iosr-Jm   Volume-12 ~ Issue-6 ~ Nov-Dec 2016

Abstract: Corruption and Fraud has been an endemic problem in the global economic affairs for ages , and recently Cybercrime has joined the litany of the cankerworm that impede economic development and social tranquility of nations. To control and manage human resource capital, in relation to stock of or supply of money, materials, and other assets that can be drawn on by a person, organization or state, to establish an effective and viable economy, individuals, organizations and governments need to maintain a truly functional law and order. It is a fact that Africa (especially Nigeria and Malaysia)................

Keywords: Law, Corruption, Fraud, Cybercrime, Business Management, Africa, Nigeria, Malaysia, and Economic Development

[1] Beattie, Andrew, 2016, Fraud History ,(www.investopedia.com/articles/finance)
[2] Clunas, Craig, et al. "china." Microsoft@Encarta@2009 "(DVD)‟ Redmond, WA; Microsoft corporation, 2008.
[3] Colander, David C. (2004), Economics, Fifth edition, McGraw Hill, Irwin; business unit, McGraw-Hill Companies, Inc, 1221 Avenue of the Americans, New York, NY 10020
[4] Ejime Paul (2016), The Guardian News on "African Union deserves visionary, dynamic leadership,‟ September 8, 2016; copyright © 2016 Guardian Newspapers
[5] Elaine Byrne (2007), The Moral and Legal Development of Corruption: Nine-teenth and Twentieth Century Corruption in Ireland – PhD Thesis, University of Limerick.

Abstract: Graph theory is one of the most research focused branch of Mathematics. It has been witnessed a tremendous growth due to a number of applications in computer communication, IT networks, molecular Physics, Chemistry, Social network and biological sciences, computational linguistics and in many other areas. Graph Parameters have a worthy role in all these applications. Many Graph parameters have been introduced and applied in various fields. The mainly used graph parameters are various types of domination numbers,..............

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Abstract: Primes less than 1012 are analyzed for occurrence of digit 3 in them. Multiple occurrences of 3's are explored. The first and last occurrences of all multiple 3's in them are determined within blocks of powers of 10 till 1 trillion.

Keywords: All occurrences, digit 3, Prime numbers.

[1] Benjamin Fine, Gerhard Rosenberger, "Number Theory: An Introduction via the Distribution of Primes," Birkhauser, (2007).
[2] Neeraj Anant Pande, "Numeral Systems of Great Ancient Human Civilizations", Journal of Science and Arts, Year 10, No. 2 (13), 2010, pp. 209-222.
[3] Neeraj Anant Pande, "Improved Prime Generating Algorithms by Skipping Composite Divisors and Even Numbers (Other Than 2)", Journal of Science and Arts, Year 15, No.2(31), 2015, pp. 135-142.
[4] Neeraj Anant Pande, "Analysis of Primes Less Than a Trillion", International Journal of Computer Science and Engineering Technology, Vol. 6, No 6, 2015, pp. 332-341.
[5] Neeraj Anant Pande, "Analysis of Occurrence of Digit 0 in Natural Numbers Less Than 10n", American International Journal of Research in Formal, Applied and Natural Sciences, Communicated, 2016..

Abstract: On the 16-hilbert problem, I will give an upper bound for the number of limit cycles in twodimensional polynomial vector fields of degree d, and I show a link between the two parts of the 16-hilbert problem.

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[1]. [Dulac, H.] (1923). Sur les cycles limites. Bull. Soc. Math. France 51, 45–188.
[2]. [Écalle, J.] (1992). Introduction aux Fonctions Analysables and Preuve Constructive de la Conjecture de Dulac. Hermann, Paris.
[3]. [Ilyashenko, J.], (1985). Dulac's memoir « On limit cycles » and related problems of the local theory of differential equations.
Russian Math. Surveys VHO, 1–49.
[4]. [Ilyashenko, Yu.], (1991). Finiteness Theorems for Limit Cycles, American Math Society, Providence, RI.
[5]. [J. Li], Hilbert's 16th problem and bifurcations of planar polynomial vector fields, Internat. J. Bifur. Chaos Appl. Sci. Engrg. 13
(2003), 47–106.

Abstract: A dominating set S V(G) is said to be a complementary tree dominating set if the induced sub graph V  S is a tree. The minimum cardinality of a complementary tree dominating set of G is called the complementary tree domination number of G and is denoted by (G). ctd  In this paper we have introduced the new type of domination named complementary tree paired domination number for connected graphs and we study the theoretical properties of this parameter and many bounds are obtained in terms of order of G and its relationship with other domination parameters are also obtained. The relation between the complementary tree paired domination number and total domination number of a tree is also discussed.

Keywords: Graph, Domination, tree, Perfect Matching

[1] J.A. Bondy Murthy, Graph Theory with Applications (Elsevier science publishing co., Inc, Newyork, N.Y.10017, 1976).
[2] E.J. Cockayne, R.M. Dawes and S.T. Hedetniemi(1980), Total domination in graphs, Networks, 10, 1980, 211-219.
[3] Jayapal Baskar Babujee, Babitha Suresh, New Constructions of Edge Bimagic Graphs from Magic Graphs, Applied Mathematics 2,
2011, 1393-1396.
[4] V.R. Kulli and B. Janakiram, The split domination number of a graph, Graph Theory Notes of New York, New York Academy of
sciences XXXXII, (1997), 16-19.
[5] Mustapha Chellai and Teresa W. Haynes , Total and paired domination numbers of a tree, AKCE J. Gaphs Combin., 1(2), (2004),
69-75.

Abstract: 1. Polidromik Number: (111, 222, 121, 525 its value same as from left to right starting number setup)

2. Horzat Number: (the number is divided by the sum of groups all number in, like in 12 sums (1+2) 3 is the Hozrat number of 12.)
3. Demloa Number: (214423, 21+23 =44 that of the sum 1st +last number =middle number )
4. UD Number : (ups and down number like 6, 9, 81, 18)
5. Kaprekar Constant: (the professor kaprekar in 1946 inventing the constant number 6174)
6. Kaprekar number: (2025 , cut in middle and ad 20+25=45 square then same previous number 2025) In this Connection,.

Keywords: Trai Rashiq bargio sutra & Constant as odd and even 8 and integer 2 up to nth term.

[1]. 17th science and technology fair 1993 "Number playing by mathematics" DT: 7-9 Th December 1993
[2]. Copyright Registration No. 10482 COPR DT: 31/08/2008
[3]. Theory of number
[4]. Real number analysis as Sequence of number as In Number
12 = 1 282 = 784
42 = 16 292 = 841
52 = 25 302 = 900…….
252 = 625 502 = 2500n………..…n2
[5]. Shown / Approved by Member secretary of Bangladesh mathematics society and chairman, math department Dhaka University.

Abstract: In the present paper we introduce some Finsler space with Euclidean space and many types of curvature forms. Finally we give some visual conditions of curvature and give the application of Finsler space and metric with curvature in theorem 1, 2, 3 and 4.

Keywords: Finsler metrics, Euclidean space, Riemannian space, Randers metric, Kropina metric, Matsumoto metric, E – Curvature, Finsler space.

[1]. Zhongmin SHEN, Lectures on Finsler Geometry Singapore World Scientific,2001
[2]. Zhongmin, SHEN,Differential Geometry of spray and Finsler Spaces, Kluwer Academic Publishers Dordrecht, 2001.
[3]. Xingyue CHEN, Zhongmin SHEN. Randers metrics with special curvature properties Osaka 1, Math 2003 40(1);87-101
[4]. Xingyue CHEN, Zhongmin SHEN .On Douglas metrics, Publ. Math Debrecen 2005 66(3-1) 503-512
[5]. O.Lungu, some curvature properties inRanders spaces. Sci. Stud Res. Math. Inform. 2009, 19(2) 3001-3008.
[6]. Dongmei TANG.A class of weak Berwald (𝛼,𝛽)- metrics with scalar flag curvature. Adv. Math. (China) 2012, 41(2):199 – 208.

Abstract: In this paper, we elaborate some existing result of fixed point theorems, that fulfill the nature of G-metric space and satisfy the ∅-maps. Previously Erdal Karapinar and Ravi Agrawal [1] have modified some existing result of fixed point theory of Samet et.al. Int. J. Anal (2013:917158, 2013) [2] and Jleli-Samet (Fixed point theory application. 2012: 210,2012) [3] in a different way.

[1]. Karapinar,E, Agarwal,R.P : Further fixed point results on G-metric spaces, Fixed point theory and application 2013,2013:154
[2]. Samet, B, Vetro, C, Vetro, F: Remarks on G-metric spaces. Int. J. Anal. 2013, Article ID 917158 (2013)
[3]. Jleli, M, Samet, B: Remarks on G-metric spaces and fixed point theorems. Fixed Point Theory Appl. 2012, Article ID 210 (2012)
[4]. Mustafa, Z, Sims, B: A new approach to generalized metric spaces. J. Nonlinear Convex Anal. 7(2), 289-297 (2006)
[5]. Banach, S: Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fundam.Math. 3, 133-181 (1922)

Abstract: In this paper we will introduce how to cluster of tangle graph. We will study clustering by normalized tangle graph cut and markov cluster. We will explain the cluster by examples. We will illustrate algorism to understand the cluster.

Keywords: Tangle graph, cluster, normalized, markov model.

[1]. M.El-Ghoul &M.M.Al-Shamiri, A study on graphs and Knots.
[2]. Van Dongen, S. (2000) Graph Clustering by Flow Simulation. PhD Thesis, University of Utrecht, The Netherlands.

Abstract: This work presents a study of three-dimensional topology optimization of some academic structures as Messerschmitt Bolkow Bolhm beam (MBB beam) and cantilever beam using the ANSYS APDL (ANSYS Parametric Design Language) based Optimality Criteria approach and the MATLAB numerical results. The basic concept solves minimum compliance problem subject to volume constraints using the Solid Isotropic Material with Penalization (SIMP) method. We compare different parameters like-stresses, displacement, and von mises stress and compliance values. In order to give a faster and better code for implementation of domain decomposition method applying to 3d structures.

Keywords: Topology optimization, SIMP method, optimality criteria, minimum compliance, material density

[1]. M.P. Bendsøe, N. Kikuchi, "‟ Generating optimal topologies in structural design using a homogenization method, "‟ Comp. Meth. Appl. Mech. Eng, 71, 1988, 197-224.
[2]. M.P. Bendsøe and Ole. Sigmund, Topology Optimization, Theory, Methods and Applications (Springer-Verlag, Berlin Heidelberg, 2003).
[3]. Ole. Sigmund, "‟A 99 line topology optimization code written in Matlab,"‟ Structural and Multidisciplinary Optimization, Springer, 21(2), 2001, 120—127.

Abstract: We define the Farey grid matrix and also, we introduce the concept of Farey grid graph and Farey grid from Farey sequence and present some observations

Keywords: Farey Sequence, Farey matrix, Farey fractions, Farey grid, Farey grid graph ,Farey grid matrix.

[1]. A.Gnanam, M.A.Gopalan, C.Dinesh, Farey Matrix, International Journal of Mathematics Trends and Technology-Volume 19 Number 1 Mar 2015.
[2]. Ivan Niven, Herbert S.Zuckerman, Hugh L.Montgomery,An Introduction to The Theory of Numbers (Fifth edition),Wiley-India Edition 2011.
[3]. Don Redmond, Number Theory An Introduction, Marcel Dekker,Inc,1996.
[4]. JozseSandor,Dragoslav S.Mitrinovic and BorislaCrstici, Handbook of Number Theory I,Springer 2006.
[5]. G.H. Hardy and E.M. Wright,An Introduction to The Theory of Numbers(Fourth edition),Oxford at The Clarendon Press 1975.

Abstract: In this article, we consider a continuous review inventory system in supply chain(consist of retailer, distributor and manufacturer) with Markovian demand. Theoperating policy is (s S) policy, that is, the maximum inventory level is Sand whenever the inventorylevel drops to, s an orderforQ(S-s)units is placed. The items are supplied to the retailers and the direct customers (Direct demand), in packs of Q items from the distribution center which has instantaneous replenishment facility from an abundant source (manufacturer).The ordered items are received after a randomtime which is assumed to be exponential distribution. The demands that occur during stock outperiod are enter into the orbit offinite size N.......

Keywords: Continuous review inventory system, positive lead time, retrialdemand, (S, S) policy.

[1]. Axsater, S. (1993). Exact and approximate evaluation of batch ordering policies for two level inventory systems. Oper. Res. 41.
777-785.
[2]. Benita M. Beamon. (1998). Supply Chain Design and Analysis: Models and Methods. International Journal of Production
Economics.Vol.55, No.3, pp.281-294.
[3]. Cinlar .E, Introduction to Stochastic 'Processes, Prentice Hall, Engle-wood Cliffs, NJ, 1975.
[4]. Clark, A. J. and H. Scarf, (1960). Optimal Policies for a Multi- Echelon Inventory Problem.Management Science, 6(4): 475-490.
[5]. Hadley, G and Whitin, T. M., (1963), Analysis of inventory systems, Prentice- Hall, Englewood Cliff,
[6]. Harris, F., 1915, Operations and costs, Factory management series, A.W. Shah Co., Chicago,48 - 52..