KMITL

Permanent URI for this communityhttps://dspace.kmitl.ac.th/handle/123456789/1

Browse

Search Results

Now showing 1 - 10 of 11

Some of the metrics are blocked by your
consent settings
The Nature and Significance of Mathematics from Contemporary Viewpoints
(2025-01-01)
Boonnam, Nathaphon
;
Hama, Rattanasak
;
Chansangiam, Pattrawut
;
Sabau, Sorin V.
This paper explores the nature and significance of mathematics, presenting it as a systematic and logical study of patterns in nature. Mathematics can be conceptualized as a pyramid consisting of three layers. The first layer is pure mathematics, which focuses on the study of abstract objects and concepts. The second layer is applied mathematics, dedicated to the development and application of mathematical methods to address specific problems. The final layer involves the applications of mathematics, where established results from pure or applied mathematics are utilized to solve concrete, real-world problems. A deep appreciation of the importance and beauty of abstract patterns requires engaging in research within pure or applied mathematics. To undertake such research, the fundamentals of pure mathematics are essential. Advances in mathematical research often lead to the development of new theories or innovative techniques for problem-solving.
Some of the metrics are blocked by your
consent settings
Sylvester matrix equation under the semi-tensor product of matrices
(2022-01-01)
Chansangiam, Pattrawut
;
Sabau, Sorin V.
We investigate the Sylvester matrix equation in which the product is given by the semi-tensor product, and all involved matrices are matrices over an arbitrary field. We discuss necessary/sufficient condition(s) for the matrix equation to have a solution or a unique solution, or infinitely many solutions. These conditions concern ranks and linear independence. Moreover, we apply a certain kind of vectorization and matrix partitioning to transform the Sylvester equation into an equivalent linear system with respect to the conventional matrix product. Our study includes the Lyapunov equation and the equation A ⋉ X = C as special cases.
Some of the metrics are blocked by your
consent settings
New transform formulae for differential transformation method with applications to the nonlinear plane autonomous systems
(2020-01-01)
Somboon, Uraiwan
;
Kasemsuwan, Jaipong
;
Sabau, Sorin V.
This work presents a new derivation technique for new differential transform formulae of a product of composite functions. The new formulae are applied to nonlinear plane autonomous systems to demonstrate their efficiency and reliability. The approximate series solutions estimated by the differential transform method (DTM) and the multistep differential transform method (MsDTM) are then compared with the flow direction of the vector fields defined by the original system and an analytical solution calculated by the phase-plane method. We found that the MsDTM results are in better agreement with the analytical solution than the DTM ones. Moreover, the MsDTM can be applied to systems whose analytical solutions are unobtainable. The approximate solutions by the MsDTM have the same direction to the flow of the vector field of the system. It follows that the proposed new formulae are reliable and efficient.
Some of the metrics are blocked by your
consent settings
THE GEOMETRY ON THE SLOPE OF A MOUNTAIN
(2020-01-01)
Chansri, P.
;
Chansangiam, P.
;
Sabau, Sorin V.
The geometry on a slope of a mountain is the geometry of a Finsler metric, called here the slope metric. We study the existence of globally defined slope metrics on surfaces of revolution as well as the geodesic’s behavior. A comparison between Finslerian and Riemannian areas of a bounded region is also studied.
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
Characterizations of positive operator-monotone functions and monotone riemannian metrics via borel measures
(2019-12-01)
Chansangiam, Pattrawut
;
Sabau, Sorin V.
We show that there is a one-to-one correspondence between positive operator-monotone functions on the positive reals, monotone Riemannian metrics, and finite positive Borel measures on the unit interval. This correspondence appears as an integral representation of weighted harmonic means with respect to that measure on the unit interval. We also investigate the normalized/symmetric conditions for operator-monotone functions. These conditions turn out to characterize monotone metrics and Morozowa-Chentsov functions as well. Concrete integral representations of such functions related to well-known monotone metrics are also provided. Moreover, we use this integral representation to decompose positive operator-monotone functions. Such decomposition gives rise to a decomposition of the associated monotone metric.
Some of the metrics are blocked by your
consent settings
The cut locus of a Randers rotational 2-sphere of revolution
(2018-01-01)
Hama, Rattanasak
;
Kasemsuwan, Jaipong
;
Sabau, Sorin V.
In the present paper, we study the structure of the cut locus of a Randers rotational 2-sphere of revolution (M, F = α + β). We show that in the case when the Gaussian curvature of the Randers surface is monotone along a meridian, the cut locus of a point q ∈ M is a point on a subarc of the opposite half bending meridian or of the antipodal parallel (Theorem 1.1). More generally, in the case when the Gaussian curvature is not monotone along the meridian, but the cut locus of a point q on the equator is a subarc of the same equator, the cut locus of any point q ∈ M different from poles is a subarc of the antipodal parallel (Theorem 1.2). Some examples are also given in the last section and some differences with the Riemannian case are pointed out.
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.

KMITL

Browse

Filters

Settings

Sort By

Results per page

Search Results