013784   Nonlaopon K;Lunnaree A;Kananthai A (Mathematics Dep, Khon Kaen Univ, Khon Kaen 40002, Thailand, Email: nkamsi@kku.ac.th) : On the solution of the n-dimensional diamond Klein-Gordon operator and its convolution. Far East J mathl Sci 2012, 63(2), 203-20.

18 ref

013783   Nandakishore L V;Udayabaskaran S (Mathematics Dep, Dr. M.G.R. Univ, Chennai-95) : Pricing double barrier options with fluctuating volatility. Far East J mathl Sci 2012, 63(1), 127-32.

In this paper, a double barrier option is considered in a market driven by the modified Black-Scholes environment with a stochastically fluctuating volatility. This is used to find the pricing formula for a double barrier option. The conditional probability density function for the same is also derived. It can be shown that the discounted stock price is a martingale under the equivalent martingale measure using the Radon-Nikodym derivative and Girsanov's theorem.

6 ref

013782   Murty M N (Physics Dep, National Institute of Science and Technology, Berhampur-761 008, Email: mnarayanamurty@rediffmail.com) : Architectures for realization of two-dimensional discrete sine transform. Ultra Scient phys Sci-Sect A 2013, 25(1), 177-87.

In this paper, two algorithms for realizing two-dimensional discrete sine transform (2-D DST) are proposed. Basing on these two algorithms, two systolic architectures are presented for implementing 2-D DST of even N. The systolic array using the algorithm-1 is a bilayer structure, which does not require any hardware/time for the transposition of the intermediate results.

10 illus, 14 ref

013781   Mishra G;Ravindra Kumar;Singh K K (Mathematics Dep, Agra College, Agra, Uttar Pradesh, Email: rkpal.maths@gmail.com) : Unsteady flow of a dusty viscous fluid through porous medium in a rectangular channel with time dependent pressure gradient. Ultra Scient phys Sci-Sect A 2013, 25(1), 169-76.

The unsteady flow of a dusty viscous incompressible fluid through porous medium in a long rectangular channel under the influence of time dependent pressure gradient has been studied. The solution of governing equations of motion is obtained by the application of Finite Fourier cosine transform and Laplace transform to study the behaviour of the flow of fluid and the dust particles through porous medium. The particular cases when the pressure gradient is (i) an absolute constant, (ii) periodic function of time, (iii) an exponentially decreasing function of time and (iv) Cte^λt, have been discussed in detail.

26 ref

013780   Matsugu Y;Takeshima T (Mathematical Sciences Dep, Faculty of Science, Shinshu University, Matsumoto-390-8621, Japn, Email: matsugu@math.shinshu-u.ac.jp) : Pointwise multipliers from A<. Far East J mathl Sci 2011, 58(2), 157-72.

Let p, q, a and b be four real numbers such that p <62> 0, q <62> 0, α <62> -1 and β -1. Let g be a holomorphic function in the unit ball B_n of Cⁿ. Then g is called a pointwise multiplier from the weighted Bergman space A^p_α(B_n) and into the other one A^q_{β(Bn) if {ƒg : ƒ ε A^pα(Bn)} ⊂ A^qβ(Bn). In the case n = 1, Zhao completely characterized the pointwise multipliers from A^pα(D) into A^qβ(D). In this paper, we prove that his result still holds even in the higher dimensional case n ≥ 2.}

5 ref

013779   Manglesh A;Gorla M G (Mathematics and Statistics Dep, Himachal Pradesh Univ, Summer Hill, Shimla-177 005, Email: raarti3025@gmail.com) : MHD free convective flow through porous medium in the presence of hall current, radiation and thermal diffusion. Indian J pure appl Math 2013, 44(6), 743-56.

An unsteady free convective flow through porous media of viscous, incompressible, electrically conducting fluid through a vertical porous channel with thermal radiation is studied. A magnetic field of uniform strength is applied perpendicular to the vertical channel. The magnetic Reynolds number is assumed very small so that the induced magnetic field effect is negligible. The injection and suction velocity at both plates is constant and is given by υ₀. The pressure gradient in the channel varies periodically with time along the axis of the channel. The temperature difference of the plates is high enough to induce the radiative heat. Taking Hall current and Soret effect into account, equations of motion, energy, and concentration are solved. The effects of the various parameters, entering into the problem, on velocity, temperature and concentration field are shown graphically.

7 illus, 16 ref

013778   Mahadevan G;Nagarajan A;Rajeswari A; Avadayappan S (Mathematics Dep, Gandhigram Rural Institute Deemed Univ, Gandhigram-624 302, Email: gmaha2003@yahoo.co.in) : Further characterization of induced paired domination number of a graph. Ultra Scient phys Sci-Sect A 2013, 25(1), 59-72.

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 perfect matching. The induced - paired domination number γ_ip(G) is the minimum cardinality taken over all 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). The authors characterized the classes of graphs whose sum of induced paired domination number and chromatic number equals to 2n - 6, for any n ≥ 4. In this paper we extend the above result and characterize the classes of all graphs whose sum of induced paired domination number and chromatic number equals to 2n - 7, for any n ≥ 4.

2 illus, 13 ref

013777   Lokeshmaran A;Elangovan R (Bio-Statistics Dep, Mahatma Gandhi Medical College & Research Institute, Pondichery-607 402, Email: lokesmaran_slams@rediff.com) : Variable selection for multivariate survival data. Ultra Scient phys Sci-Sect A 2013, 25(1), 103-16.

It is assumed for the Cox's proportional hazards model that the survival times of subjects are independent. This assumption might be violated in some situations, in which the collected data are correlated. The well-known Cox model is not valid in this situation because independence assumption among individuals is violated. For this purpose Cox's proportional hazard model is extent to the analysis of multivariate failure time data, which includes frailty models and marginal model. In this paper frailty and marginal hazard models are discussed using nonconcave penalized likelihood approach. Detailed illustrations are also provided.

1 table, 30 ref

013776   Liu L;Wu Y;You G (NO, School of Mathematics and Statistics, Henan Science and Technology Uni, Luoyang-471 003, P.R. China, Email: lujuliu@gmail.com) : Global dynamics for a TB model incorporating case detection and noninfectious TB cases. Far East J mathl Sci 2012, 63(2), 157-80.

It is recognized that the case detection and noninfectious TB cases of the active tuberculosis (TB) patients are two key factors to effectively prevent and to successfully control the transmission of tuberculosis. This paper presents the global dynamics of a tuberculosis transmission model with these key factors by constructing proper Lyapunov functions. It is proved that the disease-free equilibrium is globally asymptotically stable when the effective reproduction number R₀ is below unity; and the unique endemic equilibrium is globally asymptotically stable when the effective reproduction number RQ is above unity and the weaker condition is valid.

17 ref

013775   Li-Xiang X;Song-Hua M;Jian-Ping F (NO, College of Science, Zhejiang Lishui Univ, Lishui-323 000, P.R. China, Email: msh6209@yahoo.com.cn) : Folded excitations and periodic wave solutions for (1+1)- dimensional burgers equation. Far East J mathl Sci 2012, 63(1), 97-103.

By means of projective equation approach, a new family of exact solutions of the (1 + 1)-dimensional Burgers system is derived. Based on the derived solution, some folded excitations and periodic wave solutions are investigated.

3 illus, 16 ref

013774   Li H (NO, School of Mathematics and Information Science, Henan Univ, Kaifeng-475 004, Henan Province, People's Republic of China, Email: lihbmath@hotmail.com) : Hausdorff dimensions of the julia sets of reluctantly recurrent rational maps. Indian J pure appl Math 2013, 44(6), 849-63.

In this paper, authors considered a rational map f of degree at least two acting on Riemman sphere C that is expanding away from critical points. Assuming that all critical points of f in the Julia set J(f) are reluctantly recurrent, we prove that the Hausdorff dimension of the Julia set J(f) is equal to the hyperbolic dimension, and the Lebesgue measure of Julia set is zero when the Julia set J(f) ≠ C.

12 ref

013773   Kusmayadi T A;Sudibyo N A (Mathematics Dep, Faculty of Mathematics and Natural Sciences, Sebelas Maret Univ, Surakarta, Central Java, 57126, Indonesia, Email: trikusma@uns.ac.id) : Eccentric digraph of friendship graph and firecracker graph. Far East J mathl Sci 2012, 63(2), 221-34.

Let G be a graph with a set of vertices V(G) and a set of edges E(G). Then the distance from vertex u to vertex v in G, denoted by d(u, v), is the length of the shortest path from vertex u to v. The eccentricity of vertex u in a graph G is the maximum distance from vertex u to any other vertices in G, denoted by e(u). Vertex v is an eccentric vertex from u if d(u, v) = e(u). The eccentric digraph ED(G) of a graph G is a graph that has the same set of vertices as G, and there is an arc (directed edge) joining vertex u to v if v is an eccentric vertex from u. In this paper, we determine the eccentric digraph of a class of graphs called the friendship graph F_kⁿ and firecracker graph F_{n, k}.

1 illus, 8 ref

013772   Kumbhar S M;Thakar S (Mathematics Dep, Shivaji Univ, Kolhapur, Maharashtra-416 004, Email: snlkumbhar3@gmail.com ) : Analytical solution of burgers-like equation. Ultra Scient phys Sci-Sect A 2013, 25(1), 127-34.

In this paper author determined optimal system for one-dimensional Burgers-like equation, c_t = [V(c)c]_x + [D(c}c_x}_x. Lie group analysis is used to obtain invariant vector fields of one-dimensional Burgers-like equation. These invariant vector fields forms the Lie algebra. Certain choice of invariant vector field defines the transformation to convert the equation into a solvable partial differential equation. With help of adjoint representation table one-dimensional optimal system is obtained.

2 tables, 4 ref

013771   Ko W;Ryu K (Mathematics Dep, Korea Univ, Jochiwon-339 700, South Korea, Email: kowl@korea.ac.kr) : Positive periodic solutions of a hassell-Varley type predator-prey system. Indian J pure appl Math 2013, 44(6), 865-82.

Author studied the existence and asymptotic behavior of positive periodic solutions of diffusive Hassell-Varley type predator-prey systems with time periodic and spatially dependent coefficients. The fixed point index theory is used to obtain necessary and sufficient conditions for the existence of positive time periodic solution. Finally, we extend the existence results to the associated elliptic models.

22 ref

013770   Kimura T;Kurosawa Y;Shibata T (NO, Institute of Mathematics Tsukuba Univ, Tsukuba, Ibaraki-305 8571, Japan, Email: kimurata@math.tsukuba.ac.jp) : Some PV-equivalence. Far East J mathl Sci 2012, 63(2), 269-80.

Gives a necessary and sufficient condition for the prehomogeneity of the triplet (G x GL(n), ρ₁ Λ₁ + ρ₂ ⊗ Λ₁*, V(m₁) ⊗ V_(n) + V(m₂) ⊗ V(_n)*) (m₁ <62> n ≥ m₂). This is a generalization of Theorem 1.1 in [3]. Considers everything over the complex number field C.

7 ref

013769   Khare S;Srivastava B M L (Mathematics Dep, Govt P.G. College, Shahdol, Madhya Pradesh) : Some new integral involving I-function of one variable and E-operator. Ultra Scient phys Sci-Sect A 2013, 25(1), 19-22.

The aim of this paper is to establish some new integrals involving I-function of one variable and E-operator.

3 ref

013768   Kawakami T (Mathematics Dep, Faculty of Education, Wakayama Univ, Sakaedani Wakayama 640-8510, Japan, Email: kawa@center.wakayama-u.ac.jp) : Structure theorems in o-minimal structures. Far East J mathl Sci 2012, 63(2), 141-55.

Let G be a definably compact affine definable C^r group, X be an affine definable C^rG manifold and 1 ≤ r <60> ∞. Suppose that every orbit in X has type G/H. Authors prove that (X, π, X/G, G/H, N(H)/H) is a definable C^r-1 fiber bundle, where N(H) is the normalizer of H in G.

11 ref

013767   Kannam R;Rabert M;Sathiyamoorthi R (Statistics Dep, Annamalai Univ, Annamalainagar-608 002, Email: statkannan@yahoo.co.in) : Stochastic model for expected time to seroconversion under correlated intercontact times using SCBZ property. Ultra Scient phys Sci-Sect A 2013, 25(1), 5-14.

This paper focuses on the study of a stochastic model for predicting seroconversion time of HIV transmission under correlated intercontact times. In the estimation of expected time to seroconversion, there is an important role for the interarrival times between successive contacts and it has a significant influence. Proposed a stochastic model assuming the intercontact times between successive contacts are correlated random variables and the threshold distribution is SCBZ property. The expected time to seroconversion and its variance are derived and numerical illustrations are provided.

6 illus, 6 ref

013766   Jat R N;Saxena V (Mathematics Dep, Rajasthan Univ, Jaipur, Email: vishaljpr.raj@gmail.com) : MHD boundary layer stagnation point flow and heat generation/absorption of a micropolar fluid with uniform suction/injection. Ultra Scient phys Sci-Sect A 2013, 25(1), 27-36.

A comprehensive study of the steady laminar flow with heat generation of an incompressible electrically conducting micropolar fluid impinging on a permeable flat plate is analyzed numerically. A uniform suction or blowing is applied normal to the plate, which is maintained at a constant temperature. Also, a uniform magnetic field is applied normal to the plate and the viscous dissipation effect is taken into account. The governing partial differential equations are transformed into ordinary differential equations by using similarity variables and then solved them numerically by standard technique. The effects of the uniform suction/ blowing parameter, magnetic parameter, material parameter on the flow and heat transfer are presented graphically and discussed.

9 illus, 1 table, 35 ref

013765   Jat R N;Neemawat A;Rajotia D (Mathematics Dep, Rajasthan Univ, Jaipur-302 004, Email: jat.rn_jp20@yahoo.com) : MHD flow with heat transfer due to a pont sink. Ultra Scient phys Sci-Sect A 2013, 25(1), 199-206.

The steady two-dimensional, laminar boundary layer flow of a viscous incompressible electrically conducting fluid in a circular cone with hole at the vertex (point sink) in the presence of a uniform transverse magnetic field is studied. Taking suitable similarity variables, the governing boundary layer equations are transformed into ordinary differential equations and solved them numerically by standard technique. Numerical values of physical quantities of interest are tabulated and the velocity and temperature distributions are plotted and discussed in detail.

8 illus, 14 ref

013764   Harne S;Badshah V H;Sethiya S (Mathematics Dep, Government College, Kannod, Madhya Pradesh, Email: sanjaykeshavharne@yahoo.co.in) : Some identities involving common factors of negafibonacci and lucas numbers. Ultra Scient phys Sci-Sect A 2013, 25(1), 81-4.

In this paper author presented some identities involving common factors of Negafibonacci and Lucas numbers. Binet's formula of Negafibonacci will employ to obtain the identities.

3 ref

013763   Ghanshyam Singh;Gupta S (NO, College of Science, M.L. Sukhadia Univ, Udaipur-313 001, Email: ghanshyamsrathore@yahoo.co.in) : Bianchi type-I inflationary cosmological model in general relatvity. Ultra Scient phys Sci-Sect A 2013, 25(1), 23-6.

Bianchi type-I inflationary cosmological model in the presence of mass less scalar field with a flat potential is investigated. A determinate solution is obtained without taking any supplementary condition between the metric potentials. Various physical and geometrical features of the model are also discussed.

15 ref

013762   Garg M;Dixit M;Tripathi P K (Mathematics Dep, Nehru P.G. College, Chhibramau, Kannauj, Uttar Pradesh, Email: garg_manoj1972@yahoo.co.in) : On g- homeomorphism in topologgical spaces. Ultra Scient phys Sci-Sect A 2013, 25(1), 95-102.

16 ref

013761   Francis A;Jones L (School of computing and Mathematics, University of Western Sydney, NSW 1797, Australia, Email: a.francis@usw.edu.au) : Monomial bases for the centres of the group algebra and Iwahori-Hecke algebra of the symmetric group. Far East J mathl Sci 2011, 58(2), 119-43.

A monomial basis for Z(ZS_n), the centre of the symmetric group algebra, or Z(H_n), the centre of the corresponding Iwahori-Hecke algebra, is a basis that consists solely of monomial symmetric polynomials in Jucys-Murphy elements. In a previous paper, we showed that there are only finitely many monomial bases for Z(ZS₃) and Z(H₃). In this paper, we prove that there exist infinitely many monomial bases for Z(ZS₄, which we characterize completely. Using this result, we are able to produce three new integral bases for Z(H₄), each of which is monomial. Based on extensive computer calculations, we conjecture that our list of monomial bases for Z(H₄) is exhaustive. In addition, we provide evidence to support the conjectures that the number of monomial bases for Z(AS₅) is finite, and that no monomial bases exist for Z(H₅).

3 tables, 13 ref

013760   Feng Y (NO, School of Mathematics and Statistics, Chongqing Three Gorges Univ, Wanzhou, Chongqing-404 100, P.R. China, Email: yumingfeng25928@163.com) : Refinements of young's inequalities for matrices. Far East J mathl Sci 2012, 63(1), 45-55.

This article aims to discuss the trace and the determinant versions of Young's inequalities. Author gave refinements of the classical Young's inequality for positive numbers and improve Young's inequalities for matrices.

8 ref

013759   Elahi Y;Aziz M I A (Mathematics Dep, Technology Malaysia Univ, Skudai, 81310 Johor Bahru, Malaysia, Email: elahi.math@gmail.com) : Efficient pricings for binomial Asian option under fuzzy environment. Far East J mathl Sci 2012, 63(1), 133-40.

Asian options are important path-dependent derivatives. The aim of this paper is to compare two binomial Asian option pricings. First, authors introduce the binomial Asian option pricing. Next, author present some useful concepts and properties about Chen-Lyuu pricing formula. Here, gives a brief overview of the literature and the different depart by pricing the Asian options, using a binomial method. Next, techniques to option pricing. They first focus on Asian option and depart by pricing the Asian options, using a binomial method. Next, to more discussion in fuzzy environment.

27 ref

013758   Deka B;Deka R C (Mathematical Sciences Dep, Tezpur Univ, Napaam, Tezpur-784 028, Email: deka_b@tezu.ernet.in) : Finite element method for a class of parabolic integro-differential equations with interfaces. Indian J pure appl Math 2013, 44(6), 823-47.

In this paper, convergence of finite element method for a class of parabolic integro-differential equations with discontinuous coefficients are analyzed. Optimal L²(L²) and L²(H¹) norms are shown to hold when the finite element space consists of piecewise linear functions on a mesh that do not require to fit exactly to the interface. Both continuous time and discrete time Galerkin methods are discussed for arbitrary shape but smooth interfaces.

23 ref

013757   Cui R;Luo Y (NO, School of Mathematics and Statistics, Lanzhou Univ, Lanzho, Gandu-730 000, P.R. China, Email: cuiranran23@163.com) : Gelfand-kirillov dimension of some primitive abundant semigroups. Indian J pure appl Math 2013, 44(6), 809-22.

In this paper, the growth and Gelfand-Kirillov dimension of some primitive abundant semigroups are investigated. It is shown that for certain primitive abundant (regular) semigroup S, S as well as the semigroup algebra K[S] has polynomial growth if and only if all of its cancellattve submonoids (subgroups) T as well as K[T] have polynomial growth. As applications, it is shown that if S is a finitely generated primitive inverse monoid having the permutational property, then clKdimK[S] = GK dimK[S] = rk(S}.

15 ref

013756   Borna K;Ashrafi Payaman N A (NO, Faculty of Mathematical Sciences and Computer, Kharazmi Univ, Tehran, Iran, Email: borna@khu.ac.ir) : Dawson's chess revisited. Indian J pure appl Math 2013, 44(6), 771-94.

In this paper authors prove that in a Quasi-Dawson's Chess (a restricted version of Dawson's Chess) playing on a 3 x d board, the first player is loser if and only if d (mod)5 = 1 or d (mod) 5 = -2. Furthermore, authors have designed two algorithms that are responsible for storing the results of Quasi-Dawson's Chess games having less than d + 1 files and finding the strategy that leads to win, if there is a possibility of winning (by a wining position, author mean one from which one can win with best play). Moreover shows that the total complexity of our algorithms is O(d²). Finally authors have implemented our algorithm in C++ which admits the main results of the paper even for large values of d.

3 tables, 13 ref

013755   Bogdanowicz Z R (NO, Armament Research, Development and Engineering Center, Picatinny, New Jersey 07806, U.S.A., Email: zrb2@aol.com) : On the arc reversal and closed walks with prescribed bounds on arcs visits. Far East J mathl Sci 2012, 63(2), 281-6.

Authors consider closed walks in multidigraph G, which can visit each arc up to a given times. Gives sufficient conditions for G, so the reversal of any arc in G decreases the number of such closed walks.

6 ref

013754   Barilla D;Bisaia M;Caristi G;Puglisi A (S.E.A. Dep, University of Messina, Italy, Email: dbarilla@unime.it) : On laplace type problems (II). Far East J mathl Sci 2011, 58(2), 145-55.

In this paper, authors considered some Laplace type problems for lattices with axial symmetry and different types of obstacles. They compute the probability that a segment of random position and constant length intersects a side of the lattice.

5 illus, 4 ref

013753   Bali R;Yadav M K;Jain V C (Mathematics Dep, Rajasthan Univ, Jaipur-302 055, Email: balir5@yahoo.co.in) : Viscous fluid cosmological model with two degrees of freedom in general relativity. Ultra Scient phys Sci-Sect A 2013, 25(1), 117-26.

Viscous fluid cosmological model with two degrees of freedom is investigated. Authors assumed the coordinates to be comoving. In presence of viscosity the model is non-degenerate Petrov Type-1. There is a real physical singularity at T=0. Moreover in the absence of viscosity, author got the stiff fluid case. Some significant physical and geometrical aspects of the model are also discussed.

19 ref

013752   Bagora Menaria A (Mathematics Dep, Jaipur National Univ, Jaipur-302 027, Email: anitabagora@gmail.com) : Tilted cosmological model with electromagnetic field. Ultra Scient phys Sci-Sect A 2013, 25(1), 37-42.

Tilted Bianchi type I cosmological model in the presence of magnetic field and barotropic fluid is investigated. To determine complete solution, author have assumed that the condition p = γρ, where p being isotropic pressure, ρ the matter density and also assumed that the relation between metric potential as A=BC. Here, it is seen that Maxwell's equations F_[ij;k] = 0 is satisfied by F ₂₃ = constant. The physical and geometrical aspects of the model in the presence and absence of magnetic field together with singularity in the model are also discussed.

16 ref

013751   Azimzadeh Z;Vahidi A R;Babolian E (Mathematics Dep, Science and Research Branch, Islamic Azad Univ, 14778-93855 Tehran, Iran, Email: z.azimzadeh@yahoo.com) : Exact solutions for non-linear Duffing's equations by He's homotopy perturbation method. Indian J Phys 2012, 86(8), 721-6.

Homotopy perturbation method (HPM) is proposed to solve Duffing's equation, which yields a series solution. Then, Pade approximation yielding the analytic approximate solution with fast convergence rate and high accuracy is applied for the series solution derived from the HPM. To illustrate the ability and the reliability of the method, two examples are provided. The results reveal that the method is very effective and simple.

3 illus, 31 ref

013750   Aurangzaib;Shafie S (Mathematical Sciences Dep, Faculty of Science, Teknologi Malaysia JB Univ, 81310, Skudai, Johor, Malaysia, Email: ridafie@yahoo.com) : Unsteady MHD stagnation-point flow with heat and mass transfer in a micropolar fluid in the presence of thermophoresis and suction/injection. Indian J pure appl Math 2013, 44(6), 729-41.

The effect of suction or injection on unsteady MHD flow with heat and mass transfer in a micropolar fluid near the forward stagnation point flow with thermophoresis has been investigated. The problem is reduced to a system of non-dimensional partial differential equations, which are solved numerically using the implicit finite-difference scheme. Profiles for velocity, microrota-tion, temperature and concentration as well as the skin friction, the rate of heat and mass transfer are determined and presented graphically for physical parameters. The results show that the suction increases the skin friction, the rate of heat and mass transfer while opposite trend is observed for the case of injection. It is also found that the effect of thermophoresis is decrease the concentration boundary layer thickness.

12 illus, 2 tables, 28 ref

013749   Asmiati;Baskoro E T;Assiyatun H;Suprijanto D; Simanjuntak R;Uttunggadewa S (Combinatorial Mathematics Research Div, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandun, Jl. Ganesa 10 Bandung 40132, Indonesia, Email: asmiati308@students.itb.ac.id) : Locating-chromatic number of firecracker graphs. Far East J mathl Sci 2012, 63(1), 11-23.

Let G = (V, E) be a connected graph and c be a proper k-coloring of G. Let ∏ = {C₁, C₂, ..., C_k} be a partition of V(G), where C_i is the set of vertices receiving color i. The color code c_∏(v) of a vertex v in G is the ordered k-tuple (d(v, C₁), ..., d(v, C_k)), where (d(v, C_i)) is the distance of v to C_i. If for any two distinct vertices u, v in G, c_∏(u) ≠ C_∏ (v), then c is called a locating-chromatic coloring of G. The locating-chromatic number of graph G, denoted by χ_L(G), is the smallest k such that G admits a locating coloring with k colors. A firecracker graphs F_n,k is a graph obtained by the concatenation of n stars, each consists of k vertices, by linking one leaf from each star. In this paper, determines the locating-chromatic number of firecracker graphs F_n,k.

4 illus, 8 ref

013748   Arulpavai R;Elangovan R (Statistics Dep, Government Arts College, C. Mutlur, Chidambaram-608 001, Email: r_arulpavai@yahoo.co.in) : Stochastic model to determine the optimal manpower reserve at four nodes in series. Ultra Scient phys Sci-Sect A 2013, 25(1), 139-55.

The purpose of manpower planning is to best match future manpower demand and supply in the light of multiple objectives such as economic conditions, production/scale trends, people skills inventory, government regulations, as well as organization history and policies regarding personnel hearing, training, promotion, firing and retirement. One of the essential components of a manpower planning system is manpower forecasting, the process of anticipating the future size and nature of the manpower force. Stochastic models have been widely used in the study of manpower systems with different modes in series like training, promotion, placement, etc. There are many industries and organizations where the skilled personnel are to be recruited and they must be given prior training before employment. In human resource planning the training and induction of the right type of personnel is a pressing problem. In this paper, we consider the optimal solution for the manpower to be kept as reserve inventory at four different nodes in series. Two different models have been discussed. Numerical illustrations are provided using simulation studies.

12 illus, 10 tables, 8 ref

013747   Al-Humaidi B;Al-Lail M;Chaudhry M A (Mathematics and Statistics Dep, King Fahd Petroleum and Minerals Univ, Dhahran 31261, Saudi Arabia, Email: humaidib@kfupm.edu.sa) : Iterated integrals of the generalized complementary error function. Far East J mathl Sci 2012, 63(1), 25-43.

Iterated integrals of the complementary error functions are introduced. Some properties of these functions including integral and series representations, differentiation formulas, and recurrence relations are provided. Certain graphical and tabular representations are also presented.

2 illus, 2 tables, 10 ref

013746   Agarwal S;Pandey R K;Pradhan A (Mathematics Dep, Uttaranchal Institute of Technology, Arcadia Grant, Chandanwari, Dehradun-248 007, Email: Pradhan@iucaa.ernet.in) : Bianchi type-II string cosmological models in normal gauge for Lyra's manifold with constant deceleration parameter. Indian J Phys 2012, 86(1), 61-70.

The present study deals with a spatially homogeneous and anisotropic Bianchi-II cosmological models representing massive strings in normal gauge for Lyra's manifold by applying the variation law for generalized Hubble's parameter that yields a constant value of deceleration parameter. The variation law for Hubble's parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential form. Using these two forms, Einstein's modified field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier (Phys Rev D 28:2414, 1983) is used to construct massive string cosmological models for which we assume that the expansion (θ) in the model is proportional to the component σ¹₁ of the shear tensor åσⁱ_j. This condition leads to A = (BC)^m , where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent with the recent observations. It has been found that the displacement vector β behaves like cosmological term Λ in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the decelerating universe, whereas strings dominate in the accelerating universe. Some physical and geometric behaviours of these models are also discussed.

10 illus, 103 ref

012804   Yi H (Mathematics Dep, Kwangwoon Univ, Seoul-139 701, Korea, Email: hsyi@kwangwoon.ac.kr) : Harmonic little bloch space. Far East J mathl Sci 2012, 60(2), 229-37.

Harmonic little Bloch space can be identified with the pre-dual of the weighted harmonic Bergman space b_α¹.

6 ref

012803   Ye S;Chen Y;Luo H (Mathematics Dep, Huizhou Univ, Huizhou-516 007, P.R. China, Email: yizhichen1980@126.com) : Generalized m-power matrices and transformations. Int J mathl Combinatorics 2012, 2(Jun), 71-5.

In this paper, generalized m-power matrices and generalized m-power transformations are defined and studied. First, we give two equivalent characterizations of generalized m-power matrices, and extend the corresponding results about m- idempotent matrices and m-unit-ponent matrices. And then, we also generalize the relative results of generalized m-power matrices to the ones of generalized m-power transformations.

6 ref

012802   Vijayalekshmi A (NO, S.T. Hindu College, Nagercoli, Tamil Nadu, Email: vijimath.a@gmail.com) : Total dominator colorings in paths. Int J mathl Combinatorics 2012, 2(Jun), 89-95.

Let G be a graph without isolated vertices. A total dominator coloring of a graph G is a proper coloring of the graph G with the extra property that every vertex in the graph G properly dominates a color class. The smallest number of colors for which there exists a total dominator coloring of G is called the total dominator chromatic number of G and is denoted by Xtd(G). In this paper we determine the total dominator chromatic number in paths. Unless otherwise specified, n denotes an integer greater than or equal to 2.

1 illus, 4 ref

012801   Verma S (Applied Science and Humanities Dep, Gurgaon College of Engineering, Bilaspur, Gurgaon, Email: Shalini_bharti7@yahoo.co.in) : Comparative study of effective conditions about theorems on metrization of topological spaces. Arya Bhatta J Math Inf 2012, 4(1), 71-82.

Many great resecarchers have different new concepts and conditions to make a space to be metrizable. This paper presents an analysis of effective conditions about different theorems on metrization of topological spaces. Our aim is to study about those conditions and find their impact area.

12 ref

012800   Vaidya S K;Bantva D D (NO, Saurashtra Univ, Rajkot-360 005, Email: samirkvaidya@yahoo.co.in) : Distance two labeling of generalized cacti. Int J mathl Combinatorics 2012, 2(Jun), 103-9.

Distance two labeling of a graph G is a function f from the vertex set V(G) to the set of all nonnegative integers such that |f(x) - f(y)| ≥ 2 if d(x,y) = 1 and |f(x) - f(y)| ≥ 1 if d(x,y) = 2. The L(2, 1)-labeling number λA(G) of G is the smallest number k such that G has an L(2, 1)-labeling with max{f(v) : v ∈ V(G)} = k. Here we introduce a new graph family called generalized cactus and investigate the λ-number for the same.

15 ref

012799   Thomas U;Mathew S C (Basic Sciences Dep, Amal Jyothi College of Engineering, koovappally, P.O.-686 518, Kottayam, Kerala) : On set-semigraceful graphs. Int J mathl Combinatorics 2012, 2(Jun), 59-70.

This paper studies certain properties of set-semigraceful graphs and obtain certain bounds for the order and size of such graphs. More set-semigraceful graphs from given ones are also obtained through various graph theoretic methods.

17 ref

012798   Sonika Kumari;Vinod Kumar (NO, J.V. Jain (P.G.) College, Saharanpur, Uttar Pradesh) : Aerodunamic forces acting on two rectangular cylinders. Arya Bhatta J Math Inf 2012, 4(2), 235-42.

Presented a third-order upwind finite element method for solutions of a two-dimensional flow around two rectangular cylinders In this paper the normalized gap size S/D, between the surfaces of the two square cylinders is set at the distance of S/D =1. The Reynolds number given in the computations is 11,050.

7 illus, 7 ref

012797   Singh T P;Kusum (NO, Yamuna Instt. of Engg. & Tech., Gadholi, Y. Nagar, Email: tpsingh75@yahoo.com) : Machine repairing queue model under fuzzy environment. Arya Bhatta J Math Inf 2012, 4(2), 189-204.

Machine interference queue models play significant role in many manufacturing system and client server computing. These problems involve many parameters like breakdown rate, service rate, loss of production rale etc. Due to uncertain and uncontrollable factors in machines repairing problems, the models behave like fuzzy in nature. In this paper we propose a methodology for constructing system performance measure where breakdown rate and service rate μ are supposed triangular fuzzy number. Numerical illustration is solved successfully to demonstrate the validity to the proposed model. The fuzzy queue can be represented more accurately by using the proposed approach and the analytical results will be useful and significant for the system designer and practitioners.

9 ref

012796   Shobhalatha G;Bhat A R (NO, , ) : Congruence on semigroups. Indian J Math mathl Sci 2011, 7(1), 39-43.

This paper contains some results on congruence semigroups and σ-reflexive semigroups using the properties like weakly separative, weakly commutative, quasi commutative etc. Defining a relation 'σ'on a commutative semigroup 'S' by aσb => abⁿ = bⁿ⁺¹, baⁿ= aⁿ⁺¹ for some positive integer 'n' and any a, b in S, it is proved that 'σ'is a separative congruence on 'S'. Also it is proved that if 'S' is quasi commutative semigroup, and 'σ'be the congruence relation on 'S'then S/σ is a maximal separative homomorphic image of S. On the other hand using the permutable property it is proved that a σ-reflexive semigroup is cancellative with or without considering separative condition. This paper also contains some results on weakly commutative semigroups. One of the properties like permutable, separative etc has taken over a weakly commutative semigroup and proved that it is weakly cancellative or cancellative.

4 ref

012795   Sharma A K;Vasdev D (Mathematics Dep, Raj Rishi Govt. Autonomous College, Alwar, Rajasthan) : Inventory model for deteriorating items with multivariate demand and money inflation. Arya Bhatta J Math Inf 2012, 4(1), 23-30.

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.

5 tables, 19 ref

012794   Sharma A K;Sharma M K (Mathematics Dep, R.R. College, Alwar, Rajasthan, Email: manojsharmamath@rediffmail.com) : Non linear price dependent inventory model for non instantaneous deteriorating items with time varying holding cost. Arya Bhatta J Math Inf 2012, 4(1), 133-8.

In this paper a Deterministic Inventory Model is developed when the deterioration rate is constant. Demand rate is a function of selling price and it is non linear (Quadratic) form and the holding cost is time dependent. The planning horizon is finite the optial replenishment policy and decision rule, which minimizes the total cost, is developed. We consider shortage and it is fully backlogged. The results are illustrated with the help of numerical example. The sensitivity analysis of the solution is also discussed.

1 illus, 1 table, 9 ref