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Author: search.filters.author.Hama, Rattanasak

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    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.
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    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.
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    The theory of geodesics on some surface of revolution
    (2017-01-01)
    Hama, Rattanasak
    ;
    Kasemsuwan, Jaipong
    We study the properties of the geodesics on a Randers rotational surface of revolution by using Zermelo navigation data (hW,), where h is the induced Riemannian metric on the surface of revolution and W is the rotational wind. We are in special interested in the half-period function that can be computed by similar methods to the Riemannian case. Our result can be applied to find the structure of the cut locus of a Randers rotational 2-sphere of revolution.
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    The geometry of a randers rotational surface
    (2015-01-01)
    Hama, Rattanasak
    ;
    Chitsakul, Pakkinee
    ;
    Sabau, Sorin V.
    We study the behaviour of geodesics on a Randers rotational surface of revolution. The main tool is the extension of Clairaut relation from Riemannian case to the Randers case. Moreover, we consider the embedding problem of this surface in a Minkowski space as a hypersurface. Finally, we study the rays and poles as well as the structure of the cut locus of a Randers rotational surface of revolution of von Mangoldt type.
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