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Some Results on Riemannean Multiple barycenters

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Journal of Applied Mathematics and Physics 2014年第7期2卷 503-509页

作者： Mostafa Zahri Naji Khallaf Department of Mathematics College of Science Taibah University Madinah Saudi Arabia

A characteristic of a special case of Riemannean barycenters on the unit circle is presented. The non-uniqueness of such barycenters leads to an interesting study of the so-called multiple barycenters. In this work, w... 详细信息

关键词： Smooth Manifold Geodesic barycenter of Masses Metric Space Multiple barycenters

On Markov Chains Induced by Partitioned Transition Probability Matrices

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Acta Mathematica Sinica,English Series 2011年第3期27卷 441-476页

作者： Thomas KAIJSER Department of Mathematics and Information Coding Group Linkoping University S-581 83 LinkSping Sweden

Let S be a denumerable state space and let P be a transition probability matrix on S. If a denumerable set M of nonnegative matrices is such that the sum of the matrices is equal to P, then we call M a partition of P. Let K denote the set of probability vectors on S. With every partition M of P we can associate a transition probability function PM on K defined in such a way that if p ∈ K and M ∈M are such that ｜｜pM｜｜〉 0, then, with probability ｜｜pM｜｜ the vector p is transferred to the vector pM/｜｜pM｜｜. Here ｜｜·｜｜ denotes the/1-norm. In this paper we investigate the convergence in distribution for Markov chains generated by transition probability functions induced by partitions of transition probability matrices. The main motivation for this investigation is the application of the convergence results obtained to filtering processes of partially observed Markov chains with denumerable state space.

关键词： Markov chains on nonlocally compact spaces filtering processes hidden Markov chains Kantorovich metric barycenter

Inequalities on the Triangle

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Journal of Mathematical Research with Applications 2016年第1期36卷 51-60页

作者： Zlatko PAVI Mechanical Engineering Faculty in Slavonski Brod University of Osijek

The article deals with generalizations of the inequalities for convex functions on the triangle. The Jensen and the Hermite-Hadamard inequality are included in the *** a convex function on the triangle, we obtain a ge... 详细信息

关键词： convex function convex combination triangle barycenter

N-Body Problem Extension Hypothesis

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Journal of Physical Science and Application 2023年第1期13卷 9-14页

作者： Karol Dobrovodsky Institute of Informatics Slovak Academy of SciencesDúbravskácesta 9Bratislava 84237Slovakia

A system of mutually interacting point-mass objects is *** objects act on each other with mutual forces.A consistent relativity of motion based on the elimination of the observer is *** center of inertia of the entire system is a common reference *** and mutual quantities are defined and the relationship between them is derived.A simple method of numerical approximation of the evolution of the central motion is *** scale invariance of the classical n-body problem is used to challenge the physical correctness of the problem ***,a hypothesis is expressed about the extension of Coulomb’s law as well as Newton’s law of *** consequences of the hypothesis are illustrated by the simulation of the helium-2 atom and the simulation of the motion of the stars S2,S4716 in the vicinity of the black hole in the core of our galaxy.

关键词： barycenter partial and resultant mutual forces central and mutual inertia

Semantic model and optimization of creative processes at mathematical knowledge formation

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Natural Science 2010年第8期2卷 915-922页

作者： Victor Egorovitch Firstov Department of Mechanics and Mathematics Saratov State University

The aim of this work is mathematical education through the knowledge system and mathematical modeling. A net model of formation of mathematical knowledge as a deductive theory is suggested here. Within this model the formation of deductive theory is represented as the development of a certain informational space, the elements of which are structured in the form of the orientated semantic net. This net is properly metrized and characterized by a certain system of coverings. It allows injecting net optimization parameters, regulating qualitative aspects of knowledge system under consideration. To regulate the creative processes of the formation and realization of mathematical know- edge, stochastic model of formation deductive theory is suggested here in the form of branching Markovian process, which is realized in the corresponding informational space as a semantic net. According to this stochastic model we can get correct foundation of criterion of optimization creative processes that leads to “great main points” strategy (GMP-strategy) in the process of realization of the effective control in the research work in the sphere of mathematics and its applications.

关键词： The Cybernetic Conception Optimization of Control Quantitative And Qualitative Information Measures Modelling Intellectual Systems Neural Network Mathematical Education The Control of Pedagogical Processes Creative Pedagogics Cognitive And Creative Processes Informal Axiomatic Thery Semantic Net Net Optimization Parameters The Topology of Semantic Net Metrization The System of Coverings Stochastic Model of Creative Processes At The Formation of Mathematical Knowledge Branching Markovian Process Great Main Points Strategy (GMP-Strategy) of The Creative Processes Control Interdisciplinary Learning: Colorimetric barycenter

The Universe Is Otherwise/External Gravity

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Natural Science 2021年第9期13卷 392-397页

作者： Paul Schroeder Wind Lake WI USA

The ideas that follow provide a totally different view of the universe. These are perspectives by which to view everything without clashing over technical understandings. Sufficient examination of this model should op... 详细信息

关键词： Gravity EM Radiation/Light Universe Rotation Revolution Doppler Infinity Electrons Matter Magnetism Bumps barycenter Black Holes