012743   Balasubramanian S;Sandhya C (Mathematics Dep, Govt. Arts College(A), Karur-639 005) : Somewhat almost GS-continuous functions and somewhat almost GS-open functions. Arya Bhatta J Math Inf 2012, 4(2), 205-10.

In this paper we have made an attempt to introduce a new variety of continuous and open functions called Somewhat almost gs-continuous functions and Somewhat almost gs-open functions. Its basic properties are discussed.

11 ref

012742   Balasubramanian S;Laxmi Sarada M (Mathematics Dep, Government Arts College, Karur, Tamil Nadu, Email: mani55682@rediffmail.com) : Almost-GPR-continuity. Arya Bhatta J Math Inf 2012, 4(2), 373-80.

Object of the present paper is to study the basic properties of Almost-gpr--continuous functions.

15 ref

012741   Balasubramanian S;Chaitanya (Mathematics Dep, Government Arts College, Karur-639 005, Email: mani55682@rediffmail.com ) : Minimal αG-open sets and maximal αG-closed sets. Arya Bhatta J Math Inf 2012, 4(1), 83-94.

Object of the present paper is to study the notions of minimal αg-closed set, maximal αg-open set, minimal αg-open set and maximal αg-closed set and their basic properties are studied.

6 ref

012740   Balasubramanian S (Mathematics Dep, Govt. Arts College(A), Karur-639 005, Tamil Nadu, Email: mani55682@rediffmail.com) : Somewhat M-vg-open functions. Arya Bhatta J Math Inf 2012, 4(2), 315-20.

In this paper we tried to introduce a new variety of continuous and open functions called Somewhat M-vg-continuous function and Somewhat M-vg-open functions. Its basic properties are discussed.

9 ref

012739   Ayyappan G;Sridevi S (Mathematics Dep, Pondicherry Engineering College, Puducherry-605 014) : Tandem queue with three multiserver units and bulk service with accessible and non accessble batch in unit III with vacation. Indian J Math mathl Sci 2011, 7(1), 29-38.

This paper analyses two different queuing model (Model I and Model II) both consisting of three units connected in series separated by a buffer of finite capacity with finite number of parallel servers in each unit. Queuing model differs only on the provision of availing vacation to the servers in unit III. In Model I server can avail exponential vacation, whereas in Model II the server takes only single vacation. Customers of unit I and Unit II are served singly but in unit HI, they are served in groups according to bulk service rule. This rule admits each batch to be served only if the batch size is not less than 'a' and not more than 'b', customers arriving late can also enter service station without affecting the service time if the size of the batch being served is less than 'd' (a d" d d" b). The occurrence time and service time have negative exponential distributions. The steady state probability vector of the number of customers in the queue is obtained by using a modified geometric method. The stability condition is also obtained.

9 ref

012738   Angel Jebitha M K;Joseph J P (Mathematics Dep, Manomaniam Sundaranar Univ, Tirunelveli-627 012, Email: jebidom@gmail.com) : Domination in transformation graph G<. Int J mathl Combinatorics 2012, 1(Mar), 58-73.

Let G = (V,E) be a simple undirected graph of order n and size m. The transformation graph of G is a simple graph with vertex set V (G) ∪ E(G) in which adjacency is defined as follows: (a) two elements in V (G) are adjacent if and only if they are adjacent in G (b) two elements in E(G) are adjacent if and only if they are non-adjacent in G and (c) one element in V (G) and one element in E(G) are adjacent if and only if they are incident in G. It is denoted by G^+-+. A set S ⊆ V (G) is a dominating set if every vertex in V. S is adjacent to at least one vertex in S. The minimum cardinality taken over all dominating sets of G is called the domination number of G and is denoted by γ(G). Investigates the domination number of transformation graph. Authers determine the exact values for some standard graphs and obtain several bounds. Also proves that for any connected graph G of order n ≥ 5, γ(G^+-+) ≤. [n/2].

8 illus, 11 ref

012737   Al-Hawary T A (Mathematics Dep, Yarmouk Univ, Irbid-Jordan) : On fuzzy matroids. Int J mathl Combinatorics 2012, 1(Mar), 13-21.

Aim of this paper is to discuss properties of fuzzy regular-flats, fuzzy C-flats, fuzzy alternative-sets and fuzzy i-flats. Moreover, author characterize some peculiar fuzzy matroids via these notions. Finally, provides a decomposition of fuzzy strong maps.

13 ref

012736   Ajitha V;Princy K L;Lokesha V;Ranjini P S (Mathematics Dep, M.G. College, Iritty-670 703, Email: mohanrajvm@yahoo.co.in) : Square difference graphs. Int J mathl Combinatorics 2012, 1(Mar), 31-40.

In graph theory number labeling problems play vital role. Let G = (V,E) be a (p, q)-graph with vertex set V and edge set E. Let f be a vertex valued bijective function from V (G) → {0, 1, ..., p - 1}. An edge valued function f. can be defined on G as a function of squares of vertex values. Graphs which satisfy the injectivity of this type of edge valued functions are called square graphs. Square graphs have two major divisions: they are square sum graphs and square difference graphs. In this paper we concentrate on square difference or SD graphs. An edge labeling f. on E(G) can be defined as follows. f.(uv) = |(f(u))² - (f(v))²| for every uv in E(G). If f. is injective, then the labeling is said to be a SD labeling. A graph which satisfies SD labeling is known as a SD graph. We illuminate some of the results on number theory into the structure of SD graphs. Also, established some classes of SD graphs and established that every graph can be embedded into a SD graph.

10 illus, 8 ref

012735   Ahmad S P;Jan T R (Statistics Dep, Kashmir Univ, Srinagar, Jammu & Kashmir, Email: sprvz@yahoo.com) : Comparison of the Bayesian and maximum likelihood estimation for exponential distribution. Arya Bhatta J Math Inf 2012, 4(1), 95-100.

Exponential distributiion is the most commonly used model in reliability & life-testing analysis. For a situation where the failure rate appears to be more or less constant, the exponential distribution would be an adquate choice but no all items satisfy the condition that 'it does and age'. The maximum likelihood method (MLE) is the conventional method used for the estimation of parameters of the distribution. Bayesian method of estimation is other method of estimation which has reeived much attention and is in contention with other methods of estimation as well as explore and compare the performance of the MLE with the Bayesian method of estimation for the exponential distribution. The MLE an dBayesian method of estimation using Jeffrey and the extension of Jeffrey prior information for estimating the parameter of exponential distribution are presented. Also will explore the performance of these estimators numerically under varying conditions. The comparisons are made through simulation study on the performance of these estimators with respect to mean squared error (MSE).

1 table, 12 ref

012734   Agboola A A A;Adeleke E O;Akinleye S A (Mathematics Dep, Agriculture Univ, Abeokuta, Nigeria, Email: aaaola2003@yahoo.com) : Neutrosophic rings II. Int J mathl Combinatorics 2012, 2(Jun), 1-8.

Present paper is devoted to the study of ideals of neutrosophic rings. Neutrosophic quotient rings are also studied.

17 ref

011723   Zi-Ming W (Foundation Dep, Shandong Yingcai Univ, Jinan-250 104, P.R. China, Email: wangziming1983@yahoo.com.cn) : Implict Mann fixed point iterations for Lipschitz quasi-pseudocontractive mapping. Far East J mathl Sci 2011, 59(2), 157-71.

Authors prove a strong convergence theorem by monotone CQ method for' a family of Lipschitz quasi-pseudocontractive mappings without any compactness restriction. Results improve and extend the corresponding results announced by many others.

21 ref

011722   Zhao K (Mathematics Dep, Qiongzhou Univ, Sanya, Hainan-572 022, P.R. China, Email: kwzqzu@yahoo.cn) : Neighborhood union conditions and cycles through specified vertices. Far East J mathl Sci 2011, 59(2), 197-200.

In 1993, Bollobas and Brightwell proved that if G is a connected graph of order n ≥ 3 and S ⊆ V(G) with |S| ≥ 3, if δ(S) ≥ n/2, then S is cyclable in G. Authors prove that if G is a 2-connected graph of order n ≥ 3 and S ⊆ V(G), if NC(S) ≥ n - δ(G), then S is cyclable in G. This result generalizes Bollobas and Brightwell's result.

2 ref

011721   Zhai H C (NO, Mathematics College, Luoyang Normal Univ, Luoyang-471 022, P.R. China, Email: zhai_hc@163.com) : Two formulas of Theta function and their applications in modular equations. Far East J mathl Sci 2012, 61(2), 271-9.

By using well-known Jacobian theta function additive identities, a formula of Jacobian theta function is obtained. A product formula of theta functions is also established. To illustrate the application of these two formulas, we derive some interesting modular equations of degree three, five, seven and nine.

7 ref

011720   Zang R;Xiang W;Cao L Y (Mathematics Dep, Northeast Forestry Univ, Harbin-150 040, P.R. China, Email: zcly200153@sina.com) : Necessary condition for the proximal subgradient in uniformly gateux smooth banach space. Far East J mathl Sci 2011, 59(2), 189-95.

A necessary condition for the proximal subgradient of lower semicontinuous functions in uniformly Gateaux smooth Banach space is given.

11 ref

011719   Yaqub A (Mathematics Dep, California Univ, Santa Barbara, California, 93106, U.S.A., Email: yaqub@math.ucsb.edu) : Generalized J-rings, periodicity and commutativity. Far East J mathl Sci 2011, 59(2), 113-26.

Well-known theorem of Jacobson asserts that a ring R with the property that for every x in R, there exists an integer n(x) <62> 1 such that x^n(x) = x is necessarily commutative. With this as a motivation, author define a generalized J-ring to be a ring R such that for all x, y in a certain subset S of R, xⁿy - xyⁿ is nilpotent for some n = n(x, y)<62>1. Some conditions are considered which yield such rings commutative or periodic, or have a nil commutator ideal.

6 ref

011718   Tatari M;Vaezspour S M;Pishinian A (Mathematics Dep, Payame Noor Univ, Bojnourd, Iran, Email: m_tatari@pnu.ac.ir) : Decomposition theorem for functions in L<. Far East J mathl Sci 2012, 61(2), 259-69.

Decomposition theorem has been introduced by Coifman and Rochberg for domains in the Bergman space L_a^p(dA) on a bounded symmetric domain of C. In this article, construct an atomic decomposition on the weighted Bergman space L_a²(dv_α) on the unit ball of Cⁿ by frame theorem.

7 ref

011717   Sitthiwirattham T (Mathematics Dep, Faculty of Applied Science, King Mongkut's Technology North Bangkok Un, Bangkok-10800, Thailand) : Matching number and edge covering number on Kronecker product of P_n. Far East J mathl Sci 2011, 59(2), 127-37.

Let α'(G) and β(G) be the matching number and edge covering number, respectively. The Kronecker product G₁⊗ G₂ of graphs of G₁ and G₂ has vertex set F(G₁⊗ G₂) = F(G₁)x V(G₂) and edge set E(G₁⊗ G₂) = {(u₁v₁)(u₂v₂)|u₂u₂ ∈ E(G₂)} and v. In this paper, let G be a simple graph of order TO, author prove that α'(P_n ⊗ G) = max {nα'(G), m[n/2]} and β'(P_n ⊗ G) = min{nβ'(G), m[n/s]}.

5 illus, 3 ref

011716   Singh A P;Sharma R;Jasvinder Kaur (Mathematics Dep, S.G.R.R. (P.G.) College, Dehradun, Uttarakhand, Email: poojanubhav2007@rediffmail.com) : Optimal ordering policy for inventory model with non-instantaneous deteriorating items and stock-dependent demand. Int J mathl Sci 2013, 12(1-2), 113-21.

In this paper authors shall discuss with the optimal ordering policy for two warehouse inventory model of non-iristantaneous deteriorating items and stock-dependent demand. Here shortage is not allowed. Here the holding and deteriorating costs in both warehouses are different and assumed that the holding cost in the RW is greater than in the OW. The necessary and sufficient conditions of the existence and uniqueness of the optimal solution are shown. Numerical example is presented to demonstrate the developed model.

14 ref

011715   Siddharth A (Computer Science and Engineering Dep, Indian Institute of Technology, Pataliputra Colony, New Government Polytechnic, Patna-870 013, Email: siddharth.cs10@iitp.ac.in) : Error detection in numeric codes. Resonance 2012, 17(7), 653-71.

This article investigates the efficiency of four commonly used methods for detecting the most frequent types of errors committed by individuals while entering numeric codes.

5 tables, 10 ref

011714   Senthilkumar D;Prasad T;Sherin Joy S M (Mathematics Dep, Government Arts College, Coimbatore-641 018, Tamil Nadu, Email: senthilsenkumhari@gmail.com) : Spectral properties of class A composition operators. Far East J mathl Sci 2012, 61(2), 231-8.

Investigation concerned with some spectral properties of class A composition operators on L space are studied by using semi-hyponormal composition operator transform and quasi class A composition operators are characerized operators are characterized.

18 ref

011713   Sekar R;Raju K (Mathematics Dep, Pondicherry Engineering College, Puducherry-605 014, Email: rsekar@pec.edu ) : Effect of magnetic field dependent viscosity on soret-driven thermoconvective instability of ferromagnetic fluid in the presence of rotating anisotropic porous medium of sparse paticle suspension. Int J mathl Sci 2013, 12(1-2), 13-31.

Double diffusive effect of magnetic field dependent (MFD) viscosity on Soret driven thermoconvective instability in a ferrofluid, saturating a rotating anisotropic porous medium has been investigated theoretically. The horizontal fluid layer is assumed to be heated from below and salted from above and the Brinkman model is used. The effect of salinity has been combined in the magnetization and density of the ferrofluid. An exact solution is obtained for the case of two free boundaries. The critical thermomagnetic Rayleigh number for onset of instability is also determined numerically for sufficient large values of buoyancy magnetization parameter M₁ and results are depicted graphically. The onset of Soret driven ferrothermohaline convection is analyzed both by stationary as well as oscillatory modes using a linear stability analysis and a normal mode technique. In all the cases, it is found that the rotation and MFD viscosity tend to stabilize the system whereas destabilization of the system occurs due to the non-buoyancy magnetization parameter M₃. Further, the ratio of mass transport to heat transport decides the stabilizing factor.

8 illus, 29 ref

011712   Sato I;Itoh M (NO, Oyama National College of Technology, Oyama, Tochigi 323-0806, Japan, Email: isato@oyama-ct.ac.jp ) : Convergence of Bartholdi zeta function of a graph. Far East J mathl Sci 2012, 61(2), 179-94.

This study examines that, for a tower of finite regular graphs covered by a periodic regular graph G, the Bartholdi zeta functions of those finite regular graphs converge to the Bartholdi zeta function of G.

20 ref

011711   Sathasivam S (NO, School of Mathematical Sciences, Sains Malaysia Univ, 11800 USM, Penang, Malaysia, Email: saratha@cs.usm.my) : First order logic in neuro-symbolic integration. Far East J mathl Sci 2012, 61(2), 213-29.

In this paper, authors present a work on implementing first order logic in logic programming in Hopfield network. There are two methods of doing logic programming in Hopfield network: Wan Abdullah's approach and Pinkas's approach. Wan Abdullah's approach uses the propositional logic formulas while Pinkas's approach uses first order logic. Now, we want to upgrade Wan Abdullah's method by using Pinkas's approach. Then we investigate and compare the upgraded method with Wan Abdullah's method. Computer simulations have been carried out to demonstrate the ability of upgrading Wan Abdullah's method doing the logic programs. Computer simulations verified that the new learning method produced by higher order logic will have impressive computational, storage and learning capabilities.

7 illus, 3 tables, 15 ref

011710   Salhotra R;Salhotra R;Sahu D R (NO, Dr. Radhabai Govt. Navin Kanya College, Raipur, Chhattisgarh) : Iterative algorithms for solving generalized nonlinear mixed variational-like inequalities. Int J mathl Sci 2013, 12(1-2), 1-12.

In this paper, authors introduced the concept of partially relaxed (g, η)-strongly monotonicity of set-valued;mappings. By applying the auxiliary principle we suggest iterative algorithm to solve generalized nonlinear mixed variational-like inequalities. The convergence behaviour is also discussed. Our result generalizes some known results in literature.

15 ref

011709   Ryoo C S (Mathematics Dep, Hannam Univ, Daejeon-306 791, Korea) : Distribution of the roots of the second kind q-Genocchi polynomials. Far East J mathl Sci 2012, 61(2), 169-77.

In this paper, authors observe the behavior of complex roots of the second kind q-Genocchi polynomials G_n,q (x), using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the second kind g-Genocchi polynomials G_n,q(x). Finally, authors give a table for the solutions of the second kind g-Genocchi polynomials G_n,q(x).

5 illus, 2 tables, 8 ref

011708   Park J S (Mathematics Education Dep, Institute of Mathematics Education, Chinju National Education Univ, Jinju-660 756, South Korea, Email: parkjs@cue.ac.kr) : Some fixed point theorems using compatible maps of type (α) in M-fuzzy metric spaces. Far East J mathl Sci 2012, 61(2), 195-205.

In this paper, authors prove some fixed point theorems and present the example for six mappings satisfying the some conditions in M -fuzzy metric space. Also generalize and extend for the results of [3], [7] and [9].

11 ref

011707   Pal D;Mahapatra G S;Samanta G P (NO, Chandrahati Dilip Kumar High School (H.S.), Chandrahati-712 504, Email: g_s_mahapatra@yahoo.com) : Quota harvesting model for a single species population under fuzziness. Int J mathl Sci 2013, 12(1-2), 33-46.

Presently population dynamics is an intercoagulating subject that projects the mathematical representation, treatment and modelling of population enhancement through various applied mathematical techniques and tools. In this paper, authors have considered one dynamical model of single species population system with natural logistics growth of the population. Authors exuberate the effects of the predatiori considering constant rate of harvesting under fuzzines they consider intrinsic growth rate and total harvesting of the single species population system as fuzzy in nature and find the equilibrium points and discuss i the stability of the equilibrium points under fuzziness. Numerical example is shown to illustrate the model.

4 illus, 1 table, 28 ref

011706   Naziri-Kordkandi A (Mathematics Dep, Payame Noor Univ, P.O. Box 19395-3697, Tehran, Iran, Email: ali_naziri2001@yahoo.com) : Some results concerning the nonvoidness of spectrum and nth root of fundamental topological algebra. Far East J mathl Sci 2011, 59(2), 149-55.

Obtains some results concerning nonvoidness of spectrum and the nth roots on fundamental topological algebra and FLM algebra. Also, similar result of Gelfand-Mazur theorem in FLM algebra is studied.

11 ref

011705   Namdari M;Veisi A (Mathematics Dep, Shahid Chamran Univ, Ahvaz, Iran, Email: mandari@ipm.ir) : Subalgebra of C(X) consisting of elements with countable image versus C(X) with respect to their rings of quotients. Far East J mathl Sci 2011, 59(2), 201-12.

Showed that C_c(X) the subalgebra of C(X) consisting of elements with countable image and C(X) share some interesting properties with regard to their rings of quotients. In particular, it is shown that Q_c(X), the maximal ring of quotients of C_c(X), is metrically dense in C_c[S] = U{C_c(S) : S ∈ S}, where the filter base S contains the dense open subsets of X.

11 ref

011704   Mao L (NO, Chinese Academy of Mathematics and System Science, Beijing-100 080, P.R. China, Email: maolinfan@163.com ) : Generalization of Seifert-Van Kampen theorem for fundamental groups. Far East J mathl Sci 2012, 61(2), 141-60.

Seifert-Van Kampen theorem handles fundamental groups of those topological spaces X = U (J V for open subsets U, V ⊂ X such that U ∩ V is arewise connected. In this paper, this theorem is generalized to such a case of maybe not arcwise-connected, i.e., there are C₁, C₂, ..., C_m arcwise-connected components in U ∩ V for an integer m ≥ 1, which enables one to find fundamental groups of combinatorial spaces by that of spaces with their underlying topological graphs, particularly, that of compact manifolds by their underlying graphs of charts.

2 illus, 10 ref

011703   Maharasi S;Mahalakshmi V;Jayalakshmi S (Mathematics Dep, Sri Parasakthi College for Women, Courtallam) : Strongly regular and bi-ideals of near-subtraction semigroup. Int J mathl Sci 2013, 12(1-2), 97-102.

6 ref

011702   Lim C S;Chew C Y (NO, Taylor's Graduate School, Taylor's Univ, No.1 Jalan Taylor's, Subang Jaya, Selangor Darul Ehsan, Malaysia, Email: chiasien.lim@taylors.edu.my) : Approach to counting via equivalence relations. Far East J mathl Sci 2011, 59(2), 213-9.

Presents two main expository themes on the techniques of counting. Authors show how the concept of equivalence relation of a set can be used to shed light on the techniques of counting and then exhibit an example of how a combinatorial identity can be proven using combinatorial perspectives which in turn provides intuition for a new algebraic identity.

5 ref

011701   Lee M (Mathematics Dep, Mokwon Univ, Daejeon-302 729, Korea, Email: lmsds@mokwon.ac.kr) : Chain transitive sets with asymptotic average shadowing. Far East J mathl Sci 2012, 61(2), 207-12.

Let (X, d) be a compact metric space, and let f : (X, d) → (X, d) be a continuous map with the shadowing. Obtained that if f has the asymptotic average shadowing property, then f is mixing.

11 ref

011700   Lee M (Mathematics Dep, Mokwon Univ, Daejeon-302 729, Korea, Email: lmsds@mokwon.ac.kr) : Asymptotic average shadowing property and strong ergodicity. Far East J mathl Sci 2011, 59(2), 139-47.

Let X be a compact metric space and f : X → X be a continuous map. Authors show that if f has the asymptotic average shadowing property and the minimal points of f are dense in X, then f is strongly ergodic and totally strongly ergodic. Moreover, f is weakly mixing.

7 ref

011699   Kahraman F;Yayli Y (Mathematics Dep, Faculty of Science, Erciyes Univ, Talas, Kayseri, Turkey, Email: ferda@erciyes.edu.tr) : Spacelike maximal and timelike minimal surfaces of revolution in Minkowski 3-space. Far East J mathl Sci 2012, 61(2), 239-57.

In this paper, author study spacelike maximal and timelike minimal surfaces of revolution by using any planar spacelike and timelike profile curve in Minkowski 3-space and obtain various differential equations which characterize the profile curve of such surfaces. Also gave some examples of spacelike maximal and timelike minimal surfaces of revolution.

4 illus, 11 ref

011698   Idris N R N;Sarudin N (Computational and Theoretical Sciences, International Islamic Malaysia Univ, Kuantan 25200, Pahang, Malaysia, Email: ruzni@iiu.edu.my) : On selection of models for continuous meta analysis data with incomplete variability measures. Far East J mathl Sci 2011, 59(2), 173-87.

Choice between the fixed and random effects models for providing an overall meta analysis estimates may affect the accuracy of those estimates. When the study-level standard deviations (SDs) are not completely reported or are. "missing" selection of a meta analysis model should be done with more caution. In this article, authors examine through a simulation study, the effects of the choice of meta analysis model and the techniques of imputation of the missing SDs on the overall meta analysis estimates. The results suggest that imputation should be adopted to estimate the overall effect size, irrespective of the model used. However, the accuracy of the estimates of the corresponding standard error (SE) is influenced by the imputation techniques. For estimates based on the fixed effect model, mean imputation provides better estimates than multiple imputation, while those based on the random effects model are the more robust of the techniques imputation used.

4 illus, 2 tables, 11 ref

011697   Hatada K (Mathematics Dep, Faculty of Education, Gifu Univ, 1-1, Yanagido, Gifu City, GIFU-501 1193, Japan) : Limits of recursive sequence of means for several numbers, II. Far East J mathl Sci 2011, 59(2), 221-30.

Let k be any positive integer, Let X₁, X₂, ..., X_k be letter different from one another. Let s₁, s₂, ..., s_k be the elementary symmetric polynomials of X₁, X₂, ..., X_k with deg(s_t(X₁, ..., X_k)) = t for each 1 ≤ t ≤ k. Let _kC_t = k!/((k-t)!t!). Let b₁, b₂, ..., b_k be arbitrary positive real numbers. Put b_t,o = b_t for each 1 ≤ t ≤ k. Define sequencces (b_{t,n)^∞n = 0 for each t ∈ [1, k] recursively by bt,(n+1) = (st(b1,n, b2,n, ..., bk,n)/kCt)^1/t for all n ≥ 0. Obtains that limn≥∞ bt,n = limn→∞ b1,n for every t ∈ [1, k]. This result is regarded as another generalization of Gauss' arithmetic-geometric mean of two numbers.}

2 ref

011696   Guzman R M;Martinez R (Electricidad Dep, Instituto Tecnologia de Cumana Univ, 6101 Cumana, Edo. Sucre, Venezuela, Email: malave r@hotmail.com) : Displacement of the mechanical systems with minimal acceleration in a sub-manifold. Int J mathl Sci 2013, 12(1-2), 75-86.

Study is done on stationary mechanical systems under the hypothesis that the displacements occur with minimal normal acceleration. A field of forces is constructed such a way that guarantees its inclusion in a sub manifold of the phase apace.

5 ref

011695   Garge A S;Shirali S A (NO, Centre for Excellence in Basic Sciences, Kalina Campus, Mumbai Univ, Mumbai-400 098, Email: anuradha@cbs.ac.in) : Triangular numbers. Resonance 2012, 17(7), 672-81.

The triangular numbers, which are numbers associated with certain arrays of dots, were known to the ancient Greeks and viewed by them with reverence. Though possessing a simple definition, they are astonishingly rich in properties of various kinds, ranging from simple relationships between them and the square numbers to very complex relationships involving partitions, modular forms, etc. - topics which belong to advanced mathematics. They also possess many pretty combinatorial properties. In this expository article we survey a few of these properties.

5 illus, 10 ref

011694   Chauhan K;Roy S N (P.G. Mathematics Dep, V.K.S. Univ, Ara, Bihar, Email: kavitachauhan908@gmail.com) : Effect of perturbations in coriolis and centrifugal forces in the photogravitational restricted problem when both the primaries are point masses. Invertis J Sci Technol 2013, 6(4), 221-7.

Investigated the effect of perturbations ε and ε in the coriolis and the centrifugal forces respectively in the Photogravitational Restricted Three Body Problem when both the primaries are point mosses. It is observed that for L₄ and L₅, the range of stability increases or decreases depending upon whether the point lies in one or the other of the two parts in which the 3D space (ε, ε, p) is divided by the plane ^36ε-^-19ε (p, the radiation parameter) and the stability of the collinear points is not effected by the perturbations in the coriolis and the centrifugal forces and they remain unstable.

6 illus, 6 ref

011693   Chaiya M (Mathematics Dep, Faculty of Science, Silpakorn Univ, Nakorn Pathom 73000, Thailand, Email: malinee.c@su.ac.th) : Prescribing dilatations on three simplices. Far East J mathl Sci 2011, 59(2), 231-45.

Authors prescribe the dilatations for a continuous piecewise affine mapping on the domain that is the union of three simplices sharing two common faces. Let Q_i be a simplex in M and f_i) be an affine mapping of the form f_i(x) = A_iX, where A_i is a 3x3 transformation matrix and x ∈ Q_i. By using the singular value ecomposition theorem, we write A_i = U_iD_iV_iT, where U_i and Vj are orthogonal matrices and D_i is a non-singular diagonal matrix. Authors show that we can find affine mappings corresponding to the given dilatations and obtain a continuous piecewise affme mapping on this domain.

4 ref

011692   Bahaa G M (Mathematics Dep, Faculty of Science, Taibah Univ, Al-Madinah Al-Munawwarah, Saudi-Arabia, Email: Bahaa_Gm@hotmail.com) : Optimality conditions for infinite order parabolic control problem involving time lags. Int J mathl Sci 2013, 12(1-2), 55-73.

Distributed control problem for the parabolic operator with an infinite order and time delay is considered. The performance index has an integral form. Constraints on controls are imposed. To obtain optimality conditions for the Neumann problem, the generalization of the Dubovitskii-Milyutin Theorem given by Walczak in Refs. [35, 36], was applied.

38 ref

011691   Amer A A;Darus M (NO, School of Mathematical Sciences, Faculty of Science and Technology, Ke, Bangi 43600 Selangor D. Ehsan, Malaysia, Email: maslina@ukm.my) : On certain subclasses of univalent functions. Far East J mathl Sci 2012, 61(2), 161-7.

Let S denote the class of normalized univalent functions f in the unit disk U. The main object of this paper is to obtain necessary and sufficient conditions for a function f lie in UST(α, β). Some interesting corollaries of the main result are also mentioned

5 ref

011690   Adekeye K S (Mathematical Sciences, Redeemer's Univ, Redemption Camp, Mowe, Nigeria) : Process capability indices based on median absolute deviation. Int J mathl Sci 2013, 12(1-2), 87-95.

Process capability analysis is to predict how well the process will hold the tolerance. It is very useful for assisting product developers in selecting or designing product/process, evaluating and selecting among competing vendors and determining the bottleneck process in terms of process quality. Process capability is the performance of a process under normal and in-control conditions. Its indices are to measure the inherent variability of a process and thus to reflect its performance. To calculate the capability indices for key characteristics, most industries normally assume that the distribution of their process output is normal. However, in practice, most key quality characteristics do fails the normality test and thus the accuracy of normal based process capability indices becomes doubtful and hence they can not really reflect the performance of a process. This paper proposes the determination of the common process capability indices based on the median absolute deviation. The median absolute deviation is a robust estimate of variability when the sample data are non- normal or are skewed. Real process data and simulated process data from heavily skewed distributions are presented to demonstrate the application of the proposed indices and the results were compared with the existing indices for non-normal and skewed process data.

4 tables, 20 ref

011689   Abebimpe O;Adeniyi M O;Kolawole M K (Mathematical and Physical Sciences Dep, Osun State Univ, Osogbo, Nigeria) : Mathematical model describing the effect of vaccine on Hepatitis A virus (HAV) transmission dynamics. Int J mathl Sci 2013, 12(1-2), 47-54.

A S-I-R mathematical model of Hepatitis A virus (HAV) infection with vaccine is discussed in this work. A rigorous analysis of the model is carried out in this study. We prove that the infection will die out if the basic reproduction number R₀ <60> 1 while the HAV infection may become endemic if R₀ <62> 1. The stability of both free and endemic steady states is also studied. Numerical simulations of the results were also presented.

4 ills, 6 ref

010603   Zimba K (NO, The Vaal Technology Univ, Private Bag X021, Vanderbijlpark 1900, South Africa, Email: kennehz@vut.ac.za) : Conjugacy classes of a subgroup S<. Far East J mathl Sci 2012, 60(1), 65-82.

Let n, m be positive integers. Let S_n^m be the direct product of m copies of the symmetric group S_n of degree n. Then S_n^m is a subgroup of the symmetric group S_mn (of degree m x n). Let g 6 ∈ S_mn, of type [mⁿ], where each m-cycle contains one symbol from each set of symbols in that order on which the copies S_n of S_n^m act. Let C_m =< 9>, the cyclic group generated by g of order m. The wreath product of S_n with C_m is a split extension of S_n^m by C_m, denoted by S_n^m : C_m. It is clear that S_n^m: C_m is a subgroup of the symmetric group S_mⁿ. In [9], a method for constructing the conjugacy classes of the groups S_n^m: C_m, prime m, is given. In this paper, that method is extended to any positive integer m.

9 ref

010602   Zhou M M;Ma S H;Fang J P (NO, College of Mathematics and Physics, Zhejiang Lishui Univ, Lishui-323 000, P.R. China, Email: msh6209@yahoo.com.cn) : Solitary wave solutions and periodic wave solutions and line-soliton excitations for the (2+1)-dimensional general Ablowitz-Kaup-Newell-Segur equation. Far East J mathl Sci 2012, 61(1), 27-33.

By the Riccati equation projective approach and a linear variable separation approach, a new family of the exact solutions of the (2 + 1)-dimensional general Ablowitz-Kaup-Newell-Segur (GAKNS) equation is derived. Based on the derived solitary wave solution, author obtained some line-soliton localized excitations.

2 illus, 16 ref

010601   Zhimin L;Tao J (Education Dep, Luoding Polytechnic, Luoding-527 200, Guangdong, P.R. China, Email: zmluo@126.com ) : Asymptotic criterion for solutions of a class of integro-differential equations. Far East J mathl Sci 2012, 62(2), 189-95.

Discusses the asymptotic behaviour of a class of integro-differential equations. By making use of Bellman-Bihari inequality, we obtain the sufficient condition under that all continuable solutions of equations behave like nontrivial linear functions at + b. In particular, an example is given to show the application of the result.

7 ref

010600   Zhang Z (NO, College of Mathematics and Information Science, Wenzhou Univ, Wenzhou, Zhejiang-325 035, P.R. China, Email: zonglao@163.com) : Some properties of graph-like submanifolds in product spaces and relevant results. Far East J mathl Sci 2012, 61(1), 131-9.

Some results dealing with graph-like submanifolds in simple Riemannian product spaces or warped product spaces are given. As a byproduct, a theorem concerning harmonic functions on Riemannian manifolds is obtained.

10 ref

010599   Yaqoob N;Chinram R (Mathematics Dep, Quaid-i-Azam Univ, Islamabad, Pakistan, Email: nayaqoob@ymail.com) : On prime (m,n) bi-ideals and rough prime (m,n) bi-ideals in semigroups. Far East J mathl Sci 2012, 62(2), 145-59.

Author introduce the notion of prime (m, n) bi-ideals and rough prime (m, n) bi-ideals of semigroups. Authors show that in semigroups, the lower and the upper approximations of a prime (m, n) bi-ideal is a prime (m, n) bi-ideal.

15 ref