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Ranks, Subdegrees and Suborbital Graphs of Direct Product of the Symmetric Group Acting on the Cartesian Product of Three Sets
Gikunju David Muriuki,
Nyaga Lewis Namu,
Rimberia Jane Kagwiria
Issue:
Volume 6, Issue 1, February 2017
Pages:
1-4
Received:
17 December 2016
Accepted:
3 January 2017
Published:
2 February 2017
Abstract: Transitivity and Primitivity of the action of the direct product of the symmetric group on Cartesian product of three sets are investigated in this paper. We prove that this action is both transitive and imprimitive for all n ≥ 2. In addition, we establish that the rank associated with the action is a constant 23 Further; we calculate the subdegrees associated with the action and arrange them according to their increasing magnitude.
Abstract: Transitivity and Primitivity of the action of the direct product of the symmetric group on Cartesian product of three sets are investigated in this paper. We prove that this action is both transitive and imprimitive for all n ≥ 2. In addition, we establish that the rank associated with the action is a constant 23 Further; we calculate the subdegree...
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Linear and Non-linear Feedback Control Strategies for a 4D Hyperchaotic System
Maysoon M. Aziz,
Saad Fawzi AL-Azzawi
Issue:
Volume 6, Issue 1, February 2017
Pages:
5-13
Received:
1 January 2017
Accepted:
13 January 2017
Published:
16 February 2017
Abstract: This paper investigates the stabilization of unstable equilibrium for a 4D hyperchaotic system. The linear, non-linear and speed feedback controls are used to suppress hyperchaos to this equilibrium. The Routh-Hurwitz theorem and Lyapunov's second methods are used to derive the conditions of the asymptotic stability of the controlled hyperchaotic system. Theoretical analysis, numerical simulation and illustrative examples are given to demonstrate the effectiveness of the proposed controllers.
Abstract: This paper investigates the stabilization of unstable equilibrium for a 4D hyperchaotic system. The linear, non-linear and speed feedback controls are used to suppress hyperchaos to this equilibrium. The Routh-Hurwitz theorem and Lyapunov's second methods are used to derive the conditions of the asymptotic stability of the controlled hyperchaotic s...
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Finite Closed Sets of Functions in Multi-valued Logic
Issue:
Volume 6, Issue 1, February 2017
Pages:
14-24
Received:
3 January 2017
Accepted:
14 January 2017
Published:
20 February 2017
Abstract: The article is devoted to classification of close sets of functions in k-valued logic. We build the classification of finite closed sets. The sets contain only constants and unary functions since sets containing even a two-ary function are infinite. Formulas of the number of finite sets and minimal sets exist for all natural k. We find the numbers of closed sets containing the identity function f (x)=x or a constant for all k. We give the number of sets on levels of inclusions at k up to 10. The inclusion diagrams are present at k up to 5, at k=6 we give inclusion diagrams of sets containing only function f (x)=x and constant 0. We find isomorphic sets and use only one of the isomorphic sets to build the diagrams.
Abstract: The article is devoted to classification of close sets of functions in k-valued logic. We build the classification of finite closed sets. The sets contain only constants and unary functions since sets containing even a two-ary function are infinite. Formulas of the number of finite sets and minimal sets exist for all natural k. We find the numbers ...
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Determining Factors of Country Development and Nondevelopment
Onialisoa Mirana Rakotoarivelo,
Hanitriniaina Sammy Grégoire Ravelonirina
Issue:
Volume 6, Issue 1, February 2017
Pages:
25-38
Received:
30 December 2016
Accepted:
14 January 2017
Published:
22 February 2017
Abstract: In this paper, we study the state of a country with the determining factors of the development-nondevelopment. For doing so, we have seen that they have indicators and sub-indicators. And after having calculated the weight and value of each determining factor, we created a new index to measure a country’s development.
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Mathematical Modelling of Impact of Education on Average Age at the First Marriage in Tanzania
Fatma S. Seif,
Sara A. Khamis,
John K. Mduma,
Estomih S. Massawe
Issue:
Volume 6, Issue 1, February 2017
Pages:
39-44
Received:
14 December 2016
Accepted:
6 January 2017
Published:
23 February 2017
Abstract: This paper examines the impact of education on the average age at the first marriage to women in Tanzania. A mathematical model for the distribution of average age at the first marriage in Tanzania is established and the effect of education on the year at first marriage is estimated for the years 1999 and 2003/04. Both descriptive analysis and model estimate show that education level and education attainment have an impact on the average age at the first marriage. It is established that as one attains further studies, her age at first marriage is delayed. The model validation was presented graphically to illustrate the validity of the model where the proportion of ever married p(a,x1,x2) fitted very closely to the empirical data.
Abstract: This paper examines the impact of education on the average age at the first marriage to women in Tanzania. A mathematical model for the distribution of average age at the first marriage in Tanzania is established and the effect of education on the year at first marriage is estimated for the years 1999 and 2003/04. Both descriptive analysis and mode...
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Some Structures of Hemirings
Md. Yasin Ali,
Kanak Ray Chowdhury,
Abeda Sultana,
Nirmal Kanti Mitra
Issue:
Volume 6, Issue 1, February 2017
Pages:
45-50
Received:
27 January 2017
Accepted:
8 February 2017
Published:
1 March 2017
Abstract: Hemirings appear in a natural manner, in some applications to the theory of automata, the theory of formal languages, graph theory, design theory and combinatorial geometry. Recently, the notions of hemirings with special structures were introduced. But still now there are no complete structural properties of hemirings. In this paper we try to investigate some structures of hemirings. This is done by introducing some examples of hemirings.
Abstract: Hemirings appear in a natural manner, in some applications to the theory of automata, the theory of formal languages, graph theory, design theory and combinatorial geometry. Recently, the notions of hemirings with special structures were introduced. But still now there are no complete structural properties of hemirings. In this paper we try to inve...
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Cubic B-spline Collocation Method for One-Dimensional Heat Equation
Mohamed Hassan Khabir,
Rahma Abdullah Farah
Issue:
Volume 6, Issue 1, February 2017
Pages:
51-58
Received:
26 November 2016
Accepted:
16 January 2017
Published:
4 March 2017
Abstract: In this paper we discuss cubic B-spline collocation method. We have given the derivation of the B-spline method in general. We have applied the method for solving one-dimensional heat equation and the numerical result have been compared with the exact solution.
