001122   Shi J;Zhang C (School of Mathematics and Information Sciences, Yantai Univ, Yantai-264 005, China, Email: shijt@pku.org.cn) : Note on finite groups in which all noncyclic proper subgroups have the same order. Indian J pure appl Math 2016, 47(4), 687-90.

In the note, auther give a complete classification of finite groups in which all noncyclic proper subgroups have the same order.

4 ref

001121   Sarkar T (Mathematics Dep, Indian Institute of Technology Madras, chennai-600 036, Email: tanmaysemilo@gmail.com) : Numerical study on a nonlinear conservation law model pertaining to manufacturing system. Indian J pure appl Math 2016, 47(4), 655-71.

This paper deals with a numerical scheme applied to a conservation law model of manufacturing system incorporating yield loss. Yield loss involving a singular term has been considered. Even though an explicit form of the material density in a production system can be obtained under certain assumptions, in general, it is difficult to get an explicit form of the material density. On the other hand, the singular term in a conservation law model imposes severe challenges for the numerical approximations on regular grids. Moreover, an approximate solution often converges to a wrong weak solution. A finite volume type numerical scheme has been studied. The convergence of the numerical solution towards entropy solution (in the Kruzkov sense) is proved. Numerical experiments are presented to get the overview of density distribution and outflux of the system.

4 illus, 21 ref

001120   Samuel A E;Kayalvizhi C (Ramanujan Research Centre, P.G. and Research Dep of Mathematics Government Arts College (Autonomo, Kumbalkonam, Tamil Nadu, Email: aedward74_thrc@yahoo.co.in) : On Hamiltonian colorings of fuzzy graphs. Far East J mathl Sci 2015, 98(4), 397-425.

In this paper, we define Hamiltonian chromatic number of fuzzy graph, hamiltonian connected and semi-hamiltonian-connected fuzzy graph. Further we introduce a hamiltonian fuzzy coloring of a connected fuzzy graph G of order n is an assignment c of color (positive integer) to the vertices of G such that D(u, v) + |c(u) - c(v)| ≥ n-1 for every two distinct vertices u and v of G where D(u,v) is the length of the longest u-v path in G. The circumference cir(G) of a fuzzy graph G is the length of a longest cycle in G. Color sequences of fuzzy graphs provide some interesting theorems, corollaries, propositions as discussed here.

2 illus, 21 ref

001119   Reehana Parveen M;Sekar P (Mathematics Dep, Justice Baheer Ahmed Sayeed College, Chennai) : Merging of semilattices and their special properties. Ultra Scient phys Sci-Sect A 2015, 27(3), 229-44.

In this paper for the first time authors define the new notion of merging of semilattices. The properties of merged semilattices is studied and several interesting results are proved in this direction.

34 illus, 5 ref

001118   Reehana Parveen M;Sekar P (Mathematics Dep, Justice Baheer Ahmed Sayeed College, Chennai) : New class of n-ary semilattices and their properties. Ultra Scient phys Sci-Sect A 2015, 27(3), 223-8.

In this paper for the first time we define the new notion of n-ary semilattices under the intersection operation. Several new notions likes pseudo buds and uniform t-length n-ary semilattices are introduced and their properties analysed.

7 illus, 3 ref

001117   Ramachandran D;Mallayya V M (NO, Mar Baselios College of Engg. & Tech. Nalanchira, Trivadrum, Email: dhanyar@gmail.com) : Inverse cubic spline. Indian J Math mathl Sci 2016, 12(1), 43-54.

In this paper a formula for inverse cubic spline interpolation is derived and evaluated using a computer programme.

2 ref

001116   Rakhimov I S;Fiidow M A (Mathematics Dep, Faculty of Sciences, Putra Malaysia Univ, Malaysia, Email: risamiddin@gmail.com) : Centroids of finite dimensional associative dialgebras. Far East J mathl Sci 2015, 98(4), 427-43.

Authors introduce the concept of centroid for associative dialgebras and study its some properties. An algorithm to find centroids of algebras is given. We apply the algorithm to determine the centroids of low-dimensional dialgebras.

12 ref

001115   Rajeswari V;Gajivaradhan P (Mathematics Dep, Pachaiyappa's College, Chennai-600 030) : Groupoid semirings using chain lattices as semirings. Ultra Scient phys Sci-Sect B 2015, 27(3), 185-94.

In this paper for the first time groupoid semirings using chain lattices as semirings are introduced and their properties are analysed. Here chain lattices are used as semirings and groupoid semirings are non associative semirings of finite order, as both the groupoids G and the chain lattice are of finite order.

7 ref

001114   Rajeswari V;Gajivaradhan P (Mathematics Dep, Pachaiyappa's College, Chennai-600 030) : Matrix groupoid. Ultra Scient phys Sci-Sect A 2015, 27(3), 255-62.

In this paper for the first time groupoid matrix are introduced and their properties are analysed. A matrix groupoid or a groupoid matrix is a collection of p x q matrices with entries from a groupoid (G,*) where groupoid matrix inherits the operation of G. Clearly groupoid matrix are non associative groupoids of finite order.

5 ref

001113   Prasad P (Mahematics Dep, Indian Institute of Science, Bangalore-560 012, Email: prasad@math.iisc.ernet.in) : Kinematical conservation laws in a space of arbitary dimensions. Indian J pure appl Math 2016, 47(4), 641-53.

In a large number of physical phenomena, we find propagating surfaces which need math-ematical treatment. In this paper, we present the theory of kinematical conservation laws (KCL) in a space of arbitrary dimensions, i.e., d-D KCL. which are equations of evolution of a moving surface Ωt in d-dimensional x-space, where x = (x₁,X₂, ..., x_d) ∈ R^{d. The KCL arc derived in a specially defined ray coordinates (ξ = (ξ1,ξ2, ..., ξ_d-1), t), where ξ1,ξ2, ..., ξd-1 are surface coordinates on Ω_t and t is time. KCL are the most general equations in conservation form, governing the evolution of Ω_t with physically realistic singularities. A very special type of singularity is a kink, which is a point on Ω_t when Ω_t is a curve in R2 and is a curve on Ω_t when it is a surface in R3. Across a kink the normal n to Ω_t and normal velocity m on Ω_t are discontinuous.}

2 illus, 21 ref

001112   Prajapati U M;Gajjar S J (Mathematics Dep, ST. Xavier's College, Ahmedabad-380 009, Email: gjr.sachin@gmail.com) : Prime cordial labeling of generalized prism graph Y_m.n. Ultra Scient phys Sci-Sect A 2015, 27(3), 189-204.

In this paper the authors have proved that prism graph Y_n,2 is prime cordial except n = 1,2 and 4 and the graph Y_n,4 also prime cordial for n ≥ 3. We have also proved that the generalized prism graph Y_3.n, Y_5.n F_6.n and Y_2p,n (for odd prime p) are prime cordial for n <62> 1 and 7_4.n is also prime cordial for n <62> 2.

17 illus, 5 ref

001111   Pathak R P;Somvanshi P S (Mathematics Dep, Nationakl Institute of Mathematics, Raipur-492 001, Chhattishargh, Email: rppathak.maths@nitrr.ac.in) : Existence and uniqueness of mild solutions for impulsive fractional differential equations with nonlocal conditions. Indian J Math mathl Sci 2016, 12(1), 61-78.

This paper is mainly concerned with existence of mild solutions for the impulsive fractional differential equations with non local initial conditions in Banach space. We assume that linear part generates an analytic semigroup and transform them into suitable integral equations. With the help of fractional powers of operators and some fixed point theorems, existence results are established. Finally, an example is given to illustrate the results.

29 ref

001110   Pandey B B;Pandey S B (Mathematics Dep, Kumaun Univ, Soban Singh Jeena Campus, Alomra) : On quasi umbilical submanifold of CO-dimension-2 of almost hyperbolic manfold. Ultra Scient phys Sci-Sect A 2015, 27(3), 263-6.

Hypersurfaces immersed in an almost hyperbolic Hermitian manifold studied by Dube and Mishra. Almost hyperbolic hermite manifold have been studied by Dube. Hypersurfaces of almost hyperbolic Hermitian manifold 1,11, have been studies by Bhatt and Dube^{1. The purpose of the present paper is to study the Quasi - Umbilical submanifold of co-dimension -2 of an almost hyperbolic manifold. We have obtained the condition for this submanifold, to be W-Quasi umbilic.}

7 ref

001109   Nimbran A S (NO, , B3-304, Palm Grove Heights, Ardee City, Gurgaon, Haryana, Email: amrikn622@gmail.com) : Extending Euler's production for √2. Indian J pure appl Math 2016, 47(4), 697-703.

In this note the authors presented some sundry infinite products for A√2 and six general formulas for some rational powers of 2.

4 ref

001108   Neeradha C K;Mallayya V M (Science & Humanities Dep, Mar Baselios College of Engineering Technology, Thiruvananthapuram, Email: ckneeradha@yahoo.co.in) : Generalized form of A 4 x 4 strongly magic square. Indian J Math mathl Sci 2016, 12(1), 87-92.

In this paper, different types of magic squares is briefly described. A generic definition for the strongly magic square is given. A generalized form of a 4x4 Strongly magic square and some basic properties of generalized 4x4 strongly magic squares (R-N SMS) are also discussed.

8 ref

001107   Mohanty P M;Acharya M (NO, S.C.S. College, Puri, Email: pravat_kin@yahoo.co.in) : Some six point eleventh degree quadrature rules involving derivatives of the integrand. Indian J Math mathl Sci 2016, 12(1), 101-6.

Some six point intepolatory quadrature rules each of degree of precision eleven have been derived by considering the values of the integrand and its derivatives at the nodes. So far as the degree of precision is concerned the rules derived are at par with the corresponding Gauss-Legendre rule.

1 table, 2 ref

001106   Meng W;Yao H (College of Applied Sciences, Beijing Univ of Technology, Beijing, 100 124, P.R. China, Email: mlwhappyhappy@163.com) : Finite group with some non-abelian subgroups of non-prime-power order. Indian J pure appl Math 2016, 47(4), 733-9.

Let G be a finite group and N A(G) denote the number of conjugacy classes of all non-abelian subgroups of non-prime-power order of G. The Symbol π(G) denote the set of the prime divisors of |G|. In this paper we establish lower bounds on N A(G). In fact, we show that if G is a finite solvable group, then N A(G) = 0 orMA(G) ≥ 2^{|π(G)|-2, and if G is non-solvable, then N A(G) ≥ |π(G)| + 1. Both lower bounds are best possible.}

10 ref

001105   Matad N S (NO, New Horizon College, Marathalli, Bangalore-560 103, Email: smnanditha@gmail.com) : Invariant submanifolds in a Trans-Sasakian manifold. Indian J Math mathl Sci 2016, 12(1), 93-100.

The purpose of this paper is to study invariant submanifolds in a trans-sasakian manifold. Here we shown that an invariant submanifold of a trans-sasakian manifold is minimal.

16 ref

001104   Maruddani D A I;Rosadi D;Gunardi;Abdurakhman (Statistics Dep, Diponegoro Univ, Indonesia, Email: maruddani@undip.ac.id) : Valuation of one period coupon bond based on default time and empirical study in Indonesian bond data. Far East J mathl Sci 2015, 98(1), 57-73.

The value of corporate bond is conventionally expressed in terms of the zero coupon bond. In practice, the most common form of debt is coupon bond and allows early default before maturity as safety covenant for the bondholder. This paper studies some valuation methods for one period coupon bond, a coupon bond that only gives one time coupon at the bond period. First, we use classical model that allows the company defaults if the firm cannot fulfill its payment obligation at maturity date T. Second, we use classical first passage time model that gives bond investors the right to take over the firm if its asset value falls below a given barrier before the maturity date. Third, we give revised first passage time model that combines the two fore models. In this approach, a firm will default when its value of assets falls below a given barrier before maturity date or below the payment obligation at the maturity date. We construct a formula of probability of default for those specified models. For the empirical application, we valuate and analyze the default prediction of corporate Indonesian bonds.

3 illus, 3 tables, 22 ref

001103   Malkawi G;Ahmad N;Ibrahim H (College of Arts and Sciences, Univ Utara Malaysia 06010 Sintok, Kedah, Malaysia, Email: gassan_malkawi@yahoo.com) : Solving the fully fuzzy sylvester matrix equation with triangular fuzzy number. Far East J mathl Sci 2015, 98(1), 37-55.

This paper proposes a new method for solving the fully fuzzy Sylvester matrix equation (FFSE). This method is considered as an extension of the solution for the positive fully fuzzy linear system (FFLS). The fully fuzzy matrix system is converted into an associated linear matrix system to obtain a crisp solution. This method is able to solve FFLS and left right - fuzzy linear system (LR-FLS). A numerical example is presented to demonstrate the contributions of this paper.

23 ref

001102   Liang L;Yang G (School of Mathematics and Physics, Lanzhou Jiaotong Univ, Lanzhou-730 070, China, Email: lliangnju@gmail.com) : Lower complete intersection dimension over local homomorphisms. Indian J pure appl Math 2016, 47(4), 673-86.

It is to introduce and study a theory of lower complete intersection dimension over local homomorphisms which encompasses the theory of lower complete intersection dimension for finite modules over local rings introduced by Gerko. In particular, we show that the lower complete intersection dimension over local homomorphisms reflects the complete intersection property of base rings as expected. As an application, we prove that the converse of a theorem of Sather-Wagstaff is also true.

11 ref

001101   Lee S (Mathematics Dep, Institute of Pure and Applied Mathematics, Chonbuk National Univ, 567 Baekje-daero, Deokjin-gu Jeonju-si, Jeollabuk-do 561-756, Republic of Korea, Email: lsy189@jbnu.ac.kr) : On the Hurewicz homomorphisms in shape theory. Far East J mathl Sci 2015, 98(4), 529-38.

In this note, under suitable conditions, it can be seen that the homotopy group is isomorphic to the integral homology group of the inverse limit of a k-connected inverse system of pointed topological spaces and pointed preserving continuous maps over a directed.

14 ref

001100   Korolev M A (Steklov Mathematical Institute of Russian Academy of Sciences, 119991, Russia, Moscow, Gubkina Str., 8, Email: korolevma@mi.ras.ru) : Extreme values of the function S(T) in short intervals. Indian J pure appl Math 2016, 47(4), 603-15.

The Obtained are new estimates for the maximum and minimum of the argument of the Riemann zeta-function on very short segments of the critical line. These results are based on the Riemann hypothesis.

17 ref

001099   Khamthong K;Jermjitpornchai S;Saengsura K (Mathematics Dep, Faculty of Science, Mahasarakham Univ, Mahasarakham 44150, Thailand, Email: kittisak.s@msu.ac.th) : On the order of manoid cohypersubstitutions of some type. Far East J mathl Sci 2015, 98(4), 495-510.

8 ref

001098   Karuppiah U;Prakasam A L M (Mathematics Dep, St. Joseph's College (Autonomous), Trichy-620 002, Email: u.karuppiah@gmail.com) : Some common fixed point theorems for non-self mappings (ψϕ)-weak contractive conditions of integral type in symmetric spaces. Far East J mathl Sci 2015, 98(1), 15-35.

Authors prove some common fixed point theorems for non-self mappings ψϕ-weak contractive conditions of integral type in symmetric spaces by changing the contractive conditions which generalize the results.

14 ref

001097   Kandasamy W B V (Mathematics Dep, Indian Institute of Technology, Chennai-600 036) : Zero divisor conjecture for group semifields. Ultra Scient phys Sci-Sect B 2015, 27(3), 209-13.

In this paper the author for the first time has studied the zero divisor conjecture for the group semifields; that is groups over semirings. It is proved that whatever group is taken the group semifield has no zero divisors that is the group semifield is a semifield or a semidivision ring. However the group semiring can have only idempotents and no units. This is in contrast with the group rings for group rings have units and if the group ring has idempotents then it has zero divisors.

11 ref

001096   Harne S;Teeth M S (NO, Government College, Mandeleshwar, Madhya Pradesh) : Generalization of fibonacci sequence in case of multiplicative coupled fibonacci sequences. Ultra Scient phys Sci-Sect A 2015, 27(3), 267-73.

In this paper we generalize the Fibonacci sequence in case multiplicative coupled Fibonacci sequence. We consider two infinite sequences {α_i}^{∞ _i=0 and {β_i}∞_i-0 which have given eight initial values and we derive new identities.}

3 ref

001095   Goli C E;Adje A (UFR Mathematiques et informatique Univ Felix Houphouet-Boigny, 22 BP 582 Abidjan 22, Cote d'Ivoire, Email: golietienne@gmail.com) : Solvability for some boundary value problems with φ-Laplacian operators and general nonlinear boundary conditions. Far East J mathl Sci 2015, 98(4), 445-76.

Authors study the nonlinear second order differential equation (φ(u'))'=f(t,u,u') with f an L^{1-Caratheodory function, submitted to nonlinear boundary conditions g₁(u(0), u'(o)) = 0, g₂(u(T), u'(T))=0, where T <62> 0. We prove the existence of solutions applying topological methods. Neither of monotonicity of g₁ and g₂, nor growth conditions for f are required.}

14 ref

001094   Giraldo H;Canadas A M;Saldarriaga O (Instituto de Matematicas, Universidad de Antioquia, Calle 67 No. 53-108, Medellin, Colombia, Email: hernan.giraldo@udea.edu.co) : Some equivalences between homotopy and derived categories. Far East J mathl Sci 2015, 98(1), 1-14.

Authors prove two triangle equivalences. One is the triangle equivalence between the homotopy category of the bounded below complexes of Ext-injectives objects of a closed by subobjects and co-resolving subcategory B of an abelian category and the derived category of the bounded below complexes over B. The other triangle equivalence is between the homotopy category of the bounded cohomology and bounded below complexes over a strongly closed by cokernels of monomorphisms and auto-orthogonal subcategory of an abelian category A and the derived category of the bounded cohomology and bounded below complexes over A.

17 ref

001093   Garg M;Rathore S S (P.G. Dep of Mathematics, Nehru P.G. College, Chhibramau, Kannauj, Uttar Pradesh, Email: garg_manoj1972@yahoo.co.in) : New type of closed sets in bitopological spaces. Ultra Scient phys Sci-Sect A 2015, 27(3), 245-54.

2 illus, 19 ref

001092   Garg M (P.G. Dep of Mathematics, Nehru (P.G.) College, Chhibramau, Kannauj, Uttar Pradesh, Email: garg_manoj1972@yahoo.co.in) : New type of generalized fixed point theorem in a complete meric space. Ultra Scient phys Sci-Sect A 2015, 27(3), 173-6.

In the present paper, we prove a fixed point theorem in the form of rational expression. Our result generalizes and extends some weil known previous results.

6 ref

001091   Feng Q;Shi X T;Guo B N (Institute of Mathematics, Henan Polytechnic Univ, Jiaozuo City, Henan Province, 454 010, China) : Some properties of the Schroder numbers. Indian J pure appl Math 2016, 47(4), 717-32.

In the paper, the authors present some properties, including convexity, complete mono-tonicity, product inequalities, and determinantal inequalities, of the large Schroder numbers and find three relations between the Schroder numbers and central Delannoy numbers. Moreover, the authors sketch generalizing the Schroder numbers and central Delannoy numbers and their generating functions.

33 ref

001090   Ezeafulukwe U A;Darus M (Mathematics Dep, Faculty of Physical Sciences, Nigeria Univ, Nsukka, Nigeria, Email: uzomaka.ezeafulukwe@unn.edu.ng) : Applications of differential subordination to the generalized Dziok-Serivastava convolution operator. Far East J mathl Sci 2015, 98(1), 78-90.

In this article, we investigate some inclusion properties of the generalized Dziok-Srivastava convolution operator on some class of analytic functions. Using the principle of differential subordination, we extended the work done by Xu et al. [6] to the t-valent type and calculated some sharp results.

22 ref

001089   Escalona G E;Gonzalez E G;Panteleeva O V; Olvera J A G (NO, UPIICA - Instituto Politecnico Nacional Av. Te 950, D.F., Mexico, Email: egutierrezg@ipn.mx) : A network system reliability estimation with Weibull mixture models. Far East J mathl Sci 2015, 98(4), 511-27.

This paper reviews the problem of finite mixtures identifiability with m components and Weibull distribution. The parameter estimators are obtained with maximum likelihood and performing calculations with a random walk algorithm using Monte Carlo simulation. The Akaike information criterion and the log-likelihood value are used to compare models. Finally, an application of the finite mixtures with Weibull distribution to type I censored data to estimate and obtain reliability and hazard functions of the failure times for the user connections in a network. For the application, a database generated from June 2012 to December 2014 with type I censored data of the recorded failures during this time in an Internet service provider company was used.

1 illus, 1 table, 44 ref

001088   Elsadany A A;Awad A M (Basic Science Dep, Faculty of Computers and Informatics, Suez Canal Univ, Ismailia-41522, Egypt) : Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game. Indian J pure appl Math 2016, 47(4), 617-39.

A dynamic of a nonlinear Kopel duopoly game with heterogeneous players is presented. By assuming two heterogeneous players where one player use naive expectation whereas the other employs a technique of adaptive. The stability conditions of equilibrium points are analyzed. Numerical simulations are used to show bifurcation diagrams, phase portraits and sensitive de-pendence on initial conditions. The chaotic behavior of the game has been controlled by using feedback control method.

19 illus, 30 ref

001087   Dyavanal R S;Rathod A (Mathematics Dep, Karnatak Univ, Dharwad-580 003, Email: renukadyavanal@gmail.com) : Uniqueness theorems for meromorphic functions in annuli. Indian J Math mathl Sci 2016, 12(1), 1-10.

The main purpose of this article is to study the uniqueness theorems for meromorphic functions and some comparison between the characteristic function of the two given functions on annuli, and we extend some of the results of Nevanlinna' s value distribution theory for meromorphic functions on annuli.

10 ref

001086   Dyavanal R S;Mathai M M (Mathematics Dep, Karnatak Univ, Dharwad-580 003, Email: renukadyavanal@gmail.com) : Uniqueness of difference- Differential polynomials of meromorphic functions and its applications. Indian J Math mathl Sci 2016, 12(1), 11-30.

In this paper, it is to investigate problems on uniqueness of difference -differential polynomials sharing values and prove some results, which extends the results of Zhang, Chen and Lin [10], Zhang and Xu [11], K. Liu, X. Liu and Cao [5].

11 ref

001085   Dorsett C (Mathematics Dep, Texas A&M Univ-Commerce, Commerce, Texas 75429) : Weakly P properties and not-separation axioms for Urysohn and weakly Urysohn axioms. Ultra Scient phys Sci-Sect A 2015, 27(3), 217-22.

In a recent paper, a new category of topological properties called weakly Po properties were introduced and investigated. The search for a topological property that failed to be a weakly Po property led to the use of "not-T₀" within that paper, and the investigation of other "not-separation axioms" and other weakly Pproperties in follow up papers. Within this paper, the study of weakly P properties and "not-separation axioms" continues with the Urysohn and weakly Urysohn axioms.

13 ref

001084   Donadze G (Indian Institute of Science Education and Research, Thiruvananthapuram CET Campus, TVPM-16, Thiruvananthapuram, Kerala, Email: gdonad@gmail.com) : Anderson-Badawi conjecture for commutative algebras over infinite fields. Indian J pure appl Math 2016, 47(4), 691-6.

In [1], Anderson and Badawi conjecture that every n-absorbing ideal of a commutative ring is strongly n-absorbing. In this article we prove their conjecture in certain cases (in particular this is the case for commutative algebras over an infinite field). We also show that an affirmative answer to another conjecture in [1] implies the Anderson-Badawi Conjecture.

3 ref

001083   Daohongm Y;Zhengjie W (Qingdao Univ of Technology, Shandong, China, Email: yaosy@163.com) : Expert clustering method based on the similarity of transfer vectors. Indian J Math mathl Sci 2016, 12(1), 31-42.

In the research of multi-attribute group decision making method, determining expert weights is a critical step, an expert clustering method based on the similarity of transfer vectors is proposed. Using every judgment matrix, the transfer matrix between is obtained. After transformation into transfer vector for the similarity and the threshold of similarity division, complete expert clustering. The judgment matrix and its consistency judged by matrix deviation within class empowerment, using all kinds of expert numbers between empowerment and obtain the total weights of experts. Examples show that the method is feasible, effective, and it can give full play in the multiple attribute decision making secondary home group, so there is certain value of popularization.

4 illus, 2 tables, 11 ref

001082   Chitra D;Parvathi P (Mathematics Dep, Quaid-E-millath government, Chennai-600 002) : Fuzzy inventory model for deteriorating items with stock and time dependent demand and partial backlogging under trade credit period. Ultra Scient phys Sci-Sect A 2015, 27(3), 177-88.

In the present paper, a Fuzzy inventory model for deteriorating items has been developed with stock and time dependent demand for which the supplier permits a fixed trade credit period. This paper also assumes that excess demand is partially backlogged. All the inventory costs involved in this model are taken as triangular fuzzy numbers. Replenishment cycle length, the time at which shortage begins and the optimal total inventory cost are taken as decision variables. Sensitivity for this model is also studied. Graded mean representation is used to defuzzify the model. The advantage of proposed approach is that it is simple, gives the better result in relatively less computational work

2 illus, 3 tables, 16 ref

001081   Boua A;Kamal A A M (Univ Ibm Zohr, Faculte des Sciences, Mathematiques Dep, B.P. 8106 Equipe d'equations fonctionnelles et Applications (EEFA), Agadir, Morocco, Email: abdelkarimboua@yahoo.fr) : Some results on 3-prime near-rings with derivations. Indian J pure appl Math 2016, 47(4), 705-16.

The proved is some theorems showing that a near-rings TV must be a commutative ring if it admits one or more derivations satisfying certain constraints on a nonzero semigroup ideal of TV. Moreover, we give examples proving necessity of the conditions given.

9 ref

001080   Bhardwaj N;Kumar V;Sharma S (Mathematics Dep, JSS Academy, Noida, Email: nitinbhardwaj.mdu@gmail.com) : Two unit cold standby systems with auxiliary unit and damaged switching devic. Indian J Math mathl Sci 2016, 12(1), 79-86.

This paper deals with a two unit standby system consisting of a main unit, an auxiliary unit and a damaged switch. The standby is substitute of a main unit only, failure time distributions are taken as negatively exponential, while repair time distributions are general.

3 illus, 11 ref

001079   Areepong Y (Applied Statistics Dep, Faculty of Applied Science, King Mongkut's Univ of Technology North Bangkok, Bangkok 10800, Thailand, Email: yuaporna@kmutnb.ac.in) : Generally weighted moving average control chart for zero-inflated Poisson. Far East J mathl Sci 2015, 98(1), 103-18.

The objective of this research is to propose an approximation of average run length (ARL) by Markov chain approach (MCA) for generally weighted moving average (GWMA) control chart when observations are from zero-inflated Poisson (ZIP) distribution. The main characteristics of a control chart are the average run length (ARL₀) which is mean of false alarm times and the average delay time (ARL₁) which is mean delay of true alarm times. The ARL₀ should be sufficiently large while the process is still in-control and the ARL₁ should be small when the process goes out-of-control. The results obtained from MCA are compared with Monte Carlo simulation (MC). The results found that the numerical results obtained from MCA are as good as from MC; however, MCA is very time saving. Furthermore, the performance of GWMA chart is superior to EWMA chart for small to moderate changes.

4 tables, 17 ref

001078   Areepong Y (Applied Statistics Dep, Faculty of Applied Science, King Mongkut's Univ of Technology North Bangkok, Bangkok 10800, Thailand, Email: yupaporna@kmutnb.ac.th) : Modified exponentially weighted moving average control chart by improved square root transformation for binomial distribution. Far East J mathl Sci 2015, 98(1), 91-102.

The main objective of this paper is to study a modified exponentially weighted moving average (EWMA) control chart for detecting a change in binomial observation by improving square root transformations, named an ISRT np EWMA control chart. This chart has been developed using the normal approximation with condition as low defect level. However, many real applications are away from these assumptions due to skewness in the exact distribution. The characteristic of the control chart is average run length (ARL), the expected number of observations taken from an in-control process until the control chart falsely signals out-of-control denoted by ARL₀. An ARL₀ will be regarded as acceptable if it is large enough to keep the level of false alarms at an acceptable level. The second common characteristic is the expected number of observations taken from an out-of-control process until the control chart signals denoted by ARL₁. We compare the performance of the ISRT np EWMA chart with EWMA chart by using ARL criteria. The numerical results also indicated that ISRT np EWMA chart is an effective alternative to the traditional EWMA control chart small shifts detection.

4 tables, 7 ref

001077   Amooshahi M;Taeri B (Mathematical Sciences Dep, Isfahan Univ of Technology, Isfahan-84156-83111, Iran, Email: m.amooshahi@math.iut.ac.ir) : On integral cayley sum graphs. Indian J pure appl Math 2016, 47(4), 583-601.

Let S be a subset of a finite abelian group G. The Cayley sum graph Cay^{+(G, S) of G with respect to S is a graph whose vertex set is G and two vertices g and h are joined by an edge if and only if g + h ∈ S. We call a finite abelian group G a Cayley sum integral group if for every subset S of G, Cay+(G, S) is integral i.e., all eigenvalues of its adjacency matrix are integers. In this paper, we prove that all Cayley sum integral groups are represented by Z₃ and Zn₂, n ≥ 1, where Z_k is the group of integers modulo k. Also, we classify simple connected cubic integral Cayley sum graphs.}

2 illus, 19 ref

000040   Yoo J K;Han H (Liberal Arts and Science Dep, Chodang Univ, Muan-534 701, Email: jkyoo@chodang.ac.kr) : On the stability of the localizable spectrum II. Far East J mathl Sci 2015, 98(3), 267-80.

As shown by Eschmeier and Prunaru [10], the localizable spectrum plays an important role in the theory of invariant subspaces. In this paper, we study the localizable spectrum for bounded linear operators on Banach spaces. At first, we prove that the localizable spectrum is stable under commuting nilpotent perturbations. We also prove that if T ∈ L(X) and S ∈ L(Y) are asymptotically quasi-similar, then σ_loc(T) = σ_loc(S). Finally, we prove that if T, S ∈ L(X) are bounded linear operators with TS = ST, and C(S, T)ⁿ(I) = 0 for some integer n ∈ N and σ_T(x) ⊆ σ_S(x) for all x ∈ X, then S is decomposable if and only if T is decomposable, and moreover, σ_loc(S) = σ_loc(T).

20 ref

000039   Triyani;Nurshiami S R (Mathematics Dep, Jenderal Soedirman Univ, Dr Soeparno Street, No. 61 Purwokerto, 53122, Indonesia, Email: trianisr@yahoo.com) : Super edge magic total labeling and its dual labeling on firecracker graphs. Far East J mathl Sci 2015, 98(3), 281-92.

Super edge magic total (SEMT) labeling on a graph G = (V, E), with p vertices and q edges, is a bijective function λ : V U E → {1, 2, 3, ..., p + q} that satisfies λ,(u) + λ(uv) + λ (v) equaling a constant c (magic constant of K), and all vertices of G receive all smallest labels. Not all graphs can be labeled using SEMT labeling. A graph that can be labeled using SEMT labeling is called an SEMT graph. The study of SEMT labeling was introduced by Enomoto et al. [1]. In their paper, Enomoto et al. [1] conjectured that every tree graph is an SEMT graph. In this paper, we study the SEMT labeling (as well as dual labeling) of firecracker graphs, F_n,k.

4 illus, 8 ref

000038   Sung Y O (Applied Mathematics, Kongju National Univ, 182 Sinkwandong, Kongju-City-314 701) : Note on fuzzy idempotent relations. Far East J mathl Sci 2015, 98(3), 365-74.

The present note gives a few elementary observations concerning fuzzy idempotent relations and investigates some related properties.

8 ref

000037   Kuboye J O;Omar Z (Mathematics Dep, School of Quantitative Sciences, Universiti Utara Malaysia, Malaysia, Email: kubbysholly2007@yahoo.com) : Solving second order ordinary differential equations directly by uniform order eight block method. Far East J mathl Sci 2015, 98(3), 315-32.

The step-length k = 1 is considered in the development of a uniform order eight block method for solving second order initial value problems of ordinary differential equations directly. Multistep collocation approach is used in the derivation of the method where power series approximate solution is considered as the basis function. The basic properties of the method which include: zero-stability, order, error constant, consistency and convergence are establishisd. The developed block method is applied to solve differential problems which guaranteed the superiority of our method when compared with the existing methods.

3 tables, 21 ref