000091   Harikrishnan P K;Riyas P;Ravindran K T (P.G and Research Centre in Mathematics Dep, Payyanur College, Payyanur, Kerala, Email: pkharikrishnans@gmail.com) : Riesz theorems in 2-inner product spaces. Int Rev pure appl Math 2009, 5(2), 303-9.

Discusses the proof of 'Riesz theorems' in 2-inner product spaces. The main result holds only for a b-linear functional but not for a bilinear functional.

5 ref

000090   Golbasi O (Faculty of Arts and Science, Mathematics Dep, Cumhuriyet Univ, Turkey, Email: ogolbasi@cumhuriyet.edu.tr) : On commutativity of semiprime rings with generalized derivations. Indian J pure appl Math 2009, 40(3), 191-9.

Let R be an associative ring. An additive mapping l : R → R is called a generalized derivation if there exists a derivation d : R → R such that f(xy) = f(x)y + xd(y), for all x, y ∈ R. Explores the commutativity of semiprime rings admitting generalized derivations l and g such that one of the following holds for all x, y ∈ R. Let (f, d) and (g, h) be two generalized derivations of R. (i) f(x)y = xg(y), (ii) f([x,y]} = ± [x,y], (iii) f(x,y) = ± xoy for all x, y ∈ R.

8 ref

000089   Ghosh P K;Pal M (Applied Mathematics with Oceanology and Computer Programming Dep, Vidyasagar Univ, Midnapore) : Algorithm to compute the feedback Vertex set on trapezoid graphs. Int J mathl Sci 2009, 8(1-2), 31-43.

The feedback vertex problem is one of the important problem in graph theory. It is well known that the feedback vertex problem is jW-complete on general graphs. For weighted feedback vertex problem, an O (mn) time algorithm is available for permutation graphs and a linear time algorithm for interval graphs, where n, m are respectively number of vertices and edges of the graphs. In this paper, we shown that a trapezoid graph contains cycles of length at most four. All the cycles of length three and four of a trapezoid graph are generated. Also, an efficient algorithm is presented to compute the feedback vertex set on trapezoid graphs, which takes O(fn^{5) time, where is the cardinality of the feedback vertex set.}

10 illus, 8 ref

000088   Ghorbani S;Hasankhani A (Mathematics of Bam Dep, Shahid Bahonar Kerman Univ, Kerman, Iran, Email: sh.ghorbani@mail.uk.ac.ir) : Uniform topology on a residuated lattice induced by Fuzzy filters. Int Rev Fuzzy Math 2009, 4(1-2), 45-62.

The concept of fuzzy filters of a residuated lattice to define a uniform topology. We study some properties of this topology. Then we construct a quotient residuated lattice by a fuzzy filter and define the quotient topology on it. We discuss some properties of this topology.

13 ref

000087   Garg S K;Vaish B (Applied Science Dep, Devender Institute of Technology and Management at 5 km Stone, NH-58, opp. ITC Meerut Road, Ghaziabad-201 007, Email: garg_sudesh28@rediffmail.com) : Optimal ordering policy for deteriorating itmes with stock dependent demand and partial backlogging. Int Rev pure appl Math 2008, 4(1), 13-20.

In this paper, the model describes an [economic order quantity for a single deteriorating item with the stock dependent demand, frequency of advertisement and selling price of an item. Deterioration rate is taken as linear time dependent. Shortages, if any, are allowed and partially backlogged. The backlogging rate depends on the length of the waiting time up to the arrival of next lot. Showroom/shop capacity is assumed to be finite. The problem is illustrated numerically and the significant features of the result due to different parameters are discussed.

1 illus, 3 tables, 12 ref

000086   Gairola U C;Rawat A S (Mathematics Dep, Pauri Campus of H.N.B. Garhwal Univ, Pauri, Garhwal-246 001, Email: ucgairola@rediffmail.com) : Fixed point theorem for a finite product of metric spaces. J Mount Res 2009, 4(Dec), 77-82.

Estabiished a fixed point theorem for a pair of maps on a finite product of metric spaces. The result extend and generalize the results of Presic 1965, and Ciric-Presic 2007.

3 ref

000085   Ferrention R (Economic Sciences and Statistics Dep, Selerno Univ, Fisciano, (Sa) Italy, Email: rferrention@unisa.it) : On a remark of De Vylder. J Analysis Applic 2009, 7(1), 19-29.

Considered a remark of De Vylder with regard to a work of Dickson and underline that, considering a distribution function of the sums at risk containing trigonometric functions, the non ruin probability has, substantially, a non unlike expression.

12 ref

000084   Ferrentino R (Economic Sciences and Statistics Dep, Salerno Univ, Fisciano (Sa), Italy, Email: rferrentino@unisa.it) : Two cases of solutions of the integral equation of Cramer. J Analysis Applic 2009, 7(2), 91-108.

Object of the paper is the solution, with the use of the Laplace transform, of the integral equation of Cramer, in the case in which the distribution function of the sums at the risk is of Erlang or is mixture of two or three exponentials. It is show that the adoption of a Erlang distribution allows to express the non ruin function, solution of the equation of Cramer, in finite term and, besides, that, in the case in which the distribution function of the sums at risk is mixture of two or three exponentials, also the non ruin function is substantially of the same type.

10 ref

000083   Ferrando J C;Amigo J M (Centro De Investigaction Operativa, Universidad Miguel Herna'ndez, E-032 02 Elche (Alicante), Spain, Email: jc.ferrando@umh.es) : Erratum. Int J Math Analysis 2009, 1(2), 171-3.

Restates Lemma 2.3 of (3) to avoid a gap and revise the results of the aforementioned paper.

3 ref

000082   Fan X;Gao Y (NO, Business School, Shnghai for Science and Technology Univ, Shanghai-200 093, Email: fanfan17@126.com) : Existence of positively invariant polyhedral sets for liner time-varying systems. Int J Math Analysis 2009, 1(2), 121-32.

Existence of positively invariant polyhedral sets for linear time-varying systems is presented. State constraints and control constraints are reduced to positive invariance of some subsets of the state space for dynamical systems. Based on the mixed monotone decomposition method and two-sided comparison theorem, the robustly positively invariant sets are discussed. Necessary and sufficient conditions are given.

9 ref

000081   Dutta T K;Das M L (Pure Mathematics Dep, Calcutta Univ, 35, Ballygunge Circular Road, Kolkata-700 019) : Extensions of fuzzy ideals of semirings. Int Rev Fuzzy Math 2009, 4(1-2), 91-107.

Introduces the notions of extension of fuzzy ideal of a semiring S, fuzzy 3-weakly completely prime ideal of Sand study the relationship between fuzzy weakly completely prime ideals, fuzzy 3-weakly completely prime ideals by means of the extensions of fuzzy ideals of semiring.

8 ref

000080   Dubey S N (Mathematics Engineering Dep, Gyan Ganga Institute of Technology & Sciences, Jabalpur-482 003) : Generalized theorem on the rate of convergence of Fourier series. Int Rev pure appl Math 2009, 5(2), 267-76.

The chief object of the paper is to stretch this thread of concept by using more generalized trigonometric polynomial, i.e., the (N,p_n) means of the partial sums of the Fouries series of f(x) which essentially includes [1], [5], [7] and [10] and over and above to determine the constants also occurring in the order of approximation similar to Bernstein as shown by Meinardus {[6], p. 48-49}. In a nutshell, obtainment of constants is the key point of this research paper similar to Bernstein.

10 ref

000079   Dubey S N (Engineering Mathematics Dep, Gyan Ganga Institute of Technology & Sciences, Jabalpur-482 003) : On approximtion by Norlund means of continuous function satisfying modulus of continuity and Lipschitz condition. Int Rev pure appl Math 2009, 5(2), 161-9.

The paper is exclusively devoted to the thorough study of the approximation of the continous function f(x) possessing certain smoothness properties like modulus of continuity ω(δ), δ > 0 and Lipschitz condition of order α, 0 < a < 1 with constant M, i.e. Lip_M α by Norlund means of the partial sums of the Fourier scries of f(x). The chief object of the paper is to explore (as far as possible) all the constants which essentially occur while the process of approximation takes place. As a matter of course, these constants are significant from the comparison points of view, particularly in those circumstances when we switch over to different methods of approximation based on various summation processes.

5 ref

000078   Dong X;Gao Y (NO, School of Management, Shanghai for Science and Technology Univ, 516 Jungong Road, Shanghai-200 093, China, Email: dongxiaoxiao1983@163.com) : Relation between the proximal normal cone and the directional derivative. Int J Math Analysis 2009, 1(1), 101-8.

This paper is devoted to the relation between the proximal normal cone and the directional derivative for a function, which is uniformly directional differentiate and quasidifferentiable (in the sense of Demyanov and Rubinov). According to this relation, the proximal normal cone is represented via the quasidifferential.

8 ref

000077   Demidenko G V (NO, School of Mathematics, Pr. Koptyuga 4, Novosibirsk, Russia-630 090, Email: demidenk@math.nsc.ru) : Stability of solutions to linear differential equations of neutral type. J Analysis Applic 2009, 7(3), 119-30.

In the present paper author studied stability of solutions to systems of linear differential equations of neutral type d/dt(y(t) + Dy(t - τ)) = Ay(t) + By(t - τ), t > τ, where A, B, D are n x n numerical matrices, T> 0 is a delay parameter. Stability conditions of the zero solution to the systems are established, uniform estimates for the solutions on the half-axis {t> T} are obtained. In the case of asymptotic stability these estimates give the decay rate of the solutions at infinity.

10 ref

000076   Dash R B;Dalai D K;Mishra N (Mathematics Dep, Ravenshaw Univ, Cuttack-753 001, Email: rajani_bdash@rediffmail.com) : Class of generalised convex functions with some applications. Int Rev pure appl Math 2009, 5(2), 243-53.

Generalized the notions of B-subadditivity, antisymmetricity, A-Convexity and ∧-invexity and studied their properties in different theorems and propositions.

8 ref

000075   Das P K;Satpathy R N (NO, Seemanta Engg. College, Mayurvihar, Jharpokhria. Mayurbhanj, Orissa, Email: prasant_das40@rediffmail.com) : Extention of Minty's Lemma to invex sets in topological vector spaces and its application in complementarity problem. Int J mathl Sci 2009, 8(3-4), 183-9.

In the recent decades, computer science has played a vital role for making it possible to implement such techniques for everyday use as well as stimulating new effort for finding solutions of much more complicated problems. The study of variational inequalities and complementarity problems is also a part of this development because optimization problems can often be reduced to the solution of variational inequalities and complementarity problems. The notion of invex function introduced by M. A. Hanson gave a wide scope to analyze the variational inequality problems, complementarity problems. Minty's Lemma is one of the best tool to prove these type of problems. In this paper, we extend the Minty's Lemma to invex sets in topological vector spaces and applied in a complementarity problem.

9 ref

000074   Das A;Haque A (Mathematics Dep, Jawaharlal Nehru College, Boko-781 123, Email: dasalok_02@rediffmail.com) : Flow of a visco-elastic Rivlin-Ericksen fluid through a horizontal channel. Int Rev pure appl Math 2009, 5(2), 177-87.

The problem dealing with the steady MHD flow of an electrically conducting visco-elastic Rivlin-Ericksen fluid through a horizontal channel has been analyzed. It is assumed that the lower plate being a stretching sheet and the upper one being a permeable plate bounded by porous medium in the presence of transverse magnetic field. The fluid Motion is due to stretching of the lower plate with injection applied at the upper plate. The governing equations of the fluid have been solved by regular perturbation method for small value of stretching Reynolds number. The skin friction coefficients at both the surfaces of the channel are derived and discussed numerically through tabular forms for different values of visco-elastic parameter. The analytical expression for pressure distribution has also been calculated and presented graphically for various visco-elastic parameters involved in the solution.

5 illus, 2 tables, 13 ref

000073   Dangwal R;Sharma M K;Pandey D (Mathematics Dep, H.N.B., Garhwal Univ, Campus Pauri Garhwal, Uttara Khand, Email: dangwalrajesh@yahoo.co.in) : Health status index using intuitionistic Fuzzy approach. J Mount Res 2009, 4(Dec), 49-64.

In order to drive an operational health status index, it is difficult to define the functional status of human body. Intuitionistic fuzzy approach has been proposed for the use in expressing the health status and its index. Introduced the concept of fuzziness and Intuitionistic fuzzy set in order to study the ambiguous health status. Health status has been divided into four factors and seems to be classified into four modes. This study may be useful for those human beings, who are more concerned about their health status. If an individual knows the status of iodine, iron, vitamin A, and folic acid in his body through pathological examinations, he would be able to know the index of his health status. Higher index value, that is closer to unity, indicates a good health in terms of the efficiency of the body and resistance to fight common diseases. A lower value nearing zero may alarm him to be concerned about his level of micronutrients and take necessary steps accordingly. This methodology can be applied to other areas of medical sciences.

3 illus, 11 ref

000072   Daili N (Mathematics Dep, Faculty of Sciences, F. Abbas Univ, Setif, Algeria-190 00, Email: nourdaili_dz@yahoo.fr) : Analytic densities in number theory. part III: extensions to Epstein's zeta-function. Int J mathl Sci 2009, 8(3-4), 83-100.

In this paper, authors do some restrection on the P. Epstein's Zeta-function. We introduce two new densities. We will prove an equivalence theorem between those two densities. We prove that the Q - analytic density is the prolongement of the plane asymptotic density.

10 ref

000071   Chunling T;Xiaohui L;Yuasheng Y;Liping W (Computer Science and Engineering Dep, , Dalian Univ of Technology) : Irregular total labellings of some families of graphs. Indian J pure appl Math 2009, 40(3), 155-81.

An edge (A vertex) irregular total ϕ-labelling of a graph G is such a labelling of the vertices and edges with integers 1, ..., k that the weights of any two different edges (vertices) are distinct, where the weight of an edge (a vertex) is the sum of the label of the edge (vertex) itself and the labels of its incident vertices (edges). The minimum ϕ for which the graph G has an edge (a vertex) irregular total ϕ-labelling is called the total edge (vertex) irregularity strength of the graph G, tes (G) υ (G)). In this paper, we show the exact values of tes (G) and tυs (G) of some families of graphs, including the generalized Petersen graph P (n,ϕ), ladder L_n, Mobius ladder M_n, Knodel graph W_3,n, and flower snark and related graph.

11 illus, 12 ref

000070   Chitrakala Rani T;Sukumari C (NO, K.N.G. Arts College for Women, Thanjavur, Tamil Nadu) : Stochastic model for the cumulative effects of small reparable breakdown. Int Rev pure appl Math 2009, 5(2), 155-9.

The aim of this paper is to estimate the expected time to reach the breakdown point of a system due to successive occurrence of small break downs in (0, t] by using the applications of cumulative damage process.

2 illus, 2 tables, 5 ref

000069   Chandramouli A B;Gupta S;Bhargava A K (P. G. Studies and Research in Mathematics Dep, Meerut College, Meerut, Uttar Pradesh, Email: dr.bhargavaak@gmail.com) : Heuristic algorithm for 2 x n flow-shop problem for minimum total rental cost when transportation time and weight of jobs are included. Int Rev pure appl Math 2009, 5(2), 431-7.

A heuristic approach has been developed to find minimum total rental cost of 2 x n flow-shop problem in which transportation time and weight of jobs are included using Swapping method.

18 ref

000068   Chakraborty A;Dubey R P (Science and Humanities Dep, M.P.C.E.T., Kailash Nagar, Near Industial Estate, Bhilai, Durg-490 026, Email: anindita_c2005@yahoo.co.in) : Approximation of fixed point of nearly asymptotically nonexpansive mappings. Int Rev pure appl Math 2009, 5(2), 391-7.

Discusses the strong convergence theorem for the sequence of iterates for a finite family of nearly asymptotically nonexpansive mapping using an implicit iteration process.

9 ref

000067   Boniello C;Ferrentino R (Economic Sciences and Statistics Dep, Salerno Univ, Fisciano (Sa), Italy, Email: cboniello@unisa.it) : Application of the laplace transform to a particular case of ruin in ended times. J Analysis Applic 2009, 7(3), 157-66.

Author examined, within the classical Risk Theory, the problem of the calculation of the non ruin function in ended times and we try, with the aid of the Laplace transform, to find an explicit expression of it in the hypothesis of null incomes and in presence of a distribution function of the sums at risk of exponential type.

15 ref

000066   Bjaj R K;Garg G;Hooda D S (NO, Jaypee Information Technology Univ, Solan-173 215) : On restricted fuzzy linear regression model. Int Rev Fuzzy Math 2009, 4(1-2), 11-23.

A fuzzy linear regression model is considered where the explanatory variables are crisp and study variable is fuzzy in nature. It is assumed that some prior information is available on some regression coefficients in terms of linear restrictions. This prior information is used in estimating the regression coefficients. Through simulation study it is shown that the obtained restricted estimator is better than the unrestricted estimator in some sense of dominance.

15 ref

000065   Bisht M S (Mathematics Dep, H.N.B. Garhwal Univ, Campus Srinagar, (Garhwal), Uttarakhand-246 174) : Stability of superposed viscoelastic fluids in the presence of suspended particles through porous medium. J Mount Res 2009, 4(Dec), 65-76.

Studies the stability of superposed viscous-viscoelastic fluid in the presence of suspended particles through porous medium in which the density of viscous liquid varies exponentially negative. The instability in the porous medium of a place interface between viscous (Newtonian) and visco-elastic fluid containing suspended particles may be of interest in Geophysics, Chemical technology and Biomechanicsand is therefore studied in the present paper. The affects of a variable horizontal magnetic field and uniform rotation bearing relevancy in Geophysics are also considered.

15 ref

000064   Bhargava A K;Chandramouli A B;Gupta S (P.G. Studies and Research in Mathematics Dep, M.M.H. College, Ghaziabad, Email: dr.bhargavaak@gmail.com) : Heuristic approach to find the effect of probabilistic break down on minimum total rental cost and flow-time with stochastic processing time. Int J mathl Sci 2009, 8(1-2), 45-54.

Developed a heuristic method of 2 x n flowshop production scheduling problem in which break down of machines is probabilistic nature. To find minimum total rental cost, C.S. Swapping method is used.

19 ref

000063   Basugade A N;Rattihalli R N (Statistics Dep, Gopal Krishna Gokhale College, Kolhapur, Maharashtra, Email: anb9@rediffmail.com) : Class of selfinvertible densities. Int Rev pure appl Math 2009, 5(2), 283-92.

Some well-known statistical methods to generate a class of distributions are transformation of variables, truncation, introducing of additional parameter or the use of contour transformation. Proposes a class of densities on (0, ∞) such that the inverse of the density function is the density function itself. Studied some of their properties and illustrative examples were given. For the family of density given in (3.5) obtained maximum likelihood estimator and a moment estimator of the parameter a. Based on simulations, the performances of the proposed estimators have been studied.

3 illus 1 table, 6 ref

000062   Baruah P K;Venkatesulu M (Mathematics and Computer Science Dep, Sri Sathya Sai Univ, Prasanthinilayam, Email: baruahpk@ssu.edu.in) : Spectrum of a pair of ordinary differential operators with a matching interface conditions. Int Rev pure appl Math 2008, 4(1), 39-49.

The study of a pair of differential operators with matching interface conditions is found in the literature. These are useful to study many physical problems like propagation of acoustic waveguides in oceanography, study of step index fiber in optical fiber communication, one dimensional scattering in quantum theory, etc. Here we initiate our effort towards the study of the spectrum of such operators. In the last section of this paper we show the continuous spectrum of two physical problems namely the acoustic waveguides problem and the one dimensional scattering of particle in quantum theory.

18 ref

000061   Baruah P K;Bharadwaj B V K;Venkatesulu M (Mathemtics and Computer Science Dep, Sri Sathya Sai Univ, Prashanthi Nilayam, Andhra Pradesh-515 134) : Characterization of maximal, minimal and inverse operators and existence theorem for coupled ordinary differential operator. Int J Math Analysis 2009, 1(1), 57-82.

In the study of convection heat transfer, coupled oscillations, etc., we encounter a new class of Boundary Value Problems (BVPs) associated with a coupled system of Ordinary Differential Equations (ODEs) of the form L₁f) + M₁(g) = N₁ and L₂(f) + M₂(g) = N₂, where L₁, M₁, L₂ and M₂ are linear ordinary differential operators of orders n₁m₁, n₂ and m₂ respectively, defined on an interval [a, b], and N₁ andN₂ are nonlinear functions off and its derivatives up to order max (n₁ - 1,n₂ - l) and g and its derivatives up to order max (m₁ - 1, m₂ - 1). In the literature there does not seem to exist a systematic study of these BVPs. Before embarking upon a study of these nonlinear BVPs, it is fundamentally important to know about the associated linear BVPs. There are a lot of operators falling in between the extreme operators (maximal and minimal operators which we have discussed). In this paper, we actually study one such operators with which the BVP involving the Coupled Ordinary Differential Equations is associated, and we have finally stated and proved a basic existence-uniqueness theorem for a BVP associated with a coupled linear system. In general, for the study of IVPs for ordinary differential equations, one can follow either the classical approach or the functional theoretic approach. But we adopt the later, for it provides the sound base for further development, especially of nonlinear BVPs.

6 ref

000060   Baruah P K;Bharadwaj B V K;Venkatesulu M (Mathematics and Computer Science Dep, Sri Sathya Sai Univ, Prasanthinilayam-515 134) : Green's matrix for linear coupled ordinary differential operator. Int J Math Analysis 2009, 1(1), 25-56.

Characterize the inverse of the coupled ordinary differential operator, discuss the properties of it. Using these properties we define the Green's matrix for the operator. Then analyse the properties of the Green's matrix which leads to it's representation. Finally we have given a stepwise method, to obtain a Green's matrix for a particular linear coupled ordinary differential operator.

6 ref

000059   Bahl S;Sanjay Kumar (Statistics Dep, M.D.U., Rohtak, Haryana) : Estimation of ratio and regression estimator in two stage stratified sampling design using SRSWOR at first stage units and PPSWR at second stage units. Int Rev pure appl Math 2008, 4(1), 59-68.

Estimator for estimating finite population ratio and regression for two stage stratified sampling scheme using auxiliary information and PPS sampling at second stage is proposed. The variance of proposed ratio and regression estimators is calculated.

8 ref

000058   Babujee J B;Joshi A (Mathematics Dep, Anna Univ, Chennai-600 024, Email: baskarbabujee@yahoo.co.in) : Topological indices of some chemical trees. Int Rev pure appl Math 2009, 5(2), 189-96.

Molecules and molecular compounds are often modeled by molecular graphs. One of the most widely known topological descriptor is the Wiener index and is defined as the half sum of the shortest distance between every pair of vertices in G. The term Σd_i² is known as first Zagreb index Z_g and the degree of v_i = d_i. Obtained the exponential relationship between W and Z_g for some molecular acyclic graphs and obtained the relationship between Estrada index and Wiener index for the same graphs.

6 illus, 3 ref

000057   Babujee J B;Jagadesh R (Mathematics Dep, Anna Univ, Chennai-600 025, Email: baskarjee@yahoo.com) : Prime laveling for connected graphs. Int Rev pure appl Math 2008, 4(1), 69-79.

A graph with Vertex set V is said to have prime labeling if there exist a bijection f: V(G) → {1,2, ..., |V|} such that for each edge xy ∈ E(G),f(x) and f(y) are relatively prime. In other words the greatest common divisor of f(x) and f(y) denoted by gcd (f(x), J[y)) = 1. In this paper we prove that Triple star K_1,n,n,n, Bistar-B_n,n+1, (P_m ∪ nK₁) + N₂, (C_m ∪ nK₁) + N₂ (C _m∪ nK₁∪ P_r) and K_1,n,n,n,Bistar -B _n,n+1, (P_m∪nK₁) + N₂,( C_m∪nK₁) (C_{m1rhas prime labeling.}

1 illus, 5 ref

000056   Babjuee J B;Shobana L (Mathematics Dep, Anna Univ, Chennai-600 025, Email: baskarbabujee@yahoo.com) : Prime cordial labeling. Int Rev pure appl Math 2009, 5(2), 277-82.

A prime cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, ..., V} such that if each edge uv is assigned the label 1 if gcd (f(u),f(v)) = 1 and 0 if gcd (f(u),(v)) > 1, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by almost 1. Proves the existence of prime cordial labeling for sun graph, kite graph and coconut tree.

5 ref

000055   Ayyappan G;Subramanian A M G;Sekar G (NO, Pondicherry Engineering College, Pondicherry, Email: ayyappanpec@hotmail.com) : M/M/1 retrial queueing system with breakdowm and repair of service under non-pre-emptive priority service. Int Rev pure appl Math 2009, 5(2), 333-53.

Consider a single server retrial queueing system with breakdown and repair under Non-pre-emptive priority service in which two types of customers arrive in a Poisson process with arrival rate λ₁ for low priority customers and A, for high priority customers. Further assume that the service times follow an exponential distribution with parameters (μ₁, andμ₂ for two types of customers respectively. The breakdown of service follows an exponential distribution with parameter a and repair of service follows an exponential distribution with parameter p. The retrial is introduced for low priority customers only. Let K be the maximum number of waiting spaces for high priority customers in front of the service station. The high priority customers will be governed by the Non-preemptive priority service. We assume that the access from orbit to the service facility is governed by the classical retrial policy. This model is solved by using Matrix geometric Technique. Numerical study have been done for Analysis of Mean number of low priority customers in the orbit (MNCO), Mean number of high priority customers in the queue(MPQL),Truncation level (OCUT),Probability of server free and Probabilities of server busy with low and high priority customers and probability of server in breakdown for various values of λ₁,λ₂, μ₁,μ₂, α, β and σ in elaborate manner and also various particular cases of this model have been discussed.

15 ref

000054   Ansari Piri E;Zohri A (Mathematics Dep, Guilan Rasht Univ, Iran, Email: e_ansari@guilan.ac.ir) : Approximating sets in commutative Frechet algebras. J Analysis Applic 2009, 7(2), 85-90.

In normed algebras, the bounded approximating sets provide bounded approximate identity which; are more usefull for many purposes. Investigates some properties of approximating sets in normed algebras and generalize them for Frechet algebras.

5 ref

000053   Amudhambigai B;Jafari S;Uma M K;Roja E (Mathematics Dep, Sri Sarada College for Women, Salem-16, Tamil Nadu) : Notions via ρ-generalized Fuzzy preopen sets. Int Rev Fuzzy Math 2009, 4(1-2), 25-36.

The concepts of r-generalized fuzzy preborder, r-generalized fuzzy preexterior and r-generalized fuzzy prefrontier in the sense of Sostak[7] and Ramadan [3] are introduced. Some interesting properties and characterizations of them are investigated. Interrelations among the concepts introduced are studied with relevant examples.

11 ref

000052   Ahmadi S;Pralhad R N (Mathematics Dep, Pune Univ, Ganesh Khind Road, Pune-411 007, Email: s_ahmadi@iau-tnb.ac.ir) : Effect of explosion on avalanche dynamics. Int Rev pure appl Math 2009, 5(2), 293-302.

Flow of an artificial release of an avalanche has been modeled from the concepts of underwater explosions dynamics with appropriate modifications to the studies. Numerical approach has been adopted for observing effect of density (ρ), viscosity (μ), eddy viscosity (η|), and snow slab height (H), on flow parameters with appropriate initial and boundary conditions from the concepts from Fracture Mechanics. One of the added advantages of the present model over the earlier models is that, the present model accounts for the concepts of residual stress and gravitational stress in the basic momentum equations. The results indicate that, the model gives higher results in comparison to the natural release of avalanches. In addition to the above, the model has been studied for the rate of mass flow, which is generally one of the flow parametric requirements at the time of design of control structure for the avalanches.

3 illus, 3 tables, 8 ref

000051   Agrawal R R;Siddiqui M A (NO, M.P. Christain College of Engg. and Technology, Bhilai, Chhatisgarh, Email: raksha_mukesh@yahoo.com) : Approximation of beta type linear positive operators. Int Rev pure appl Math 2009, 5(2), 379-84.

Introduces a sequence of linear positive operators of beta type. Using the Bhoman Korovkin uniform convergence criterion proves theorem on convergence. In addition gives some estimates by these operators.

5 ref

000050   Agrawal A;Ghatol A A;Agrawal V P;Nayse S (NO, BITS, Pilani, Goa Campus) : Structural modeling & analysis of medical image diagnosis system: a graph theoretic approach. Int Rev pure appl Math 2009, 5(2), 197-228.

An attempt has been made to develop an integrated systems model for the structure of the medical image diagnosis system (MIDS) in terms of its different components and interactions between them using graph theory & matrix algebra. The complete MIDS is viewed as a system which is comprised of a number of subsystems. All such subsystems are identified which are responsible for the overall performance of a diagnosis procedure. The MIDS is thus defined in terms of all of its concerned structural constituents. All the possible interactions, interdependencies, influence and effects between different subsystems are shown in the block diagram form. A classification of all the subsystems and their sub subsystems have been detailed in a hierarchical tree form. This non-mathematical model is then modeled mathematically using different approaches, first with the help of graph theory, then by a variable adjacency matrix and finally by a unique representation multinomial known as a permanent function. A graphical representation of distinct terms of different groups and subgroups is given and the interpretation of the graphical representations as subsets of real life situation are explored. The permanent function helps to carry out the structural analysis of the diagnosis system in terms of strength, weakness, improvement, and optimization by correlating the properties of a medical imaging system with its structure. A physical meaning has been associated with each term of the permanent function. All of the terms in (N + 1) groups are arranged in standard œ (sigma) format. Generalization of the permanent matrix and its permanent function are also presented. The coefficients of similarity and dissimilarity are identified and compared. A top-down approach for complete analysis of a medical image diagnosis system is given. Who will be the beneficiaries from this has also been indicated. Finally a step-by-step approach has been proposed in this paper to help generate a new algorithm for software coding.

7 illus, 3 tables, 34 ref

000049   Adhami A Y;Bari A;Rabbani Q (Statistics and Operations Research Dep, Aligarh Muslim Univ, Aligarh, Email: yusufstats@gmail.com) : Algorithm for the mixed-integer concave qudratic bilevel programming problem. Int Rev pure appl Math 2009, 5(2), 355-61.

Gives an algorithm to solve mixed integer concave quadratic bilevel programming problems where leader tries to minimize a concave quadratic objective function with mixed-integer decision variables. The follower's objective function is a linear function in continuous decision space. At the end, numerical example is given to illustrate the algorithm.

13 ref

020002   Sharma R K (Mathmatics Dep, PSIT, Kanpur, Email: rjmthspsit@gmail.com) : Estimation of mortality of an urban population. Indian J scient Res 2010, 1(1), 75-6.

Mortality is an important factor of population change. The study of mortality is useful for analyzing the current conditions. An attempt has been made to evaluate the current mortality measures such as CDR, IMR,ASMR etc. for an urban population through analysis of data obtained on mortality survey of 500 sample urban households.

2 illus, 1 table, 5 ref

020001   Kannan R;Thirumurugan A;Sathiyamoorthi R; Malarvizhi G (Statistics Dep, Annamalai Univ, Annamalainagar-608 002) : Stochastic model with antigenic diversity threshold of HIV transmission using order statistics. Biosci Res Bull 2010, 26(1), 45-55.

Focuses on the study of a stochastic model for predicting the seroconversion time of HIV transmission using order statistics. In the estimation of expected time to seroconversion, there is an important role for the inter-arrival times between successive contacts and it has a significant influence. It is assumed that the inter-arrival times between the contacts distributed as the smallest order statistics. The mean time to seroconversion and its variance are derived and numerical illustration is provided.

4 illus, 4 tables, 5 ref

020000   Jayakumar S;Arunraj B (Mathematics Dep, A V V M Sri Puspam College, Poondi-613 503) : Evaluating the medical diagnosis system with an emphasis on related environmental factors using fuzzy modeling. Biosci Res Bull 2010, 26(1), 57-67.

Used the fuzzy relation on evaluating the diagnosis system with an emphasis on related environmental factors. In the modern concept, disease is due to a disturbance in the delicate balance between man and his environment. The influence of age on susceptibility and the complicated environment in which he is living are considered more crucial in disease arise. An attempt has been made in certain level to enlighten those hidden points. For this, we formed an index for the diagnosis and its related factors, which is based on the multistep transmission process of fuzzy relation.

7 tables, 5 ref

014675   Zahran A M;Zeyada F M;Azab Abd-Allah M;Khalaf M M (Mathematics Dep, Faculty of Science, Al Azhar Univ, Assiut, Egypt) : Separation axioms in L-fuzzifying topology. Far East J mathl Sci 2008, 31(3), 447-69.

Introduced and study T0-, T1-, T₂ (Hausdorff)-, T3 (regularity)-, T₄ (normality)-, R0-, R1 -separation axioms in Z-fuzzifying topology where L is a complete residuated lattice. Sometimes we add more conditions on L such as the completely distributive law or the double negation law.

13 ref

014674   Yadav S;Prasad B (Mathematics Dep, D.A.V. P.G. College, Azamgarh, Uttar Pradesh) : Shock formation in the presence of entropy gradients in magnetic field. Acta Cienc Indica-Math 2009, 35(3), 997-1007.

The steepening of a normal compression wave into a shock in a homentropic flow field is understood well through the method of characteristics. In a non-homentropic flow field, however, shock formation from a compression wave is more complex. The effects of entropy (or sound speed) gradients on a shock formation from a compression wave are determined using a wave front expansion in Cartesian and in spherical polar coordinates in magnetic field. The latter problem has application to the intense energy focusing of sonoluminescence, particularly when applied to a spherically collapsing gas. The principal result is an analytical criterion for the time and place of shock formation, for a wave propagating into a magnetic field of smoothly varying entropy.

7 ref

014673   Yadav R B S;Rai B N;Singh B N P (P.G. Dep of Maths, M.U., Bodh-Gaya, Bihar) : Investigation on red shift and behaviour of a test practical in general relativity. Acta Cienc Indica-Math 2009, 35(3), 943-5.

The present paper provides an investigation on red shift and behaviour of a test practical by taking a suitable metric in general relativity.

4 ref

014672   Wang T;Zhou W;Zhang X (College of Fundamental Studies, Shanghai Univ of Engineering Science, Shanghai 201620, P.R. China) : Mean square exponential stability of uncertain nonlinear time delay neutral systems with markovian jumping parameters. Far East J mathl Sci 2008, 31(3), 501-13.

This paper studies the problem of mean square exponential stability (MSBS) for a class of uncertain nonlinear time delay neutral systems with Markovian jumping parameters by the method of constructing Lyapunov-Krasovskii function. The system under consideration is subjected to time delay in the state and bounded nonlinear term. Our attention is to obtain sufficient conditions which ensure the system is MSES and shows that a robust stabilizing state feedback controller can be constructed through solving a couple of linear matrix inequalities.

9 ref