009586   Thomas B;Scaria J (Statistics Dep, Sree Sankara College, Kalady, Ernakulam Dist., Kerala-683 574, Email: baijukolathu@yahoo.co.in) : Concomitants of records from cambanis type bivariate gamma distribution. Sci Soc 2012, 10(1), 45-52.

Let X_i, i= 1,2,...,be a sequence of independently and identically distributed random variables having the same absolutely continuous distribution function F(x). The random variable X_j is called an upper record (or simply a record) if its value exceeds that of all previous observations. Thus X_j is a record if X_j <62> X_i for all i = 1, 2,... j-1. An analogous definition deals with lower record values. Let R_n denote the nth record value in the sequence of X values. The corresponding random variable Y, i.e. the Y value paired with the X value R_n is called the n'h record concomitant and will be denoted by R_[n]. This paper deals with the distribution theory of record concomitants from the Cambanis type bivariate gamma distribution.

15 ref

009585   Rajarajeswari P;Uma N (Mathematics Dep, Chikkanna Art College, Tirupur, Tamil Nadu (INDIA), Email: prajarajeswari29@gmail.com) : Off-line signature verification and forgery detection using pixel based fuzzy logic technique. J Innovative Res Solut 2013, 1(2), 77-81.

A simple, passive scheme to achieve the offline signature verification and forgery detection is proposed. This approach is based on the fuzzy technique of the Takagi-Sugeno model. The ultimate goal of fuzzy logic is to deal with reasoning, inexact or fuzzy concepts. The parameters considered in this approach are the pixel comparison of the signatures, pixel area of the signature and the distance taken from the centre of the image. From these parameters, the efficiency rates are calculated. Based on these efficiency rates, the rule based fuzzy technique is framed to evaluate the testing process [1],[l0]. The trained genuine specimen signatures are compared with the tested signatures, based on this algorithm; the signature is accepted or rejected. The experimental results show that the proposed scheme indentifies the two types of forgeries: unskilled and skilled forgeries effectively. The accuracy rate of our proposal is found to be about 85 to 89%.

4 illus, 12 ref

008499   Wang X;Xue Y (Mathematics Dep, North China Univ, Taiyuan, Shanxi-030 051, P.R. China, Email: wangxiaohong198502@163.com) : Analysis of HFMD in China using a SEIQR model. Far East J mathl Sci 2011, 58(1), 83-98.

This paper presents a mathematical model of hand-foot-and-mouth disease (HFMD) that incorporates quarantine in the children population. The model consists of susceptible, exposed, infectious, quarantined and recovered subgroups and considers the exposed (infected by HFMD virus but not infectious) individuals may transmit virus to the others. The model simulations agree with the HFMD data reported by the Chinese Ministry of Health. We estimate that the basic reproduction number R0= 1.0121 for the HFMD transmission in China and predict that the number of the HFMD is increasing but will eventually maintain at a stable level!. Also perform some sensitivity analysis of RQ in terms of the model parameters and demonstrate that quarantine is very effective on controlling the spread of the disease.

5 illus, 1 table, 17 ref

008498   Vijender C;Srisailam A (Mathematics Dep, Osmania Univ, Hyderabad-500 007, Email: asmou22@yahoo.com) : Parametric study of point-image-quality assessment of an optical system with an amplitude apodiser". Ultra Scient phys Sci-Sect A 2012, 24(2), 361-8.

In this paper, a parametric study of some of the most important corollaries of the Green's function of an optical system has been carried out. The parameters chosen for this study are Full-Width at half-Maximum Negative amplitude, second order movement and Ripple Factor, The results obtained have been discussed with the help of graphs and tables.

6 illus, 6 tables, 8 ref

008497   Vijaya S (Mathematics Dep, Annamalai Univ, (India)) : Stochastic model with variable threshold in HIV infection. Ultra Scient phys Sci-Sect A 2012, 24(2), 311-18.

In the study of HIV infection the progression of the disease takes place with the passage of time. This is due to the increasing the antigenic diversity level of the Retrovirus. As and when the total antigenic diversity crosses a threshold level, the sero conversion takes place. The threshold itself is considered to be a random variable. In this paper assuming that the antigenic diversity threshold satisfies the property known as Setting the Clock Back to Zero (SCBZ) property, the expected time to sero conversion and its variance are derived. The results are augumented with suitable numerical illustrations.

4 illus, 4 tables, 7 ref

008496   Udo-Utun X;Siddiqui Z U;Balla M Y;Afuwape A U;Mshelia E D (Mathematics and Statistics Dep, Maiduguri Univ, Maiduguri, Nigeria, Email: xvior@yahoo.com) : On integral representation of casual operators. Far East J mathl Sci 2011, 59(1), 57-63.

In this work-authors advance a contribution toward tackling the solvability of the problem of representing causal operators with classical Volterra integral operators. Authors have combined notions from Nemytskii operator theory and frequency domain methods to achieve our results.

9 ref

008495   Tiwari R K;Chaurasiya N K;Badal D (Mathematics Dep, G.B.S. College, Mauranipur) : Closedown time dependent bulk queue with multiple vacations. Ultra Scient phys Sci-Sect A 2012, 24(2), 391-404.

In this paper a Closedown time concent is introduced in a Bulk queuing model closedown time dependent a M^x/G(a,b)/queuing system with multiple vacation is considered. After completing a service, if the queue length is ξ, where ξ, <60>a, then the server performs closedown work. After that the server leaves for multiple vacation of random length, irrespective of queue length. After a vacation, when it returns. If the queue length is less than 'a', it leaves for another vacation and so on, until he finds 'a' customers in the queue. After a vacation, if the server finds at least 'a' customers waiting for service, say, then he serves a batch of size min (ξb) customers, where b ≥a. Various Characteristics of the queueing system and a cost model with the numerical result for a particular case of the model are presented in this paper.

1 illus, 1 table, 10 ref

008494   Thangam T;Bageerathi K;Thangavelu P (Mathematics Dep, Govindammal Aditanar College for Women, Tiruchendur-628 215, Email: sivarathi_2006@yahoo.in) : On Fuzzy feebly open sets and fuzzy feebly closed sets. Ultra Scient phys Sci-Sect A 2012, 24(2), 379-90.

In this paper authors introduce the concept of fuzzy feebly open and fuzzy feebly closed sets by using arbitrary complement function and by using fuzzy semi closure operators of a fuzzy topological space where [0, 1] → [0, 1] is a function and investigate some of their basic properties of a fuzzy topological space.

10 ref

008493   Sudarsana I W (Combinatorial and Applied Mathematics Research Group, Tadulako Univ, Jalan Soekarno-Hatta Km. 8, Palu 94118, Indonesia, Email: sudarsanaiwayan@yahoo.co.id) : Goodness of long path with respect to multiple copies of small wheel. Far East J mathl Sci 2011, 59(1), 47-55.

Denotes by W_n for a wheel on n + 1 vertices. The notation tW₄ represents a graph with t copies of wheel W₄. In this note, authors discuss the goodness of path P_n on n vertices with respect to tW₄. This result provides the Ramsey number R(G, tW₄) when G is a disjoint union of paths.

11 ref

008492   Singh G P;Tyagi A (Mathematics Dep, Pacific institute of Engineering, Pacific Academy of Higher education, Udaipur-313 024, Email: gajendrasingh237@gmail.com) : Magnetized Bianchi type III anti-stiff fluid consmological models with time dependent <65> and variable magnetic permeability. Ultra Scient phys Sci-Sect A 2012, 24(2), 347-54.

Behavior of cosmological constant in homogeneous Bianchi type-III universe is investigated for magnetized anti-stiff perfect fluid distribution. The magnetic permeability is assumed as a variable quantity. The magnetic field is due to an electric current produce along x- axis, thus F₂₃ is the only non vanishing component of electromagnetic field tensor. For the complete determination of the model we assume a condition between metric potential A = Cⁿ. Physical and Geometrical features of model in presence and absence of magnetic field are also discussed.

36 ref

008491   Shrivastava R;Rajput A;Singh S K (NO, Govt. Science & Commerce Benazeer College, Bhopal, Email: rajeshraju0101@rediffmail.com) : Common fixed point theorem for fuzzy type mapping hilbert space. Ultra Scient phys Sci-Sect A 2012, 24(2), 255-8.

6 ref

008490   Sharma A K;Vasdev D (Mathematics Dep, Raj Rishi Govt. Autonomous College, Alwar, Rajasthan) : Inventory model for time dependent deteriorating items with holding cost as a quadratic function of time. Asian sci 2012, 7(1), 21-4.

This paper deals with an inventory model in which shortages are allowed and partially backlogged. It is also assumed that the demand is a function of stock and selling price and the money value is subject to inflation.

4 illus, 4 tables, 10 ref

008489   Sebastian S;Jacob M K;Mary V M;Divyamary Daise S (Mathematics Dep, St. Albert's College, Kochi-682 018) : On Q-fuzzy prime ideals of Q-rings. Ultra Scient phys Sci-Sect A 2012, 24(2), 355-60.

Notion of Q-rings, Q-ideals, Q-prime ideals and their fuzzy counterparts are introduced and analyzed. Also gave a characterization of O-fuzzy prime ideals of a fuzzy ring.

4 ref

008488   Ryoo C S (Mathematics Dep, Hannam Univ, Daejeon-306 791, Korea) : Note on q-extension of the second kind Bernoulli numbers and polynomials. Far East J mathl Sci 2011, 58(1), 75-82.

In this paper, authors construct q-extension of the second kind Bernoulli numbers B_n,q and polynomials B_n,qq(x). From these numbers and polynomials, we derive some interesting properties and identities.

7 ref

008487   Ryoo C S (Mathematics Dep, Hannam Univ, Daejeon-306 791) : Note on the (h,q)-extension of the second kind euler numbers and polynomials. Far East J mathl Sci 2011, 58(1), 31-7.

In this paper, we construct new (h, q)-extension of the second kind Euler numbers and polynomials and obtain some properties of these numbers and polynomials.

7 ref

008486   Robbins N (Mathematics Dep, San Francisco State Univ, San Francisco, CA 94132, U.S.A., Email: nrobbins@sfsu.edu) : On prime that have a prescribed integer as a primitive root. Far East J mathl Sci 2011, 58(1), 61-6.

Let t be a fixed integer such that t ≥ 2 and t ≠ a² and obtain sufficient conditions that the odd prime p has t as a primitive root.

1 ref

008485   Robbins N (Mathematics Dep, San Francisco State Univ, San Francisco, CA 94132, U.S.A., Email: nrobbins@sfsu.edu) : On divisor partitions. Far East J mathl Sci 2011, 59(1), 103-12.

If n is a natural number, let p*(n) denote the number of partitions of n all of whose parts are divisors of n. Obtains some formulas for p*(n) when n has few divisors.

2 ref

008484   Rawat K S;Uniyal N (Mathematics Dep, H.N.B. Garhwal Univ Campus Badshahi Tahul, Tehri (Garhwal)-249 199, Email: drksrawathnbgu@rediffmail.com) : Decomposition of curvature tensor field in a tachibana recurrent space. Ultra Scient phys Sci-Sect A 2012, 24(2), 424-8.

Takano have studied decomposition of curvature tensor in a recurrent space. Sinha and Singh have been studied on decomposition of recurrent curvature tensor fields in a Finsler space. Further, Negi and Rawat have studied decomposition of recurrent curvature tensor field in a Kaehlerian space. In the present paper, authors have studied the decomposition of curvature tensor field R^h_iik... in terms of two vectors and a tensor field. Also several theorems have been investigated and proved.

14 ref

008483   Ravindra kumar;Singh K K;Sharma A K (Mathematics Dep, Agra College, Agra, Uttar Pradesh, Email: rkpal.maths@gmail.com) : MHD flow of visco-elastic [oldroyd (1958) model] liquid of first order through porous media between two parallel flat plates. Ultra Scient phys Sci-Sect A 2012, 24(2), 273-8.

Present paper is concerned with the oscillatory motion of conducting visco-elastic [Oldroyd (1958) model] liquid of first order through porous medium between two infinite flat plates both of which execute simple harmonic motion in the plane of plates with different amplitudes and frequencies under the influence of an uniform magnetic field applied perpendicular to the flat plates. Some particular cases have also been discussed in detail.

19 ref

008482   Rajput A;Dwivedi P K (CSA, Govt. PG College, Sehore, Email: dranilrajput@hotmail.com) : Non compatible mappings in fuzzy metric spaces. Ultra Scient phys Sci-Sect A 2012, 24(2), 299-302.

In this paper authors have proved some common fixed point theorems for the class of four non compatible mappings in fuzzy metric spaces. These results are proved without exploiting the notion of continuity and without imposing any condition on t-norm.

12 ref

008481   Prasanna Kumar K N;Kiranagi B S;Bagewadi C S (Mathematics Dep, Kuvempu Univ, Shimoga, Karnataka) : Food web cycle-green plants and nutrients concatenated to terrestial organism-oxygen consumption-decomposer organism-dead organic matter-accentuation-a trophication model. Asian sci 2012, 7(1), 90-106.

System of green plants absorbing nutrients vis-a-vis decomposer organisms attested to terrestrial organisms dissipating consumption of oxygen due to cellular respiration and parallel system of consumption of dead organic matter concatenated to oxygen due to cellular respiration that contribute to the dissipation of the velocity of production of decomposer organisms vis-a-vis terrestrial organisms is investigated. It is shown that the time independence of the contributions portrays another system by itself and constitutes the equilibrium solution of the original time independent system. A system of nutrients consolidated with dead organic matter that reduces the dissipation coefficient of the green plants correlated to decomposer organism annexed to the oxygen consumption-terrestrial organism system. With the methodology reinforced and revitalized with the explanations, we write the governing equations with the nomenclature for the systems in the foregoing. Further papers extensively draw inferences upon such concatenation process thus consummating the fait accompli desideratum of the food web cycle, towards which the consubstantiation process was undertaken for execution.

10 ref

008480   Pandian S;Balachandran Y;Purushothaman G (NO, College of Arts and Science, Thiruvalluvar Univ, Vandavasi, Tamilnadu, Email: pandianapr51@gmail.com) : Asymptotic behavior of solutions of first-order nonlinear neutral impulsive differential equation with positive and negative coefficients. Far East J mathl Sci 2011, 59(1), 73-87.

This paper is concerned with first order nonlinear impulsive neutral differential equation with positive and negative coefficients with unbounded delays. Sufficient conditions are obtained, for every solution tends to a constant as t → ∞.

10 ref

008479   Owolabi K M (Mathematics and Applied Mathematics Dep, Western Cape Univ, Private Bag X17, Bellville, 7535, Cape Town, South Africa, Email: mkowolax@yahoo.com) : Contradictory log case problem of homogeneous second order ordinary differential equation, power series approach. Far East J mathl Sci 2011, 58(1), 21-9.

Power series method of solving homogeneous linear ordinary Flower series method of solving homogeneous linear ordinary differential equations with analytic coefficients could and in practice be applied to various examples. To illustrate the different ways of surmounting the obstacles connected with the different forms which the roots of the indicial equation can take for the simple equations for which transformations are available, the power series method is comparatively tedious. But for the general equation with analytic coefficients, for which constant coefficient reducing transformation is not available, power series method remains the most effective method of attack.

8 ref

008478   Mishra G;Ravindra Kumar;Singh K K (Mathematics Dep, Agra College Agra, Uttar Pradesh, Email: rkpal.maths@gmail.com) : Oscillatory blood flow through porous medium in a stenosed artery. Ultra Scient phys Sci-Sect A 2012, 24(2), 369-73.

Purpose of this paper is to study the oscillatory flow of blood through porous medium in a rigid tube with a mild stenosis. Here we assumed that the blood behaves as a Newtonian fluid and the maximum height of the roughness is very small compared with the radius of the unconstricted tube. The expressions are given for the instantaneous flow rate, resistive impedance and wall shear stress.

2 illus, 12 ref

008477   Mathur P K;Singh A (Mathematics Dep, Saifia Science College, Bhopal, Madhya Pradesh) : Certain simultaneous five tuple series equations involving laguerre polynomials. Ultra Scient phys Sci-Sect A 2012, 24(2), 419-23.

Lowndes have obtained the solution of some dual series equations involving laguerre polynomials and then solved triple series equations involving laguerre polynomials. Singh, Rokne and Dhaliwal obtained closed form solution of triple series equations involving Laguerre polynomials and Srivastava have also obtained the solutions of certain dual series equations involving Laguerre polynomials. In the present paper, an exact solution has been obtained for the simultaneous five tuple series equations involving Laguerre polynomials by Noble's modified multiplying factor technique.

11 ref

008476   Mahadevan G;Nagarajan A;Rajeswari A (Mathematics Dep, Gandhigram Rural Univ, Gandhigram-624 302, Email: gmaha2003@yahoo.co.in) : Characterization of induced paired domination number of a graph. Ultra Scient phys Sci-Sect A 2012, 24(2), 337-46.

Concept of induced paired domination number of a graph was introduced by D.S.Studer, T.W. Haynes and L.M. Lawson11, with the following application in mind. In the guard application an induced paired dominating set represents a configuration of security guards in which each guard is assigned one other as a designated backup with in (as in a paired dominating set), but to avoid conflicts (such as radio interference) between a guard and his/her backup, we require that the backup each guard be unique. Since among the guards only designated partners are adjacent to each other, we reduce the possibility of conflicts in communication. A set S ⊆ V is a induced -paired dominating set if S is a dominating set of G and the induced subgraph <60>S<62> is a set of independent edges. The induced - paired domination number γ_ip (G) is the minimum cardinality taken over all induced paired dominating sets in G. The minimum number of colours required to colour all the vertices so that adjacent vertices do not receive the same colour and is denoted by χ(G). Mahadevan, G characterized the classes of all graphs whose sum of induced paired domination number and chromatic number of order up to 2n - 5. In this paper we characterize the classes of all graphs whose sum of induced paired domination number and chromatic number equals to 2n-6, for any n ≥ 4.

2 illus, 11 ref

008475   Liu J (Mathematics Dep, Guangdong Institute of Education and Information, Guangzhou-510 631, P.R. China, Email: junfengliu6688@163.com) : Invariant subspaces for polynomially bounded operators of class C_.0 on a banach space. Far East J mathl Sci 2011, 58(1), 39-47.

In this paper, we show that every polynomially bounded operator of class C.₀ ON A Banach space whose spectrum contains the unit circle has a nontrivial invariant closed subspace.

10 ref

008474   Leerawat U;Prabpayak C (Mathematics Dep, Kasetsart Univ, Bangkok, Thailand, Email: fsciutl@ku.ac.th) : On outer (θ, φ)-derivations of BCI-algebras. Far East J mathl Sci 2011, 58(1), 49-60.

In this paper, a notion of the outer (θ, φ) -derivation of a BCI-algebra is introduced and certain properties in BCI-algebra and p-semisimple BCI-algebra are obtained. Moreover, we show that d(A) ⊆ 6(A) for all ideal A of X if and only if d is regular, provided 6 is an automorphism on X.

14 ref

008473   Jin S S;Lee Y H (Mathematics Education Dep, Gongju National Education Univ, Gongju-314 711, Republic of Korea) : Fixed point aproach to the stability of the functional equation deriving from quadratic and additive mappings. Far East J mathl Sci 2011, 58(1), 1-20.

In this paper, we investigate the stability of the functional equation f(2x + y)+ f(2x -y) + 2f(z) - f(x + y)-f(x-y)- 2f(2x) = 0 by using the fixed point theory in the sense of Cadariu and Radu.

20 ref

008472   George R;Johnson T P (Mathematics Dep, St. Peter's College, Kolenchery-682 311, Ernakulam, Kerala) : On the lattice of principal L-topologies. Far East J mathl Sci 2011, 58(1), 67-74.

Investigated the lattice structure of the set of principal i-topologies on a given set X. It is proved that the lattice of principal L-topologies is atomic and even not modular. It is complete and it has dual atoms if and only if membership lattice L has dual atoms and this lattice is semi-complemented.

15 ref

008471   Gangele R K;Choube S K (Mathematics and Statistics Dep, Dr. Sir Hari Singh Gour Univ, Sagar, Madhya Pradesh) : Estimator for population mean using power transformation and auxiliary information. Ultra Scient phys Sci-Sect A 2012, 24(2), 249-54.

8 ref

008470   Fu J;Zhao J (Mathematics Dep, Communication China Univ, Beijing-100 024, P.R. China, Email: fujy@cuc.edu.cn) : Classification of irreducible weight W(a,b) modules with a finite dimensional weight space. Far East J mathl Sci 2011, 59(1), 9-102.

Authors obtain that every simple weight module V over the Lie algebra W(a, b), which has an infinite dimensional weight space, satisfies that all non-trivial weight spaces are infinite dimensional. As a corollary, we also have that V is a Harish-Chandra module if V has a non-trivial finite dimensional weight space.

9 ref

008469   Charles Dorsett (NO, , Texas A&M Univ-Commerce) : Finite sets, separation axioms, and equivalences of open and closed images. Ultra Scient phys Sci-Sect A 2012, 24(2), 374-8.

Within this paper nonempty finite sets are further characterized using closed images and the R₀ and R₁ separation axioms, and equivalences of open and closed images are given for T₁ and R₀ spaces.

5 ref

008468   Caristi G;Stoka M (S.E.A. Dep, Messina Univ, Italy) : Laplace type problem for lattice with axial symmetric and different obstacles type (I). Far East J mathl Sci 2011, 58(1), 99-118.

In this paper, Authors consider a lattice with the cell composed of two rectangles represented in Figures 1, 3 and 5, cell composed by three rectangles in Figure 7 and cell composed by In - 1 rectangles in Figure 9 and they compute the probability that a segment of random position and constant length intersects a side of the lattice.

10 illus, 4 ref

008467   Bhattacharya D;Prasad N (NO, Ramgarh College, Ramgarh Dep of Mathematics Dist., Ramgarh Jharkhand-829 122) : Quasi-P normal operators linear operators on hilbert space for which T+T* and T*T commute. Ultra Scient phys Sci-Sect A 2012, 24(2), 269-72.

6 ref

008466   Bali R;Kumawat M (Mathematics Dep, Rajasthan Univ, Jaipur-302 055) : C-field cosmological models with bulk viscosity and variable G in flat FRW space-time. Ultra Scient phys Sci-Sect A 2012, 24(2), 259-68.

Cosmological models with variable gravitational constant (G) and bulk viscosity in C-field cosmology for flat FRW space-time are investigated. To get the deterministic model of the universe, we have assumed G = R^Π where R is the scale factor and n is a constant. Under this assumption, author investigated two C-field cosmological models for two cases: (i) ζθ = constant, (ii) ζ = constant, θ = ζ is 3R/R where ζ is the coefficient of bulk viscosity, θ the expansion in the model. The physical and geometrical aspects of the models and the effect of bulk viscosity related with the observation are discussed.

23 ref

008465   Bagh S;Pal M K (Statistics Dep, Sambalpur Univ, Orissa, Email: sbagh55@hotmail.com) : Random algebraic polynomials with non-identically distributed normal coefficients. Ultra Scient phys Sci-Sect A 2012, 24(2), 303-10.

Asymptotic estimate for the expected number of real zeros of a random algebraic polynomial Q_n(x, ω = Σⁿ_j=0 a_j(ω) (n/j)^1/2 x^j. Where the coefficients a_j (ω) are independently normally distributed random variables defined on a probability space (Ω, F, P ), ω ∈ Ω is known. In this paper authors provide the asymptotic value for the expected number of zeros of the integration of Q_n(x, ω) with respect to x.

6 ref

008464   Bageerathi K;Thangam T (Mathematics Dep, Govindammal Aditanar College for Women, Tiruchendur-628 215, Email: sivarathi_2006@yahoo.in) : Generalization of fuzzy alpha-boundary. Ultra Scient phys Sci-Sect A 2012, 24(2), 405-18.

Author has recently introduced the concepts of fuzzy boundary, fuzzy check semi-boundary and fuzzy pre boundary where [0, 1] → [0, 1] is a function. The purpose of this paper is to introduce the concept of fuzzy -alpha boundary and investigate some of their basic properties of a fuzzy topological space.

10 ref

008463   Aramaki J (Science Div, Faculty of Science and Engineering, Tokyo Denki Univ, Hatotyama-Machi, Saitama 350-0394, Japan, Email: aramaki@mail.dendai.ac.jp) : Quasilinear elliptic system in three-dimensional space associated with superconductivity. Far East J mathl Sci 2011, 59(1), 1-45.

Considered a nonlinear elliptic system associated with superheating field in the theory of superconductivity in a three-dimensional domain. According to a formal analysis of Chapman [5] and the rigorous arguments of Bates and Pan [3], the superheating field is associated with some nonlinear elliptic system. In two-dimensional domain, Pan and Kwek [15] conjectured that the results still hold for a system with a more general nonlinearity, and the author extended the results in the previous papers, Aramaki [1, 2]. Considers such a system with general nonlinearity in a three-dimensional domain. Authors also examine the asymptotically decay estimate in the place away from the boundary of the solutions.

16 ref

008462   Abbasi A;Habibi S (Pure Mathematics Dep, Faculty of Mathematical Sciences, Guilan Univ, P.O. Box 41335-19141, Rasht, Iran, Email: aabbasi@guilan.ac.ir) : Zer-divisor graph in commutative rings with decomposable zero ideal. Far East J mathl Sci 2011, 59(1), 65-72.

Authors study some graph properties of zero-divisor graph of a commutative ring R where the zero ideal is decomposable. It is obtained that the girth is 3 and the diameter of the zero-divisor is greater than or equal to 2 for n ≥ 2. It is also obtained the conditions that the zero-divisor graph is not planar.

13 ref

007359   Thomas B;Scaria J (Statistics Dep, Sree Sankara College, Kalady-683 574, Email: baijukolathu@yahoo.co.in) : Concomitants of order statistics from morgenstern type bivariate two-sided power (TSP) distribution. Sci Soc 2012, 10(2), 155-62.

Authors study the distribution theory of concomitants of order statistics from the bivariate Morgenstern family with marginals given by the recently proposed two-sided power (TSP) distribution.

19 ref

006349   Vahidi A R;Babolian E;Cordshooli G A (Mathematics Dep, Shahr-e-Rey Branch, Islamic Azad Univ, Tehran 18155-144, Iran, Email: alrevahidi@yahoo.com) : Numerical solutions of duffing's oscillator problem. Indian J Phys 2012, 86(4), 311-15.

In this paper, author approximate the solution of Duffing's equation by converting it to a system of the first order ordinary differential equations and using Adomian's decomposition method. This approach shows that for different versions of Duffing's equation in identical conditions, the order of response polynomial is considerably lower than the polynomial obtained from direct application of Adomian's decomposition method. Therefore, the order of computations and the running time of applied softwares will reduce.

1 table, 16 ref

006348   Uchimura Y;Saito K (NO, Graduate School of Science and Technology, Maijo Univ, Shiogamaguchi 1-501, Tempaku-ku, Nagoya 468-5802, Japan, Email: m0951501@ccmailg.maijo-u.ac.jp) : Improvement of Howard's policy iteration method for application to policies modeled by periodic Markov chains. Far East J mathl Sci 2011, 57(2), 113-32.

Describes an improvement of the policy iteration method proposed by R. A. Howard. The conventional method decides an optimal policy from a set composed of many policies modeled by Markov chains with rewards that have a limiting distribution. Thus, the conventional method cannot decide it when the set includes policies modeled by periodic Markov chains because they do not have a limiting distribution. This condition is too severe to apply it. Therefore, we have improved this method to decide it, even if the set includes policies modeled by periodic Markov chains.

4 illus, 2 tables, 3 ref

006347   Park J (Mathematics Dep, Hanseo Univ, Seosan-si, Chungnam-do-356 706, Korea, Email: jkpark@hanseo.ac.kr) : Generalizations of Simpson-like type inequalities for differentiable (α, m)- convex mappings. Far East J mathl Sci 2011, 57(2), 139-51.

Authors obtain new generalizations and some refinements of Simpson-like type inequalities based on s-convex mappings in the second sense.

12 ref

006346   Naika M S M;Sushanbairy K;Manjunatha M (Mathematics Dep, Bangalore Univ, Central College Campus, Bangalore-560 001, Email: msmnaika@rediffmail.com) : Certain identities for a continued fraction of Eisenstein. Far East J mathl Sci 2011, 57(2), 205-26.

Eisenstein recorded twenty elegant continued fraction expansion in his papers. In this paper, we establish several modular relations for a continued fraction of Eisenstein using Ramanujan's modular equations. We establish two integral representations and also explicit evaluations of continued fraction of Eisenstein.

26 ref

006345   Mei Li Y;Xiang Y (Mathematics Dep, Huaihua Univ, Huaihua, Hunan-418 008, People's Republic of China, Email: liym74@yahoo.com) : Effect of genotyping errors on the robustness of composite linkage disequilibrium measures. J Genet 2011, 90(3), 453-7.

Concluded that composite linkage disequilibrium (LD) measures be adopted in population-based LD mapping or association mapping studies since it is unaffected by Hardy-Weinberg disequilibrium. Although some properties of composite LD measures have been recently studied, the effects of genotyping errors on composite LD measures have not been examined. In this report, we derived deterministic formulas to evaluate the impact of genotyping errors on the composite LD measures Δ_AB and rAB, and compared the robustness of Δ_AB and r_AB in the presence of genotyping errors. The results showed that Δ_AB and r_AB depend on the allele frequencies and the assumed error model, and show varying degrees of robustness in the presence of errors. In general, whether there is HWD or not, r_AB is more robust than A'AB except some special cases and the difference of robustness between A_AB and r_AB is becomes less severe as the difference between the frequencies of two SNP alleles A and B becomes smaller.

1 illus, 4 tables, 15 ref

006344   Lee M (Mathematics Dep, Mokwon Univ, Daejeon-302 729, Korea, Email: lmsds@mokwon.ac.kr) : Average shadowing property on closed sets. Far East J mathl Sci 2011, 57(2), 171-9.

Let f be a diffeomorphism of a closed n-dimensional C^∝ manifold M, and p be a hyperbolic periodic point of f. Let Λ (p) be a nontrivial closed set containing p. In this paper, suppose f has the average shadowing property on Λ (p). Then, we show that if f has the C¹-stably shadowing property, then it is hyperbolic.

8 ref

006343   Kyei K A (Statistics Dep, Venda Univ, Private Bag X5050, Thohoyandou 0950, South Africa, Email: kyei61@gmail.com ) : Determinants of childhood mortality in South Africa: using categorical data modeling. J hum Ecol 2012, 37(1), 47-56.

Childhood mortality is of great interest to social scientists and policy makers concerned about the quality of life in less developed countries. Thus, the importance of the study of childhood mortality cannot be exaggerated. The levels of infant and child mortality are the two sensitive and widely used indicators of socio-economic development. The childhood mortality rate is a refined and sensitive index of the total cultural milieu of a community or a country. It reflects among other things, the state of public health and hygiene, the environmental sanitation, cultural mores about feeding and clothing, socio-economic development, and above all. the people's attitude towards the dignity and value of human life itself. It is the simple statistical index which conveys the idea of whether environmental hazards are controlled effectively or not, in developing countries, especially in Africa. The childhood mortality situation in South Africa has been investigated in this research using South African Demographic and Health Survey II data. About ten socio-economic, demographic, environmental and health-related variables were analyzed using categorical data modeling (catmod) analysis. On the basis of the analysis, the study concludes that education of parents, marital status as well as the occupation of mother, the survival of the penultimate child, duration of breastfeeding, anti-natal check-ups and availability of toilets in the residence are the determinants of childhood mortality in South Africa.

006342   Kubo F;Nakamura N;Ohno K;Wada S (Mathematics Dep, Faculty of Science, Toyama Univ, Gofuku Toyama, 930-8555, Japan, Email: fkubo@sci.u-toyama.ac.jp) : Barbour path of operator monotone functions. Far East J mathl Sci 2011, 57(2), 181-92.

This paper is concerned with the properties of a path ϕ(x) of operator monotone functions which has the following form: φ(x) = [αx + β(1-x)]/[x + γ(1-x)] where α, β, γ are positive continuous functions on (0, ∞) and X ∈ [0, 1].

6 ref

006341   Kondo M (NO, School of Information Environment, Tokyo Denki Univ, Inzai, 270-1382, Japan) : Characterization of some types of filters in commutative residuated lattices. Far East J mathl Sci 2011, 57(2), 193-203.

Authors consider fundamental properties of some types of filters implicative, positive implicative and fantastic filters) of integral commutative residuated lattices and prove that for any integral commutative residuated lattice X and filter F of X, (a) F is an implicative filter if and only if X/F satisfies a = a² (= a x a) for all a, b ∈ X/F, that is, a relatively pseudo-complemented distributive lattice, or equivalently, a {∧, ∨, →>, 1}-reduct of Heyting algebra; (b) F is a positive implicative filter if and only if X/F satisfies the condition a = (a → b) → a for all a, b ∈ X/F; (c) F is a fantastic filter if and only if X/F satisfies the condition sup{a, b} = (a → b) → b = (b → a) →> a for all a, b ∈ X/F. It follows from this characterization that, for any filter F of an integral commutative residuated lattice, it is a positive implicative filter if and only if it is an implicative and fantastic filter.

9 ref