Search Results

Now showing 1 - 6 of 6

Some of the metrics are blocked by your
consent settings
Finsler Metrics Induced by a Similarity Function
(2020-01-01)
Kumankat, Nisachon
;
Pantaragphong, Praiboon
;
Sabau, Sorin V.
In the present paper, the geometrical properties of a topological space endowed with a similarity was studied. Its relation with weighted quasi-metrics and Finsler metrics of Randers type was discussed. Finally, some applications to bioinformatics and computer science by relating similarities to dynamic programming algorithms are considered. In conclusion, the space containing the real-world data is non-symmetric and non-linear.
Some of the metrics are blocked by your
consent settings
Geodesic distance Kernels
(2017-01-01)
Somboon, Uraiwan
;
Pantaragphong, Praiboon
;
Sabau, Sorin V.
In this paper, the authors deals with non-symmetric kernels induced by weighted quasi-metrics on Hilbert spaces and they study their fundamental properties. These are new and original. Such kind of metrics is obtained from Finsler metrics for example. We show that the use of such kernels may provide a solution to the conflict between positive definiteness of the kernel and the curvature of the underlying space.
Some of the metrics are blocked by your
consent settings
Kosambi-Cartan-Chern (KCC) theory for higher-order dynamical systems
(2016-02-01)
Harko, Tiberiu
;
Pantaragphong, Praiboon
;
Sabau, Sorin V.
The Kosambi-Cartan-Chern (KCC) theory represents a powerful mathematical method for the investigation of the properties of dynamical systems. The KCC theory introduces a geometric description of the time evolution of a dynamical system, with the solution curves of the dynamical system described by methods inspired by the theory of geodesics in a Finsler spaces. The evolution of a dynamical system is geometrized by introducing a nonlinear connection, which allows the construction of the KCC covariant derivative, and of the deviation curvature tensor. In the KCC theory, the properties of any dynamical system are described in terms of five geometrical invariants, with the second one giving the Jacobi stability of the system. Usually, the KCC theory is formulated by reducing the dynamical evolution equations to a set of second-order differential equations. In this paper, we introduce and develop the KCC approach for dynamical systems described by systems of arbitrary n-dimensional first-order differential equations. We investigate in detail the properties of the n-dimensional autonomous dynamical systems, as well as the relationship between the linear stability and the Jacobi stability. As a main result we find that only even-dimensional dynamical systems can exhibit both Jacobi stability and instability behaviors, while odd-dimensional dynamical systems are always Jacobi unstable, no matter their Lyapunov stability. As applications of the developed formalism we consider the geometrization and the study of the Jacobi stability of the complex dynamical networks, and of the Cold Dark Matter (CDM) cosmological models, respectively.
Some of the metrics are blocked by your
consent settings
Jacobi Stability Analysis of Scalar Field Models with Minimal Coupling to Gravity in a Cosmological Background
(2016-01-01)
Dǎnilǎ, Bogdan
;
Harko, Tiberiu
;
Mak, Man Kwong
;
Pantaragphong, Praiboon
;
Sabau, Sorin V.
We study the stability of the cosmological scalar field models by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory. In this approach, we describe the time evolution of the scalar field cosmologies in geometric terms, by performing a "second geometrization" and considering them as paths of a semispray. By introducing a nonlinear connection and a Berwald-type connection associated with the Friedmann and Klein-Gordon equations, five geometrical invariants can be constructed, with the second invariant giving the Jacobi stability of the cosmological model. We obtain all the relevant geometric quantities, and we formulate the condition for Jacobi stability in scalar field cosmologies. We consider the Jacobi stability properties of the scalar fields with exponential and Higgs type potential. The Universe dominated by a scalar field exponential potential is in Jacobi unstable state, while the cosmological evolution in the presence of Higgs fields has alternating stable and unstable phases. We also investigate the stability of the phantom quintessence and tachyonic scalar field models, by lifting the first-order system to the tangent bundle. It turns out that in the presence of a power law potential both of these models are Jacobi unstable during the entire cosmological evolution.
Some of the metrics are blocked by your
consent settings
Inequalities for Kronecker products and Hadamard products of positive definite matrices
(2009-01-01)
Chansangiam, Pattrawut
;
Hemchote, Patcharin
;
Pantaragphong, Praiboon
The purpose of this paper is to develop inequalities for Kronecker products and Hadamard products of positive definite matrices. A number of inequalities involving powers, Kronecker powers, and Hadamard powers of linear combination of matrices are presented. In particular, Hölder inequalities and arithmetic mean-geometric mean inequalities for Kronecker products and Hadamard products are obtained as special cases.
Some of the metrics are blocked by your
consent settings
The matrix analog of the Kneser-Süss inequality
(2006-07-01)
Pranayanuntana, Poramate
;
Hemchote, Patcharin
;
Pantaragphong, Praiboon
The Brunn-Minkowski theory is a core part of convex geometry. At its foundation lies the Minkowski addition of convex bodies which led to the definition of mixed volume of convex bodies and to various notions and inequalities in convex geometry. Various matrix analogs of these notions and inequalities have been well known for a century. We present a few new analogs. The major theorem presented here is the matrix analog of the Kneser-Süss inequality.

KMITL

Browse

Filters

Settings

Sort By

Results per page

Search Results