Search results for "9(39)"

showing 10 items of 677 documents

Refined Finiteness and Degree Properties in Graphs

2020

Summary In this article the finiteness of graphs is refined and the minimal and maximal degree of graphs are formalized in the Mizar system [3], based on the formalization of graphs in [4].

Discrete mathematicsDegree (graph theory)maximum degreeApplied Mathematicsgraph theory68v20vertex degree05c07Computational MathematicsQA1-939MathematicsMathematicsMathematicsofComputing_DISCRETEMATHEMATICSminimum degreeFormalized Mathematics
researchProduct

Fuzzy functions: a fuzzy extension of the category SET and some related categories

2000

<p>In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -> L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.</p>

Discrete mathematicsFuzzy classificationL-relationFuzzy topologylcsh:MathematicsFuzzy setlcsh:QA299.6-433Fuzzy subalgebralcsh:AnalysisFuzzy groupType-2 fuzzy sets and systemslcsh:QA1-939DefuzzificationAlgebraFuzzy mathematicsL-fuzzy functionFuzzy numberFuzzy set operationsGeometry and TopologyFuzzy categoryMathematics
researchProduct

About Aczél Inequality and Some Bounds for Several Statistical Indicators

2020

In this paper, we will study a refinement of the Cauchy&ndash

Discrete mathematicsInequalityGeneral Mathematicsmedia_common.quotation_subjectlcsh:Mathematics010102 general mathematicsstatistical indicatorsMathematics::Analysis of PDEsVariation (game tree)lcsh:QA1-93901 natural sciences0103 physical sciencesComputer Science (miscellaneous)010307 mathematical physicsCauchy–Buniakowski–Schwarz inequality0101 mathematicsEngineering (miscellaneous)MathematicsSequence (medicine)media_commonMathematics
researchProduct

Quasi-pseudometric properties of the Nikodym-Saks space

2003

[EN] For a non-negative finite countably additive measure μ defined on the σ-field Σ of subsets of Ω, it is well known that a certain quotient of Σ can be turned into a complete metric space Σ (Ω), known as the Nikodym-Saks space, which yields such important results in Measure Theory and Functional Analysis as Vitali-Hahn-Saks and Nikodym's theorems. Here we study some topological properties of Σ (Ω) regarded as a quasi-pseudometric space.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsFunctional analysislcsh:MathematicsQuasi-pseudometric spaceMathematics::General Topologylcsh:QA299.6-433lcsh:AnalysisPseudometric spacelcsh:QA1-939Space (mathematics)Measure (mathematics)Complete metric spaceNikodym-Saks spaceGeometry and TopologyQuotientMathematicsApplied General Topology
researchProduct

Rearrangement and convergence in spaces of measurable functions

2007

We prove that the convergence of a sequence of functions in the space of measurable functions, with respect to the topology of convergence in measure, implies the convergence -almost everywhere ( denotes the Lebesgue measure) of the sequence of rearrangements. We obtain nonexpansivity of rearrangement on the space , and also on Orlicz spaces with respect to a finitely additive extended real-valued set function. In the space and in the space , of finite elements of an Orlicz space of a -additive set function, we introduce some parameters which estimate the Hausdorff measure of noncompactness. We obtain some relations involving these parameters when passing from a bounded set of , or , to th…

Discrete mathematicsMathematics::Functional AnalysisSequenceConvergence in measureLebesgue measureMeasurable functionlcsh:MathematicsApplied Mathematicslcsh:QA1-939Space (mathematics)TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESSet functionData_FILESDiscrete Mathematics and CombinatoricsHausdorff measureAlmost everywhereAnalysisMathematics
researchProduct

Fixed-Point Theorems in Complete Gauge Spaces and Applications to Second-Order Nonlinear Initial-Value Problems

2013

We establish fixed-point results for mappings and cyclic mappings satisfying a generalized contractive condition in a complete gauge space. Our theorems generalize and extend some fixed-point results in the literature. We apply our obtained results to the study of existence and uniqueness of solution to a second-order nonlinear initial-value problem.

Discrete mathematicsPure mathematicsArticle Subjectlcsh:MathematicsFixed-point theoremGauge (firearms)Space (mathematics)lcsh:QA1-939Nonlinear systemSettore MAT/05 - Analisi MatematicaInitial value problemOrder (group theory)UniquenessCoincidence pointfixed point gauge spaces initial-value problemAnalysisMathematics
researchProduct

Remarks on G-Metric Spaces

2013

In 2005, Mustafa and Sims (2006) introduced and studied a new class of generalized metric spaces, which are called G-metric spaces, as a generalization of metric spaces. We establish some useful propositions to show that many fixed point theorems on (nonsymmetric) G-metric spaces given recently by many authors follow directly from well-known theorems on metric spaces. Our technique can be easily extended to other results as shown in application.

Discrete mathematicsPure mathematicsArticle Subjectlcsh:MathematicsInjective metric spaceEquivalence of metricslcsh:QA1-939Intrinsic metricConvex metric spaceUniform continuityMetric spaceSettore MAT/05 - Analisi MatematicaG-metric space metric space fixed pointMetric (mathematics)Metric mapMathematicsInternational Journal of Analysis
researchProduct

Construction of chaotic dynamical system

2010

The first‐order difference equation xn+ 1 = f(xn ), n = 0,1,…, where f: R → R, is referred as an one‐dimensional discrete dynamical system. If function f is a chaotic mapping, then we talk about chaotic dynamical system. Models with chaotic mappings are not predictable in long‐term. In this paper we consider family of chaotic mappings in symbol space S 2. We use the idea of topological semi‐conjugacy and so we can construct a family of mappings in the unit segment such that it is chaotic. First published online: 09 Jun 2011

Discrete mathematicsPure mathematicsincreasing mappingDifferential equationChaoticinfinite symbol spaceBinary numberFunction (mathematics)Space (mathematics)Nonlinear Sciences::Chaotic Dynamicstopological semi‐conjugacyModeling and SimulationQA1-939Orbit (dynamics)chaotic mappingbinary expansionUnit (ring theory)MathematicsAnalysisMathematicsCoupled map latticeMathematical Modelling and Analysis
researchProduct

Periodic and Chaotic Orbits of a Neuron Model

2015

In this paper we study a class of difference equations which describes a discrete version of a single neuron model. We consider a generalization of the original McCulloch-Pitts model that has two thresholds. Periodic orbits are investigated accordingly to the different range of parameters. For some parameters sufficient conditions for periodic orbits of arbitrary periods have been obtained. We conclude that there exist values of parameters such that the function in the model has chaotic orbits. Models with chaotic orbits are not predictable in long-term.

Discrete mathematicsQuantitative Biology::Neurons and CognitionGeneralizationMathematical analysisChaoticBiological neuron modelFunction (mathematics)stabilityDynamical systemStability (probability)dynamical systemModeling and Simulationiterative processRange (statistics)Orbit (dynamics)QA1-939chaotic mappingnonlinear problemAnalysisMathematicsMathematicsMathematical Modelling and Analysis
researchProduct

Caristi Type Selections of Multivalued Mappings

2015

Multivalued mappings and related selection theorems are fundamental tools in many branches of mathematics and applied sciences. In this paper we continue this theory and prove the existence of Caristi type selections for generalized multivalued contractions on complete metric spaces, by using some classes of functions. Also we prove fixed point and quasi-fixed point theorems.

Discrete mathematicsSelection (relational algebra)Article Subjectlcsh:MathematicsMULTIVALUED CONTRACTION MAPPINGSType (model theory)Fixed pointlcsh:QA1-939METRIC SPACESMetric spaceFIXED-POINT THEOREMSettore MAT/05 - Analisi MatematicaPoint (geometry)Settore MAT/03 - GeometriaAnalysisMathematicsJournal of Function Spaces
researchProduct