iosr-Jm   Volume-12 ~ Issue-2 ~ Mar-Apr 2016

Abstract: This paper covers our computational work and the algorithms designed and implemented in the construction of the main program designated for the determination of the tensor product of representations for the symmetric groups 𝑆𝑛,1≤𝑛≤14 including a flow – diagram of the main program. We have also been able to design the program of the diagram of the tensor product of permutations. Some algorithms are followed by simple examples for illustrations.

[1]. K. Chen and w. Lee: "A general method to calculate all irreduciblerepresentations of a finite groups" Britain J. phys. A. math. Gen-19 (1989).
[2]. ML. Curtis: "Matrix Groups "2 nd. Ed Springer- verlag New york1984.
[3]. C. Curtis and I. Reiner: "Representation theory of finite groups andassociative algebras", John wiley and sone, New York (1962).
[4]. L. Dornhoff: "Group representation theory". Part A, Marcel Dekker,Inc-New York (1971).
[5]. H. DynyaAbdulkamid: "Some Identities relation to partitions andrepetitions of parts" M. SC. Thesis (2000).

Abstract:This paper models the Kenyan Secondary school students' enrollment data using Markov chain model. The 2011 student cohort is observed from time of entry to the time of graduating from the system after the expected four years in Kenya's secondary school level of education. The cohort formed the study target population. The model was used to determine the Country's secondary school completion and dropout rate, retention rate and, the expected duration of schooling by sex.

Key words: Absorbing States, Absorbing Markov Chain, Transition Rates, Dropout Rates, Completion Rates, Fundamental Matrix

[1]. Beck, J. R. &Pauker, S. G. (1983),"The Markov Process in Medical Prognosis", Med Decis Making3, 419–458.
[2]. Dworkin, J. B. (2005),"Retention: How important is it really? and graduation rates", http://www.pnc.edu/co/Retention.pdf .
[3]. Kenya National Bureau of statistics. Statistical Abstract, 2015, KNBS;

[4]. Mose J. N., Odhiambo E. A., Ojunga O. S., & Onyango F., (2014), "Application of Markov Chain Model in Studying Progression
of secondary School Students by Sex During the Free Secondary Education: A case study of Kisii central District." International
Journal of Mathematical Theory and Modelling, iiste 4(4):73-84
[5]. Musiga, L. A., Owino, J. O. & Weke, P. G. (2010), "Modeling a Hierarchical System with a Single Absorbing State, University of
Nairobi .

Abstract: In this paper, we prove the conjecture that the four star 1, 1 1, 1 1, m 1, n K  K  K  K is a relaxed skolem mean graph if m n  8 for n 1, 2, 3, ... and m 1, 2, 3, ... .
Keywords: Relaxed skolem mean graph and star.

[1]. J. C. Bermond, Graceful graphs, radio antennae and French windmills, Graph theory and Combinatorics, Pitman, London, (1979), 13 – 37.
[2]. V. Balaji, D. S. T. Ramesh and A. Subramanian, Skolem Mean Labeling, Bulletin of Pure and Applied Sciences, vol. 26E No. 2, 2007, 245 – 248.
[3]. V. Balaji, D. S. T. Ramesh and A. Subramanian, Some Results on Skolem Mean Graphs, Bulletin of Pure and Applied Sciences, vol. 27E No. 1, 2008, 67 – 74.
[4]. V.Balaji, D.S.T. Ramesh and A.Subramanian, Some Results On Relaxed Skolem Mean Graphs, Bulletin of Kerala Mathematics Association, Vol.5(2), December 2009, 33-44.
[5]. V. Balaji, D.S.T. Ramesh and A.Subramanian, Relaxed Skolem Mean Labeling, Advances and Applications in Discrete Mathematics, Vol.5 (1), January 2010, 11-22.

Abstract: In this paper we will introduce new type of representations of the symmetric groups we call them the triangular representations of the symmetric groups and we will study the first of them which we call it the first triangular representation of the symmetric groups when p divides (n-1).

Keywords: symmetric group,group algebra 𝐾𝑆𝑛 ,𝐾𝑆𝑛−module,Specht module ,exact sequence .

[1]. Adalbert Kerber, Axel Kohnert, Modular irreducible representations of the Symmetric group as linear Codes ,European Journal of
Combinatorics 25(2004) 1285-1299.
[2]. H.K. Farahat, On the Natural Representation of the Symmetric groups, Proc .Glasgow Math.Assoc.5(1962),121-136.
[3]. M.H .Peel, On the Second Natural Representation of the Symmetric groups. Glasgow Math .Journal vol.10 part1(1969),25-37.
[4]. M.H .Peel, Hook Representation of the Symmetric groups ,Glasgow Math .Journal vol.12 part 2(1971),136-149.
[5]. M.H.Peel, Specht Modules and Symmetric groups .Journal of Algebra.vol.36 No.1(1975)88-97).

Abstract: The conditions under which the Wreath Products of Permutation groups would be transitive, primitive and faithful were highlighted by Suleiman Ahmad (2006) see [2]. These properties, under the highlighted conditions are established in [1].In this communication, we enumerate the establishment of such properties under the given conditions; our goal is achievable by relying on existing theorems and enumerating an elaborate example.
Keywords: Group actions, Wreath products, Automorphism, Transitive Permutation groups, K  transitive, Primitivism, Faithfulness.

[1]. Chun P.B, Choji N.M, Adidi C.S, Ajai P.T (2014) "The Transitivity, Primitivity and Faithfulness of the Wreath Products of
Permutation groups" IOSR Journal of Mathematics.
[2]. Ahmad, Suleiman(2006) "On the wreath Products of Permutation groups" Department of Mathematics, University of Jos.
[3]. Audu, M.S. "On Transitive Permutation Groups". African Matimatika,Journal of African Mathematical Union, series 2, Vol.5 (155-
160)
[4]. Ezenwanne, I.U. "Transitive, Primitivism and Wreath Product of Permutation Group" University of Jos.
[5]. Apine, E. (1991). "On Permutation Groups of Prime-Power Order"University of Jos.

Abstract: In this paper,we study the existence of a random attractor for a stochastic dynamical system generated by nonlinear damped wave equation with multiplicative white noise defined on R3.First we proving the existence of the pullback absorbing set and the pullback asymptotic compactness of the cocycle in a certain parameter region by using uniform estimate then we prove the existence of a random attractor.
Keywords: Stochastic wave equation ; nonlinear damping ; random attractor ; pullback asymptotic compactness.

[1]. R. Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1997.
[2]. H. Crauel, Random point attractors versus random set attractors, J. London Math. Soc, 63 (2002) 413-427.
[3]. ]Zhaojuan Wang,Shengfan Zhou,Random attactor for non-Autonomous stochastic strongly damped wave equation on unbounded domains,Journal of Applied Analysis and Computation ,5(2015) 363-387.
[4]. Feireisl E,Global attractors for semilinear damped wave equations with supercritical exponent, Journal of Differential Equations,116( 1995) 431-447.
[5]. H.Crauel,A.Debussche,and F.Flandoli,Random attractors,J.Dynamics and Differential equations ,9 (1997) 307-341.

Abstract: In a many biological and physical sciences studies, a set of techniques have been developed to analyse the relationship between the circular and linear data derived from the geographical positioning system (GPS) telemetry to describe animal movement. Yet, many of the models used by ecologists do not provide a link between the circular and linear variables. This chapter demonstrates the application of the circular-linear regression in describing such a relationship......
Keywords: Animal movement, circular statistics, von Mises, regression model, GPS tracking, turn angles

[1]. Agostinelli, C. and Lund, U. (2011). R package 'circular': Circular statistics (version 0.4-3). URL https://rforge.r-project. org/projects/circular.
[2]. Batschelet, E. (1981). Circular Statistics in Biology. Mathematics in Biology. Academic Press.
[3]. Birkett, P. J., Vanak, A. T., Muggeo, V. M. R., Ferreira, S. M., and Slotow, R. (2012). Animal perception of seasonal thresholds: Changes in elephant movement in relation to rainfall patterns. PLoS ONE, 7(6):e38363.
[4]. Cain, M. L. (1985). Random search by herbivorous insects: A simulation model. Ecology, 66(3):pp. 876–888.
[5]. Cain, M. L. (1989). The analysis of angular data in ecological field studies. Ecology, 70(5):pp. 1540–1543.

Abstract: Multiple encryptions in a practical system refers to encrypting the data more than once i.e., twice or trice to increase the security levels. As long as the cipher is unbreakable the encryption schemes remains strong. In view of the known attacks encrypting the data more than once will strengthen the security levels. In this paper we proposed a triple encryption scheme by using two keys generated by the mathematical structures from the number-theoretic concepts.
Keywords: Fibonacci numbers, Lucas numbers, Fibonacci-Lucas, Affine, Vignere transformations.

[1] A. ChandraSekhar, D. Chaya Kumari, S. Ashok Kumar "Symmetric Key Cryptosystem for Multiple Encryptions",International Journal of Mathematics Trends and Technology (IJMTT). V29 (2):140-144 January 2016. ISSN:2231-5373.
[1] A. Chandra Sekhar, Prasad Reddy. P.V.G.D, A.S.N.Murty, B.Krishna Gandhi "Self-Encrypting Data Streams Using Graph Structures" IETECH International Journal Of Advanced Computations PP 007-009, 2008, vol 2.
[2] A.P.Stakhov " The Golden matrices and a new kind of cryptography" chaos, solutions and Fractals 32(2007) pp1138-1146.
[3] A.P.Stakhov " The Golden section and modern harmony mathematics. Applications of Fibonacci numbers" ,kluwer Academic publishers (1998). pp393-399
[4] A. Chandra Sekhar, K.R. Sudha and Prasad Reddy. P.V.G.D "Data Encryption Technique Using Random Generator" IEEE International Conference on Granular Computing GrC-07, Nov 2-4, 2007, Silicon Valley, USA, PP 576-579.

Abstract: This paper describes a methodology designed to support the decision-making process by the banks to meet the demand. In order to determine an optimum number of servers, queuing theory is applied. The effect of queuing in relation to the time spent by customers to access bank services is increasingly becoming a major source of concern. This is because keeping customers waiting too long could result to cost to them (waiting cost). Providing too much service capacity to operate a system involves excessive cost.......
Keywords: Service; FIFO; M/M/s; Poisson distribution; Queue; Service cost; Utilization factor; Waiting cost; Waiting time, optimization.

[1]. Kembe, M. M, Onah, E. S, Iorkegh, S ; A Study of Waiting And Service Costs of A Multi-Server Queuing Model In A Specialist Hospital; International Journal of Scientific & Technology Research; Volume 1, Issue 8(2012)
[2]. Mohammad Shyfur Rahman chowdhury, Mohammad Toufiqur Rahman and Mohammad Rokibul Kabir; Solving Of Waiting Lines Models in the Bank Using Queuing Theory Model the Practice Case: Islami Bank Bangladesh Limited, Chawkbazar Branch, Chittagong; IOSR Journal of Business and Management; Volume 10, Issue 1 (2013)
[3]. Ajay Kumar Sharma, Dr.Rajiv Kumar, Dr.Girish Kumar Sharma; Queuing theory approach with Queuing Mode; International Journal of Engineering Science Invention; Volume 2, Issue 2(2013)
[4]. M.E. El-Naggar; Application of Queuing Theory to the container terminal at Alexandria seaport; Journal of Soil Science and Environmental Management; Volume 1, Issue 4 (2010)
[5]. Operations Research – Theory and Application by J.K.Sharma, Macmillan Publishers, 2013 Edition, Page;559-61