Search results for "General Mathematics"

showing 10 items of 3795 documents

L -valued bornologies on powersets

2016

In M. Abel and A. ostak (2011) [1], the concept of an L-fuzzy bornology was introduced. Actually, an L-fuzzy bornology on a set X is a certain ideal in the family LX of L-fuzzy subsets of a set X. Here we propose an alternative approach to fuzzification of the concept of bornology. We define an L-valued bornology on a set X as an L-fuzzy subset B of the powerset 2X satisfying L-valued analogues of the axioms of a bornology. Basic properties of L-valued bornological spaces are studied. Our special interest concerns L-valued bornologies induced by fuzzy metrics and relative compactness-type L-valued bornologies in ChangGoguen L-topological spaces.

Discrete mathematicsIdeal (set theory)Logic010102 general mathematicsFuzzy set02 engineering and technology01 natural sciencesFuzzy logicFuzzy topologyAlgebraSet (abstract data type)Artificial Intelligence0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processing0101 mathematicsAxiomMathematicsFuzzy Sets and Systems
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Very Narrow Quantum OBDDs and Width Hierarchies for Classical OBDDs

2014

In the paper we investigate a model for computing of Boolean functions – Ordered Binary Decision Diagrams (OBDDs), which is a restricted version of Branching Programs. We present several results on the comparative complexity for several variants of OBDD models. We present some results on the comparative complexity of classical and quantum OBDDs. We consider a partial function depending on a parameter k such that for any k > 0 this function is computed by an exact quantum OBDD of width 2, but any classical OBDD (deterministic or stable bounded-error probabilistic) needs width 2 k + 1. We consider quantum and classical nondeterminism. We show that quantum nondeterminism can be more efficient …

Discrete mathematicsImplicit functionBinary decision diagram010102 general mathematics02 engineering and technologyFunction (mathematics)Computer Science::Artificial IntelligenceComputer Science::Computational Complexity01 natural sciencesCombinatoricsNondeterministic algorithmComputer Science::Logic in Computer SciencePartial function0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processing0101 mathematicsBoolean functionQuantumQuantum computerMathematics
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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
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Some fixed point results via R-functions

2016

We establish existence and uniqueness of fixed points for a new class of mappings, by using R-functions and lower semi-continuous functions in the setting of metric spaces. As consequences of this results, we obtain several known fixed point results, in metric and partial metric spaces. An example is given to support the new theory. A homotopy result for operators on a set endowed with a metric is given as application.

Discrete mathematicsInjective metric spaceApplied Mathematics010102 general mathematics01 natural sciencesConvex metric spaceIntrinsic metric010101 applied mathematicsMetric spaceMetric (mathematics)Metric mapGeometry and Topology0101 mathematicsMetric differentialFisher information metricMathematicsFixed Point Theory and Applications
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Common fixed points for self-mappings on partial metric spaces

2012

Abstract In this paper, we prove some results of a common fixed point for two self-mappings on partial metric spaces. Our results generalize some interesting results of Ilić et al. (Appl. Math. Lett. 24:1326-1330, 2011). We conclude with a result of the existence of a fixed point for set-valued mappings in the context of 0-complete partial metric spaces. MSC:54H25, 47H10.

Discrete mathematicsInjective metric spaceApplied Mathematics010102 general mathematicsEquivalence of metricscommon fixed point01 natural sciencesConvex metric spaceIntrinsic metric010101 applied mathematicsMetric spacepoints of coincidence0-complete partial metric spaceSettore MAT/05 - Analisi Matematicaψ-contractions.Metric (mathematics)Metric mapGeometry and Topology0101 mathematicsCoincidence pointMathematicsFixed Point Theory and Applications
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VECTOR-VALUED FUNCTIONS INTEGRABLE WITH RESPECT TO BILINEAR MAPS

2008

Let $(\Omega, \Sigma, \mu)$ be a $\sigma-$finite measure space, $1\le p \lt \infty$, $X$ be a Banach space $X$ and ${\cal B} :X\times Y \to Z$ be a bounded bilinear map. We say that an $X$-valued function $f$ is $p-$integrable with respect to ${\cal B}$ whenever $\sup\{\int_\Omega\|{\cal B}(f(w),y)\|^pd\mu: \|y\|=1\}$ is finite. We identify the spaces of functions integrable with respect to the bilinear maps arising from H\"older's and Young's inequalities. We apply the theory to give conditions on $X$-valued kernels for the boundedness of integral operators $T_{{\cal B}}(f) (w)=\int_{\Omega'}{{\cal B}}(k(w,w'),$ $f(w'))d\mu'(w')$ from ${\mathrm L}^p(Y)$ into ${\mathrm L}^p(Z)$, extending t…

Discrete mathematicsIntegrable systemGeneral MathematicsBanach spaceFunction (mathematics)Space (mathematics)Measure (mathematics)Omegavector-valued functionsbilinear mapBounded function42B3047B35Vector-valued functionMathematics
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Generalized quasidisks and conformality II

2015

We introduce a weaker variant of the concept of three point property, which is equivalent to a non-linear local connectivity condition introduced in [12], sufficient to guarantee the extendability of a conformal map f from the unit disk onto a domain to the entire plane as a homeomorphism of locally exponentially integrable distortion. Sufficient conditions for extendability to a homeomorphism of locally p-integrable distortion are also given.

Discrete mathematicsIntegrable systemPlane (geometry)Applied MathematicsGeneral Mathematics010102 general mathematicsA domainConformal map01 natural sciencesUnit diskHomeomorphism010101 applied mathematicsDistortion (mathematics)Point (geometry)0101 mathematicsMathematicsProceedings of the American Mathematical Society
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A decomposition theorem for compact-valued Henstock integral

2006

We prove that if X is a separable Banach space, then a measurable multifunction Γ : [0, 1] → ck(X) is Henstock integrable if and only if Γ can be represented as Γ = G + f, where G : [0, 1] → ck(X) is McShane integrable and f is a Henstock integrable selection of Γ.

Discrete mathematicsIntegrable systemSelection (relational algebra)MultifunctionHenstock integralIf and only ifGeneral MathematicsBanach spacePettis integralKurzweil–Henstock–Pettis integral selectionSeparable spaceMathematicsDecomposition theorem
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An integral representation for decomposable measures of measurable functions

1994

We start with a measurem on a measurable space (Ω,A), decomposable with respect to an Archimedeant-conorm ⊥ on a real interval [0,M], which generalizes an additive measure. Using the integral introduced by the second author, a Radon-Nikodym type theorem, needed in what follows, is given.

Discrete mathematicsIntegral representationMarkov kernelMeasurable functionApplied MathematicsGeneral MathematicsDiscrete Mathematics and CombinatoricsInterval (graph theory)Type (model theory)Space (mathematics)Measure (mathematics)MathematicsAequationes Mathematicae
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Polynomial identities with involution, superinvolutions and the Grassmann envelope

2017

Let A be an algebra with involution ∗ over a field of characteristic zero. We prove that in case A satisfies a non-trivial ∗-identity, then A has the same ∗-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution. As a consequence we give a positive answer to the Specht problem for algebras with involution, i.e., any T-ideal of identities of an algebra with involution is finitely generated as a T-ideal.

Discrete mathematicsInvolution (mathematics)Pure mathematicsInvolutionGrassmann algebraSuperinvolutionGeneral MathematicsApplied MathematicsPolynomial identityGrassmann numberSuperinvolutionMathematics (all)Exterior algebraMathematics
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