Kernel systems on L-ordered sets

This paper presents fuzzy versions of kernel operators and kernel systems on L-ordered sets and establishes a one-to-one correspondence between them.     

Semigroups Based on L-Valued Logic and Its Ideals

In this paper, we introduce the concepts of semigroups based on complete residuated lattice-valued logic (L-valued logic, for short), and discuss the structures and the properties of subsemigronps and ideals in the theory of L-semigroups.AMS Subject Classification (2000) 20M     

The L-L estimates of solutions to one-dimensional damped wave equations and their application to the compressible flow through porous media

We first obtain the L^p-L^q estimates of solutions to the Cauchy problem for one-dimensional damped wave equation

     

L-fuzzy Q-convergence structures

In this paper, we construct a topological category of pretopological L-fuzzy Q-convergence spaces, which contains the category of topological L-fuzzy Q-convergence spaces as a bireflective full subcategory. Considering the connections with L-fuzzy topology, it is proved that the category of topological L-fuzzy Q-convergence spaces is isomorphic to the category of topological L-fuzzy quasi-coincident neighborhood spaces, and the latter is isomorphic to the category of L-fuzzy topological spaces. Moreover, we find that our pretopological L-fuzzy Q-convergence spaces can be characterized as a kind of L-fuzzy quasi-coincident neighborhood spaces, which is called strong L-fuzzy quasi-coincident neighborhood space.     

Some fixed point results on L-embedded Banach spaces

In this paper we prove that w-fixed point property and w^★-fixed point property are equivalent concepts for L-embedded Banach spaces which are duals of M-embedded spaces. Similar results will be obtained with respect to the normal structure. These equivalences will be applied to establish new fixed point results for different examples. We will also prove the existence of fixed points for both nonexpansive and asymptotically regular mappings defined on subsets of L-embedded Banach spaces which are sequentially compact for the abstract measure topology. We will check that our results do not hold in the case of the weak topology.     

Approximating Orders in Meet-Continuous Lattices and Regularity Axioms in Many Valued Topology

It is shown that in a meet-continuous lattice L endowed with a multiplicative auxiliary order ≺ the family of all members of L which satisfy the axiom of approximation, i.e. α = {β ∈ L : β ≺ α}, is closed under finite infs and arbitrary sups. This is a key ingredient of a meet-continuous lattice proof that both regularity and complete regularity of many valued topology have subbasic characterizations. As a consequence, the frame law can now be eliminated from some fundamental results on completely regular L-valued topological spaces (e.g., this is the case in regard to the Tychonoff embedding theorem). The grant MTM2006-14925-C02-02 from the Ministry of Education and Science of Spain and FEDER is gratefully acknowledged by the second named author.     

Robustness Comparisons of Some Classes of Location Parameter Estimators

Asymptotic biases and variances of M-, L- and R-estimators of a location parameter are compared under ε-contamination of the known error distribution F ₀ by an unknown (and possibly asymmetric) distribution. For each ε-contamination neighborhood of F ₀, the corresponding M-, L- and R-estimators which are asymptotically efficient at the least informative distribution are compared under asymmetric ε-contamination. Three scale-invariant versions of the M-estimator are studied: (i) one using the interquartile range as a preliminary estimator of scale: (ii) another using the median absolute deviation as a preliminary estimator of scale; and (iii) simultaneous M-estimation of location and scale by Huber's Proposal 2. A question considered for each case is: when are the maximal asymptotic biases and variances under asymmetric ε-contamination attained by unit point mass contamination at ∞? Numerical results for the case of the ε-contaminated normal distribution show that the L-estimators have generally better performance (for small to moderate values of ε) than all three of the scale-invariant M-estimators studied.     

L-topological vector spaces and families of L-fuzzy pseudo-norms

In this paper, the concept of a family of L-fuzzy pseudo-norms on vector spaces is proposed and the characterization of L-vector topologies in terms of a family of L-fuzzy pseudo-norms is presented. As applications of the characterization, the Hausdorff separation property, convergence of molecule nets and boundedness of L-sets in L-topological vector spaces are investigated.     

Coreflective hull of finite strong L-topological spaces

This paper is concerned with the interaction between the logic features of the table of truth values and categorical properties of L-topological spaces and L-co-topological spaces. On one hand, it is shown that for each unital quantale L, the category of Alexandroff strong L-co-topological spaces is the coreflective hull of finite strong L-co-topological spaces. On the other hand, in the case that the quantale L is the unit interval [0,1] equipped with a continuous t-norm, it is shown that the category of Alexandroff strong [0,1]-topological spaces is the coreflective hull of finite strong [0,1]-topological spaces if and only if the continuous t-norm is an ordinal sum of the ?ukasiewicz t-norm whose set of idempotent elements is a well-ordered subset of [0,1] under the usual order.     

Duality of dams via mountain processes

We consider a G/M/1-type dam having finite capacity and a general release rule, and construct a ‘dual’ M/G/1-type dam with state-dependent jump sizes and without dry periods whose content process has the same stationary density (up to some transformation). For the dual dam the stationary distribution can be computed in closed form.     

On some functional relations between Mordell-Tornheim double L-functions and Dirichlet L-functions

In the past decade, many relation formulas for the multiple zeta values, further for the multiple L-values at positive integers have been discovered. Recently Matsumoto suggested that it is important to reveal whether those relations are valid only at integer points, or valid also at other values. Indeed the famous Euler formula for ζ(2k) can be regarded as a part of the functional equation of ζ(s). In this paper, we give certain analytic functional relations between the Mordell-Tornheim double L-functions and the Dirichlet L-functions of conductor 3 and 4. These can be regarded as continuous generalizations of the known discrete relations between the Mordell-Tornheim L-values and the Dirichlet L-values of conductor 3 and 4 at positive integers.     

Nonlinear diffusions, hypercontractivity and the optimal L-Euclidean logarithmic Sobolev inequality

The equation u_t=Δ_p(u^1/(p−1)) for p>1 is a nonlinear generalization of the heat equation which is also homogeneous, of degree 1. For large time asymptotics, its links with the optimal L^p-Euclidean logarithmic Sobolev inequality have recently been investigated. Here we focus on the existence and the uniqueness of the solutions to the Cauchy problem and on the regularization properties (hypercontractivity and ultracontractivity) of the equation using the L^p-Euclidean logarithmic Sobolev inequality. A large deviation result based on a Hamilton-Jacobi equation and also related to the L^p-Euclidean logarithmic Sobolev inequality is then stated.     

Algorithmic approximations for the busy period distribution of the M/M/c retrial queue

In this paper we deal with the main multiserver retrial queue of M/M/c type with exponential repeated attempts. This model is known to be analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused by the retrial feature. For this reason several models have been proposed for approximating its stationary distribution, that lead to satisfactory numerical implementations. This paper extends these studies by developing efficient algorithmic procedures for calculating the busy period distribution of the main approximation models of Wilkinson [Wilkinson, R.I., 1956. Theories for toll traffic engineering in the USA, The Bell System Technical Journal 35, 421–514], Falin [Falin, G.I., 1983. Calculations of probability characteristics of a multiline system with repeated calls, Moscow University Computational Mathematics and Cybernetics 1, 43–49] and Neuts and Rao [Neuts, M.F., Rao, B.M., 1990. Numerical investigation of a multiserver retrial model, Queueing Systems 7, 169–190]. Moreover, we develop stable recursive schemes for the computation of the busy period moments. The corresponding distributions for the total number of customers served during a busy period are also studied. Several numerical results illustrate the efficiency of the methods and reveal interesting facts concerning the behavior of the M/M/c retrial queue.     

Omega theorems related to the general Euler totient function

We prove an omega estimate related to the general Euler totient function associated to a polynomial Euler product satisfying some natural analytic properties. For convenience, we work with a set of L-functions similar to the Selberg class, but in principle our results can be proved in a still more general setup. In a recent paper the authors treated a special case of Dirichlet L-functions with real characters. Greater generality of the present paper invites new technical difficulties. Effectiveness of the main theorem is illustrated by corollaries concerning Euler totient functions associated to the shifted Riemann zeta function, shifted Dirichlet L-functions and shifted L-functions of modular forms. Results are either of the same quality as the best known estimates or are entirely new.     

Self-approximation of Dirichlet L-functions

Let d be a real number, let s be in a fixed compact set of the strip 1/2<σ<1, and let L(s,χ) be the Dirichlet L-function. The hypothesis is that for any real number d there exist ‘many’ real numbers τ such that the shifts L(s+iτ,χ) and L(s+idτ,χ) are ‘near’ each other. If d is an algebraic irrational number then this was obtained by T. Nakamura. ?. Pańkowski solved the case then d is a transcendental number. We prove the case then d≠0 is a rational number. If d=0 then by B. Bagchi we know that the above hypothesis is equivalent to the Riemann hypothesis for the given Dirichlet L-function. We also consider a more general version of the above problem.     

Points of Weak-Norm Continuity in the Unit Ball of Banach Spaces

Using the M-structure theory, we show that several classical function spaces and spaces of operators on them fail to have points of weak-norm continuity for the identity map on the unit ball. This gives a unified approach to several results in the literature that establish the failure of strong geometric structure in the unit ball of classical function spaces. Spaces covered by our result include the Bloch spaces, dual of the Bergman space L¹_a and spaces of operators on them, as well as the space C(T)/A, where A is the disc algebra on the unit circle T. For any unit vector f in an infinite-dimensional function algebra A we explicitly construct a sequence {f_n} in the unit ball of A that converges weakly to f but not in the norm.     

Analysis of an M/G/∞ queue with batch arrivals and batch-dedicated servers

We analyze an M/G/∞ queue with batch arrivals, where jobs belonging to a batch have to be processed by the same server. The number of jobs in the system is characterized as a compound Poisson random variable through a scaling of the original arrival and batch size processes.     

q-Dedekind type sums related to q-zeta function and basic L-series

The main purpose of this paper is to define new generating functions. By applying the Mellin transformation formula to these generating functions, we define q-analogue of Riemann zeta function, q-analogue Hurwitz zeta function, q-analogue Dirichlet L-function and two-variable q-L-function. In particular, by using these generating functions, we will construct new generating functions which produce q-Dedekind type sums and q-Dedekind type sums attached to Dirichlet character. We also give the relations between these sums and Dedekind sums. Furthermore, by using *-product which is given in this paper, we will give the relation between Dedekind sums and q-L function as well.     

Maximal theorems of Menchoff-Rademacher type in non-commutative Lq-spaces

Estimates for maximal functions provide the fundamental tool for solving problems on pointwise convergence. This applies in particular for the Menchoff-Rademacher theorem on orthogonal series in L₂[0,1] and for results due independently to Bennett and Maurey-Nahoum on unconditionally convergent series in L₁[0,1]. We prove corresponding maximal inequalities in non-commutative L_q-spaces over a semifinite von Neumann algebra. The appropriate formulation for non-commutative maximal functions originates in Pisier's recent work on non-commutative vector valued L_q-spaces.