Pure and Applied Mathematics Journal

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Volume 6, Issue 4, August 2017

  • The Development of Napoleon’s Theorem on the Quadrilateral in Case of Outside Direction

    Mashadi, Chitra Valentika, Sri Gemawati, Hasriati

    Issue: Volume 6, Issue 4, August 2017
    Pages: 108-113
    Received: 6 May 2017
    Accepted: 14 June 2017
    Published: 18 July 2017
    DOI: 10.11648/j.pamj.20170604.11
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    Abstract: In this article we discuss Napoleon’s theorem on the rectangles having two pairs of parallel sides for the case of outside direction. The proof of Napoleon’s theorem is carried out using a congruence approach. In the last section we discuss the development of Napoleon’s theorem on a quadrilateral by drawing a square from the midpoint of a line conn... Show More
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  • Galois and Post Algebras of Compositions (Superpositions)

    Maydim Malkov

    Issue: Volume 6, Issue 4, August 2017
    Pages: 114-119
    Received: 10 June 2017
    Accepted: 22 June 2017
    Published: 20 July 2017
    DOI: 10.11648/j.pamj.20170604.12
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    Abstract: The Galois algebra and the universal Post algebra of compositions are constructed. The universe of the Galois algebra contains relations, both discrete and continuous. The found proofs of Galois connections are shorter and simpler. It is noted that anti-isomorphism of the two algebras of functions and of relations allows to transfer the results of ... Show More
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  • A Study of Congruence on (n, m)-semigroup

    Jiangping Xiao

    Issue: Volume 6, Issue 4, August 2017
    Pages: 120-123
    Received: 1 June 2017
    Accepted: 29 June 2017
    Published: 31 July 2017
    DOI: 10.11648/j.pamj.20170604.13
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    Abstract: Congruence is a special type of equivalence relation which plays a vital role in the study of quotient structures of different algebraic structures. The purpose of this paper is to study the quotient structure of (n, m)-semigroup by using the notion of congruence in (n, m)-semigroup. Firstly, the concept of homomorphism on (n, m)-semigroup is intro... Show More
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  • Cervical Cancer and HIV Diseases Co-dynamics with Optimal Control and Cost Effectiveness

    Geomira George Sanga, Oluwole Daniel Makinde, Estomih Shedrack Massawe, Lucy Namkinga

    Issue: Volume 6, Issue 4, August 2017
    Pages: 124-136
    Received: 22 June 2017
    Accepted: 7 July 2017
    Published: 4 August 2017
    DOI: 10.11648/j.pamj.20170604.14
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    Abstract: The deterministic model for co-infection of cervical cancer and HIV (Human Immunodeficiency Virus) diseases is formulated and rigorously analyzed. The optimal control theory is employed to the model to study the level of effort is needed to control the transmission of co-infection of cervical cancer and HIV diseases using three controls; prevention... Show More
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