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Region Mathematics-a New Direction in Mathematics: Part-1
Issue:
Volume 5, Issue 3, June 2016
Pages:
39-59
Received:
23 March 2016
Accepted:
13 April 2016
Published:
25 April 2016
Abstract: In this paper the author introduces a new direction in Mathematics called by “Region Mathematics” to the world mathematicians, academicians, scientists and engineers. The purpose of developing ‘Region Mathematics’ is not just for doing a generalization of the existing rich volume of classical Mathematics, but it has automatically happened so by this work. To introduce the ‘Region Mathematics’, we begin here with introducing three of its initial giant family members: Region Algebra, Region Calculus and Multi-dimensional Region Calculus. Three more of its initial giant family members: Theory of Objects, Theory of A-numbers (Number Theory) and Region Geometry will follow in the sequel work. The development of the subject ‘Region Mathematics’ is initiated from its zero level for all its initial giant family members. The subject is expected to grow very fast with time to take its own shape, and it will surely cater to all branches of Science, Engineering, and others wherever an element of mathematics needs to be done. With the introduction of Region Mathematics, all existing branches of mathematics will get wide horizontal shifts in the academic universe of science, mathematics, engineering, social science, statistics, etc. with many more alternative new approaches and new thoughts.
Abstract: In this paper the author introduces a new direction in Mathematics called by “Region Mathematics” to the world mathematicians, academicians, scientists and engineers. The purpose of developing ‘Region Mathematics’ is not just for doing a generalization of the existing rich volume of classical Mathematics, but it has automatically happened so by thi...
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Region Mathematics-a New Direction in Mathematics: Part-2
Issue:
Volume 5, Issue 3, June 2016
Pages:
60-76
Received:
23 March 2016
Accepted:
13 April 2016
Published:
3 May 2016
Abstract: This is sequel to our earlier work [11] in which we introduced a new direction in Mathematics called by “Region Mathematics”. The ‘Region Mathematics’ is a newly discovered mathematics to be viewed as a universal mathematics of super giant volume containing the existing rich volume of mathematics developed so far since the stone age of earth. To introduce the ‘Region Mathematics’, we began in [11] by introducing three of its initial giant family members: Region Algebra, Region Calculus and Multi-dimensional Region Calculus. In this paper we introduce three more new topics of Region Mathematics which are : Theory of Objects, Theory of A-numbers and Region Geometry. Several new kind of Numbers are discovered, and consequently the existing ‘Theory of Numbers’ needs to be updated, extended and viewed in a new style.
Abstract: This is sequel to our earlier work [11] in which we introduced a new direction in Mathematics called by “Region Mathematics”. The ‘Region Mathematics’ is a newly discovered mathematics to be viewed as a universal mathematics of super giant volume containing the existing rich volume of mathematics developed so far since the stone age of earth. To in...
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Optimal Control and Hamiltonian System
Issue:
Volume 5, Issue 3, June 2016
Pages:
77-81
Received:
16 April 2016
Accepted:
28 April 2016
Published:
10 May 2016
Abstract: In this paper, an optimal control for Hamiltonian control systems with external variables will be formulated and analysed. Necessary and sufficient conditions which lead to Pantryagin’s principle are stated and elaborated. Finally it is shown how the Pontryagin’s principle fits very well to the theory of Hamiltonian systems. The case of Potryagin’s maximum principle will be considered in detail since it is capable of dealing with both unbounded continuous controls and bounded controls which are possibly discontinuous.
Abstract: In this paper, an optimal control for Hamiltonian control systems with external variables will be formulated and analysed. Necessary and sufficient conditions which lead to Pantryagin’s principle are stated and elaborated. Finally it is shown how the Pontryagin’s principle fits very well to the theory of Hamiltonian systems. The case of Potryagin’s...
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Arithmetic and Matricial Calculation
Raoelina Andriambololona,
Ravo Tokiniaina Ranaivoson,
Wilfrid Chrysante Solofoarisina
Issue:
Volume 5, Issue 3, June 2016
Pages:
82-86
Received:
29 April 2016
Accepted:
9 May 2016
Published:
25 May 2016
Abstract: We present a study on written numeration and arithmetic using matricial formalism for the writing of numeral basis and number. The underlying idea is simple, it consists to consider the numeral representation of number as a matrix representation of an intrinsic number in a basis which represents the numeral system. Then the matrix calculation and linear algebra tools are extensively utilized to simplify arithmetic operations and to remove many inconsistencies existing in arithmetic. Owing to the adopted convention, four dispositions are obtained for the writing of number components according to the disposition in row matrix or column matrix and in decreasing or increasing order. The writing in line from Left handside to the Right handsideby increasing order (called LRi) is shown to be much more logical and coherent with the addition and the multiplication rules than the usual one which starts from the left handside to the right handside by decreasing order (LRd). In the LRi disposition, rules for the addition and multiplication of integers number are derived.
Abstract: We present a study on written numeration and arithmetic using matricial formalism for the writing of numeral basis and number. The underlying idea is simple, it consists to consider the numeral representation of number as a matrix representation of an intrinsic number in a basis which represents the numeral system. Then the matrix calculation and l...
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Numeral System Change in Arithmetic and Matricial Formalism
Raoelina Andriambololona,
Ravo Tokiniaina Ranaivoson,
Hanitriarivo Rakotoson
Issue:
Volume 5, Issue 3, June 2016
Pages:
87-92
Received:
12 May 2016
Accepted:
25 May 2016
Published:
7 June 2016
Abstract: The main goal of this paper is to present a method to tackle the numeral system change problem using matricial formalism. In a previous work, we have described an approach which permits to use matricial formalism and matricial calculation in writing numeration and arithmetic. The present paper is focused on the study of the problem of numeral system change in the framework of this approach. The cases of integer numbers and of more general numbers are given.
Abstract: The main goal of this paper is to present a method to tackle the numeral system change problem using matricial formalism. In a previous work, we have described an approach which permits to use matricial formalism and matricial calculation in writing numeration and arithmetic. The present paper is focused on the study of the problem of numeral syste...
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