*-algebras). Our theory is homotopy invariant, has long exact sequences and a Milnor sequence, and satisfies Bott periodicity. On C ^*-algebras it gives the ordinary K-theory, and on the space of continuous functions on a countable direct limit X of compact Hausdorff spaces, it gives the representable K-theory of X. (We do not claim that our theory is in general a representable functor.) We also define an equivariant version, and discuss several related groups.Partially supported by a National Science Foundation Postdoctoral Fellowship.     

Stability and queueing time analysis of a reader-writer queue with alternating exhaustive priorities

This paper considers a reader-writer queue with alternating exhaustive priorities. The system can process an unlimited number of readers simultaneously. However, writers have to be processed one at a time. Both readers and writers arrive according to Poisson processes. Writer and reader service times are general iid random variables. There is infinite waiting room for both. The alternating exhaustive priority policy operates as follows. Assume the system is initially idle. The first arriving customer initiates service for the class (readers or writers) to which it belongs. Once processing begins for a given class of customers, this class is served exhaustively, i.e. until no members of that class are left in the system. At this point, if customers of the other class are in the queue, priority switches to this class, and it is served exhaustively. This system is analyzed to produce a stability condition and Laplace-Stieltjes transforms (LSTs) for the steady state queueing times of readers and writers. An example is also given.     

A Simple Proof of the Borel Extension Theorem and Weak Compactness of Operators

Let T be a locally compact Hausdorff space and let C ₀(T) be the Banach space of all complex valued continuous functions vanishing at infinity in T, provided with the supremum norm. Let X be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of X-valued -additive Baire measures on T is given, which is more natural and direct than the existing ones. Using this result the integral representation and weak compactness of a continuous linear map u: C ₀(T) X when c ₀ X are obtained. The proof of the latter result is independent of the use of powerful results such as Theorem 6 of [6] or Theorem 3 (vii) of [13].     

L ∞ Algebra Representations

It is shown that the direct sum of an L algebra and a module over it has a natural L algebra structure.     

On Decomposing an Abelian p-Group Under a p′-Operator Group

Let A be a p-group acting on a finite Abelian p-group P. We give a necessary and sufficient condition on an A-irreducible decomposition of ₁(P) = _i1U_i for the existence of an A-indecomposable decomposition of P = _i1R_i such that ₁(R_i) = U_i for all i I. This readily implies a main result of [1].2000 Mathematics Subject Classification: 20D15     

Symmetry Classification for Jackson Integrals Associated with the Root System BC n

The Jackson integrals associated with the non-reduced root system are defined as multiple sums which are generalization of the Bailey's very-well-poised ₆₆ sum. They are classified by the number of their parameters when they can be expressed as a product of the Jacobi elliptic theta functions. The sums which appear in the classification list coincide with those investigated individually by Gustafson and van Diejen.