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** Authors are invited to submit manuscripts for December 2019 issue.

** November 2019 issue of AARF Journals is officially released.

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S.No Particular Pdf Page No.
1
  • SOME VALUABLE RESULTS ON GOLDEN RATIO


Rajiv Kumar

Abstract:
Mathematician Mark Barr proposed using the first letter in the name of Greek sculptor Phidias, phi, to symbolize the golden ratio.


1-8
2
  • ON ANALYSES OF PRIME GAMMA RINGS AND PRIME GAMMA RADICALS


Ranu Paul

Abstract:
The prime ideals and prime radicals in the projective product of Gamma-rings are extensively studied in this paper. It is shown that the projective product of any two gamma rings can never be prime unless the two component gamma rings are factor gamma rings in which case the prime nature cannot be predicted.


9-17
3
  • ON SUMMABILITY FACTORS FOR GENERALIZED ABSOLUTE NΓ–RLUND SUMMABILITY


Zakawat U. Siddiqui & Bahr E. G. Basi

Abstract:
In this paper we determine the necessary and sufficient conditions to obtain summability factors in transition from |N, pn, qn| boundedness to πœ‘βˆ’ 𝑁 ,π‘žπ‘›,𝛿 k summability.


18-25
4
  • A PROMINENT OBSERVATION ON A NUMBER


Rajiv Kumar

Abstract:
In this paper we discuss some prominent observation on a number 𝑁=π‘π‘žπ‘ž+1 , wβ„Žπ‘’π‘Ÿπ‘’ 𝑝 π‘Žπ‘›π‘‘ π‘žare prime numbers.


26-30
5
  • ANALYSIS OF MATCHED ASYMPTOTIC EXPANSIONS METHOD TO PROVIDE APPROXIMATION SOLUTIONS TO DIFFERENTIAL EQUATIONS


Ayele Tulu Yadate , Daba Meshesha Gusu

Abstract:
This study is attempted to introduce some of the basic concepts of asymptotic analysis and provide approximation solutions to differential equations that cannot easily be solved explicitly. The study is divided in to three parts.


31-49
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