005965   Balasubramanian S (Mathematics Dep, Government Arts College(A), Karur-639 005, Email: mani55682@rediffmail.com ) : Contra vg-open and contra vg-closed mappings. Arya Bhatta J Math Inf 2015, 7(1), 29-40.

Aim of this paper is to introduce and study the concepts of contra vg-open and contra vg-closed mappings and the interrelationship between other contra-closed maps.

34 ref

005964   Babusci D;Dattoli G;Palma E D;Petropoulou E N (NO, , INFN-Laboratori Nazionali di Frascati via E. Fermi 40-00044 Frascati, Italy) : Humbert-bessel functions stirling numbers and probability distributions in coincidence problems. Far East J mathl Sci 2015, 96(6), 661-9.

Humbert-Bessel is a multi-index function with various applications in electromagnetism. New families of functions sharing some similarities with Bessel functions are often introduced in the mathematical literature, but at a closer analysis they are not new, in the strict sense of the word, and are shown to be expressible in terms of already discussed forms. This is indeed the case of the remodified Bessel functions, whose properties have been analyzed within the context of coincidence problems in probability theory. In this paper, we show that these functions are particular cases of the Humbert-Bessel ones.

6 ref

005963   Alazemi A;Bani-Ata M I A A (Mathematics Dep, Kuwait Univ, Kuwait, Email: alazmi@sci.kuniv.edu.kw) : On certain properties of baer triples (V, G, K)F₂ of type_n. Far East J mathl Sci 2015, 96(6), 725-34.

Aim of this paper is to prove certain properties of Baer triples (V, G, K)_F2 of type n, where G ≅ 2^{n is an elementary abelian.}

5 ref

005962   Adlakha N;Taneja G (Mathematics Dep, Maharshi Dayanand Univ, Rohtak, Haryana, Email: nadlakha59@gmail.com) : Reliability model for a single unit system used for communication through satellites. Arya Bhatta J Math Inf 2015, 7(1), 119-26.

Present paper deals with the study of a reliability analysis of a model for a single unit system used for communication through satellites. The Satellite news gathering network using transportable VSATs (Very Small Aperture Terminals), sometimes called 'fly-away' stations, are transported by car or aircraft and set up at a location where news reporters am transmit video signals to a hub located near the company's studio. In the present study, stochastic analysis of a transportable VSAT used for voice communication and satellite news gathering has been carried out. On requirement, the system is unpacked and assembled. After the assembling process, it becomes operative for the purpose. System is disassembled when requirement is over. Various measures of system effectiveness have been obtained by making use of regenerative point technique.

5 tables, 7 ref

005001   Sukstrienwong A (Information Technology Dep, School of Science and Technology Bangkok Univ, 40/4 Rama IV Rd., Klong-Toey Bangkok, Thailand, Email: anon.su@bu.ac.th) : Method of genetic algorithm for forming student groups based on heterogeneous grouping. Far East J mathl Sci 2014, 95(1), 95-110.

Presently, forming student groups has been considered an essential approach in collaborative learning. Several approaches exist to assist the teachers in universities to form student groups; however, most of the existing literature seems to provide evidence for the success of the peer response technique within language classes. It motivates this research to propose a genetic algorithm approach for group formation based on heterogeneous grouping. Hence, authors propose an approach for the grouping of the students, regarding prior educational knowledge in order to achieve better group composition. It involves balancing students at different levels of knowledge in the appropriate groups in order to learn from peers. The case study is conducted to this paper to demonstrate the efficiency of the algorithm. An experimental result indicates that our approach can optimally generate groups in the effective way.

2 tables, 6 ref

005000   Silalahi B P (Mathematics Dep, Faculty of Mathematics and Natural Sciences, Bogor Agricultural Univ, JL. Meranti, Kampus IPB Darmaga Bogor, 16680, Indonesia, Email: bibparuhum1@yahoo.com) : Sharper analysis of upper bound for the iteration complexity of an interior-point method using primal-dual full-newton step algorithm. Far East J mathl Sci 2014, 95(1), 69-80.

Use of interior-point methods to solve linear optimization problems has become a great attention to the researchers. The most important thing is that the interior-point methods have the best complexity compared to other methods and also efficient in practice. The worst upper bound for the iteration complexity of this method is polynomial. Roos, Terlaky and Vial presented an interior-point method using primal-dual full-Newton step algorithm that requires the best known upper bound for the iteration complexity of an interior-point method. In this paper, authors present their method with a slightly better iteration bound.

3 illus, 13 ref

004999   Pipattanajinda N (Program of Mathematics Faculty of Sciences and Technology, Kamphaeng Phet Rajabhat Univ, Kamphaeng Phet, Thailand, Email: nirutt.p@gmail.com) : Graphs with non-singularity. Far East J mathl Sci 2014, 95(1), 1-17.

Graph is said to be non-singular if the adjacency matrix is non-singular. In this paper, authores give the non-singular graph with loop complement, which is also non-singular. In particular, the non-singularity of some special classes of graphs is revealed.

8 tables, 9 ref

004998   Pavani R;Calio F (Mathematics Dep, Politecnico di Milano 20133 Milano, Italy, Email: raffaella.pavani@polimi.it) : About an artificial time approach for iterative numerical solution of fredholm integral equations of the first kind. Far East J mathl Sci 2014, 95(1), 51-68.

Iterative method exploiting artificial time iteration is presented and applied to the solution of Fredholm integral equations of the first kind, discretized by a collocation method based on Variation Diminishing Schoenberg (VDS) spline approximations. Convergence theorem of iterative method is provided. The presented iterative method is also used to solve known problems discretized by both classical Galerkin and quadrature methods. More, the choice of the linear discrete regularization operator is discussed within the context of Tikhonov, regularization. Numerical results are reported to show the effectiveness of the presented approach.

2 illus, 2 tables, 16 ref

004997   Karuppiah U;Dharsini A M P (Mathematics Dep, St. Joseph's College (Autonomous), Trichy-620 002, Email: u.karuppiah@gmail.com) : Some fixed point theorems satisfying (S, T)-contractive condition in partially ordered partial metric space. Far East J mathl Sci 2014, 95(1), 19-50.

In this paper, we prove some commori fixed point theorems for four mappings by changing the almost generalized (S, T) -contractive condition [43], and combine this idea with the concept of partial metric in such spaces which generalize the theorems of Shobkolaeia et al. [43].

43 ref

004996   Jin H (Mathematics Dep, Jeju National Univ, Jeju 690-756, Republic of Korea, Email: hjin@jejunu.ac.kr) : Mathematical closures of multiphase flow models. Far East J mathl Sci 2014, 95(1), 111-32.

Authors discuss two-pressure two-phase flow models. Multiphase flow equations are defined through an ensemble average of microphysical equations characterized by distinct phases. A central problem for multiphase flow models is closure, or the proper definition of averages of nonlinear terms. Here various proposed closures are compared. We introduce physical constraints closures should satisfy to conserve the total energy and phase entropy and to satisfy boundary conditions at the edges of the mixing zones. A closure which satisfies these constraints is identified. Authors consider, compressible multiphase flow with surface tension and transport.

19 ref

004995   Gupta M K;Tomar N K (Mathematics Dep, Indian Institute of Technology, Patna-800 013) : Proportional derivative observer design for rectangular linear descriptor systems. Bhartiya Vaigyanik Evam Audyogik Anusandhan Patrika 2015, 23(1), 48-53.

New method is proposed to design a proportional derivative (PD) observer for rectangular linear time invariant descriptor systems. The method is based on the effects of full column rank matrix transformations. By these transformations, given descriptor systems has been transformed into a equivalent system satisfying certain conditions. These full column rank matrices are derived from the coefficient matrices of the given descriptor system using simple matrix theory. Sufficient conditions for the existence of observers are given and proved. An illustrative example is provided to demonstrate the effectiveness of the proposed method.

1 illus, 34 ref

004994   Charkrit S (Mathematics Dep, Maejo Univ, Chiang Mai 50290, Thailand, Email: sita_char@yahoo.com) : Alternative method for solving nonlinear differential equations via integral equations. Far East J mathl Sci 2014, 95(1), 81-93.

Alternative method is proposed for finding the solution of the n-order nonlinear initial value problem (IVP). By using the Laplace transforms, the IVP is converted into the Volterra integral form. Then the successive approximation is applied to obtain the solution. In addition, the formulation of the solution is constructed for the convenience of the calculation. Several examples illustrate the efficiency and the simplicity of the proposed method.

25 ref

003079   Yoo J K (Liberal Arts and Science Dep, Chodang Univ, 419 Sungnamri Muangun 534-701, Chonnam, Korea) : Totally paranormal operators with property δ have invariant subspaces. Far East J mathl Sci 2014, 94(2), 239-49.

Suppose H is a complex Hilbert space and T ∈ L(H) is a bounded linear operator. In this paper, we show that if T ∈ L(H) is a totally paranormal with no eigenvalues, then H_T({λ}) = N(λI - T) for all λ, ∈ C. We also show that if T ∈ L(H) is a totally paranormal with no eigenvalues, then T is algebraic if and only if the spectrum σ(T) is finite. Finally, it is shown that that if T ∈ L(H) is a totally paranormal operator on a complex Hilbert space H with property (5), then T has a nontrivial invariant subspace. As a corollary, every hyponormal operator with (8) has a nontrivial closed invariant subspace.

25 ref

003078   Yamagishi H (Science and Engineering Dep, Tokyo Denki Univ, Hatoyama, Saitama 350-0394, Japan, Email: hizuru@mail.dendai.ac.jp) : Certain quadruple family of superelliptic curves associated with (p, p)-extension. Far East J mathl Sci 2015, 96(1), 1-14.

Let p ≠ 3 be an odd prime and k be a field containing a primitive pth root of unity. We construct cubic polynomials f(t), g(t), h(t) with coefficients in K, a certain transcendental extension field of k, such that all of the ranks of Jacobian variety of the curves f(t)y^{p = f(x), g(t)yp = f(x), h(t)yP = f(x), g(t)h(t)yp = f(x) over K(t) are positive.}

8 ref

003077   Welyyanti D;Baskoro E T;Simanjuntak R; Uttunggadewa S (Combinatorial Mathematics Research Div, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandun, Jl. Ganesa 10 Bandung 40132, Indonesia, Email: deswelyyanti@students.itb.ac.id ) : The locating-chromatic number of disconnected graphs. Far East J mathl Sci 2014, 94(2), 169-82.

The paper generalizes the notion of locating-chromatic number of a graph such that it can be applied to disconnected graphs as well. In this sense, not all the graphs will have finite locating-chromatic numbers. We derive conditions under which a graph has a finite locating-chromatic number. In particular, we determine the locating-chromatic number of a uniform linear forest, namely a disjoint union of some paths with the same length.

5 illus, 4 tables, 11 ref

003076   Venkaiah V C (School of Computer and Information Sciences, Hyderabad Univ, Gachibowli, Hyderabad-500 046, Email: venkaiah@hotmail.com) : Necklaces: generalizations. Resonance 2015, 20(6), 542-55.

A q-ary necklace of length n is an equivalence class of q-coloured strings of length n under rotation. In this article, we study various generalizations and derive analytical expressions to count the number of these generalized necklaces. Also discussed are the various relations among the generalized necklaces, circulant matrices, and tw-istulant matrices.

003075   Udayabaskaran S;Karthikeyan T;Lalitha D (Mathematics Dep, Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Tech, Chennai-600 062, Email: udayabaskaran.s@gmail.com) : Stochastic model of cytotoxic T lymphocyte mediated control of HIV. Far East J mathl Sci 2015, 96(1), 15-28.

In this paper, a stochastic analogue of the model of HIV dynamics presented in Wodarz and Nowak [2] is developed. Based upon the stochastic model, a long-term immunological control of HIV is predicted. Therapy regimes which can convert a HIV progression into a state of long-term non-progression are also designed.

5 illus, 3 ref

003074   Thakur D S (Mathematics Dep, Rochester Univ, Rochester, New York 14627, USA, Email: dinesh.thakur@rochester.edu) : Notion of twenty-two shrutis frequency ratios in hindustani claasical music. Resonance 2015, 20(6), 515-31.

This is an expository article with the intent of briefly explaining the possible logic behind a 22-shruti model for the system of musical notes in Hindustani (i.e., North Indian) classical music. It will also be explained how this model is consistent with the Chatus-saaranaa (meaning 'four translations') tuning procedure described in the famous manuscript Natya Shastra by Bharat Muni, dated somewhere between second century BC to third century AD.

12 ref

003073   Song J;Ma Z;Yang J (College of Computer Science and Technology, Southwest Univ of Nationalities, Chengdu 610041, P.R. China, Email: 2671382678@qq.com) : Asymptotic property of impulsive difference equations with delays. Far East J mathl Sci 2015, 96(1), 87-96.

By establishing a singular impulsive delay difference inequality and using the properties of "ρ-cone", several sufficient conditions ensuring the invariant set and the attracting set for impulsive difference equations with delays are obtained. The results have extended and improved the related earlier results.

8 ref

003072   Selvaraj C;Umamaheswaran A (Mathematics Dep, Periyar Univ, Salem-636 011, Email: selvavlr@yahoo.com) : χ-injective and gorenstein χ-injective modules. Far East J mathl Sci 2014, 94(2), 203-16.

In this paper, authors study the notion of Gorenstein X -injective module with respect to its complete injective resolution and give its characterization, where χ^{<124> = U_χ and χ = {N ∈ R-ModN is finitely presented and Ext_R1(N, M) = 0, ∀M ∈ U_χ}. Authors prove that (i) the class of all χ-injective modules and the class of all Gorenstein χ-injective modules are injectively resolving, respectively, (ii) if R is a coherent ring, then every R-module M has an χ-injective cover. Finally, we show that if 0 → M₁ → M₂1 → M₃ → 0 is an exact sequence of R-modules with M₂ and M₃ Gorenstein χ-injective R-modules, then M₁ is Gorenstein χ-injective if and only if Ext_R1(G', M1) = 0 for all χ-injective R-modules G.}

8 ref

003071   Prasertsang P;Sompong S (Sciences Dep, Faculty of Science and Engineering Kasetsart Univ, Chalermprakiat Sakon Nakhon Province Campus Sakon Nakhon 47000, Thailand, Email: patarawadee@gmail.com) : (i, j)-m_X-α-boundary and exterior sets in biminimal structure spaces. Far East J mathl Sci 2015, 96(1), 97-111.

Concepts of m_X-α -boundary and exterior sets in biminimal structure spaces were introduced, which found some characterizations and several properties of those sets.

13 ref

003070   Paranjape K H (NO, Indian Institute of Science Education and Research Mohali, Sector 81 SAS Naga, Manauli PO Punjab-140 306, Email: kapil@iisermohali.ac.in) : Grothendieck and the concept of space. Resonance 2015, 20(6), 500-5.

A very brief introduction to Grothendieck's concepts of algebraic schemes and algebraic spaces.

1 illus, 3 ref

003069   Paranjape K H (NO, Institute of Science Education and Research Mohali, Sector 81 SAS Naga, Manauli PO Punjab-140 306, Email: kapil@iisermohali.ac.in) : Glossary of some mathematical terms. Resonance 2015, 20(6), 491-9.

M S Narasimhan's article in this issue on page 482 contains several mathematical terms. In this glossary, we try to briefly explain some of them.

003068   Narasimhan M S (Distinguished Associate, NMI, IISc and Honorary Fellow, TIFR Centre, Bengaluru, Email: narasim@math.tifrbng.res.in) : Alexander the great the mathematical genius grothendieck. Resonance 2015, 20(6), 483-90.

Alexander Grothendieck was one of the greatest mathematicians of the twentieth century. His work revolutionized algebraic geometry and he made tremendous contributions to the concepts, content and techniques of this field, advancing it to an unprecedented level. Moreover, his work had enormous influence in other areas of mathematics like number theory, topology, homological algebra and functional analysis. His unifying vision provided the framework and tools for solving famous and long-standing problems in algebraic geometry and number theory: for example, Weil conjectures by Deligne, Mordell conjecture by Faltings and Modular conjecture -Fermat's 'last' theorem by Wiles-Taylor.

11 ref

003067   Mulyono;Sumardi H;Suwilo S (Mathematics Dep, Univ of Sumatera Utara Jl. Bioteknologi No 1 FMIPA USU Medan 20155, Indonesia) : Scrambling index of primitive two-colored two cycles whose lengths differ by 1. Far East J mathl Sci 2015, 96(1), 113-32.

Two-colored digraph is a digraph each of whose arc is colored by red or blue. An (h, l) -walk is a walk consisting of h red arcs and l blue arcs. The scrambling index of a two-colored digraph is the smallest positive integer h + l. over all nonnegative integers h and l, such that for each pair of vertices u and v there is a vertex w such that there exist an (h, l) -walk from H to w and an (h, l) -walk from v to w. We study the scrambling index of primitive two-colored digraph consisting of two cycles whose lengths differ by 1. Authors present a lower bound and an upper bound for the scrambling index for such two-colored digraph. We then show that the lower and the upper bounds are sharp bounds.

4 ref

003066   Mbaye A;Toure S D;Diop K;Sanghare M (Departement de Mathmatiques et Informatique, Facult des Sciences et Techniques, Universit Cheikh Anta Diop de Dakar, Senegal, Email: abdoulaye_m@hotmail.com) : On SCI-duo-rings. Far East J mathl Sci 2014, 94(2), 183-8.

Let R be a duo ring. A unital R-module M is said to have property (I) if every injective endomorphism of Mis an automorphism. The ring R is called SCI-duo-ring if every R-module with property (7) is finitely cogenerated. In this note, we show that the following conditions are equivalent: (i) R is an Artinian principal ideal duo ring; (ii) R is an SC7-duo-ring.

10 ref

003065   Mashuri;Purwanto B S (Mathematics Dep, Universitas Jenderal Soedirman Jl. Dr. Soeparno No. 61 Purwokerto, 53122, Indonesia) : Wave group evolution in KdV-type model. Far East J mathl Sci 2015, 96(1), 29-42.

Improvement of uni-directional wave model so called AB equation was proposed to study wave groups that appeared in the wave tanks of hydrodynamic laboratory [2]. The model was revised version of the KdV equation and could be interpreted as a higher order KdV equation for wave above finite depth and in certain approximation it became the KdV equation. In this paper, we will focus to investigate the evolution of the envelop of modulated wave which is described by the nonlinear Schrodinger equation (NLS). We derive the NLS-type equation from the AB equation. The asymptotic method is used to find the equation. The signs of the coefficients of the NLS-type equation that determine whether experimentally relevant wave groups are possible exist or not will be compared by the other NLS-type equations. The effect of the dispersion relation and the nonlinearity terms of the model to existence of experimentally relevant wave groups will be presented.

4 illus, 1 table, 5 ref

003064   Marva M (Departamento de Fisica y Mathematics, Universidad de Alcala, 28871 Alcala de Henares, Spain, Email: marcos.marva@uah.es) : Supersolutions of degenerated logistic equation type. Far East J mathl Sci 2014, 94(2), 161-7.

In this paper, authors provide a method for building up a strictly positive supersolution for the steady state of a degenerated logistic equation type, i.e., when the weight function vanishes on the boundary of the domain. This degenerated system is related in obtaining the so-called large solutions. Previously, this problem was handled as the limit case of non degenerated approaching problems. Our method can be adapted straightforwardly to degenerated boundary value problems.

14 ref

003063   Maria Susai Manuel M;Srinivasan K;Dilip D S; Dominic Babu G (Science and Humanities Dep, R.M.D. Engineering College, Kavaraipettai-601 206, Email: mmariasusai@gmail.com) : Asymptotic properties of solutions of higher order nonlinear generalized α-difference equations. Far East J mathl Sci 2014, 94(2), 189-202.

In this paper, the authors discuss the asymptotic behaviour of solutions of higher order generalized α-difference equation of the form Δ_α^{n(l)u(k) + f(k, u(k), Δ_α(l)u(k), ..., Δ_α(l)n-1u(k)) = 0,k ∈ [0, ∞), (1) where the function f is defined on [0, ∞) x Rn and l is a positive real.}

15 ref

003062   Luangmalawat B;Humphries U;Tangmanee S (Mathematics Dep, King Mongkut's Univ of Technology Thonburi, Thailand, Email: budsaraphorn@gmail.com) : Wavelet analysis on southern Thailand rainfall data. Far East J mathl Sci 2014, 94(2), 149-59.

Wavelet transform with the Morlet wavelet function was applied to study the periodic oscillation of rainfall variability in southern Thailand. Using the white noise time series as a background for hypothesis testing of the monthly rainfall of 62 years (1951 to 2012), the wavelet power spectrum shown that in the east coast, there were two periodic oscillations of period 4-8 months and 8-16 months, meanwhile in the west coast the rainfall having one periodic oscillation with 8-16 months.

9 illus, 12 ref

003061   Liu R;Ge F (College of Fundamental Studies, Shanghai Univ of Engineering Science, Shanghai 201620, P.R. China, Email: ruirui0516@163.com) : Positive solutions on fractional boundary value problem with changing sign nonlinearity on the half-axis. Far East J mathl Sci 2014, 94(2), 217-38.

In this paper, we obtain the existence results of positive solutions of fractional order with changing sign on the half-axis in a Banach space by using a fixed point theorem on cone. Examples illustrating our main results are also given.

16 ref

003060   Kim Y K;Min W K (Mathematics Dep, Myongji Univ, Youngin 449-728, Korea, Email: ykkim@mju.ac.kr) : σ-preopen sets and σ-precontinuous functions on spaces with σ-structures. Far East J mathl Sci 2014, 94(2), 251-62.

Authors introduce the notions of σ-preopen sets and σ-precontinuous functions on sets with σ structures, and study some basic properties of such notions. We investigate characterizations for the σ-precontinnity by using the σ-interior, σ-closure, σ-pre-interior and σ-pre-closure operators. In particular, we investigate the relationships among σ-continuity and σ-semicontinuity and σ-precontinuity.

4 ref

003059   Kanasri N R;Singthongla P (Mathematics Dep, Khon Kaen Univ, Khon Kaen-40002, Thailand, Email: naraka@kku.ac.th) : Alternating sel series expansion and generalized model construction for the real number system via alternating series. Far East J mathl Sci 2014, 94(2), 129-47.

Authors present an algorithm for constructing an alternating series expansion for real numbers, which yields generalized versions of three alternating series expansions, namely, alternating Sylvester series, alternating Engel series and alternating Luroth series expansions. Using this alternating series expansion, a generalized model for the real number system is also constructed.

8 ref

003058   Bashammakh S A;Babusail R;Alqahtani H S (Mathematics Dep, Faculty of Sciences (Girls) King Abdulaziz Univ, Jeddah, Saudi Arabia, Email: h.s.alqahtani@hotmail.com) : Left derivations of incline algebras and related set. Far East J mathl Sci 2015, 96(1), 43-62.

In this paper, authors introduce the notion of left derivations of incline algebras, and prove some results on left derivations of an incline and integral incline. Also, we define the fixed set of left derivations on incline and show that it is a subincline and the fixed set of left derivations on incline is an ideal, principal ideal and model.

1 table, 18 ref

003057   Abdelkarim A A (NO, Jerash Private Univ, Jerash, Jordan) : On products of uniformly continuous functions. Far East J mathl Sci 2015, 96(1), 63-71.

In this note, authors show that if f(x) is a bounded continuous and of bounded variation on an interval I = (a, ∞), then f is uniformly continuous. If, furthermore, g is a uniformly continuous function on I, then fg is uniformly continuous. Let f(x) be a differentiable unbounded function defined on an interval (a, ∞). Then f(x) is not uniformly continuous if and only if lim sup |f'(x)| = ∞ on (a, ∞). On an interval (a, ∞), a differentiable function greater than an increasing differentiable function which is not uniformly continuous is not uniformly continuous. And increasing differentiable function which is less than a uniformly continuous differentiable function is uniformly continuous.

2 illus, 2 ref

002183   Yang M (Mathematics Dep, Incheon National Univ, Yeonsoo-Gu Songdo-Dong 12-1 Incheon 406-772, Korea, Email: mhyang@incheon.ac.kr) : Herglotz space associated with the state space of a ultiscale system. Far East J mathl Sci 2014, 93(2), 211-27.

Let S be a Schur muliplier in a multiscale system. A Herglotz space L(S) can be constructed from the state space H(S) of a quasi-coisometric linear system whose transfer function is S. For a Caratheodory operator Φ, there is a multiscale linear system whose state space L(Φ) is related to the space L(S), where S = (I + Φ)^-1.(I-Φ).

8 ref

002182   Xavier G B A;Gerly T G;Nasira Begum H (Mathematics Dep, Sacred Heart College (Autonomous) Tirupattur, Vellore District-635 601, Email: brittoshc@gmail.com) : Finite series of polynomials and polynomial factorials arising from generalized q-difference operator. Far East J mathl Sci 2014, 94(1), 47-63.

In this paper, the authors define q-difference operator Δ_q and present some significant results on the inverse of the q-difference operator of the tth order using generalized polynomial factorial and Stirling number of the second kind. Suitable numerical examples are also provided to illustrate the main results.

10 ref

002181   Tiwari S K (Applied Science and Humanities Dep, Ajay Kumar Garg Engineering College, Ghaziabad) : Phie-confomally flat generalized Sasakian space form. Int J latest Technol Engng Mgmt appl Sci 2015, 4(6), 82-5.

In this article authors studied generalized sasakian space forms which are φ-conformally flat, φ-conharmonically flat, φ-projectively flat and prove that they are η-einstein manifolds under suitable assumptions. 2000 Mathematical subject classification 53D15,53C25.

11 ref

002180   Subramanian N;Priya C;Saivaraju N (Mathematics Dep, SASTRA Univ, Thanjavur-613 401, Email: nsmaths@yahoo.com ) : Randomness of lacunary statistical convergence of χ<. Far East J mathl Sci 2014, 94(1), 89-111.

Mursaleen introduced the concepts of statistical convergence in random 2-normed spaces. Recently, Mohiuddine and Aiyup defined the notion of lacimary statistical convergence and lacunary statistical Cauchy in random 2-normed spaces. In this paper, we define and study the notion of lacunary statistical convergence and lacunary statistical Cauchy sequences in random on χ^{2 over p-metric spaces defined by sequence of modulus functions and prove some theorems which generalize the result due to Mohiuddine and Aiyup results.}

38 ref

002179   Sarathi M P;Ansari M A (Electronics and Communications Engineering Dep, Amity School of Engineering and Technology, Amity Univ, Sector 125, Noida, Uttar Pradesh-201 301, Email: psmangipudi@amity.edu) : Novel algorithm for brain slice retrieval from brain MR image databases. Indian J ind appl Math 2015, 6(1), 80-94.

Paper presents a brain slice retrieval scheme in magnetic resonance (MR) brain volumes acquired from biomedical image sensors. The proposed scheme inputs a 2D brain MR image slice and outputs visually similar slices present in the brain MR volume database. It could be of immense help to the medical practitioners. It might prove to be a useful diagnostic aid and serve as a teaching aid for students in the medical field. Brain MRI artefacts like noise and scanner inhomo-geneities are serious impediments to accurate retrieval. The challenge then is to device an algorithm which is fast, accurate and is robust to variability in tissue intensity values caused by imaging artefacts. To this end, our scheme tries to overcome these hurdles and devise an algorithm which is shown to be robust to inter- and intra-slice intensity variations and geometrical transformations. The edge information of the lesions is extracted via combining multi-resolution methods and spatial methods. The multi-resolution property of wavelets is inherently robust to the present bias fields. The local structure information is then utilised for successful retrieval of similar slices from the brain volumes. The feature point representation of the edge information is shown to be better in comparison to the existing algorithms.

13 illus, 2 tables, 22 ref

002178   Rakesh Kumar;Som B K (School of Mathematics, Shri Mata Vaishno Devi Univ, Katra 182320, Email: rakesh_stat_kuk@yahoo.co.in) : M/M/1/N queuing system with reverse balking, reverse reneging, and retention of reneged customers. Indian J ind appl Math 2015, 6(1), 73-9.

In this paper, we study a single server finite capacity Markovian queuing system with reverse balking, reverse reneging, and retention of reneged customers. We derive the steady-state solution of the model and obtain some important measures of performance. Sensitivity analysis of the model is also performed with a numerical example.

4 tables, 9 ref

002177   Pooja;Manchanda P;Kumar J (Mathematics Dep, Guru Nanak Dev Univ, Amritsar, Punjab, Email: poojarai_44@yahoo.com) : Regularization of 2D backward heat equation using heatlets. Indian J ind appl Math 2015, 6(1), 36-48.

Heatlets were introduced by Shen and Strang [1999. Journal of Differential Equations, 161, pp 403-421] to solve the heat equation using wavelet expansion of the initial data. In this paper, we regularize the 2D backward heat equation and, in general, ill-posed Cauchy problems using heatlets. Authors use the quasi-reversibility method to find approximate solutions to ill-posed Cauchy problems and then apply Holder-continuous dependence inequalities obtained by Ames and Hughes [2005, Semigroup Forum, 70, pp. 127-145] to relate the solutions of original and approximate problem.

18 ref

002176   Paichit P;Areepong Y;Sukparungsee S (Applied Statistics Dep, Faculty of Applied Science, King Mongkut's Univ of Technology North Ba, Bangkok 10800, Thailand, Email: yupaporna@kmutnb.ac.th) : Average run length of Ewma chart for sarma (P, Q)_L processes. Far East J mathl Sci 2014, 93(2), 229-41.

Exponentially weighted moving average (EWMA) control chart is very effective in detecting small shifts in process mean and vastly used in a great variety of practical applications such as economic industry health and in other areas. There are several situations in which the process is serially correlation such as in the chemical and process industries. For example, the dynamics of the process will induce correlations in observations that are closely spaced in time. The average run length (ARL) is a traditional measurement of the performance of control chart. The main purpose of this paper is to derive analytical solutions for the ARL of an EWMA control chart for seasonal autoregressive and moving average of order P, Q (SARMA (P, Q)_L) process with exponential white noise. In this paper, the ARL is the unique solution to the integral equation under some weak regularity conditions. Checking the accuracy of results, the results obtained from exact solutions with numerical integral equation based on Gauss-Legendre rule were compared. An excellent agreement between the exact solutions and numerical solutions was found. This fact is an additional indication that the exact solutions are sufficiently high accuracy.

3 tables, 18 ref

002175   Ouannas A;Ahlem G (LAMIS Laboratory, Mathematics and Computer Science Dep, Tebessa Univ, Algeria, Email: ouannas_adel@yahoo.fr) : General synchronization approach for general chaotic systems in continuous-time. Far East J mathl Sci 2015, 96(2), 231-9.

Based on Lyapunov stability theory, a universal control method is proposed to derive a new synchronization criterion for general chaotic systems. The derived criterion is established in the form of simple algebraic conditions to achieve global synchronization between coupled of continuous-time chaotic systems in n-D. This simple criterion is applicable to a large class of chaotic systems. To demonstrate the efficiency of the new design control, the suggested method is applied to some typical chaotic systems.

2 illus, 16 ref

002174   Ogata S;Zhao H L (Mathematical Institute, Tohoku Univ, Sendai 980-8578, Japan, Email: ogata@math.tohoku.ac.jp) : Characterization of gorenstein toric fano n-folds with indes n and fujita's conjecture. Far East J mathl Sci 2014, 94(1), 65-88.

We give a characterization of Gorenstein toric Fano varieties of dimension n with index n among toric varieties. As an application, we give a stronger version of Fujita's freeness conjecture and also give a simple proof of Fujita's very ampleness conjecture on Gorenstein toric varieties.

10 ref

002173   Mumtong W;Pongsumpun P;I-Ming T (Mathematics Dep, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Ladkrabang Bangkok 10520, Thailand, Email: kppuntan@kmitl.ac.th) : Analysis of model for menstrual cycle with the effect of body mass index. Far East J mathl Sci 2014, 93(2), 243-66.

Menstrual cycle is the tissue that peeled off from the lining of the uterus. It is caused by changes in female hormones associated with ovulation. Obesity often affects the balance of estrogen hormone, hormone for ovulation control that may cause menstrual abnormalities. If there is no ovulation, then there would be no menstruation occurs. This article has examined the above factors that affect the balance of hormones on the control of the ovulation cycle.

5 illus, 28 ref

002172   Liao Y H;Chung L Y (Applied Mathematics Dep, National Pingtung Univ, Pingtung 900 Taiwan, Email: twincos@ms25.hinet.net) : Minimal consistent core: an converse consitent enlargement and alternative axiomatizations. Far East J mathl Sci 2014, 94(1), 113-28.

In order to investigate how extensive the violation of converse complement-consistency is, a converse complement-consistent enlargement of the minimal consistent core is firstly proposed. By focusing on both the agents and their actions, we further propose some revised reductions to axiomatize the minimal consistent core.

10 ref

002171   Khan I U;Ansari M A (Electronics and Communication Engineering Dep, Integral Univ, Lucknow, Email: imranuk79@gmail.com) : Data partitioning and MDC for the SPECk coder for real-time applications over wireless channel. Indian J ind appl Math 2015, 6(1), 57-72.

In this paper, overview of error concealment scheme data partitioning of H.264/AVC and Set Partitioning Embedded Block (SPECK) coder is discussed. This paper refers to the reference software joint model 4.2(JM-4.2) for H.264/AVC. SPECK coder is a zero-block coder based on inter-subband correlation. In this paper, performance of H.264/AVC for various data partitioning conditions may be discussed, also SPECK coder is proposed and analysis of multiple descriptive coding on Speck coder is carried out. Both subjective and objective results show that there is significant improvement in video quality than direct decoding.

13 illus, 9 tables, 33 ref

002170   Khampakdee J (Mathematics Dep, Faculty of Science Mahasarakham Univ, Mahasarakham-44150, Thailand, Email: jeeranunt.k@msu.ac.th) : β-open sets in biclosure spaces. Far East J mathl Sci 2014, 94(1), 33-45.

The purpose of this paper is to introduce the concept of β-open sets in biclosure spaces and investigate their fundamental properties. Moreover, we give the concepts of (3-open maps and β-continuous maps and their characterizations.

6 ref

002169   Karim S A A (Fundamental and Applied Sciences Dep, Univ Teknologi PETRONAS Bandar Seri Iskandar, 31750 Tronoh Perak Darul Ridzuan, Malaysia, Email: samsul_ariffin@petronas.com.my ) : Shape preserving by using rational cubic ball interpolant. Far East J mathl Sci 2015, 96(2), 211-30.

Paper discusses the positivity and monotonicity preserving by using rational cubic Ball interpolant of the form cubic/quadratic with three parameters. The sufficient conditions for the positivity and monotonicity are derived with two parameters for controlling the final resulting interpolating curves (positive and monotone). The degree of smoothness attained is C. Four data sets are chosen in order to test the capability of the proposed rational cubic Ball interpolation for positivity and monotonicity preserving. From all graphical results, rational cubic Ball with three parameters gives smooth interpolating curves and visually pleasing for scientific visualization.

3 illus, 9 tables, 19 ref