#### Version-2 (Mar-Apr 2015)

**Version-1**
**Version-2**
**Version-3**
**Version-4**
**Version-5**
**Version-6**

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Paper Type |
: | Research Paper |

Title |
: | A Method of Designing Block Cipher Which Involves a Key Bunch Matrix with Polynomial Entries over F2 |

Country |
: | India |

Authors |
: | SAJU M I || LILLY P L |

**Abstract: **In this paper , we have devoted our attention to the development of block cipher , which involves a key bunch matrix , an additional matrix , and key matrix utilized in the development of a pair of functions called permute and substitute , over a finite extension field of F2 . The entries of the matrices are polynomials over F2, this create confusion and diffusion for each round of the iteration process of the encryption algorithm. The security of this process depends upon the size of the extension field. This cipher cannot be broken by any cryptanalytic attack generally available in the literature of cryptography.

**Key words:** Function field, Key bunch matrix, Permute, Primitive polynomial, Substitute.

[1]. Dr.V.U.K. Sastry, K.Shirisha, A Novel Block Cipher Involving a Key Bunch Matrix, International Journal of Computer Applications, 55(16), 2012, 1-6(6)

[2]. Dr. V.U.K. Sastry, K.Shirisha, A Block Cipher Involving a Key Bunch Matrix and Including another Key Matrix supplemented with Xor Operation, International Journal of Computer Applications, 55(16), 2012, 7-10(4)

[3]. Dr. V.U.K. Sastry, K.Shirisha, A Block Cipher Involving a Key Bunch Matrix and Including Another Key Matrix supported with Modular Arithmetic Addition, International Journal of Computer Applications 55(16), 2012, 11-14(4)

[4]. Dr. V.U.K. Sastry, K.Shirisha, A Block Cipher Involving a Key Bunch Matrix and an Additional Key Matrix, Supplemented with Modular Arithmetic Addition and Supported by Key-Based Substitution, International Journal of Advanced Computer Science and Applications (IJACSA), 3(12), 2012, 110-115(6)

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Paper Type |
: | Research Paper |

Title |
: | Area and side measurement relation of two right angled triangle (Relation All Mathematics) |

Country |
: | India |

Authors |
: | Deshmukh Sachin Sandipan |

**Abstract: **In this research paper ,two right angled triangle relation explained with the help of formulas. This relation explained in two part i.e. Area relation and Sidemeasurement relation.Right angled triangle can be narrowed in segment and as like right angled triangle called Seg right angled triangle.Seg right angled triangle always become in zero area. Very feamas pyathagoras theoram proof with the help of Relation All Mathematics methode. also we are given proof of DGP theorem i.e. "In a right angled triangle ,the square of hypoténuse is equal to the subtract of the square of the sidemeasurement and four times the area". We are trying to give a new concept "Relation All Mathematics" to the world .I am sure that this concept will be helpful in Agricultural, Engineering, Mathematical world etc.

**Keywords:** Area, Perimeter, Relation , Seg-right angled triangle , B- Sidemeasurement

[1]. Surrounding agricultural life.

[2]. Answers.yahoo.com ( www.answers.yahoo.com )

[3]. Wikipedia , Google and other search engines. ( www.wikipedia.org )

[4]. This paper is next part of previous paper "Area and perimeter relation of square and rectangle(Relation All Mathematics)"

DOI:10.9790/5728-10660107 , [http://iosrjournals.org/iosr-jm/pages/v10(6)Version-6.html

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Paper Type |
: | Research Paper |

Title |
: | Existence of Semi Primitive Root Mod Pα |

Country |
: | India |

Authors |
: | Dr. K.Vijayalakshmi |

**Abstract: **We know that the smallest positive integer f such that af 1 mod m is called the exponent of 'a' modulo
m and is denoted by expma. We say that 'a' is a semi-primitive root mod m if expma =
2
(m)
. We proved that
there exists a semi-primitive root for mod m when m = p, 2 p(for2), 22.p and 2if 3. Also it was
established that there exists a semi-primitive root for mod m when m = p1p2 where p1 and p2 are distinct odd
primes and at least one prime is of the form 4n+3.In this paper we discuss the existence of semi primitive root
mod pαwhenever it exists for mod p. we have If 'a'

[1]. Introduction to Analytic Number Theory, Springer International Student Edition.

[2]. An Introduction to Theory of Numbers by Ivan Niven, Herbert S. Zuckerman – Wiley Eastern Limited.

[3]. Elementary Number theory by David M .Burton.

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Paper Type |
: | Research Paper |

Title |
: | Note on Fisher's Method of Constructing An Efficient Estimator |

Country |
: | India |

Authors |
: | U.B.AITHAL |

**Abstract: **Fisher (1925), in his famous paper, gave a method of constructing an efficient estimator by using a successive approximation. If there exists a root-n consistent estimator of the parameter and if the probability density function satisfies certain regularities conditions, it is possible to construct an efficient estimator of the parameter. This can be done by a single approximation ( Lehman and Casella, 1998). In order to distinguish between the efficient estimators, Rao( (1961, 1963) introduced the concept of second order efficiency (s.o.e.) of an estimators. In this note, we consider the estimator obtained by using two iterations in the approximation and obtain its s.o.e. following the definition of Rao. It follows from this derivation that we can construct a second order efficient estimator, if it exists, by using any root-n consistent estimator of the parameter.

**Keywords:** and phrases: First order efficient estimator, maximum likelihood estimator, root-n consistent estimator, second order efficiency.

[1]. Aithal,B.U and Nagnur,B.N (1990) Second order efficiency of the BAN estimators for the multinomial family.Comm.Statist.Theory.Meth. 19(5)1763-1776.

[2]. Cox , D.R. and Hinkley, D.V. (1974) : Theoretical statistics, Chapman and Hall, London, 279-363.

[3]. Efron, B. (1975): "Defining the Curvature of a Statistical of a Statistical Problem with applications to second order efficiency", Ann,Statist, 3.

[4]. Fisher, R.A. (1925): "Theory of Statistical Estimation", Canb.Phil.Soc. 22, 700-725.

[5]. Gudi,S.V and Nagnur,B.N (2004) Deficiency of Two Estimator in One-Parameter Exponential Family of DistributionComm.Statist.Theory.Meth 33(8) 1779-1800.

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Paper Type |
: | Research Paper |

Title |
: | Properties of NANO GB-Closed Maps |

Country |
: | India |

Authors |
: | A. Dhanis Arul Mary || I. Arockiarani |

**Abstract: **The aim of this paper is to introduce a new class of maps called nano gb-closed maps in nano
topological spaces. Also some characterizations and several properties concerning nano gb-closed maps and
strongly nano gb-closed maps are derived. 2010 AMS Subject Classification: 54A05, 54C08.

**Keywords**: nano gb-closed sets, nano gb-open sets, nano gb-closed maps, strongly nano gb-closed maps.

[1]. D. Andrijevic, On b-open sets, Mat. Vesnik 48(1996), no.1-2, 59-64.

[2]. Ahmad Al-Omari and Mohd. Salmi Md. Noorani, On generalized b-closed sets, Bull. Malays. Math. Sci. Soc. (2)32(1)(2009), 19-

30.

[3]. Ahmed I. El-maghrabi, More on -generalized closed sets in topology, Journal of Taibah University for science 7(2013),114-119

[4]. M. Caldas and S. Jafari, On some applications of b-open sets in topological spaces, Kochi, J. Math.2(2007), 11-19.

[5]. J. Donntchev, Contra continuous functions and strongly-S closed spaces, Internat. J. Math. Sci. 19(1996), 303-310.

[6]. E. Ekici and Caldas, Slightly -continuous functions, Bol. Soc. Parana. Mat. (3) 22 (2004), no. 2, 63-74.

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Paper Type |
: | Research Paper |

Title |
: | On a Finsler space with Binomial metrics |

Country |
: | India |

Authors |
: | Ghanashyam Kr. Prajapati |

**Abstract: **In this paper, we study a class of (, ) -Finsler metrics called Binomial (, ) -metrics on an n
-dimensional differential manifold M and get the conditions for such metrics to be Berwald, Douglas and
Projectively flat. Further, we prove that a Binomial (, ) -metric is of scalar flag curvature and isotropic S
-curvature if and only if it is isotropic Berwald metric with almost isotropic flag curvature.
2010 Mathematics Subject Classifications: 53B40, 53C60.
Keywords: (, ) -metric , Berwald space, Douglas space, Finsler space, projectively flat, scalar flag
curvature.

[1]. Z. Shen and S. S. Chern, Riemann-Finsler Geometry, (Nankai Tracts in Mathematics, World Scientific, 2004).

[2]. B.Najafi, Z.Shen and A.Tayebi, Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties, Geom.

Dedicata., 131, 2008 , 87-97.

[3]. S.Bacso and M.Matsumoto, On Finsler spaces of Douglas type, A generalization of the notion of Berwald space, Publ. Math.

Debrecen., 51, 1997, 385-406.

[4]. B.Li, Y.Shen and Z.Shen, On a class of Douglas metrics, Studia Sci. Math. Hungarica, 46(3), 2009, 355-365.

[5]. G.Hamel, Uber die Geometrien in denen die Geraden die Kurzesten sind, Math. Ann., 57, 1903, 231-264.

[6]. Z.Shen and G.Civi Yildirim, On a Class of Projectively Flat metrics with Constant Flag Curvature, Canadian Journal of Mathematics.,

60, 2008, 443-456.

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Paper Type |
: | Research Paper |

Title |
: | Analytical Approximate Solutions of Fifth Order More Critically Damped Systems in the case of Smaller Triply Repeated Roots |

Country |
: | Bangladesh |

Authors |
: | Md. Mahafujur Rahaman || Md. Mizanur Rahman |

**Abstract: **In order to look into the transient behavior of vibrating systems, the Krylov-Bogoliubov-Mitropolskii
(KBM) method is extensively used. The method was initially devised to obtain the periodic solutions of second
order nonlinear differential systems with small nonlinearities. In this article, the method has been modified to
investigate the solutions of fifth order more critically damped nonlinear systems. A fifth order more critically
damped nonlinear differential system is considered and asymptotic solutions are studied when the triply
eigenvalues are small and the other two equal eigenvalues are large. The results obtained by the presented
modified KBM method agree with those obtained by the fourth order Runge-Kuttamethod satisfactorily.

**Keywords**: KBM, nonlinearity, more critically damped system, asymptotic solution, eigenvalues

[1]. N. N. Krylov and N. N.Bogoliubov, Introduction to Nonlinear Mechanics(New Jersey, Princeton University Press, 1947).

[2]. N. N.Bogoliubov and Y.Mitropolskii, Asymptotic Methods in the Theory of Nonlinear Oscillations (New York, Gordan and Breach, 1961).

[3]. I. P.Popov, A Generalization of the Bogoliubov Asymptotic Method in the Theory of Nonlinear Oscillations (in Russian), Dokl. Akad. USSR, 3, 1956, 308-310.

[4]. I. S. N. Murty and B. L. Deekshatulu, and G.Krishna, On an Asymptotic Method of Krylov-Bogoliubov for Over-damped Nonlinear Systems, J. Frank. Inst.,288, 1969, 49-65.

[5]. M. A. Sattar, An asymptotic Method for Second Order Critically Damped Nonlinear Equations, J. Frank. Inst., 321, 1986, 109-113.

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Paper Type |
: | Research Paper |

Title |
: | (M, N)-Jordan Left Derivation on Matrix Ring |

Country |
: | Iraq |

Authors |
: | Rajaa C. Shaheen || A. H. Majeed |

**Abstract: **In this paper ,we introduced a new definition which is the definition of (m,n)-Jordan left derivation and we prove that any (m,n)-Jordan left derivation on the full matrix ring is identically zero also we describe the structure of (m,n)-Jordan left derivation on the upper triangular matrix ring .

**Keywords:** Left derivation , Jordan Left Derivation.

[1]. M.Bresar and J.Vukman ,On left derivation and related mappings, Proc.Amer .Math. Soc.110(1990),no.1,7-16.

[2]. Q.Deng,On Jordan left derivation ,Math.J.Okayama Univ.34(1992)145-147.

[3]. N.M.Ghosseire,On Jordan left derivations and generalized Jordan left derivations of matrix rings,Bulletin of the Iranian mathematical society vol.38 no.3(2012),pp 689-698.

[4]. B.Hvala.Generalized derivation in rings,Comm.Algebra26(1998),no.4,1147-1166.

[5]. W.Jingand S.Lu,Generalized Jordan derivations on prime rings and standard operator algebras,Taiwanese J.Math.7(2003),no.4,605-613.

[6]. K.W.Jun and B.D.Kim,Anote on Jordan left derivations,Bull.Korean Math.Soc.33(1996),no.2,221-228.

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Paper Type |
: | Research Paper |

Title |
: | Basic Minimal Dominating Functions of Euler Totient Cayley Graphs |

Country |
: | India |

Authors |
: | K.J. Sangeetha || B. Maheswari |

**Abstract: **Graph Theory is the fast growing area of research in Mathematics. The concepts of Number Theory,
particularly, the "Theory of Congruence" in Graph Theory, introduced by Nathanson[8], paved the way for the
emergence of a new class of graphs, namely, "Arithmetic Graphs". Cayley graphs are another class of graphs
associated with the elements of a group. If this group is associated with some arithmetic function then the
Cayley graph becomes an Arithmetic graph.
The Cayley graph associated with Euler Totient function is called an Euler Totient Cayley graph and in this
paper we study the Basic Minimal Domination Functions of Euler Totient Cayley graphs.

**Keywords**: Euler Totient Cayley Graph, Minimal Dominating Functions, Basic Minimal Dominating
Functions.

[1]. Allan, R. B., Laskar, R. C. − On domination and independent domination numbers of a graph, Discrete Math, 23 (1978), 73-76.

[2]. Arumugam, S. − Uniform Domination in graphs, National Seminar on graph theory and its Applications, January (1983).

[3]. Arumugam, S., Rejikumar, K. − Fractional independence and fractional domination chain in graphs. AKCE J Graphs. Combin., 4

(2) (2007), 161 – 169.

[4]. Berge, C. − The Theory of Graphs and its Applications, Methuen, London (1962).

[5]. Cockayne, E. J., Hedetniemi, S. T. − Towards a theory of domination in graphs, Networks, 7 (1977), 247 – 261.

[6]. 6. Haynes, T. W., Hedetniemi, S. T., Slater, P. J − Fundamentals of domination in graphs, Marcel Dekker, Inc., New York (1998).

[7]. Madhavi, L. − Studies on domination parameters and enumeration of cycles in some Arithmetic Graphs, Ph.D.Thesis,submitted to

S.V.University, Tirupati, India, (2002).

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Paper Type |
: | Research Paper |

Title |
: | Special Double Sampling Plan for Truncated Life Tests Based On Generalised Log-Logistic Distribution |

Country |
: | India |

Authors |
: | D. Malathi || Dr. S. Muthulakshmi |

**Abstract: **The design of special double sampling plan is proposed for the truncated life tests assuming that the lifetime of a product follows generalized log-logistic distribution . The minimum sample sizes of the special double sampling plan are determined to ensure that the median life is longer than the given life at the specified consumer's confidence level. The operating characteristic values are analysed.The minimum median ratios are obtained so as to meet the producer's risk at the specified consumer's confidence level. Numerical illustrations are provided to explain the use of constructed tables. The efficiency of special double sampling plan is analysed with single sampling plan.

[1]. Rao G.S., Kantam R.R.L., Rosaiah K. and Pratapa Reddy J.(2012) Acceptance Sampling Plans for Percentiles based on the Inverse Rayleigh distribution, Electron. J. App. Stat. Anal, Vol.5,No.2 ,164-177.

[2]. Rosaiah K. and Kantam R.R.L.(2005) Acceptance Sampling based on the Inverse Rayleigh Distribution,Economic Quality Control,Vol 20, No.2, 277-286.

[3]. Aslam M.and Jun C.H.(2010) A Double Acceptance Sampling plan for generalized log-logistic distributions with known shape parameters ,Journal of Applied Statistics,Vol.37,No.3,405-414.

[4]. Kantam R.R.L., Rosaiah K. and Rao G.S.(2001) Acceptance sampling based on life tests: log-logistic models, Journal of Applied Statistics,Vol.28,121-128.

[5]. Rao G.S., Kantam R.R.L.(2010) Acceptance sampling plans from truncated life tests based on the log-logistic distribution for percentiles, Economic Quality Control,Vol.25,No.2,153-167.

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Paper Type |
: | Research Paper |

Title |
: | Intuitionistic Fuzzy Perfectly Regular Weakly Generalized Continuous Mappings |

Country |
: | India |

Authors |
: | P. Rajarajeswari || L. Senthil Kumar |

**Abstract: **The purpose of this paper is to introduce and study the concepts of intuitionistic fuzzy perfectly regular weakly generalized continuous mappings and intuitionistic fuzzy perfectly regular weakly generalized open mappings in intuitionistic fuzzy topological space. Some of their properties are explored.

**Keywords:** Intuitionistic fuzzy topology, Intuitionistic fuzzy regular weakly generalized closed set, Intuitionistic fuzzy regular weakly generalized open set, Intuitionistic fuzzy perfectly regular weakly generalized continuous mappings, Intuitionistic fuzzy perfectly regular weakly generalized open mappings.

[1]. Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 20, 1986, 87–96.

[2]. Chang, C. L. Fuzzy topological spaces, J. Math. Anal. Appl., Vol. 24, 1968, 182–190.

[3]. Çoker, D., An introduction to intuitionistic fuzzy topological spaces, Fuzzy sets and systems, Vol. 88, 1997, 81–89.

[4]. Gurcay, H., A. Haydar, D. Çoker, On fuzzy continuity in intuitionistic fuzzy topological spaces, Jour. of Fuzzy Math, Vol. 5, 1997, 365–378.

[5]. Hanafy, I. M., Intuitionistic fuzzy γ continuity, Canad. Math Bull, Vol. 52, 2009, 544–554.

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Paper Type |
: | Research Paper |

Title |
: | A Completion for Distributive Lattices |

Country |
: | India |

Authors |
: | C. Ganesa Moorthy || S. G. Karpagavalli |

**Abstract: **A completion for a class of lattices is constructed and it is observed that a congruence relation on a given lattice can be extended to its completion.

**Key words:** Complete lattice, Congruence relation. AMS Subject Classification (2010): 06B23,06D10,18B35.

[1]. G.Gratzer, General lattice theory, Academic press, New York, 1978.

[2]. F.Wehrung, A solution to Dilworth's congruence lattice problem, Advances in Mathematics, 216(2007)610-625