Some Results on Riemannean Multiple Barycenters

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, we deal with a smooth one-dimensional manifold S1 only. Some theoretical and computational analysis is listed.

CALCULATION FOR KERNEL OF INTERVAL GREY NUMBER BASED ON BARYCENTER APPROACH

The kernel of interval grey number is most likely the real number,which can be used to represent whitenization value of interval grey number.A novel method for calculating kernel of interval grey number is constructed based on the geometric barycenter of whitenization weight function in the two-dimensional coordinate plane,and the calculation of kernel is converted to the calculation of barycenter in geometric figures.The method fully considers the effect of all information contained in whitenization weight function on the calculation result of kernel,and is the extension and perfection of the existing methods in the scope of application.

The Barycenter Property for Robust and Generic Diffeomorphisms

Let f ： Md →Md（d 〉 2） be a diffeomorphism on a compact C^∞ manifold on M. If a diffeomorphism f belongs to the Cl-interior of the set of all diffeomorphisms having the barycenter property, then f is Ω-stable. Moreover, if a generic diffeomorphism f has the barycenter property, then f is 12-stable. We also apply our results to volume preserving diffeomorphisms.

Habitat Suitability and Distribution Pattern Response to Global Climate Change in a Widespread Species,the Asiatic Toad(Bufo gargarizans)

The distribution and diversity of the species are closely related to the global climate.As the most widely distributed species of Bufonidae in China,the study of the distribution pattern and habitat suitability of the Asiatic toad under climate change can help us understand the reply pattern of Bufonidae habitat to climate change.Here,combined with the Maxent model and GIS technology,the effects of climate change on the distribution pattern and habitat suitability of the Asiatic toad were comprehensively analyzed.The results show that the rainfall during the wettest season(Bio16)and the mean temperature of the driest season(Bio9)have a considerable impact on the distribution of the Asiatic toad.In the next 30 to 50 years,across the overall spacial scale of the Chinese mainland,the habitat of the Asiatic toad will be primarily in the eastern part of China and less in south part,while its distribution area will expand to the midwest and northwest parts of China.Overall,the area in which it can be distributed will be reduced and suitable habitat will shift to some regions of higher latitude and elevation.In a word,we systematically analyzed the changes of the distribution pattern and habitat suitability of the Asiatic toad with climate change,and we aim to provide data on how climatic variation may impact amphibians.

N-Body Problem Extension Hypothesis

A system of mutually interacting point-mass objects is considered.All objects act on each other with mutual forces.A consistent relativity of motion based on the elimination of the observer is introduced.The center of inertia of the entire system is a common reference point.Central 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 presented.The scale invariance of the classical n-body problem is used to challenge the physical correctness of the problem formulation.Subsequently,a hypothesis is expressed about the extension of Coulomb’s law as well as Newton’s law of gravity.The 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.

The Universe Is Otherwise/External Gravity

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 open minds and add enhanced views for those uncomfortable with current cosmology.

Semantic model and optimization of creative processes at mathematical knowledge formation

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.

On Markov Chains Induced by Partitioned Transition Probability Matrices

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.

SOLUTION OF OPTIMAL TR A NSPORTATION PROBLEMS USING A MULTIGRID LINEAR PROGR AMMING APPROACH

We compute and visualize solutions to the Optimal Transportation(OT)problem for a wide class of cost functions.The standard linear programming(LP)discretization of the continuous problem becomes intractable for moderate grid sizes.A grid refinement method results in a linear cost algorithm.Weak convergence of solutions is established and barycentric projection of transference plans is used to improve the accuracy of solutions.Optimal maps between nonconvex domains,partial OT free boundaries,and high accuracy barycenters are presented.