016446   Bali R;Poonia L (Mathematics CSIR Emeritus Scientist Dep, Rajasthan Univ, Jaipur-302 004, Email: balir5@yahoo.co.in ) : Inflationary scenario in spatially homogeneous bianchi type IX space-time with flat potential in general relativity. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 361-6.

Inflationary scenario in spatially homogeneous Bianchi Type IX space-time is investigated. To get the deterministic result, we have considered the potential V(φ) is constant and the scale factor R <126> e^Ht where H is Hubble constant. We findthat spatial volume (R³) increases exponentially. Thus inflationary scenario exists in Bianchi Type IX space time. The Higgs field decreases slowly. The expansion (θ) is constant, shear (σ) is zero and deceleration parameter (q) = - 1 which indicate that the model represents de-Sitter universe. The model also gives accelerating phase of the universe.

14 ref

016445   Balasubramanian K;Subramanian N (Mathematics Dep, Srninvasa Ramanujan Centre, Sastra Univ, Kumbakonam-612 001, Email: k_bala27@yahoo.co.in) : Riesz almost lacunary multiple triple sequence spaces of Γ<. Far East J mathl Sci 2017, 101(2), 343-60.

In this paper, authors introduce a new concept for Riesz almost lacunary Γ³ sequence spaces strong P-convergent to zero with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We also introduce and study statistical convergence of Riesz almost lacunary Γ³ sequence spaces and also some inclusion theorems are discussed.

14 ref

016444   Balasubramanian K;Subramanian N (Mathematics Dep, Srinivasa Ramanujan Centre, Sastra Univ, Kumbakonam-612 001, Email: k_bala27@yahoo.co.in) : On generalized difference sequence space of integrated sequence of fuzzy real numbers over p-metric spaces defined by musielak-modulus function. Far East J mathl Sci 2017, 101(2), 329-42.

In this article, we introduce the sequence spaces associated with the integrated sequence space defined by Musielak. We study some basic topological and algebraic properties of these spaces. We also investigate some inclusion relations related to these spaces.

10 ref

016443   Aydin F T;Yuce S (Mathematical Engineering Dep, Yildiz Technical Univ, Faculty of Chemical and Metallurgical Engineering, Davutpasa Campus, 34220 Esenler, Istanbul, Turkey, Email: sayuce@yildiz.edu.tr) : Dual Pell quaternions. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 328-39.

In this paper, Authors defined dual Pell quaternions. Also, we investigated the relations between dual Pell quaternions which connected with Pell and Pell-Lucas numbers. Furthermore, we gave the Binet formulas and Cassini-like identities for these quaternions.

22 ref

016442   Arshaduzzaman M (Mathematics Dep, College of Science al Baha Univ, Al Baha Kingdom of Saudi Arabia, Email: shyan.zaman@gmail.com) : Fuzzy management on human centered systems. Ultra Scient phys Sci-Sect B 2016, 28(5-7), 155-7.

In this paper the author discusses Fuzzy or non-Fuzzy, the best defined management is fuzzy, i.e. it is better to use in governing a human centered system not the conventional mathematical apparatus (specially when the mathematical apparatus leads to extremely large computational efforts) but the apparatus of fuzzy sets and algorithms.

2 illus, 8 ref

016441   Arman;Suparwanto A;Salmah (Mathematics Dep, Faculty of Mathematics and Natural Sciences, Gadjah Mada (UGM) Yogyakarta, Indonesia, Email: armanfmipa@gmail.com) : The necessary and sufficient condition of input-output group decoupling for linear descriptor systems with index one. Far East J mathl Sci 2017, 101(2), 261-87.

In this paper, we study the problem of input-output group decoupling for regular linear descriptor systems of index at most one. The problem is handled in geometric setting. Necessary and sufficient conditions for a solution of the input-output group decoupling problem are established. Finally, we give other equivalent formulations of the input-output group decoupling problem for linear descriptor system with index one.

19 ref

016440   Alam T (College of Business Administration, Al Kharj Prince Sattam bin Abdulaziz Univ, P.O. Box No.: 165, Zip Code: 11942, Al Kharj, Kingdom of Saudi Arabia, Email: t.alam@psau.edu.sa) : Brief review of the cuts in integer programming problem. Ultra Scient phys Sci-Sect B 2016, 28(5-7), 149-54.

The paper presents an overview of various cuts which are used in obtaining the integer solution to an Integer Programming Problem. The decision variables of any problem that must assume non-fractional values may be categorized as an integer programming. The Cut is a device for reducing the feasible region. Whereas the feasible region is a set of feasible solution. Numerous mathematicians and researchers developed various Cuts for different Integer programming problem from time to time. An optimal solution is achieved in a minimum number of phases after using a developed Cut. Integer programming problems are widely used in many applications like Production planning, Scheduling, Telecommunications networks, Cellular network, etc.

41 ref

015555   Zhan G (Mathematics Dep, Zhejiang Univ of Technology, Hangzhou, 310023, Zhejiang, P.R. China, Email: zhangp@ziut.edu.cn) : Julia set of λ exp(z)/z with real parameters λ. Indian J pure appl Math 2017, 48(2), 271-83.

In this paper, we investigate the Julia set of the family λ exp(z)/z with real parameters λ. We look for what values of real parameters λ such that the Julia set of λ exp(z)/z does not coincide with the whole plane, and thus gives a complete classification for real parameters, which is similar to Jang's result of a family of transcendental entire functions. Moreover, We also discuss the shape and size of Fatou sets and Julia sets of λ exp(z)/z with real parameters λ when the Julia sets are not the whole plane.

23 ref

015554   Vanitha L;Ramachandran C;Bulboaca T (Mathematics Dep, Univ College of Engineering, Anna Univ, Villupuram-605 103, Email: swarna.vanitha@gmail.com) : Classes of k-uniformly convex and starlike functions involving the generalzed fox-wright function. Far East J mathl Sci 2016, 99(7), 1081-1107.

In this paper, we discuss the mapping properties of various subclasses of k-uniformly convex and starlike functions involving the generalized Fox-Wright function.

34 ref

015553   Unai A (Mathematical Information Science Dep, Tokyo Univ of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan, Email: unai@rs.kagu.tus.ac.jp) : Sub- and super-solutions method for some quasilinear elliptic operators. Far East J mathl Sci 2016, 99(6), 851-67.

In this paper, an existence theorem of weak solutions for some quasilinear elliptic equations involving monotone operators are proved which is not necessarily of potential type. Our existence theorem is a natural generalization of the following well-known semilinear problem: -div(M(x)∇u) = g(u) + f in Ω with Dirichlet boundary condition. The proof is based on the sub- and super-solutions method.

6 ref

015552   Tarhadi;Bachtiar A A (Mathematics Education Dep, Terbuka Universitas, Indonesia, Email: tarhadi.fkip@gmail.com) : Helicity of Pekeris, Accad and Shkoller flow. Far East J mathl Sci 2016, 99(6), 813-30.

Helicity of PAS (Pekeris-Accad-Shkoller) flow is the scalar product of velocity vflow and its curl, in a Euclidean space. Since PAS flow is a Beltrami flow with a property Cv = curlv, with C is a constant, the helicity of PAS flow can be determined by integrating the scalar product between vectors v and v and multiply with Λ. This paper will explain the process of calculating the helicity of PAS.

1 illus, 5 ref

015551   Tang Z;Gong C (Mathematics Dep, Soochow (Suzhou) Univ, Suzhou 215006, P.R. China, Email: zmtang@suda.edu.cn) : On the stability and regularity of the multiplier ideals of monomial ideals. Indian J pure appl Math 2017, 48(2), 167-76.

Let a ⊆ C[x₁, ..., x_d] be a monomial ideal and J(a) its multiplier ideal which is also a monomial ideal. It is proved that if a is strongly stable or squarefree strongly - 42 - stable then so is J(a). Denote the maximal degree of minimal generators of a by d(a). When a is strongly stable or squarefree strongly stable, it is shown that the Castelnuovo-Mumford regularity of J(a) is less than or equal to d(a). As a corollary, one gets a vanishing result on the ideal sheaf J(a) on P^d-1 associated to J(a) that Hⁱ(P^d-1; J(a) (s-i)) = 0, for all i <62> 0 and ≥ d(a).

14 ref

015550   Shashikala P (Studies in Mathematics Dep, Mysore Univ, Manasagangotri, Mysuru-570 006, Email: shaship2010@gmail.com ) : Extraction of orthogonal polynomials from generating function for reciprocal of odd numbers. Indian J pure appl Math 2017, 48(2), 177-85.

In the present paper the orthogonality relations, exhibited by both numerator and denominator polynomials of both even and odd order convergents of a regular C-fraction of a power series with coefficients as reciprocal of odd numbers are described. The two sequences of convergents are nothing but diagonal and upper diagonal Pade approximants for the power series. The two orthogonal polynomials extracted from denominators are shown to be classical orthogonal polynomials and two orthogonal polynomials extracted from numerators are shown to be non-classical orthogonal polynomials.

15 ref

015549   Selvanayaki N;Ilango G (Mathematics Dep, Akshaya College of Engineering and Technology, Coimbatore, Tamilnadu, Email: selvanayaki.nataraj@gmail.com) : αgrw-separation AXIOMS. Far East J mathl Sci 2016, 99(7), 1037-45.

In this paper, we introduce αgrw-separation axioms and study some of their properties in topological spaces. Also, we study relationships among these separation axioms with the well known axioms T₀, T₁ and T₂.

10 ref

015548   Saikia N;Boruah C (Mathematics Dep, Rajiv Gandhi Univ, Rono Hills, Doimukh-791 112, Email: nipennak@yahoo.com) : Congruences for l-regular overpartition for l ∈ {5,6,8}. Indian J pure appl Math 2017, 48(2), 295-308.

Let A__l(n) denote the number of overpartitions of a non-negative integer n with no part divisible by l, where l is a positive integer. In this paper, we prove infinite family of congruences for A_₅(n) modulo 4, A_₆(n) modulo 3, and A_₈(n) modulo 4. In the process, we also prove some other congruences.

22 ref

015547   Ranmmechai S;Nakprasit K (Mathematics Dep, Faculty of Science, Khon Kaen Univ, Khon Kaen, Thailand, Email: r.sawitree@kkumail.com) : Flexible coloring of graphs. Far East J mathl Sci 2016, 99(6), .

Li et al. [2] introduced the notion of a flexible coloring in hypergraphs. A flexible coloring of a hypergraph His an assignment of list of one or more colors to each vertex such that, for each edge, we can choose a color from the color list of each vertex so that an edge is strongly colored. In this paper, we present the study of flexible coloring in graphs. The smallest summation of sizes of color lists of all vertices from flexible coloring with t allowable colors of G is denoted by F_t(G). We find F_t(G), for all possible t, where Gis a path, a cycle, a tree, a wheel graph, a hypercube graph, a complete graph, or a complete k-partite graph. Moreover, we find F_t(G x H) and F_t(G ∨ H), where G x H denotes the Cartesian product of G and H, G ∨ H denotes the join of Gand H, and each graph is a path, a cycle, or a complete graph.

3 ref

015546   Permana D;Effendie A R;Pasaribu U S;Indratno S W;Suprayogi (Statistics Research Div, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandun, Indonesia, Email: donypermana27@gmail.com) : Modelling of dynamical interest rates using binomial and trinomial trees. Far East J mathl Sci 2016, 99(6), 909-20.

Interest rate is an important factor in the field of economics and finance. Thus, modelling of interest rate is very useful in developing many principles in that field. Until now, a lot of models have been designed for interest rate. Various methods have been used to develop the models. There are deterministics, stochastics and combination methods of both. One of the simple stochastics method is using binomial and trinomial trees. In this paper, the methods are reviewed analytically. Basically, the methods have a principle which is almost the same. Both formulas are a little bit different. Modelling of interest rate using trinomial tree is applied to data of interest rates monthly in Indonesia. Here, model parameters are variated thereby producing a variety of models. The resulting models are used for fitting and forecasting of interest rate for the next month. The results are compared by using the mean square error to determine the best model.

5 illus, 3 tables, 11 ref

015545   Panichkitkosolkul W;Meedech N (Mathematics and Statistics Dep, Faculty of Science and Technology, Thammasat Univ, Phathum Thani, 12121, Thailand, Email: wararit@mathstat.sci.tu.ac.th ) : Testing on the ratio of normal means with a known coeffieicnt of variation. Far East J mathl Sci 2016, 99(7), 1047-60.

This paper proposes an asymptotic test and an approximate test for the ratio of normal means with a known coefficient of variation. The asymptotic test was based on the expectation and variance of the estimator of the ratio of normal means. The approximate test used the approximate expectation and variance of the estimator by Taylor series expansion. A Monte Carlo simulation study was conducted to compare the performance of the two statistical tests. Simulation results showed that the two proposed tests performed well in terms of empirical type I errors and powers.

2 table, 23 ref

015544   Ostrovska S (Mathematics Dep, Atilim Univ, Ankara, Turkey, Email: sofia.ostrovska@atilim.edu.tr) : On the images of entire functions under the limit q-bernstein operator. Indian J pure appl Math 2017, 48(2), 205-10.

The limit q-Bernstein operator B_q comes out naturally as the limit for the sequence of q-Bernstein operators in the case 0 <60> q <60> 1: Alternatively, it can be viewed as a modification of the Szasz-Mirakyan operator related to the Euler distribution. In this paper, a necessary and sufficient condition for a function g to be an image of an entire function under B_q is presented.

12 ref

015543   Oguro T;Sekigawa K (Science Div, School of Science and Engineering, Tokyo Denki Univ, Saitama, 350-0394, Japan, Email: oguro@mail.dendai.ac.jp) : On an integral formula for compact almost Kahler manifolds. Far East J mathl Sci 2016, 99(6), 885-907.

In this paper, the curvature identities derived from the integral formula for any compact almost Kahler manifold together with its application to a special class of compact Kahler manifold are discussed.

14 ref

015542   Nimbran A S;Levrie P (NO, , B3-304, Palm Grove Heights, Ardee City, Gurgaon, Haryana, Email: amrikn622@gmail.com) : Some continued fractions for π and G. Indian J pure appl Math 2017, 48(2), 187-204.

Authors present here two classes of infinite series and the associated continued fractions involving p and Catalan's constant based on the work of Euler and Ramanujan. A few sundry continued fractions are also given.

20 ref

015541   Mohammadi M H (NO, Institute of Mathematics National Academy of Sciences of Republic of A, Armenia, Email: mohamadi.mh.edu@gmail.com) : Three-dimensional mathematical modeling of heat transfer by stream function and its numerical solution. Far East J mathl Sci 2016, 99(7), 969-81.

This paper states the mathematical modeling of heat transfer in the Garnissage furnace in two dimensional case, and the modeling is based on the stream function. We invoke the three conservation laws of physics, i.e. the mass, the momentum, and the energy conservation laws to derive the continuity equation, the Navier-Stokes equations, and the energy equation. The Stefan condition will be applied to demonstrate the free boundary between solid and liquid phase. First we express the system by stream functions, and then we convert it to the variational formulation (weak formulation), and after that we perform the finite element method to achieve the numerical solution of the system.

1 illus, 20 ref

015540   Mashuri;Reorita R (Mathematics Dep, Universitas Jenderal Soedirman, Jl. Dr. Soeparno No. 61 Purwokerto, 53122, Indonesia, Email: mashuri_unsoed@yahoo.com) : On the bichromatic wave propagation over varying bottom. Far East J mathl Sci 2016, 99(6), 837-50.

The propagation of water wave over varying bottom using AB equation as governing equation is discussed. The AB equation is an improvement of the KdV equation and can be interpreted as higher KdV equation for wave above finite depth and under certain approximation it becomes the KdV equation [3]. We solve the equation using asymptotic method with bichromatic wave as a signal input, then we apply the varying bottom to the operators of AB equation that contain exact dispersion relation. We observe the propagation of the wave that produced over a slope bottom and find the position of maximal amplitude and amplification of the wave. Comparison the result with the AB equation for flat bottom to study the different characteristic of each other will be studied.

7 illus, 5 ref

015539   Makaje N;A Phon-on (Mathematics and Computer Science Dep, Faculty of Science and Technology, Prince of Songkla Univ, Pattani Campus, Pattani 94000, Thailand, Email: manifatam@gmail.com - 39 - ) : Modified SP-interative scheme for solving nonlinear equations. Far East J mathl Sci 2016, 99(7), 1021-36.

In this paper, we establish a new second order iteration method, called the MSP-iteration, for solving nonlinear equations. We give a sufficient condition for the convergence of MSP-iteration on the interval which brackets the root. By using some numerical examples underthesameconditions,wecomparetheconvergencespeed between the MSP-iteration, the Kang et al.-iteration and the SP-iteration.

6 tables, 15 ref

015538   Liu Z;Wang G;Huangyan (College of Sciences, Hezhou Univ, Hezhou Guangxi, 542899, Email: gx.lzw@163.com) : On the diophantine equation x<. Far East J mathl Sci 2016, 99(6), 831-6.

Let k, n be fixed positive integers with n <62> 2. Using some properties of simple continued fractions of square roots of nonsquare positive integers, we prove that if either k not identical to 2(mod4) or k ≡ 2(mod4) and k <62> 2ⁿ⁺¹ then the equation x² - kxy + y² = 2ⁿ has no positive integer solutions (x, y) with gcd(x,y) = 1.

10 ref

015537   Li M;Wang J (Mathematics Dep, Soochow Univ, Suzhou 215006, P.R. China, Email: ntzdwangjian@163.com) : On K_p,q-factorization of complete bipartite multigraphs. Indian J pure appl Math 2017, 48(2), 221-31.

Let λK_m,n be a complete bipartite multigraph with two partite sets having m and n vertices, respectively. A K_p,q-factorization of λK_m,n is a set of edge-disjoint K_p,q-factors of λK_m,n which partition the set of edges of λK_m,n. When p = 1 and q is a prime number, Wang, in his paper [On K_1,q-factorization of complete bipartite graph, Discrete Math., 126: (1994), 359-364], investigated the K_1,q-factorization of K_m,n and gave a sufficient condition for such a factorization to exist. In papers [K_1,k-factorization of complete bipartite graphs, Discrete Math., 259: 301-306 (2002),; K_p,q-factorization of complete bipartite graphs, Sci. China Ser. A-Math., 47: (2004), 473-479], Du and Wang extended Wang's result to the case that p and q are any positive integers. In this paper, we give a sufficient condition for λK_m,n to have a K_p,q-factorization. As a special case, it is shown that the necessary condition for the K_p,q-factorization of λK_m,n is always sufficient when p : q = k : (k + 1) for any positive integer k.

17 ref

015536   Li H;Xu P (School of Mathematics and Statistics, Henan Univ, Kaifeng 475004, P.R. China, Email: lihbmath@henu.edu.cn) : Hyperbolic dimension and poincare critical exponent of rational maps. Indian J pure appl Math 2017, 48(2), 285-94.

Authors study the Poincare series of rational maps. By investigating the property of conical Julia set and dissipative measure, we prove that the Poincare critical exponents are equal to the hyperbolic dimensions for a large class of rational maps.

9 ref

015535   Khan M N I;Jun J B (Computer Science Dep, College of Computer, Qassim Univ, P.O. Box 5588 Buraidah 51452, Saudi Arabia, Email: mnazrul@rediffmail.com) : On an invariant submanifold - 38 - in a f_λ (5, 3)-structure manifold. Far East J mathl Sci 2016, 99(7), 959-67.

Invariant submanifolds of an almost complex manifold have been studied by Yano and Schouten [11]. Yano and Ishihara [10]also studied invariant submanifolds of almost contact manifold. Other works that authors who studied the invariant submanifold are included in [3, 4, 7]. In this paper, we have defined an invariant submanifold in a f_λ-structure manifold and studied its properties in relation with the manifold.

11 ref

015534   Ibrahim M A H;Mamat M;Ghazali P L;Salleh Z (NO, Faculty of Entrepreneurship and Business Universiti Malaysia Kelantan, Malaysia, Email: hery.i@umk.edu.my) : The scaling of hybrid method in solving unconstrained optmization method. Far East J mathl Sci 2016, 99(7), 983-91.

In this paper, the solution of unconstrained optimization problems has been suggested by using scaling of BFGS-SD method. This method is globally convergent with inexact line searches for general convex functions. The number of iterations and CPU-time of this method has been compared with those of the original BFGS method.

2 illus, 1 table, 12 ref

015533   Huang C H;Chi E C;Hsieh Y L;Xu B C;Liao Y H (Graduate Institute of Educational Administration, National Pingtung Univ, Pingtung 900, Taiwan, R.O.C) : Alternative reduction and related axiomatic results for an extended shapley value. Far East J mathl Sci 2016, 99(7), 1109-17.

By considering both the agents and the activity levels, we define the agent-action reduction and related consistency to characterize the extended Shapley value proposed by Nouweland et al. [4].

5 ref

015532   Gongopadhyay K;Mazumder S (NO, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S.A.S. Nagar, Punjab-140 306, Email: krishnendug@gmail.com) : Existence of an invariant form under a linear map. Indian J pure appl Math 2017, 48(2), 211-20.

Let F be a field of characteristic different from 2 and V be a vector space over F. Let J: α → α^J be a fixed involutory automorphism on F. In this paper we answer the following question: given an invertible linear map T: V → V, when does the vector space V admit a T-invariant nondegenerate J-hermitian, resp. J-skew-hermitian, form?

8 ref

015531   Ghosh A (NO, Durgapur Women's College, Durgapur, West Bengal, Email: amitava1729@gmail.com) : Monotonicity of strata in the stratification of the cone of totally positive matrices. Indian J pure appl Math 2017, 48(2), 245-57.

According to a theorem of Bjorner [5], there exists a stratified space whose strata are labeled by the elements of [u, v] for every interval [u, v] in the Bruhat order of a Coxeter group W, and each closed stratum (respectively the boundary of each stratum) has the homology of a ball (respectively of a sphere). In [6], Fomin and Shapiro suggest a natural geometric realization of these stratified spaces for a Weyl group W of a semi-simple Lie group G, and then prove its validity in the case of the symmetric group. The stratified spaces arise as links in the Bruhat decomposition of the totally non-negative part of the unipotent radical of G. In this article, we verify the topological regularity property of the strata formed as a result of Bruhat partial ordering on the elements of theWeyl group (of rank 4) of a semi-simple simply connected algebraic group G which is SL(4,R) in our case here. The Weyl group here is the Coxeter group S₄.

11 ref

015530   Gaur A;Sharma A (Mathematics Dep, Delhi Univ, Delhi-110 007, Email: gaursatul@gmail.com) : Eulerian graphs and automorphisms of a maximal graph. Indian J pure appl Math 2017, 48(2), 233-44.

Let R be a commutative ring with identity. Let Γ(R) denote the maximal graph corresponding to the non-unit elements of R, i.e., Γ(R) is a graph with vertices the non-unit elements of R, where two distinct vertices a and b are adjacent if and only if there is a maximal ideal of R containing both. In this paper, we have shown that, for any finite ring R which is not a field, Γ(R) is a Euler graph if and only if R has odd cardinality. Moreover, for any finite ring R ≡ R₁ x R₂ x ... x R_n, where the R_i is a local ring of cardinality p_i^a_i for all i, and the p_i's are distinct primes, it is shown that Aut(Γ(R)) is isomorphic to a finite direct product of symmetric groups. We have also proved that clique(G(R)') = <67>(G(R)') for any semi-local ring R, where G(R)' denote the comaximal graph associated to R.

1 illus, 7 ref

015529   Edward Samuel A;Kayalvizhi C (Mathematics PG and Research Dep, Ramanujan Research Centre, Government Arts College (Autonomous), Kumbakonam-612 001, Email: aedward74_thrc@yahoo.co.in) : Hamiltonian fuzzy partition coloring. Far East J mathl Sci 2016, 99(7), 1061-79.

In this paper, we define hamiltonian fuzzy partition. Further, we introduce a hamiltonian fuzzy partition coloring, connecting the hamiltonian fuzzy partition of union and join, hamiltonian partition achromatic fuzzy number, hamiltonian fuzzy path partition and provide some related results, theorems, observations, remarks, examples discussed.

2 illus, 16 ref

015528   Dorsett C (Mathematics Dep, Texas A&M University-Commerce, Texas 75429, U.S.A., Email: charles.dorsett@tamuc.edu ) : Not-separation axioms. Far East J mathl Sci 2016, 99(6), 803-12.

In a recent paper, a new category of topological properties called weakly P properties were introduced and investigated. Within that paper, the search for a topological property that failed to be weakly P led to the use of "not-T₀". As a result, questions concerning the "not-separation axioms" arose leading to the work in this paper.

4 ref

015527   Chung Y L;Mohd M H;Swaminathan A;Lee S K (School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia, Email: chungyaoliang@gmail.com) : Starlikeness of triple integral operators. Far East J mathl Sci 2016, 99(6), 793-801.

The main objective of this work is to obtain sufficient conditions for an analytic function defined in the open unit disk to be starlike of order β by using third-order differential inequalities. We shall give some conditions for f defined by triple integral operator to be starlike of order β.

14 ref

015526   Augustin T K;Adama C;Hermith K A A;Adou Kablan J (NO, Institut National Polytechnique Houphouet-Boigny de Yamoussoukro, BP 2444 Yamoussoukro, Cote d'Ivoire, Email: latourci@yahoo.fr) : Exponential stability of variable coefficients rayleigh beams with indefinite damping under a force control in moment and velocity. Far East J mathl Sci 2016, 99(7), 993-1020.

Authors study the stabilization of a nonhomogeneous Rayleigh beam via an internal damping and the boundary controls feedbacks and demonstrate how the damping term can affect the decay rate asymptotically. Using the approach used by [29, 30] to study these perturbed systems, we obtain the stability and establish the spectrum determined growth condition for the system. Moreover, when - 36 - the damping is indefinite, we provide a condition on how "negative" the damping can without destroying the exponential stability.

33 ref

015525   Aldhafeeri S (Mathematics Dep, College of Basic Education, PAAET, Kuwait, Email: saldhafeeri@yahoo.com) : On permutation characters of A₇ and steiner system S(2, 3, 7). Far East J mathl Sci 2016, 99(6), 775-92.

The purpose of this paper is to study the relation between the permutation characters of the alternating group A₇ and the automorphisms of the Steiner systems S(2,3,7) on one hand, and prove that Foulkes Conjecture holds for all possible wreath products S₁₂ on the other hand.

2 illus, 4 tables, 4 ref

015524   Al-Shaalan K H (Science Dep, King Abdul-aziz Military Academy, Kingdom of Saudi Arabia, Email: khshaalan@gmail.com) : On commutativity of near-rings with generalized derivations. Indian J pure appl Math 2017, 48(2), 259-69.

In this paper we prove some theorems of commutativity for near-rings with generalized derivations. As a consequence of the results obtained, we generalize some published results. Also, we give some examples to show that some conditions in some results obtained are not redundant.

15 ref

015523   Adi-Kusumo F;Winanda R S (Mathematics Dep, Faculty of Mathematics and Natural Sciences, Universitas Gadjah Mada, Sekip Utara, Yogyakarta 55281, Indonesia, Email: f_adikusumo@ugm.ac.id) : Bifurcation analysis of the cervical cancer cells, effector cells, and IL-2 compounds interaction model with immunotherapy. Far East J mathl Sci 2016, 99(6), 869-83.

Authors consider a mathematical model that describes the interaction between the cervical cancer cells, effector cells, and IL-2 compounds. The interaction depends on many factors, such as enzyme reaction process, protein reactions, medical factors, etc. The cervical cancer is a malignant tumor caused by human papilloma virus (HPV). The virus inactivates the p53 and pRb genes which play an important role in the normal cell division and apoptosis. The other important components are the immune system which is designed to detect the presence of antigens. While the effector cells is needed to destroy the HPV-infected cells by stimulation of IL-2. A cancer treatment by using a part of tumor tissue to enhance the immune responses by in-vitro fertilisation is called immunotherapy. We assume that the interactions between these components follow biochemical reactions which is modelled by Michaelis-Menten kinetics function. In this paper, we analyze the dynamics of the system and study the bifurcation related to the variation of its parameter values.

3 illus, 18 ref

015522   Abdelrahim R;Omar Z (Mathematics Dep, College of Art and Sciences, Universiti Utara Sintok, Kedah, Malaysia) : One step block method for the direct solution of third order initial value problems of ordinary differential equations. Far East J mathl Sci 2016, 99(6), 945-58.

One step block method for direct solution of third order initial value problems is considered in this paper. The polynomial basis function is interpolated at two off-step points and collocated at all points. Besides proven to be convergent, numerical examples show that the method competes with the existing methods in terms of accuracy.

1 illus, 2 tables, 12 ref

014594   Yilmaz S;Unluturk Y;Savci U Z (Dokuz Eylul Univ, Buca Educational Faculty, 35150, Buca-Izmir, Turkey, Email: suha.yilmaz@deu.edu.tr) : On dual curves of constant breadth according to dual bishop frame in dual lorentzian space D<. Int J mathl Combinatorics 2016, 1(1), 8-17.

In this work, dual curves of constant breadth according to Bishop frame are defined, and applications of their differential equations are solved for special cases in dual Lorentzian space D^{3₁₃₁. These characterizations are made by obtaining special solutions of differential equations which characterize closed dual curves of constant breadth according to Bishop frame in dual Lorentzian space D3₁.}

18 ref

014593   Wali RS;Patil V R (Mathematics Dep, Bhandari and Rathi College, Guledagudd, Karnataka) : On minimal rgwε-locally open sets and maximal rgwε-locally closed sets in topological spaces. Int J multidiscipl Res Dev 2017, 4(7), 28-32.

In this paper, a - 35 - new class of sets called minimal rgwε-locally open sets and maximal rgwε-closed sets in topological spaces are introduced, which are sub classes of rgwε-locally open sets and rgwε-locally closed sets. Also we introduce and study maximal rgwε-locally open sets and minimal rgwε-locally closed sets in topological spaces and also study τ_rgw?lc-min and τ_rgw?lc-max spaces.

6 ref

014592   Waghamore H P;Rajeshwari S (Mathematics Dep, Central College Campus, Bangalore Univ, Bangalore-560 001, Email: harinapw@mail.com) : Generalization of nonlinear differential polynomials sharing 1-points. Far East J mathl Sci 2017, 101(1), 1-13.

In this paper, authors generalize two theorems on the uniqueness of nonlinear differential polynomials sharing 1-points, which improves a result of Lahiri and Pal [7].

10 ref

014591   Vernold Vivin J;Venkatachalam M;Mohanapriya N (Mathematics Dep, Univ College of Engineering Nagercoil, Anna Univ, Constituent College, Konam, Nagercoil-629 004, Email: vernoldvivin@yahoo.in) : On b-chromatic number of some line, middle and total graph families. Int J mathl Combinatorics 2016, 1(1), 116-125.

A proper coloring of the graph assigns colors to the vertices, edges, or both so that proximal elements are assigned distinct colors. Concepts and questions of graph coloring arise naturally from practical problems and have found applications in many areas, including information theory and most notably theoretical computer science. A b-coloring of a graph G is a proper coloring of the vertices of G such that there exists a vertex in each color class joined to at least one vertex in each other color class. The b-chromatic number of a graph G, denoted by φ(G), is the largest integer k such that G may have a b-coloring with k colors. In this paper, the authors obtain the b-chromatic number for line, middle and total graph of some families such as cycle, helm and gear graphs.

9 illus, 20 ref

014590   Udayabaskaran S;Viswanath J;Kothandaraman M (NO, School of Basic Sciences Vel Tech Rangarajan Dr.Sagunthala R&D Instit, Avadi, Chennai, Tamilnadu-600 062, Email: udayabaskaran.s@gmail.com) : New class of perishable single product inventory systems with compulsory waiting period for reordering. Far East J mathl Sci 2016, 99(8), 1245-60.

A new class of continuous review single product perishable inventory systems is analysed. A compulsory waiting period (CWP) for reordering is introduced. Reorder for instantaneous replenishment can be placed only after the expiry of a CWP even if the inventory level of the system reaches zero before the expiry of the CWP. Stationary mean number of replenishment, mean number of demand satisfied and mean number of demand lost are found explicitly. Numerical illustration is given to validate the model.

4 illus, 11 ref

014589   Udayabaskaran S;Ranganathan N G (School of Basic Science, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Techn, Avadi, Chennai-600 062, Email: - 34 - udayabaskaran.s@gmail.com) : Stochastic analysis of invasion of exotic species. Far East J mathl Sci 2017, 101(1), 73-101.

We consider a microscopic stochastic model of invasion of exotic species in a lake system in a random environment. We obtain the speed of the invasion when the spatial density of the invasion is controlled by changing the offspring generating mechanism of invaders at the infected lake.

2 illus, 2 tables, 11 ref

014588   Tripathi B K;Pandey K B;Tiwari R B (Mathematics Dep, L.E. College, Morbi-363 642, Email: brijeshkumartripathi4@gmail.com) : Nonholonomic frames for finsler space with (α, β)-metrics. Int J mathl Combinatorics 2016, 1(1), 109-15.

The purpose of present paper to determine the two special Finsler spaces due to deformations of some special Finsler space with help of (α,β)-metrics. Consequently, we obtain the non-holonomic frame for the (α,β)-metrics, such as (I) L = (α^{2/α-β) β2/α = αβ2/(α-<98>) i.e. product of Matsumoto metric and Kropina metric and (II) L = (α + β) β2/α = β2 + β2/α i.e. product of Randers metric and Kropina metric.}

14 ref

014587   Torunbalci Aydin F;Yuce S (Mathematical Engineering Dep, Yildiz Univ, 34220, Istanbul, Turkey) : Some new generalizations of the Lucas sequence. Int J mathl Combinatorics 2017, 1(1), 36-51.

In this paper, we investigate the generalized Lucas, the generalized complex Lucas and the generalized dual Lucas sequence using the Lucas number. Also, we investigate special cases of these sequences. Furthermore, we give recurrence relations, vectors, the golden ratio and Binet's formula for the generalized Lucas and the generalized dual Lucas sequence.

17 ref

014586   Tahmasbzadehbaee Z;Abdollahzadeh Ahangar H; Mojdeh D A (Basic Science Dep, Technical and Vocational Univ, Babol branch-Alzahra, Babol, I.R. Iran, Email: ztahmasb@yahoo.com) : Note on the strong defining numbers in graphs. Int J mathl Combinatorics 2016, 1(1), 126-9.

A defining set (of vertex coloring) of a graph G = (V,E) is a set of vertices S with an assignment of colors to its elements which has a unique extension to a proper coloring of G. A defining set S is called a strong defining set if there exists an ordering set {v₁, v₂, ..., v|V|-|S|} of the vertices of G-S such that in the induced list of colors in each of the subgraphs G-S, G-(S∪{v₁}),G-(S∪{v₁, v₂}), ..., G-(S∪{v₁, v₂, ..., v|V|-|S|-1}) there exists at least one vertex whose list of colors is of cardinality 1. The strong defining number, denoted sd(G, k), of G is the cardinality of its smallest strong defining set, where k ≥ χ(G). In the paper, [D.A. Mojdeh and A.P. Kazemi, Defining numbers in some of the Harary graphs, Appl. Math. Lett. 22 (2009), 922-926], the authors have studied the strong defining number in Harary graphs and posed the following problem: sd(H_2m,3m+2, χ) = 2m if m is even and sd(H_2m,3m+2, χ) = 2m + 1 when m is odd. In this note we prove this problem.

9 ref