The individual ergodic theorem on the IF-events with product

The ergodic theory and particularly the individual ergodic theorem were studied in many structures. Recently the individual ergodic theorem has been proved for MV-algebras of fuzzy sets (Riečan in Czech Math J 50(125):673–680, 2000; Riečan and Neubrunn in Integral, measure, and ordering. Kluwer, Dordrecht, 1997) and even in general MV-algebras (Jurečková in Int J Theor Phys 39:757–764, 2000). The notion of almost everywhere equality of observables was introduced by Riečan and Jurečková (Int J Theor Phys 44:1587–1597, 2005). They proved that the limit of Cesaro means is an invariant observable for P-observables. In Lendelová (Int J Theor Phys 45(5):915–923, 2006c) showed that the assumption of P-observable can be omitted. In this paper we prove the individual ergodic theorem on family of IF-events and show that each P {\mathcal{P}} -preserving transformation in this family can be expressed by two corresponding P^\flat,P^\sharp {\mathcal{P}}^\flat,{\mathcal{P}}^\sharp -preserving transformations in tribe T. {\mathcal{T}}.     

NMG-代数中同态核的结构刻画

逻辑代数上的Bosbach态与Riečan态是经典概率论中Kolmogorov公理的两种不同方式的多值化推广,也是概率计量逻辑中语义计量化方法的代数公理化,是非经典数理逻辑领域中的重要研究分支.现已证明具有Glivenko性质的逻辑代数上的Bosbach态与Riečan态等价,并且逻辑代数的Glivenko性质是研究态算子的构造和存在性的重要工具,因而是态理论中的研究热点之一.研究了NMG-代数基于核算子的Glivenko性质,证明NMG-代数具有核基Glivenko性质的充要条件是该核算子是从此NMG-代数到其像集代数的同态,并给出NMG-代数中同态核的结构刻画.这里,NMG-代数是刻画序和三角模<（[0,1/2,T_NM]）,（[1/2,1,T_M]）>的逻辑系统NMG的语义逻辑代数.     

States on semi-divisible residuated lattices

Given a residuated lattice L, we prove that the subset MV(L) of complement elements x ^* of L generates an MV-algebra if, and only if L is semi-divisible. Riečan states on a semi-divisible residuated lattice L, and Riečan states on MV(L) are essentially the very same thing. The same holds for Bosbach states as far as L is divisible. There are semi-divisible residuated lattices that do not have Bosbach states. These results were obtained when the authors visited Academy of Science, Czech Republic, Institute of Comp. Sciences in Autumn 2006.     

Example Verifications Using Alphabet Axioms

This paper is supplementary to [KoS98]. It illustrates by means of examples the use of alphabet axioms as presented in [KoS98]. Furthermore a brief overview of μCRL [GrP94] and its proof theory [GrP93] are added. Received April 1995 / Accepted in revised form March 1998     

Some principles of coordinated decision making in distributed systems

Conclusion The proposed approach leads to flexible decision support algorithms and procedures that easily adapt to changing requirements. The application of the proposed principles is illustrated in [12] with the object of allowing for the specific features of the problem and accelerating convergence of distributed decision support systems. The application of these principles to the construction of various control procedures and decision support scheme is demonstrated in [13–19]. At the present time, in connection with active transition to the market and operation in a rapidly changing reality, we can expect an increase in demand for algorithms, procedures, and schemes that divide the domains of competence, sharply delineate the domains of responsibility, and clearly separate the fields of action of the “center” and the “periphery” [11]. The need for such procedures will also be felt in financial management support [26–27] and in macro/micro economic modeling and forecasting [20–26]. This is due to the fact that in our rapidly changing world we are often unable to identify several separate criteria for optimization. We are often forced to look for a decision which is admissible by a whole range of formal and informal criteria and is stable under small perturbations of both the criteria and the external conditions [28–30]. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 161–175, March–April, 1996.     

Every Linear Pseudo BL-Algebra Admits a State

We show that every linear pseudo BL-algebra, hence every representable one, admits a state and is good. This solves positively the problem on the existence of states raised in Dvurečenskij and Rachůnek (Probabilistic averaging in bounded communitative residuated ℓ-monoids, 2006), and gives a partial answer to the problem on good pseudo BL-algebras from [Di Nola, Georgescu and Iorgulescu (Multiple Val Logic 8:715–750, 2002) Problem 3.21]. Moreover, we present that every saturated linear pseudo BL-algebra can be expressed as an ordinal sum of Hájek’s type of irreducible pseudo linear pseudo BL-algebras. The paper has been supported by the Center of Excellence SAS—Physics of Information—I/2/2005, the grant VEGA no. 2/3163/23 SAV and by Science and Technology Assistance Agency under the contract no. APVT-51-032002. Bratislava, Slovakia.     

The stability of long action chains in XCS

 XCS [1, 2] represents a new form of learning classifier system [3] that uses accuracy as a means of guiding fitness for selection within a Genetic Algorithm. The combination of accuracy-based selection and a dynamic niche-based deletion mechanism achieve a long sought-after goal–the reliable production, maintenance, and proliferation of the sub-population of optimally general accurate classifiers that map the problem domain [4]. Wilson [2] and Lanzi [5, 6] have demonstrated the applicability of XCS to the identification of the optimal action-chain leading to the optimum trade-off between reward distance and magnitude. However, Lanzi [6] also demonstrated that XCS has difficulty in finding an optimal solution to the long action-chain environment Woods-14 [7]. Whilst these findings have shed some light on the ability of XCS to form long action-chains, they have not provided a systematic and, above all, controlled investigation of the limits of XCS learning within multiple-step environments. In this investigation a set of confounding variables in such problems are identified. These are controlled using carefully constructed FSW environments [8, 9] of increasing length. Whilst investigations demonstrate that XCS is able to establish the optimal sub-population [O] [4] when generalisation is not used, it is shown that the introduction of generalisation introduces low bounds on the length of action-chains that can be identified and chosen between to find the optimal pathway. Where these bounds are reached a form of over-generalisation caused by the formation of dominant classifiers can occur. This form is further investigated and the Domination Hypothesis introduced to explain its formation and preservation.     

Building online trust through privacy practices

This study applies Mayer et al. [24] trust model to an Internet context. A model is presented linking privacy policy, through trustworthiness, to online trust, and then to customers’ loyalty and their willingness to provide truthful information. The model is tested using a sample of 269 responses. The findings suggest that consumers’ trust in a company is closely linked with the perception of the company’s respect for customer privacy. Trust in turn is linked to increased customer loyalty that can be manifested through increased purchases, openness to trying new products, and willingness to participate in programs that use additional personal information.     

Synthesis of continuous-valued logic functions defined in tabular form

The choice table provides one of the techniques for the representation of functions in continuous-valued logic [1]. The need to synthesize functions from choice tables arise in the design of hybrid [2] and analog [3] computers, and also in other applications of continuous-valued logic that are surveyed in [4]. The structure of the original table is determined by the external specification of the device or unit being designed. Algorithms are available for the synthesis of continuous-valued logic functions from choice tables of a special form, for instance, from ordered choice tables [ It is noted in [ that a general algorithm to synthesize a continuous-valued logic function from an arbitrary choice table is still unknown. In the present article, we derive a criterion that decides whether a given choice table defmes some continuous-valued logic function and construct a simple algorithm to synthesize the function from the table. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 42–49, March–April, 1998.     

The inclusion-exclusion principle for IF-events

The probabilistic version of the inclusion-exclusion principle is generalized for IF-events. Two versions of the generalized formula, corresponding to different t-conorms applied for defining the union of IF-events are shown.     

Tensor products of MV-algebras

 The structure of MV-module over a PMV-algebra was defined in [5]. In this paper we test this notion in the important problem of scalar extension. The tensor product ⊗ _mv defined in [11] is generalized and another tensor product, ⊗ _o , is studied in relation with the corresponding tensor product of ℓ-groups [9]. Using tensor products we get the free MV-modules over a totally ordered PMV-algebra. Dedicated to Prof. Ján Jakubíik on the occasion of his 80th birthday     

A Note on the Stability of Gauss–Jordan Elimination for Diagonally Dominant Matrices

Peters and Wilkinson [2] state that “it is well known that Gauss–Jordan is stable” for a diagonally dominant matrix, but a proof does not seem to have been published [1]. The present note fills this gap. Gauss–Jordan elimination is backward stable for matrices diagonally dominant by rows and not for those diagonally dominant by columns. In either case it is forward stable. Received February 28, 2000     

Calculations of two-dimensional test problems by the method of adaptive viscosity

The paper is concerned with calculations of two-dimensional test gas dynamic problems through a new artificial viscosity grid method. A detailed account of this method is given in [1, 2]; it was extended in [3] to two and three dimensions. The equations are considered in a rectangle and in step-shaped regions using Cartesian coordinates and Euler variables, and they are closed by the gas law of ideal polytropic gas. Test problems are taken from [4–6]. A comparison of the solution of these problems as obtained by the AAV method and other methods put forward in [4–6] is made.     

A coarsening finite element strategy in image selective smoothing

We introduce the coarsening of finite element computational grid strategy into the method proposed by Kačur and Mikula in [11] for the numerical solution of the Perona–Malik model modified in the sense of Catté, Lions, Morel and Coll. It improves the efficiency of the method, while the solution tends to be more flat during the selective smoothing process applied to the image. The numerical approximation consists of Rothe's method in time and linear finite elements on unstructured adaptively coarsened meshes in space. Received: 2 September 1996 / Accepted: 24 February 1997     

Fabrication of LIGA-Acceleration Sensors by Aligned Molding

 A technology for the fabrication of movable LIGA-Microstructures by molding was developed, which enables the cheaper production of e.g. LIGA-Acceleration Sensors [1]. For this purpose an aligned molding process had to be developed. The realized experimental setup consists of two subsystems, the molding machine and the alignment arrangement [2]. After aligning a substrate it is transported into the molding machine. An effective and extremely precise dimension translation system is required. Although during molding temperature changes appear and high forces are applied, the dimension stability during the molding process has to be guaranteed. The presented system and setup deals successfully with these conditions. An alignment quality of ±10 μm is realized. Using the aligned molding technology temperature compensated LIGA-acceleration sensors [1] were fabricated. The proper function of the sensors was demonstrated. Received: 30 October 1995/Accepted: 11 December 1995     

Construction of convex continuations for functions defined on a hypersphere

Construction of convex continuations for functions defined on the vertices of some combinatorial polyhedra, in particular the permutation polyhedron and the arrangement polyhedron, has been studied in [1, 2]. Subsequently this result has been generalized to functions defined at the extreme points of an arbitrary polyhedron [3]. For purposes of combinatorial optimization [4-6] it is relevant to consider the existence and construction of convex continuations from continua, in particular, when the function is defined on a hypersphere in thek-dimensional space. Unfortunately, passage to the limit from discrete sets to continua does not produce positive results in this case. We are thus forced to develop special approaches to investigating the existence of convex continuations of functions defined on continua. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 27–36, March–April, 1998.     

Some Differential-Geometric Remarks on a Method for Minimizing Constrained Functionals of Matrix-Valued Functions

In [3] an approach is given for minimizing certain functionals on certain spaces , where Ω is a domain in some Euclidean space and N is a space of square matrices satisfying some extra condition(s), e.g. symmetry and positive-definiteness. The approach has the advantage that in the associated algorithm, the preservation of constraints is built in automatically. One practical use of such an algorithm its its application to diffusion-tensor imaging, which in recent years has been shown to be a very fruitful approach to certain problems in medical imaging. The method in [3] is motivated by differential-geometric considerations, some of which are discussed briefly in [3] and in greater detail in [4]. We describe here certain geometric aspects of this approach that are not readily apparent in [3] or [4]. We also discuss what one can and cannot hope to achieve by this approach. David Groisser is an Associate Professor of Mathematics at the University of Florida. Dr. Groisser conducts research in pure and applied differential geometry. His current interests include the geometry of shape spaces and applications of differential geometry to image-analysis.     

A Multi-formalism Approach for the Validation of UML Models

Our approach is based on UML models. They are edited with the rational Rose^™ tool [Rat96] and complemented with annotations that state several constraints. The class diagram is the starting point of a translation process that produces formal specifications in Z [Spi92] and Lustre [CHP87]. The RoZ tool is used to translate the class diagram into Z automatically. The Z and Lustre specifications are used to validate the UML models by means of a prover and a testing environment. Received February 2000 / Accepted in revised form December 2000     

Approximation of functions by means of a new generalized Bernstein operator

In this paper we first use a probabilistic method to construct a linear positive polynomial operatorL _{m, r} ^α,β Bernstein type, depending on a non-negative integer parameterr and on two real parameters α and β, such that 0≤α≤β. Then we investigate the approximation properties of this operator mapping into itself the Banach spaceC[0,1] of real-valued continuous functions on [0,1]. A special attention is accorded to the case of the operatorL _m,r=L _m,r ^0,0 . We prove that the remainder of the approximation formula of a functionfεC[0,1] byL _m,r f can be represented either by means of divided differences, or in an integral form, obtained by using a classical theorem of Peano. We give also an asymptotic estimate for this remainder. The operatorL _m,r enjoys the variation diminishing property—in the sense of I. J. Schoenberg [15]. By extending the known inequalities of T. Popoviciu [12] and G. G. Lorentz [7], we evaluate the orders of approximation in terms of the modulus of continuity of the functionf or of its derivative. In the last section of this paper we determine the point spectrum of the operatorL _m,r and , finally, we present a quadrature formula which can be constructed by means of this operator. Dedicated to Professor Aldo Ghizzetti on his 75th birthday     

A simple approximation algorithm for the weighted matching problem

We present a linear time approximation algorithm with a performance ratio of 1/2 for finding a maximum weight matching in an arbitrary graph. Such a result is already known and is due to Preis [STACS'99, Lecture Notes in Comput. Sci., Vol. 1563, 1999, pp. 259-269]. Our algorithm uses a new approach which is much simpler than the one given by Preis and needs no amortized analysis for its running time.