Some types of filters in BL algebras

In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters and quotient algebras that are constructed via these filters.     

Partial quasi-metrics

In this article we introduce and investigate the concept of a partial quasi-metric and some of its applications. We show that many important constructions studied in Matthews's theory of partial metrics can still be used successfully in this more general setting. In particular, we consider the bicompletion of the quasi-metric space that is associated with a partial quasi-metric space and study its applications in groups and BCK-algebras.     

Isomorphism theorems on generalized effect algebras based on atoms

A well-known fact is that every generalized effect algebra can be uniquely extended to an effect algebra in which it becomes a sub-generalized effect algebra and simultaneously a proper order ideal, the set-theoretic complement of which is its dual poset. We show that two non-isomorphic generalized effect algebras (even finite ones) may have isomorphic effect algebraic extensions. For Archimedean atomic lattice effect algebras we prove “Isomorphism theorem based on atoms”. As an application we obtain necessary and sufficient conditions for isomorphism of two prelattice Archimedean atomic generalized effect algebras with common (or isomorphic) effect algebraic extensions.     

On derivations of lattices

In this paper, we introduce the notion of derivation for a lattice and discuss some related properties. We give some equivalent conditions under which a derivation is isotone for lattices with a greatest element, modular lattices, and distributive lattices. We characterize modular lattices and distributive lattices by isotone derivation. Moreover, we prove that if d is an isotone derivation of a lattice L, the fixed set Fix_d(L) is an ideal of L. Finally, we prove that D(L) is isomorphic to L in a distributive lattice L.     

Continuous approximations of product implication in MV-algebras with product

Recently, MV-algebras with product have been investigated from different points of view. In particular, in [EGM01], a variety resulting from the combination of MV-algebras and product algebras (see [H98]) has been introduced. The elements of this variety are called ŁΠ-algebras. Even though the language of ŁΠ-algebras is strong enough to describe the main properties of product and of ukasiewicz connectives on [0,1], the discontinuity of product implication introduces some problems in the applications, because a small error in the data may cause a relevant error in the output. In this paper we try to overcome this difficulty, substituting the product implication by a continuous approximation of it. We investigate the resulting algebras, called ŁΠ_q -algebras, and we show that these algebras constitute a quasivariety which is generated by the class of all ŁΠ _q -algebras whose lattice reduct is the unit interval [0,1] with the usual order.     

Multilevel norms forH −1/2

We give some estimates related to finite element multilevel splittings and Sobolev norms of negative order. Basically, results for the positive order case are carried over by duality. In particular, semi-orthogonal splittings based on piecewise constants are studied for Sobolev spaces of order −1/2. Numerical experiments are provided for the screen problem.     

Error analysis of thermal equation with moving ends

A mathematical model of the linear thermodynamic equations with moving ends, based on the Stefan Problem is considered. In this work, we are interested in obtaining existence, uniqueness and regularity using the Galerkin method and mainly to establish an error estimates of solutions in Sobolev spaces for the semi-discrete problem, with discretization of space variable, continuous time and for the completely discrete problem with discretization of space variable and time.     

Regular ordered semigroups in terms of fuzzy subsets

Given a set S, a fuzzy subset of S (or a fuzzy set in S) is, by definition, an arbitrary mapping f : S → [0, 1] where [0, 1] is the usual interval of real numbers. If the set S bears some structure, one may distinguish some fuzzy subsets of S in terms of that additional structure. This important concept of a fuzzy set was first introduced by Zadeh. Fuzzy groups have been first considered by Rosenfeld, fuzzy semigroups by Kuroki. A theory of fuzzy sets on ordered groupoids and ordered semigroups can be developed. Some results on ordered groupoids-semigroups have been already given by the same authors in [N. Kehayopulu, M. Tsingelis, Fuzzy sets in ordered groupoids, Semigroup Forum 65 (2002) 128-132; N. Kehayopulu, M. Tsingelis, The embedding of an ordered groupoid into a poe-groupoid in terms of fuzzy sets, Inform. Sci. 152 (2003) 231-236; N. Kehayopulu, M. Tsingelis, Fuzzy bi-ideals in ordered semigroups, Inform. Sci. 171 (2004) 13-28] where S has been endowed with the structure of an ordered semigroup and defined “fuzzy” analogous for several notions that have been proved to be useful in the theory of ordered semigroups. The characterization of regular rings in terms of right and left ideals is well known. The characterization of regular semigroups and regular ordered semigroups in terms of left and right ideals or in terms of left, right ideals and quasi-ideals is well known as well. The characterization of regular le-semigroups (that is lattice ordered semigroups having a greatest element) in terms of right ideal elements and left ideal elements or right, left and quasi-ideal elements is also known. In the present paper we first give the main theorem which characterizes the regular ordered semigroups by means of fuzzy right and fuzzy left ideals. Then we characterize the regular ordered semigroups in terms of fuzzy right, fuzzy left ideals and fuzzy quasi-ideals. The paper serves as an example to show that one can pass from the theory of ordered semigroups to the theory of “fuzzy” ordered semigroups. Some of our results are true for ordered groupoids in general.     

Online querying of d-dimensional hierarchies

In this paper we describe a distributed system designed to efficiently store, query and update multidimensional data organized into concept hierarchies and dispersed over a network. Our system employs an adaptive scheme that automatically adjusts the level of indexing according to the granularity of the incoming queries, without assuming any prior knowledge of the workload. Efficient roll-up and drill-down operations take place in order to maximize the performance by minimizing query flooding. Updates are performed on-line, with minimal communication overhead, depending on the level of consistency needed. Extensive experimental evaluation shows that, on top of the advantages that a distributed storage offers, our method answers the vast majority of incoming queries, both point and aggregate ones, without flooding the network and without causing significant storage or load imbalance. Our scheme proves to be especially efficient in cases of skewed workloads, even when these change dynamically with time. At the same time, it manages to preserve the hierarchical nature of data. To the best of our knowledge, this is the first attempt towards the support of concept hierarchies in DHTs.     

Order results for Krylov-W-methods

We consider ROW-methods for stiff initial value problems, where the stage equations are solved by Krylov techniques. By using a certain ‘multiple Arnoldi process’ over all stages the order of the fully-implicit one-step scheme can be preserved with low Krylov dimensions. Explicit estimates for minimal order preserving dimensions are derived. They depend on the parameters of the method only, not on the dimension of the ODE. Stability restrictions usually require larger dimensions, of course, but this can be done adaptively. These results justify to adopt the step size control of the underlying ROW-method. The widely used ROW-methods of order 4 are discussed in detail and numerical illustrations are given. For the special class of semilinear systems with stiffness in a constant linear part we establish the order 2 of B-consistency for these Krylov-W-methods. This work was supported by the Deutsche Forschungsgemeinschaft.     

On convergence of splitting iteration methods for non-Hermitian positive-definite linear systems

A new splitting iteration method is presented for the system of linear equations when the coefficient matrix is a non-Hermitian positive-definite matrix. The spectral radius, the optimal parameter, and some norm properties of the iteration matrix for the new method are discussed in detail. Based on these results, the new method is convergent under reasonable conditions for any non-Hermitian positive-definite linear system. Finally, the numerical examples show that the new method is more effective than the Hermitian and skew-Hermitian splitting iterative (or positive-definite and skew-Hermitian splitting iterative) method in central processing unit time.     

On d-solvability for linear differential equations

The aim of this paper is to investigate the possibility of solving a linear differential equation of degree n$n$ by means of differential equations of degree less than or equal to a fixed d$d$, 1≤d<n$1\le d<n$. This paper recovers and extends work of G. Fano, M. F. Singer and E. Compoint. Representations of algebraic Lie algebras are the main tool.     

Pseudocomplemented lattice effect algebras and existence of states

We prove that in every pseudocomplemented atomic lattice effect algebra the subset of all pseudocomplements is a Boolean algebra including the set of sharp elements as a subalgebra. As an application, we show families of effect algebras for which the existence of a pseudocomplementation implies the existence of states. These states can be obtained by smearing of states existing on the Boolean algebra of sharp elements.     

Using integral equations and the immersed interface method to solve immersed boundary problems with stiff forces

We propose a fast, explicit numerical method for computing approximations for the immersed boundary problem in which the boundaries that separate the fluid into two regions are stiff. In the numerical computations of such problems, one frequently has to contend with numerical instability, as the stiff immersed boundaries exert large forces on the local fluid. When the boundary forces are treated explicitly, prohibitively small time-steps may be required to maintain numerical stability. On the other hand, when the boundary forces are treated implicitly, the restriction on the time-step size is reduced, but the solution of a large system of coupled non-linear equations may be required. In this work, we develop an efficient method that combines an integral equation approach with the immersed interface method. The present method treats the boundary forces explicitly. To reduce computational costs, the method uses an operator-splitting approach: large time-steps are used to update the non-stiff advection terms, and smaller substeps are used to advance the stiff boundary. At each substep, an integral equation is computed to yield fluid velocity local to the boundary; those velocity values are then used to update the boundary configuration. Fluid variables are computed over the entire domain, using the immersed interface method, only at the end of the large advection time-steps. Numerical results suggest that the present method compares favorably with an implementation of the immersed interface method that employs an explicit time-stepping and no fractional stepping.     

?ukasiewicz transform and its application to compression and reconstruction of digital images

We define the ?ukasiewicz transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “?ukasiewicz Transform Based” (?TB) algorithm for image processing, demonstrating its applicability.     

A Runge-Kutta discontinuous Galerkin method for the Euler equations

This paper presents a Runge-Kutta discontinuous Galerkin (RKDG) method for the Euler equations of gas dynamics from the viewpoint of kinetic theory. Like the traditional gas-kinetic schemes, our proposed RKDG method does not need to use the characteristic decomposition or the Riemann solver in computing the numerical flux at the surface of the finite elements. The integral term containing the non-linear flux can be computed exactly at the microscopic level. A limiting procedure is carefully designed to suppress numerical oscillations. It is demonstrated by the numerical experiments that the proposed RKDG methods give higher resolution in solving problems with smooth solutions. Moreover, shock and contact discontinuities can be well captured by using the proposed methods.     

Two-level Stabilized Finite Element Methods for the Steady Navier–Stokes Problem

In this article, the two-level stabilized finite element formulations of the two-dimensional steady Navier–Stokes problem are analyzed. A macroelement condition is introduced for constructing the local stabilized formulation of the steady Navier–Stokes problem. By satisfying this condition the stability of the Q₁–P₀ quadrilateral element and the P₁–P₀ triangular element are established. Moreover, the two-level stabilized finite element methods involve solving one small Navier–Stokes problem on a coarse mesh with mesh size H, a large Stokes problem for the simple two-level stabilized finite element method on a fine mesh with mesh size h=O(H²) or a large general Stokes problem for the Newton two-level stabilized finite element method on a fine mesh with mesh size h=O(|log h|^1/2H³). The methods we study provide an approximate solution (u^h,p^h) with the convergence rate of same order as the usual stabilized finite element solution, which involves solving one large Navier–Stokes problem on a fine mesh with mesh size h. Hence, our methods can save a large amount of computational time.     

Extension of ENO and WENO schemes to one-dimensional sediment transport equations

Essentially nonoscillatory and weighted essentially nonoscillatory schemes are high order resolution schemes constructed for the hyperbolic conservation laws. In this paper we extend these schemes to the one-dimensional bed-load sediment transport equations. The difficulties that arise in the numerical modelling come from the fact that a nonconservative product is present in the system. Our specific numerical approximations for the nonconservative product are based on two ideas. First is to include the influence of that term in the system upwinding and the second is to define the numerical approximation in such a way that the obtained scheme solves the system for the quiescent flow case exactly. As a consequence, the resulting schemes give excellent results, as it can be seen from the numerical tests we present. On the opposite, the numerical results obtained by applying the pointwise evaluation of nonconservative product on the same tests present unacceptably large numerical errors.     

Maintenance routing for train units: The interchange model

Train units need regular preventive maintenance. Given the train units that require maintenance in the forthcoming 1–3 days, the rolling stock schedule must be adjusted so that these urgent units reach the maintenance facility in time. In this paper, we present an integer programming model for solving this problem, give complexity results, suggest solution methods, and report our computational results based on practical instances of NS Reizigers, the main Dutch operator of passenger trains.