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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
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 connecting each of the angle points of each square, where each of the squares is constructed on any quadrilateral and forming a square by using the row line concept.
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...
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Galois and Post Algebras of Compositions (Superpositions)
Issue:
Volume 6, Issue 4, August 2017
Pages:
114-119
Received:
10 June 2017
Accepted:
22 June 2017
Published:
20 July 2017
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 the modern algebra of functions to the algebra of relations, and vice versa, to transfer the results of the modern algebra of relations to the algebra of functions. A new Post algebra is constructed by using pre-iterative algebra and by adding relations as one more universe of the algebra. The universes of relations and functions are discrete or continuous. It is proved that the Post algebra of relations and the Galois algebra are equal. This allows to replace the operation of conjunction by the operation of substitution and to exclude the operation of exist quantifier.
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 ...
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A Study of Congruence on (n, m)-semigroup
Issue:
Volume 6, Issue 4, August 2017
Pages:
120-123
Received:
1 June 2017
Accepted:
29 June 2017
Published:
31 July 2017
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 introduced. Then, the concept of congruence on (n, m)-semigroup is defined, and some basic properties are studied. Finally, it is proved that the set of congruences on an (n, m)-semigroup is a complete lattice. All these generalize the corresponding notions and results for usual binary and ternary semigroups.
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...
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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
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, screening and treatment control strategies. Numerical solutions show a remarkable decrease of infected individuals with HPV (Human Papilloma Virus) infection, cervical cancer, cervical cancer and HIV, cervical cancer and AIDS (Acquire Immunodeficiency Syndrome), HIV infection and AIDS after applying the combination of the optimal prevention, screening and treatment control strategies. However, Incremental Cost-Effective Ratio (ICER) shows that the best control strategy of minimizing cervical cancer among HIV-infected individuals with low cost is to use the combination of prevention and treatment control strategies.
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...
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