Wyniki wyszukiwania - BazTech

1

Invariant Structures and Dependence Relations

Janicki R., Kleijn J., Koutny M., Mikulski Ł.

Fundamenta Informaticae

|

2017

|

Vol. 155, nr 1/2

1--29

EN

A step trace is an equivalence class of step sequences which can be thought of as different observations of the same underlying concurrent history. Equivalence is determined on basis of a step alphabet that describes the relations between events in terms of potential simultaneity and sequentialisability. Step traces cannot be represented by standard partial orders, but require so-called invariant structures, extended order structures that capture the phenomena of mutual exclusion and weak causality. In this paper, we present an effective way of deciding whether an invariant structure represents a step trace over a given step alphabet. We also describe a method by which one can check whether a given invariant structure can represent a step trace over any step alphabet. Moreover, if the answer is positive, the method provides a suitable step alphabet.

2

Some fixed point theorems for almost (GF, δb)-contractions and application

Nashine H. K., Agarwal R. P., Shukla S., Gupta A.

Fasciculi Mathematici

|

2017

|

Nr 58

123--143

EN

We propose a new notion of multi-valued almost (GF, δb)-contractions involving rational terms under δ-distance on b-metric spaces and give its relevance to fixed point results in orbitally complete b-metric spaces. An ordered version of our main result is also proved with some weaker contractive conditions. Some examples are given to show the usability of the results proved herein. Moreover, application of our result to the nonlinear integral equation is given.

3

Decomposition of Relations and Concept Lattices

Berghammer R., Winter M.

Fundamenta Informaticae

|

2013

|

Vol. 126, nr 1

37--82

EN

We introduce the decomposition of an arbitrary relation into a sequential composition of three relations, viz. of a mapping with a partial order and then the transpose of a mapping. After presenting some basic properties, we investigate the specific classes of junkfree, irreducible and minimal decompositions and show that for all relations a minimal decomposition exists. We also study decompositions with regard to DedekindMacNeille completions and concept lattices. These constructions are closely related to decompositions of relations. In our setting the fundamental theorem of concept lattices states that concept lattices are minimal-complete decompositions and all such decompositions are isomorphic. As a further main result we prove that the cutDedekindMacNeille completion of the order that belongs to the minimal decomposition of a relation is isomorphic to the concept lattice of that relation. Instead of considering binary relations on sets, we will work point-free within the general framework of allegories. This complement-free approach implies that the results of the paper can be applied to all models of these algebraic structures, including, for instance, lattice-valued fuzzy relations.

4

Visualisation of concurrent processes

Mikulski Ł, Piątkowski M.

Control and Cybernetics

|

2013

|

Vol. 42, no. 3

699-725

EN

Mazurkiewicz traces are a widely used model for describing the languages of concurrent systems computations. The causal structure of atomic actions occurring in a process modeled as a trace generates a partial order. Hasse diagrams of such order are very common structures used for presentation and investigation in the concurrency theory, especially from the behavioural perspective. We present effective algorithms for Hasse diagrams construction and transformation. Later on, we use them for enumeration of all linearisations of the partial order that represents a concurrent process. Additionally, we attach the flexible visual implementation of all considered Algorithms.

5

Continuity of scale parameter estimators with respect to stochastic orders

Bartoszewicz J., Frąszczak M.

Probability and Mathematical Statistics

|

2012

|

Vol. 32, Fasc. 1

57--67

EN

Lehmann and Rojo [8] proposed a concept of invariance of stochastic orders and related probability metrics with respect to increasing transformations of random variables. Bartoszewicz and Benduch [3] and Bartoszewicz and Frąszczak [4] applied a concept of Lehmann and Rojo to new settings. In the paper these results are applied to the problem of robustness in the sense of Zieliński [11], [12]. Metrics related to some stochastic orders are used to study the continuity (robustness) of scale parameter estimators when contaminations of the models are generated by stochastic orders. The exponential model is considered in detail.

6

Properties of partial order in generalised inverse semigroups

Lipińska J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

|

2011

|

Vol. 10, nr 1

145-149

EN

In this paper we show that among the idempotent elements of a generalised inverse semigroup isomorphic to a pseudogroup of transformations on a topological space, is the largest element. We also show how to obtain the smallest element in some inverse semigroups.

7

The method of data envelopment analysis as a tool for compiling a rating list

Gierulski W.

Operations Research and Decisions

|

2010

|

Vol. 20, No. 1

41-59

EN

The paper presents the method of Data Envelopment Analysis (DEA) as a tool for compiling rating lists in tasks of ordering elements of assemblages. We describe the differences that result from applying a one-dimensional model and multi-dimensional model, where in the latter a so-called partial order is created for incomparable elements in the assemblage being ordered. The example used to illustrate the issues discussed is the analysis of teaching results in a student group.

8

Limit points of random iterations of monotone maps

Sikora R.

Bulletin of the Polish Academy of Sciences. Mathematics

|

1998

|

Vol. 46, no 4

351-363

EN

We consider random iterations of a monotone, continous map f of a partially ordered compact Polish space. We prove that, under additional assumptions, all limit point of the trajectories are fixed points of f a.s. If the fixed points are isolated, then almost all trajectories are convergent. Invariant measure are supported on the sets of fixed points.