iosr-Jm   Volume-15 ~ Issue-1 ~ Jan-Feb 2019

Abstract: Let B = (Q, *, Ʃ, δ, q0, F) and B = (Q', Δ , Ʃ, δ', q0', F') be two Finite Group Automata. Then a mapping Ψ : B → B' is said to be a Finite Group Automata Homomorphism or simply FGA Homomorphism if 1.Ψ(a*b) = Ψ(a) Δ Ψ(b), 2.Ψ(δ(a,n)) = δ' (Ψ(a),n), 3.Ψ(q0) = q0', 4.a ϵ F if and only if Ψ(a) ϵ F'. Let B = (Q, *, Ʃ, δ, q0, F) and B' = (Q', Δ , Ʃ, δ', q0', F') be two Finite Group Automata. Let f : B → B' be a FGA homomorphism. Then (1) if S is a Finite Subgroup Automata of B, then f(S) is a Finite Subgroup Automata of B'. (2) If B is Finite Abelian Group Automaton, then f(B) is Finite Abelian Subgroup Automaton of B. (3) If N is a Finite Normal Subgroup Automaton of B, then f(N) is a Finite Normal Subgroup Automaton of B'.

Key Word:Finite Group Automata, Finite Group Automata Homomorphism (FGA Homomorphism)

[1]. Dr.K.Muthukumaran And S.Shanmugavadivoo , " Finite Sub-Group Automata" Accepted In "Iosr Journal Of Mathematics", A
Journal Of "International Organization Of Scientific Research"
[2]. Dr.K.Muthukumaran And S.Shanmugavadivoo , " Finite Abelian Automata" Accepted In "Iosr Journal Of Mathematics", A
Journal Of "International Organization Of Scientific Research"
[3]. S.Shanmugavadivoo And Dr.K.Muthukumaran , "Ac Finite Binary Automata" "Iosr Journal Of Mathematics", A Journal Of
"International Organization Of Scientific Research"
[4]. S.Shanmugavadivoo And Dr. M.Kamaraj, "Finite Binary Automata" "International Journal Of Mathematical Archive",
7(4),2016, Pages 217-223.
[5]. S.Shanmugavadivoo And Dr. M.Kamaraj, "An Efficient Algorithm To Design Dfa That Accept Strings Over The Input Symbol
A,B,C Having Atmost X Number Of A, Y Number Of B, & Z Number Of C" "Shanlax International Journal Of Arts, Science
And Humanities" Volume 3, No. 1, July 2015,Pages 13-18

Abstract: Let B = (Q, *, Ʃ, δ, q0, F) and B' = (Q', Δ , Ʃ, δ', q0', F') be two Finite Group Automata. Then a mapping Ψ : B → B' is said to be a Finite Group Automata isomorphism or simply FGA isomorphism if 1. Ψ is a FGA homomorphism, 2.Ψ is 1-1 and 3.Ψ is onto. Examples of isomorphic Finite Group Automata are given. If there is a FGA isomorphism from B onto B' , there will be a FGA isomorphism from B' onto B. More generally, FGA Isomorphism is an equivalence relation among finite group automata.

Key Word: Finite Group Automata, Finite Group Automata Homomorphism and Finite Group Automata isomorphismi= 0,1,2)

[1]. Dr.K.Muthukumaran And S.Shanmugavadivoo , " Finite Sub-Group Automata" Accepted In "Iosr Journal Of Mathematics", A Journal Of "International Organization Of Scientific Research"
[2]. Dr.K.Muthukumaran And S.Shanmugavadivoo , " Finite Abelian Automata" Volume 14, Issue 2, Ver.Ii (March – April 2018) , "Iosr Journal Of Mathematics" , A Journal Of "International Organization Of Scientific Research"
[3]. S.Shanmugavadivoo And Dr.K.Muthukumaran , "Ac Finite Binary Automata" Volume 14, Issue 1, Ver.Iii (Jan. – Feb. 2018) , "Iosr Journal Of Mathematics", A Journal Of "International Organization Of Scientific Research"
[4]. S.Shanmugavadivoo And Dr. M.Kamaraj, "Finite Binary Automata" "International Journal Of Mathematical Archive", 7(4),2016, Pages 217-223.
[5]. S.Shanmugavadivoo And Dr. M.Kamaraj, "An Efficient Algorithm To Design Dfa That Accept Strings Over The Input Symbol A,B,C Having Atmost X Number Of A, Y Number Of B, & Z Number Of C" "Shanlax International Journal Of Arts, Science And Humanities" Volume 3, No. 1, July 2015,Pages 13-18

Abstract: In this paper a new method is proposed to solve Quasi-Concave Quadratic Programming problems in which the objective function is in the form of product of two linear functions and constraints functions are in the linear inequalities form. In this method we convert the problem into Multi-Objective Linear Programming problem by splitting those two linear functions and considering them as different maximize/ minimize (depending on main objective function type) type linear objective functions under same constraints and then solve the problem by Chandra Sen's method. For developing this method, we use programming language MATLAB 2017. To demonstrate our propose method, numerical examples are also illustrated.

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Abstract: The article provides a general solution of Fermat quadratic equation, analyzes the behavior of different classes of the basic solutions of the equation. The author shows the possibility to use the solutions for generating prime numbers and proving Landau's hypothesis and Goldbach's binary hypothesis. Numerical calculations are made to explain the general relationships.

Keywords and phrases: Theory of numbers, natural numbers, prime numbers, Goldbach's binary hypothesis,
Landau's hypothesis

[1]. Romanov V. N., Study of fundamental problems of number theory. Saint-Petersburg, Publishing company "Asterion", 2015 (in Russian)..

Abstract: The problem of null-controllability for linear non-autonomous system of the form.......

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Abstract: Based on a previous summary on the the frequently-used properties of the floor function, this article collects till 2018 more frequently-used properties of the floor function. This is an update the previous summary and is helpful for scholars of mathematics and computer science and technology.

Keywords: Floor function, Inequality, Number theory, Discrete mathematics

[1]. Rosen K H. Elementary Number Theory and Its Applications(6th edition). Addison-Wesley, 2011.
[2]. Wang Xingbo, "A Mean-value Formula for the Floor Function on Integers", Mathproblems Journal, 2012,2(4),136-143
[3]. Graham R L, Knuth D E and Patashnik O, Integer Functions. Ch.3 in Concrete Mathematics: A Foundation for Computer Science,
2nd ed. Reading, MA: Addison-Wesley, pp.67-101, 1994, ISBN 0-201-55802-5.

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[5]. Pan C D and Pan CB, Elementary Number Theory (3rd Edition), Press of Peking University, 2013

Abstract: A set Dof a graph G  (V,E) is a dominating set if every vertex in V \ D is adjacent to some vertex in D. The domination number of G is the minimum cardinality of a dominating set. In this paper, complementary circuit domination number is defined and some of its properties are studied..

Keywords: Domination number, complementary circuit domination number

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[3]. Muthammai S., M. Bhanumathi and P. Vidhya,Complementary Tree Domination Number of a Graph,
International Mathematical Forum, 2011, (6), 1273 - 1282.
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Abstract: Musical talent is a gift of nature and a matter of aptitude not instinct. Some people are born with greater aptitude and they develop skills on musical instrument much faster than do others and rise to ability to consistently and doggedly work to improve, usually in tiny increments in all areas of musical talents. In the minds of many people this skill is unnecessary because you either have it or you don't. This paper has carefully traced the trend of growth and development of musical talents in Nigeria as is anchored in the activities of the musical society of Nigeria,. It x-rayed in details one of the talented products of Muson, Tunde Jegede, a composer and multi instrumentalist in contemporary.........

Keywords: African Messiah, Musical Talent, nationalistic movement, Africanism.

[1]. Adeniji, O. (1999) "Music in the Art house" in Guardian Newspapers, April 23, P.25
[2]. Akinsanya, O.A (2005). Message from the Festival planning Committee Chair. The Muson Festival, 2005
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[4]. Blacking, J. (1973). How musical is Man? London: Faber and Faber P.89
[5]. Bergarthan, B, and Boardman, E. (1979). Musical Growth in the Elementary child. Fourth Edition, Holt, Rinchart, Wisconsin

Abstract: Data mining is an important method for analysis the huge data that contained many types of variables. Data mining is widely used in many fields such as commerce, marketing, medicine, ...,etc. It is also an important field with contributions from many sciences. The important techniques of data mining include the classification tree, the regression tree and the clustering. In this paper, we will be interested with the two first techniques. The third technique is presented in another paper. These two techniques will be applied on the practical clinical data, containing different types variables, such as "nominal", "ordered", "numeric", "binary", "repeated measures". The different packages..........

Keywords: Data mining; Classification; Regression; Trees; Cross-validation Errors

[1]. J. Han and M. Kamber, Data mining: Concepts and techniques (Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, 2000).
[2]. D. J. Hand, H. Mannila and P. Smyth, Principles of data mining: Adaptive computation and Machine learning (The MIT Press, 2001).
[3]. T. Hothorn, K. Hornik, C. Strobl and A. Zeile, Party: A laboratory for recursive partitioning, R package version 1.0, 23, 2015.
[4]. T. Therneau, B. Atkinson and B. Ripley, rpart: Recursive partitioning and regression trees, R package version 4, 2015,1-9.
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Abstract: In this paper, we shall introduce the extension of 𝛼𝛽− statistical convergence of order 𝛾 in probability to double sequences. The study will also establish some inclusion relations between 𝛼𝛽− statistical convergences of order 𝛾 and 𝛼𝛽− statistical convergences of order 𝛾in probabilityof double sequences. Finally, we will give a condition under which a double sequence of random variables will converge to a unique limit under two different (𝛼,𝛽) of double sequences and also to prove that if this condition violates then the limit value of 𝛼𝛽− statistical convergence of order 𝛾 in probability of double sequence of random variables for two different (𝛼,𝛽) of double sequence may not be equal..

Keywords: Statistical convergence, Double sequence, 𝛼𝛽− statistical convergences 2010 Mathematics Subject Classification: Primary 40F05, 40J05, 40G05

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