Normally Distributed Probability Measure on the Metric Space of Norms

Horváth, Ákos G.

doi:10.1016/s0252-9602(13)60076-4

Cited by 9 publications

(7 citation statements)

References 13 publications

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“…The distance of two normed spaces can be measured by the Hausdorff distance of their unit balls. This motivated the investigations of [9]. We recall it in this section.…”

Section: The Probability Space Of Normsmentioning

confidence: 89%

“…We shall public it in a forthcoming paper since the scope of the present one is still too high. This paper is based on three previous papers of the author ( [7], [8], [9]). These contain some definitions and theorems which will be generalized here and some others which we mention and use now.…”

Section: Introductionmentioning

confidence: 99%

“…This paper is based on three previous papers of the author ( [7], [8], [9]). These contain some definitions and theorems which will be generalized here and some others which we mention and use now.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Minkowski space with changing shape

Horváth

2014

Aequat. Math.

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Abstract. In earlier papers we changed the concept of the inner product to a more general one, to the so-called Minkowski product. This product changes on the tangent space hence we could investigate a more general structure than a Riemannian manifold. Particularly interesting such a model is when the negative direct component has dimension one and the model shows a certain space-time character. We will discuss this case here. We give a deterministic and a non-deterministic (random) variant of such a model. As we showed, the deterministic model can be defined also with a "shape function". Mathematics subject classification (2000). 46C50, 46C20, 53B40.

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“…The distance of two normed spaces can be measured by the Hausdorff distance of their unit balls. This motivated the investigations of [9]. We recall it in this section.…”

Section: The Probability Space Of Normsmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

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Generalized Minkowski space with changing shape

Horváth

2014

Aequat. Math.

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“…The construction of probability measures over a set of convex bodies in metric spaces is proposed by researchers [25]. The model considers n-dimensional Euclidean spaces and the probability space of norms are defined by unit ball.…”

Section: Related Workmentioning

confidence: 99%

Construction and Simulation of Composite Measures and Condensation Model for Designing Probabilistic Computational Applications

Bagchi

2018

Symmetry

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The probabilistic algorithms are widely applied in designing computational applications such as distributed systems and probabilistic databases, to determine distributed consensus in the presence of random failures of nodes or networks. In distributed computing, symmetry breaking is performed by employing probabilistic algorithms. In general, probabilistic symmetry breaking without any bias is preferred. Thus, the designing of randomized and probabilistic algorithms requires modeling of associated probability spaces to generate control-inputs. It is required that discrete measures in such spaces are computable and tractable in nature. This paper proposes the construction of composite discrete measures in real as well as complex metric spaces. The measures are constructed on different varieties of continuous smooth curves having distinctive non-linear profiles. The compositions of discrete measures consider arbitrary functions within metric spaces. The measures are constructed on 1-D interval and 2-D surfaces and, the corresponding probability metric product is defined. The associated sigma algebraic properties are formulated. The condensation measure of the uniform contraction map is constructed as axioms. The computational evaluations of the proposed composite set of measures are presented.

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“…Thus, from practical point of view the deterministic models are more important. We must mention here that the measure of a random model is based on the following observation: on the space of norms such a geometric measure can be defined in such a way that its push-forward onto the line of the absolute-time has normal distribution (see [6]).…”

Section: Introductionmentioning

confidence: 99%

Relativity Theory in Time-space Manifold

Horváth¹

2016

ujpa

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The concept of time-space defined in an earlier paper of the author is a certain generalization of the so-called space-time. In this paper we introduce the concept of time-space manifolds. In the homogeneous case, a time-space manifold is a differentiable manifold with such tangent spaces which have a certain fixed time-space structure. We redefine the fundamental concepts of global relativity theory with respect to this general situation. We study the concepts of affine connection, parallel transport, curvature tensor and Einstein equation, respectively.1991 Mathematics Subject Classification. 83D05, 83F05, 83A05, 51P05; 2010 Physics and Astronomy Classification Scheme. 03.30+p, 04.20Cv, 04.20Jb.

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Normally Distributed Probability Measure on the Metric Space of Norms

Cited by 9 publications

References 13 publications

Generalized Minkowski space with changing shape

Generalized Minkowski space with changing shape

Construction and Simulation of Composite Measures and Condensation Model for Designing Probabilistic Computational Applications

Relativity Theory in Time-space Manifold

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