iosr-Jm   Volume-12 ~ Issue-5 ~ Sep-Oct 2016

Abstract: Product of consecutive integers is expressible by the products of falling factorials which have connection with compositions of a positive integer. There exists a recurrence relation involving falling factorials which has close connection with the ordered compositions and the ordered integers of amazing properties. The ordered compositions and integers hold some arithmetic rhythms.

Keywords: Sequence; Recurrence; Falling factorial; Composition; Summand.

[1]. Andrews G.E., The Theory of Partitions, Cambridge University Press, 1998, Chapter 4, p54.

[2]. Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with formulas, Graphs, and

[3]. Mathematical Tables, 9th printing, New York: Dover, 1972.
[4]. Bera Soumendra, Relationships between Ordered Compositions and Fibonacci Numbers Journal of Mathematics Research, Vol.7, No.3, 2015.

Abstract: A subgroup H of G is malnormal in G if for any g 2 G such that g =2 H the intersection H \ g1Hg is trivial. Most subgroups are neither normal nor malnormal, so the study of the intersection pattern of conjugates of a subgroup is an interesting problem. It is closely connected to the study of the behavior of di_erent lifts of subspaces of topological spaces in covering spaces. Malnormality of a subgroup has been generalized in di_erent ways. One of them, namely the height, introduced in [3], has been used by Agol in [1] and [2] in his proof of Thurston's conjecture that 3-manifolds are virtual bundles

[1]. I. Agol, The virtual Haken conjecture. With an appendix by Agol, Daniel Groves, and Jason Manning, Doc. Math. 18 (2013), 1045{1087.
[2]. I. Agol, D. Groves, and J. Manning, Residual _niteness, QCERF and _llings of hyperbolic groups, Geom. Topol. 13 (2009), 1043{1073.
[3]. R. Gitik and E. Rips, Heights of Subgroups, MSRI preprint 027-95.
[4]. R. Gitik, M. Mitra, E. Rips, and M. Sageev, Widths of Subgroups, Trans. AMS 350 (1998), 321{329.
[5]. G.C. Hruska and D.T. Wise Packing subgroups in relatively hyperbolic groups, Geom. Topol. 13 (2009), 1945{1988.

Abstract: In this paper we present desensitization of gonadotropin responses to kisspeptin in the female rat Analyses of LH and FSH secretion at different developmental and metabolic states using recent generations of the Weibull distribution. We conclude that continuous administration of Kisspeptin to female rats, with remarkable differences being detected between LH and FSH responses, in different developmental and metabolic states. The physiological roles of kisspeptin in the dynamic regulation of gonadotropin secretion in the female rat..............

Keywords: Gonadotropin, Kisspeptin, FSH, LH, Hazard rate function, Cumulative Failure rate function, Reliability function, Mean life time.

[1]. Casanueva FF, Dieguez C. Neuroendocrine regulation and actions of leptin. Front Neuroendocrinol 20: 317–363, 1999.
[2]. Castellano JM, Navarro VM, Fernandez-Fernandez R, Castano JP,Malagon MM, Aguilar E, Dieguez C, Magni P, Pinilla L, Tena-Sempere M. Ontogeny and mechanisms of action for the stimulatory effect of kisspeptin on gonadotropin-releasing hormone system of the rat.Mol Cell Endocrinol 257–258: 75–83, 2006.
[3]. Castellano JM, Navarro VM, Fernandez-Fernandez R, Nogueiras R,Tovar S, Roa J, Vazquez MJ, Vigo E, Casanueva FF, Aguilar E,Pinilla L, Dieguez C, Tena-Sempere M. Changes in hypothalamicKiSS-1 system and restoration of pubertal activation of the Reproductive axis by kisspeptin in under nutrition. Endocrinology 146: 3917–3925,2005.
[4]. Castellano JM, Navarro VM, Fernandez-Fernandez R, Roa J, Vigo E,Pineda R, Dieguez C, Aguilar E, Pinilla L, Tena-Sempere M. Expressionof hypothalamic KiSS-1 system and rescue of defective gonadotropic responses by kisspeptin in streptozotocin-induced diabetic male rats. Diabetes 55: 2602–2610, 2006.

Abstract: This paper investigates an optimal replacement policy N for the maintenance problem with two types of failures and one repairman. In proposed model it is assumed that the system experiences with two types of failures namely repairable failures and non repairable failures. When repairable failure occurs, the repairs will be repaired once by the repairman. The repair is not as good as new. The successive working times after repair are stochastically decreasing and form a decreasing alpha series process while............

Keywords: Renewal Reward theorem, Renewal Process, Alpha series Process, Replacement policy N, Long-run Average cost Rate (ACR).

[1] Barlow, R.E and Hunter, L.C, 'Optimum Preventive Maintenance Policies', Operations Research, Vol. 08, pp.90-100, 1959.
[2] Braun W.J, Li Wei and Zhao Y.Q, 'Properties of the geometric and related process', Naval Research Logistics, Vol.52, pp.607-617, 2005.
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Abstract: Child mortality is regarded as one of the most revealing measures of society's ability to meet the needs of its people. The Millennium Development Goal 4 (MDG 4) advocates a reduction of under-five mortality rate by two-thirds between 1990 and 2015. The main objective of this study was to develop a validated set of statistical models and select the most appropriate model between logistic regression and Neural Networks to predict mortality among children under five and to compare the influence of selected risk factors on the probability of death before the age of 5 years among children in Ghana

Keywords: Logistic Regression, Neural Networks, Children under five years,

[1]. Bâra, A., & Lungu, I. (2012). Improving Decision Support Systems with Data Mining Techniques. INTECH Open Access Publisher.
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Abstract: The aim of this research paper is to establish some new identities involving generalized H–function of two variables.

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Abstract: I give a relativistic proof to the Fermat's last theorem : no three positive integers a, b, and c satisfy the ...........

[1] Andrew Wiles, Modular elliptic curves and Fermat's last Théorème, Annal of mathematics, 142, 443-551, 1995
[2] M. Sghiar, Des applications génératrices des nombres premiers et cinq preuves de l'hypothèse de Riemann, Pioneer Journal of Algebra, Number Theory and its Applications, Volume 10, Numbers 1-2, 2015, Pages 1-31. http://www.pspchv.com/content_PJANTA.html
[3] M. Sghiar, La relativité et la théorie des nombres (déposé au Hal : 01174146), accepté par IOSR Journal of Mathematics (IOSR-JM).

Abstract: Let G= (V,𝐸) be an intutitionistic fuzzy graph. Mahioub M. Q. Shubatah introduced the concept of perfect domination in intuitionistic fuzzy graphs. In this paper we study some theorem in perfect dominating sets of IFG. Also define connected perfect domination in intutionistic fuzzy graph and perfect domination in constant intuitionistic fuzzy domination number are discussed. Obtain some interesting results for this new parameter in IFG and constant IFG.

Keywords: Intuitionistic fuzzy graph, constant Intuitionistic fuzzy graph, perfect domination number, connected perfect domination number in IFG.

[1]. K. Atanassov, Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag, New
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Abstract: In this paper, we investigate the effects thermo-diffusion on unsteady MHD natural convective flow past an infinite vertical plate in presence of heat absorption. The dimensionless governing equations are solved numerically using Galerkin finite element method. The numerical results for some special cases were compared with previously published work and were found to be in good agreement. The effects of various pertinent flow parameters on velocity, temperature and concentration are shown graphically where as skin friction, Nusselt number and Sherwood number are presented in tabular form.

Keywords: Thermo-diffusion, Unsteady, MHD, Heat absorption, Finite element method

[1] Dursunkaya, Z and Worek,W. M (1992), Diffusion-thermo and thermal-diffusion effects in transient and steady natural convection
from vertical surface. Int. J. Heat Mass Transfer, Vol. 35(8), pp.2060–2065.
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Embedded in a Porous Medium. Mathematics, XI, Vol. 4, pp. 11–21.
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three dimensional free convection over a permeable stretching surface with radiation, Physics Letters, Section A, Vol. 372 (3),
pp. 263 – 272.

Abstract: In this paper the concept of connected edge geodetic domination number of a graph is introduced. A set of vertices S of a graph G is a connected edge geodetic domination set ( CEGD set) if it is edge geodetic set, a domination set of G and the induced sub graph <S> is connected. The connected edge geodetic domination number (CEGD number) of G, γgce (G) is the cardinality of a minimum CEGD set. CEGD number of some...........

Keywords: Edge geodetic number, geodetic domination number, edge geodetic domination number, connected edge geodetic domination number

[1] P. Arul Paul Sudhahar, M. Mohammed Abdhul Khayyoom and A. Sadiquali. Edge Monophonic Domination Number of Graphs. J. Adv. Mathematics. Vol 11. 10 pp 5781 – 5785. (Jan 2016)
[2] P. Arul Paul Sudhahar, M. Mohammed Abdhul Khayyoom and A. Sadiquali. Connected Closed Monophonic Number of Graphs. Indian J. Res. Found., 5, 17 - 21 (2016)
[3] P. Arul Paul Sudhahar, A. Sadiquali and M. Mohammed Abdhul Khayyoom. The Monophonic Geodetic Domination Number of Graphs, J. Comp. Math. Sci. Vol7(1),pp 27-38(Jan 2016).
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Abstract: We survey the results of ranks of discrete tropical divisors on tropical curves. Moreover, we found both upper and lower bounds for ranks of a given divisor, which help us quickly find the exact value of the ranks of discrete tropical divisors

Keywords: Tropical Geometry, Discrete Tropical Divisor, Tropical Rank, Tropical Riemann-Roch Theorem, Metric Graph

[1]. Matthew Baker and Serguei Norine. Riemann-Roch and Abel-Jacobi theory on a finite graph. Adv. Math., 215(2):766–788, 2007.
[2]. Andreas Gathmann and Michael Kerber. A Riemann-Roch theorem in tropical geometry. Math. Z., 259(1):217–230, 2008.
[3]. Grigory Mikhalkin and Ilia Zharkov. Tropical curves, their Jacobians and theta functions. In Curves and abelian varieties, volume 465 of Contemp. Math., pages 203–230. Amer. Math. Soc., Providence, RI, 2008.
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Abstract: Homotopy Perturbation Method (HPM) is an elegant and powerful method to solve linear and nonlinear partial differential equations. As we know to get an exact solution of nonlinear partial differential equation is very difficult, so any kind of perturbative approach is acceptable depending on its criteria. Homotopy Perturbation Method provides an analytical solution by using the initial conditions. It is interesting to note that only a few terms are required to obtain..........

Keywords:Homotopy perturbation method, Approximate solutions, Exact solution, Fisher's equation, Initial condition.

[1]. J.H. He, Homotopy perturbation technique, Comput. Methods. Appl. Mech. Engrg. vol. 178, P-257-262, 1999.
[2]. J.H. He, A coupling method of a homotopy technique and a perturbation technique for non-linear problems, Internat. J. Non-Linear
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Abstract: The aim of this paper is to define the concepts of soft -open setsand soft  -closed sets in soft topological spaces by studying the basics of soft set theory formulated by D. Molodstov.

Keywords: soft set, soft topology, soft open sets and soft closed sets..

[1]. I. Arockiarani and A. Arokia Lancy, "Generalized soft gβ closed sets and soft gsβ closed sets in soft topological spaces," International Journal of Mathematical Archive 4(2), 2013, 17-23.
[2]. M.I. Ali, F.Feng, X.Liu, W.K.Min, M.Shabir, "On some new operations in soft set theory," Computers and Mathematics with Applications, 57, 2009, 1547-1553.
[3]. J. Krishnaveni and C. Sekar, "Soft semi connected and soft locally semi con- nected properties in soft topological spaces," International Journal of Mathematics and soft Computing, 3(3), 2013, 85-91.
[4]. D. Molodtsov, "Soft set theory-first results," Computers and Mathematics with Applications, 37(4-5), 1999, 19-31.
[5]. D.Molodtsov, V.Y. Leonov, D.V.Kovkov, "Soft sets technique and its application," Nechetkie Sistemy i Myagkie Vychisleniya 1(1), 2006, 8-39.

Abstract: The aim of this paper is to define the concepts of soft -open setsand soft  -closed sets in soft topological spaces by studying the basics of soft set theory formulated by D. Molodstov

Keywords: soft set, soft topology, soft open sets and soft closed sets..

[1]. I. Arockiarani and A. Arokia Lancy, "Generalized soft gβ closed sets and soft gsβ closed sets in soft topological spaces," International Journal of Mathematical Archive 4(2), 2013, 17-23.
[2]. M.I. Ali, F.Feng, X.Liu, W.K.Min, M.Shabir, "On some new operations in soft set theory," Computers and Mathematics with Applications, 57, 2009, 1547-1553.
[3]. J. Krishnaveni and C. Sekar, "Soft semi connected and soft locally semi con- nected properties in soft topological spaces," International Journal of Mathematics and soft Computing, 3(3), 2013, 85-91.
[4]. D. Molodtsov, "Soft set theory-first results," Computers and Mathematics with Applications, 37(4-5), 1999, 19-31.
[5]. D.Molodtsov, V.Y. Leonov, D.V.Kovkov, "Soft sets technique and its application," Nechetkie Sistemy i Myagkie Vychisleniya 1(1), 2006, 8-39.

Abstract: In this paper we consider prime graph of R (denoted by PGR ) of an associative ring R (introduced by Satyanarayana, Syam Prasad and Nagaraju [22]). We also consider zero divisor graph of a finite associative ring R (denoted by ZDGR ). It is proved that every prime graph is a subgraph of the zero divisor graph but the converse need not be true. An example of a ring for which PG(R) ≠ ZDG(R) was presented.

Keywords: Prime graph, Associative ring,zero divisor graph

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Abstract: In this paper, we introduce and study sets called 𝜌 -closed set and 𝜌 -open set. Also we have investigated some of their basic properties

Keywords: p– closed set, 𝜌 – open set

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