000052   Boikanyo O A;Choudhary B (Mathematics Dep, Botswana Univ, Private Bag 0022, Gaborone, Botswana, Email: boikanyoa@yahoo.co.uk) : Two common fixed point theorems for weakly compatible mappings satisfying a general contractive condition of integral type. Far East J mathl Sci 2008, 30(3), 437-56.

The first important result on fixed points for contractive type mappings is the well-known Banach Fixed Point Theorem. Branciari [3] established a fixed point theorem for mappings on complete metric spaces satisfying a contractive inequality of integral type. In this paper, we prove two fixed point theorems for weakly compatible mappings on metric spaces satisfying a general contractive inequality of integral type.

9 ref

000051   Bhowmik M;Pal M (Applied Mathematics with Dep, Oceanology and Computer Programming, Vidyasagar Univ, Midnapore-721 102, Email: monoranjan_bhowmik@rediffmail.com) : Generalized intuitionistic fuzzy matrices. Far East J mathl Sci 2008, 29(3), 533-54.

Generalized intuitionistic fuzzy matrices (GIFMs) are defined. In fact, all GIFMs are intuitionistic fuzzy matrices (IFMs) but all IFMs are not GIFMs. Also, some operations are valid for IFMs but they are not valid for GIFMs. The relational properties, i.e., four types of reflexivity and irreflexivity, symmetricity and transitivity are studied here. Finally, some new operations over GIFMs are studied here.

29 ref

000050   Bhoosnurmath S S;Prasad K S L N (Mathematics Dep, Karnatak Univ, Dharwad-580 003, Email: ssbmath@gmail.com) : Value distribution of some differential polynomials. Bull Calcutta Mathl Soc 2009, 101(1), 55-62.

Value distribution theorem for meromorphic functions having few poles from which we obtain several interesting results which improve some results of W. Doeringer, C.C. Yang, A.P. Singh, G.P. Barker and others.

14 ref

000049   Bera G H (Mathematics Dep, St. Paul's Cathedral Mission College, 33/1, Raja Rammohan Roy Sarani, Kolkata-700 009, Email: g_bera@rediffmail.com) : Numerical solution of some integral equations arising in elasticity theory. Bull Calcutta Mathl Soc 2009, 101(2), 181-6.

Simple method based on a polynomial approximation of a function is employed to obtain approximate solution of some Fredholm's integral equations of second kind arising in elasticity theory. The numerical results obtained by the present method, when compared with results available in the literature, show the usefulness of the method.

2 illus, 2 tables, 6 ref

000048   Bassey U N (Mathematics Dep, Ibadan Univ, Ibadan, Nigeria, Email: unbassey@yahoo.com) : Theorem on sequential convergence. Far East J mathl Sci 2008, 30(2), 221-5.

Let E := (E, τ) be a locally convex algebra with identity, β(x) denote the radius of boundedness of an element x in E, and D(E) denote the set of all elements x ∈ E such that β(x) < 1. If E is pseudo-complete, then prove that every τ-convergent sequence of elements x_n ∈ D(E) is Mackey-convergent.

9 ref

000047   Basavanagoud B;Mathad V N (Mathematics Dep, Karnatak Univ, Dharwad-580 003, Email: bgouder1@yahoo.co.in) : On pathos qlick graph of a tree. Proc Natn Acad Sci India-Sect A 2008, 78(Pt 3), 219-23.

The concept of pathos qlick graph is introduced to study on trees. Presents a characterization of the graphs whose pathos qlick graphs are Hamiltonian, Eulerian, planar, outerplanar, minimally nonouterplanar and maximal outerplanar.

2 illus, 7 ref

000046   Banerjee D;Dutta R K (Mathematics Dep, Visva-Bharati, Santiniketan-731 235, Email: dibyendu192@rediffmail.com) : Relative order of functions analytic in the unit disc. Bull Calcutta Mathl Soc 2009, 101(1), 95-104.

Author considered relative order of a function analytic in the unit disc with respect to an entire function and after proving several theorems, presents an integral representation of the relative order.

5 ref

000045   Bali R;Gupta R (Mathematics Dep, Rajasthan Univ, Jaipur-302 004, Email: balir5@yahoo.co.in) : Bianchi type IX non-static barotropic perfect fluid cosmological model in general relativity. Proc Natn Acad Sci India-Sect A 2008, 78(Pt 3), 225-9.

Bianchi type IX barotropic perfect fluid cosmological models are investigated assuming that shear (σ) is proportional to the expansion (φ). This leads to a = bⁿ where a and b are metric potentials and n is the constant. For the realistic picture of the universe in terms of cosmic time t, n = 2 and 3/2. The physical and geometrical aspects of the models are discussed in detail.

8 ref

000044   Badshah V H;Meena G (Mathematics Dep, Vikram Univ, Ujjain-456 010) : Common fixed point theorems for a pair of semi compatible self maps in a sequentially compact D-metric space. Ultra Scient phys Sci 2008, 20(1), 149-56.

The aim of this paper is to obtain a common fixed point theorem for the pair of semi-compatible self maps in a sequentially compact D-metric space, one of them is continuous and by using a functional inequality.

8 ref

000043   Assale L A;Boni T K;Nabongo D (Institut National Polytechnique Houphouet-Boigny de Yamoussoukro, BP 1093 Yamoussoukro, Cote d'Ivoire, Email: assale@inphb.edu.ci) : Numerical quenching for a quasilinear parabolic equation. Far East J mathl Sci 2008, 29(3), 613-27.

Deals with the study of the numerical approximation for the following initial-boundary value problem {u_t = (φ(u_x))_x -u^-p, x ∈ (0, 1), t ∈ (0, T), u_t(0, t) = 0, (u_x(1, t) = 0, t ∈ (0, T), u(x, 0) = u₀(x) > 0, x ∈ [0, 1], where p > 0, ϕ(s) is positive, increasing and sϕ"(s) ≤ 0 for positive values of s. We show that the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its semidiscrete quenching time. We also prove that, under some assumptions, the semidiscrete quenching time converges to the real one when the mesh size goes to zero. Finally, we give some numerical experiments to illustrate our analysis.

2 tables, 16 ref

000042   Alaca A;Alaca S;Williams K S (Centre for Research in Algebra and Number Theory, School of Mathematics and Statistics, Carleton Univ, Ottawa, Ontario, Canada K1S 5B6, Email: aalaca@connect.carleton.ca) : Liouville's sextenary quadratic forms. Far East J mathl Sci 2008, 30(3), 547-56.

Liouville's asserted formulae for the number of representations of a positive integer by each of the sextenary quadratic forms x² + y² + z² + t² + 2u² + 2v², x² + y² + 2z² + 2t² + 2u² + 2v² and x² + 2y² + 2z² 2t² + 2u² + 4v² are proved.

8 ref

000041   Ahmed N;Barua D P (Mathematics Dep, Gauhati Univ, Guwahati-781 014) : Magnetohydrodynamic three dimensional inclined flow past a porous plate with variable suction and sinusoidal temperature in presence of a heat sink. Far East J mathl Sci 2008, 30(2), 325-57.

The problem of a three dimensional inclined flow of a viscous incompressible electrically conducting fluid past an infinite inclined porous plate with variable suction in the presence of a heat sink, a uniform free stream and a uniform magnetic field applied in a direction normal to the plate is considered. The heated plate is subjected to a variable temperature distribution across its breadth together with first order velocity slip conditions; the slip parameter being very small. The expressions for the velocity and temperature fields are obtained. Further, the expressions for the skin friction at the plate in the main flow and transverse flow directions, the rate of heat transfer at the plate in terms of the Nusselt number are obtained in non-dimensional forms. The natures of the aforementioned expressions are demonstrated in figures and tables for different values of the parameters involved.

9 illus, 22 tables, 14 ref

023515   Warbhe M S;Khobragade N W (Mathematics Dep, MJP Educational Campus, RTM Nagpur Univ, Nagpur-440 033) : Transient thermoelastic problem of a thin circular plate due to partially distributed heat supply. J Indian Acad Math 2008, 30(2), 447-55.

In this paper, an attempt is made to determine the temperature, displacement and stress functions at any point of a thin circular plate of thickness 2h occupying the space D : {O ≤ r ≤ a,-h ≤ z ≤ h} ∈ R³, where r = √x² + y², with the stated boundary conditions by applying finite Marchi-Fasulo integral transform and Laplace transform techniques.

6 ref

023514   Victorbabu B R;Sivalinga Prasad P (Statistics Dep, Acharya Nagarjuna university, Guntur-522 510, Email: victorsugnanam@yahoo.co.in) : Construction of four and six level second order rotatable designs using incomplete block designs with unequal block sizes. Int J agric statist Sci 2009, 5(1), 1-11.

Construction of four and six level second order rotatable designs using symmetrical unequal block arrangements with two unequal block sizes is suggested. It is observed that this method leads to designs with lesser number of design points in some cases.

3 tables, 11 ref

023513   Unhale S I;Chaudhary M S (Mathematics Dep, Maharashtra College of Arts, Commerce, and Science, Mumbai-400 008, Email: a-subhash@indiatimes.com) : On distributional generalized laplace transformation. J Indian Acad Math 2008, 30(2), 403-12.

The object of this paper is to obtain the inversion formula and uniqueness theorem for the distributional generalized Laplace transformation.

3 ref

023512   Tyagi V K;Goel S (Statistics Dep, M.M. (P.G.) College, Modinagar-201 204, Email: vnaytyagi@gmail.com) : Profit analysis of three unit cold standby system with correlated failures and repairs. Int J agric statist Sci 2009, 5(1), 123-30.

Three-unit standby system is discussed wherein two units are operative and arranged in series and one is cold standby. On the failure of a unit, inspection is carried out to detect whether the unit needs to be replaced or can be repaired. Also the failure and repair times of each unit are assumed to be correlated by taking their joint density as a bivariate exponential. Various measures of system effectiveness are obtained by making use of regenerative point technique.

3 illus, 9 ref

023511   Talawar A S;Wali K S (Statistics Dep, Karnatak University, Dharwad-580 003, Email: Talwar_as@hotmail.com) : Epidemic model of intermediate class with initial preventive measure. Int J agric statist Sci 2009, 5(1), 35-41.

Birth and death process in the population are usually assumed to be independent of the disease status, however, the survival and reproduction of a host can be affected by an infectious disease. One way of protecting the newborns and susceptible population from disease is the reduction of number of susceptible individuals through immunizations (by means of vaccinations). Hence in the present paper, we considered the epidemic model of the intermediate classes (SEIR) with Initial Preventive Measure. We have formulated both deterministic and stochastic versions of the model. The model is analyzed with the help of basic reproductive rate (R_φ and compared it with that in the absence of initial preventive measure. We have also shown that the Kolmogorov differential difference equations in the model can be solved mathematically by applying the method proposed by Billard (1974).

11 ref

023510   Sundar P;Sadhasivam V (Mathematics Dep, Kandaswami Kandar's College, Velur-638 182) : Oscillation criteria for second order natural difference equations with positive and negative coefficients. J Indian Acad Math 2008, 30(2), 515-32.

Concerned with the following class of forced second order netural difference equations with positive and negative coefficients of the form Δ² [x(n) ± Σ^l_{i = 1} c_i(n) x(n-τ_i)] + Σ^M_{i = 1} P_I(n)x(n-δ_i) - Σ^r_{i = 1} q(v>i(n)x(n-σ_i) = f(n), n↑ n_o (*). Sufficient conditions have been obtained for the oscillation of both bounded and unbounded solutions of (*). Several examples are inserted to illustrate the results.

15 ref

023509   Subramanian C (Statistics Dep, Annamalai University, Annamalai Nagar-608 002, Email: manistat@yahoo.co.in) : Designing quick switching system-3 through the inflection point. Int J agric statist Sci 2009, 5(1), 107-12.

Romboski has studied the quick switching system (QSS) by taking pairs of single sampling plan. Designing procedure for QSS-3 (n; C_n, C_T) given p^* and h^* is discussed. Numerical illustration is also presented.

2 tables, 8 ref

023508   Srivastava K K;Rai V N;Dube L K (Maths & Statistics Dep, N.D. Univ. of Agric. & Tech., Kumarganj, Faizabad-224 229, Email: lkdube04@yahoo.com) : Goodman's technique approach for heating of a solid cylinder under the influence of periodic temperature. Int J agric statist Sci 2009, 5(1), 199-203.

Deals with a mathematical model for drying of a solid cylinder. The dimensionless temperature distribution expression is obtained by using the extension of Goodman 's technique. For quasi-steady state the expressions for dimensionless temperature distribution, their average values and generalized time rate of average values are obtained. The specific heat rate and heat utilization factor are calculated for thin cylinder.

5 ref

023507   Srinivasan S;Sulaiman A;Sathiyamoorthi R (Mathematics Dep, B.S.A. Crescent Engineering College, Chennai-600 048) : Estimation of the expected time to reorder in inventory control. J Indian Acad Math 2008, 30(2), 425-33.

In inventory control problems, the objective is to determine the optimal size of the inventory or the optimal reorder size, given the related costs. The depletion of the inventory takes place due to the demands at the successive random epochs. The reorder point or critical inventory level is a fixed one and reorders are made when inventory on hand reaches this level. In this paper an estimate of the time at which the stock level will come down to the critical inventory level is determined using the shock model approach. Numerical illustrations are also provided.

4 ref

023506   Srinivasa Rao V;Srinivasa Rao K;Vivekananda Murthy M (Statistics & Mathematics Dep, Agricultural College, Bapatia, Guntur-522 101, Email: vs_raoin@yahoo.co.in) : Complete three graded stochastic model. Int J agric statist Sci 2009, 5(1), 305-15.

Manpower planning is very much useful for human resource management in large organizations. This paper deals with a three graded manpower planning model having direct recruitment in all grades with an assumption that the recruitment process, promotion process and leaving processes are considered as Poisson. By using the difference- differential equations the transient and steady- state behaviour of the model is developed and analysed in the light of the parametric' values. The average grade size of the employees, the grade size variability and the covariance of the grade sizes are simulated.

3 tables, 9 ref

023505   Srihari K;Kishan N;Anand Rao J (Mathematics Dep, Mahatma Gandhi Institute of Technology, Gandipet, Hyderabad) : MHD three dimensional couete flow through a porous medium with heat transfer and viscous dissipation. J Indian Acad Math 2008, 30(2), 567-85.

The Couette flow of a viscous incompressible fluid through a porous medium between two infinite horizontal parallel porous flat plates is considered, taking into account viscous dissipative heat under the influence of transverse magnetic field. The stationary plate and the plate in uniform motion are subjected to transverse sinusoidal injection and constant suction of the fluid respectively. The flow becomes three-dimensional due to this type of injection velocity. The governing equations of the motion are solved by using finite difference method. In the presence of magnetic field, the effect of injection parameter R_e, permeability parameter K on main flow, cross flow and skin friction components are described graphically. Temperature profile and numerical values of heat transfer coefficient N_u of air and water in the presence of dissipative heat are given, to observe the effects of various flow parameters encountered in the equations.

8 illus, 2 tables, 11 ref

023504   Srihari K;Kishan N;Anand Rao J (Mathematics Dep, Mahatma Gandhi Institute of Technology, Gandipet, Hyderabad) : MHD three dimensional couette flow through a porous medium with heat transfer and viscous dissipation. J Indian Acad Math 2008, 30(2), 371-88.

The Couette flow of a viscous incompressible fluid through a porous medium between two infinite horizontal parallel porous flat plates is considered, taking into account viscous dissipative heat under the influence of transverse magnetic field. The stationary plate and the plate in uniform motion are subjected to transverse sinusoidal injection and constant suction of the fluid respectively. The flow becomes three-dimensional due to this type of injection velocity. The governing equations of the motion are solved by using finite difference method. In the presence of magnetic field, the effect of injection parameter R_e, permeability parameter K on main flow, cross flow and skin friction components are described graphically. Temperature profile and numerical values of heat transfer coefficient N_u of air and water in the presence of dissipative heat are given, to observe the effects of various flow parameters encountered in the equations.

10 illus, 20 tables, 11 ref

023503   Singh Y (Statistics Dep, University of Rajasthan, Jaipur-302 004) : On duals of some partially balanced incomplete block designs. Int J agric statist Sci 2009, 5(1), 43-7.

Purpose is to discuss duals of some two associate class partially balaned incomplete block (PBIB) designs.

1 table, 12 ref

023502   Sharma V D;Gudadhe A S (Mathematics Dep, Arts Commerce & Science College, Kiran Nagar, Amravati, Email: alka_gudadhe@yahoo.com) : Scale invariant optical correlation. J Indian Acad Math 2008, 30(2), 469-76.

In the recent years fractional calculus is a flourishing field of active research. The fractional transform has been rediscovered in quantum mechanics, in optics and in signal processing recently. The fractional Fourier transform is rich in applications covering number of subjects like optics, signal processing, image reconstruction, pattern recognition, tomography etc. In pattern recognition correlation provides information concerning the translation of the pattern. The role of correlation is well known in object recognition. Fractional Fourier, fractional Mellin based correlation control and estimate specific ranges. In particular fractional Fourier transform is used to control the ranges of translation where as fractional Mellin transform is used to control ranges of rotation and scaling. The aim of present paper is to introduce distributional fractional Mellin transform with analytically theorem Inversion and Uniqueness theorem are also proved.

7 ref

023501   Sharma P;Awasthi J (Mathematics & Astronomy Dep, Lucknow Univ, Lucknow-226 007, Email: poonambaba@yahoo.com) : Some classes of univalent analytic functions with respect to symmetric points having negative coefficients. J Indian Acad Math 2008, 30(2), 457-68.

Paper deals with two classes Ts (α,β) and Ts (α,β) which are subclasses of starlike and convex functions with respect to symmetric points. Coefficients theorems, distortion theorems, closure theorems are obtained for these two classes. Also convex linear combination, radii of convexity are obtained for these two classes.

6 ref

023500   Satheesh S;Sandhya E (NO, , Neelolpalam, S. N. Park Road, Trichur-680 004, Email: ssatheesh1963@yahoo.co.in) : Geometric gamma max-infinitely divisible models. Int J agric statist Sci 2009, 5(1), 99-105.

Transformation of gamma max-infinitely divisible laws viz., geometric gamma max-infinitely divisible laws is considered in this paper. Some of its distributional and divisibility properties are discussed and a random time changed extremal process corresponding to this distribution is presented. A new kind of invariance (stability) under geometric maxima is proved and a max-AR(l) model corresponding to it is also discussed.

11 ref

023499   Ramaraj T;Nirmala G (Mathematics Dep, A.V.V.M. Sri Pushpam College, Poondi-613 503) : Advantage of genetic algorithm with neuro fuzzy network. J Indian Acad Math 2008, 30(2), 359-69.

Optimization is an esoteric technique used only in the History of Mathematics and Operations research activities. With the advent of computers, optimization has became a part of Computer aided design activities. Genetic Algorithms are stochastic in nature with statistical probabilistic transition rules. Usually GA keeps a pool of chromosomes at the same time and these chromosomes can evolve with the Genetic operators. After a number of generations the population will contain hopefully, chromosomes with better fitness values. Even under the best conditions only local optimal solution can be expected. As a numerical example, a design problem of a chemical process is used. This problem has three design variables and two responses. The Multiple Adaptive Neuro Fuzzy Inference System (MANFIS) network is used to model the response surfaces of this process. There are two output nodes corresponding to the two responses, which can be viewed as consisted of two independent ANFIS networks.

6 illus, 3 tables, 7 ref

023498   Rama Mohan S;Verma S M;Reddy Y R;Raju G S S (Operations Research & S. Q. C. Dep, Rayalaseema University, Kurnool-518 002, Email: seeverma@rediffmail.com) : Reliability indices for 3-unit system in the presence of chance CCS failures. Int J agric statist Sci 2009, 5(1), 297-304.

Discusses the presence of chance common cause shock failures in addition to individual failures in system reliability analysis. The formulae for system reliability and Mean Time Between Failures (both series and parallel configurations) are derived for a three unit identical system which is affected by chance common cause shock failures in addition to individual failures. Also, these measures are compared in the presence of chance CCS failures as well as individual failures with that of the situation when chance CCS failures are not affecting the system. Numerical illustrations are also given in this paper to support the model.

3 illus, 2 tables, 5 ref

023497   Rajesh N (Mathematics Dep, Kongu Engineering College, Perundural, Erode-638 052, Email: nrajesh_topology@yahoo.co.in) : On b-locally closed sets in bitopological spaces. J Indian Acad Math 2008, 30(2), 551-6.

The purpose of this paper is to introduce the notions of b-locally closed sets, blc*-sets, blc**-sets in bitopological spaces and some different notions of pairwise LC-continuous functions namely, pairwise bLC-contiriuous functions, pairwise bLC*-continuous functions, pairwise bLC**-continuous functions. Several examples are provided to illustrate the behaviour of these new classes of sets and functions.

4 ref

023496   Punam;Singh M;Ashok Kumar (Statistics Dep, M.D. University, Rohtak-124 001) : Steady state solution of serial and non serial queuing processes with reneging and balking due to long queue and some urgent message. Int J agric statist Sci 2009, 5(1), 283-7.

O Brien (1954), Jackson (1954), Hunt(1955) and Maggu (1970) studied the problems of serial queues in the steady state with poisson assumptions. In these studies, it is assumed that unit is not allowed to balk or renege at any stage and must go through each service channel without leaving the system. Barrer (1955) obtained the steady state solution of a single channel queuing model having Poisson input, exponential holding time, random selection where impatient customers leave the service facility after a wait of certain time. Singh (1984) studied the problem of serial queues introducing the concept of reneging. Singh and Vikram (1997) obtained the solutions of serial and non serial queuing processes with reneging and balking phenomenon. In our present work, the steady state solutions are obtained for general queuing process in which (1) N service channels in series are linked in series with M non serial channels having reneging and blking phenomenon. (2) In M non serial channels, there is reneging and balking due to long queue and some urgent messages. (3) The service discipline follows SIRO rule (service in random order) instead of FIFO nile (Fist in first out). (4) Waiting space is infinite.

9 ref

023495   Patel N;Shrivastava P;Parihar C L (Applied Science Dep, Institute of Engineering & Technology, Devi Ahilya Univ, Indore-452 017, Email: n_patel_1978@yahoo.co.in) : Factorization of pel and-pell-lucas polynomials. J Indian Acad Math 2008, 30(2), 557-65.

In this paper, we-given zeros of Pell and Pell-Lucas Polynomials and hence factorized them. Then as a particular case, author factorization of Pell and Pell-Lucas numbers.

4 ref

023494   Noushima Humera G;Ramana Murthy M V; Rafiuddin;Chenna Krishna Reddy M (Mathematics Dep, N.S.A.K. Center for PG Studies & Research, New Mallapally, Hyderabad) : Unsteady viscoelastic memory flow and heat transfer over a continuous porous moving horizontal surface. J Indian Acad Math 2008, 30(2), 325-31.

Ohmic disspitaion effect on unsteady boundary layer flow and heat transfer of an incompressible memory fluid electrically conducting over a continuous porous moving horizontal non-conducting surface in the presence of transverse magnetic field, an oscillating free stream and volumetric rate of heat generation (or absorption is investigated, neglecting induced magnetic field in comparison to the applied magnetic field. The velocity and temperature distributions are obtained numerically and presented in graphical form. The expressions of skin friction coefficient and rate of heat transfer in terms of Nusselt number at the surface are derived, numerically and their numerical values for various values of physical parameters are presented in Tabular form.

3 illus, 2 tables, 12 ref

023493   Nayak S S;Kunichi M C (Statistics Dep, Gulbarga University, Gulbarga-585 106, Email: ssnayak2006@rediffmail.com) : Limit points for subsequences of record values. Int J agric statist Sci 2009, 5(1), 13-23.

Obtained the limit points for subsequences of record values under the set up of De Haan and Resnick (1973).

9 ref

023492   Narmada S (Mathematics Dep, Kerela Univ, Kariavation, Thirunanathapuram, Kerela) : Reliability analysis of a repairable and non-repairable two unit system subject to common external environment and hardware failures. J Indian Acad Math 2008, 30(2), 351-7.

This paper presents two Markov models to evaluate the reliability analysis of a standby system subject to common external environment and hardware failures. In model II repair process is initiated as soon as one of the two active units fails. Various measures of system effectiveness are obtained. To make the study more practicable, graphical illustrations are given at the end.

2 illus, 6 ref

023491   Mujumdar N S;Sharma K C (Engineering Sciences Dep, Bharati Vidyapeeth Univ College of Engineering, Dhankawadi, Pune-411 043, Email: mujum66@yahoo.com) : Polymeric fluid flow using ECTN model in a cylindrical converging pipe. J Indian Acad Math 2008, 30(2), 333-43.

Flow dynamics of polymeric fluids through a horizontal converging pipe arising from constant and variable pressure gradients. The non-dimensional stress model and the equations of motion [2] are analysed and analytical expressions are derived for velocity vector, the stress components for fully developed steady flow using energetically crosslinked transient network (ECTN) model [1]. In this study, the rates of segment creation and loss formed by physical and energetic interactions are assumed to be constants. The analysis clearly shows that the velocity profile depends on the parameters Nm and the flow slows down axially as against Newtonian flow in a converging cylindrical pipe.

ref

023490   Mondal C R (Mathematics Dep, North Eastern Hill Univ, Shillong-793 022) : Internal waves in a two layered fluid. J Indian Acad Math 2008, 30(2), 533-49.

An initial value investigation is made of the development of internal wave motion generated by harmonic pressure distribution of fixed frequency in a fluid which is composed of two layers of different densities, the upper layer being of finite depth and the lower layer being of unlimited depth. The formal solution in terms of infinite integrals is obtained in a straightforward way by applying Laplace and Fourier transformations. The wave integral is subjected to an asymptotic which follows essentially a method due to Bleistein [1966], and which remains uniform even near the critical line produced by the coalescing of the pole and the stationary point of the wave spectrum.

14 ref

023489   Misra U K;Sahoo N C;Paikray S K (Mathematics Dep, Berhampur Univ, Berhampur-760 007) : Note on |N, p<. J Indian Acad Math 2008, 30(2), 481-7.

In this paper establish a theorem on |N, p^α_n, δ|k -Summability of an infinite series.

2 ref

023488   Meshram D K;Khobragade N W;Durge M H (Mathematics Dep, MJP Educational Campus, RTM Nagpur Univ, Nagpur-480 033, Email: khoprage_nw@rediffmail.com) : Inverse transient thermoelastic problem of an infinite rectangular slab. J Indian Acad Math 2008, 30(2), 413-24.

This paper is concerned with an inverse transient thermoelastic problem to determine the unknown temperature, displacement and stress functions on the edge z = h of an infinite rectangular slab occupying the space - ∞ < x < ∞, - ∞ < y < ∞, 0 ≤ z ≤ h by applying double Fourier integral transform. The temperature T(x,y, Z,t)|z= ξ = f(x, y,t) for a fixed value of ξ, 0 < ξ <h is a known function of x, y and t.

5 ref

023487   Mehta M N;Yadav R (Mathematics Section, AS & H Dep, S.V. National Institute of Technology & Engineering, Surat-395 007) : Solution of longitudinal dispersion phenomena occurring in two phase flow through porous media. J Indian Acad Math 2008, 30(2), 345-50.

An Approximate solution of longitudinal dispersion phenomena occurring in two phase miscible fluid flow through porous media has been obtained by using the method of small parameter. The longitudinal dispersion coefficient is assumed to be directly proportional to the concentration and the velocity component in direction of x-axis is considered directly proportional to ratio of distance x and time T.

8 ref

023486   Mahurpawar V;Deo S D (Mathematics Dep, Govt. Auto P.G. College, Chhindwara, Madhya Pradesh) : Six dimensional static plane symmetric space-time with cosmic strings in biometric relativity. J Indian Acad Math 2008, 30(2), 477-80.

Nil contribution of the cosmic strings to the higher six dimensional static plane symmetric space-time in biometric relativity is obtained and it is observed that the resulting space-time can be reduced to the conformal one.

2 ref

023485   Kawale S (Statistics Dep, Dr. B.A.M. University, Aurangabad-431 004, Email: ksunila@rediffmail.com) : Production inventory model with two rates of production and deterioration. Int J agric statist Sci 2009, 5(1), 211-15.

Attempt is made to develop a single product deterministic production model with backorders. It is assumed that the deterioration rate is changed with production rate. When production rate is increased, rate of deterioration is also increased. For this model, the total cost per unit time as a function of Q₁, Q₂ and S are computed.

8 ref

023484   Javaid S;Gupta S N;Khalid M M (Statistics and O.R. Dep, Aligarh Muslim University, Aligarh-202 002, Email: shakeel.jd@operamail.com) : Optimization with fractional objective under random parameters. Int J agric statist Sci 2009, 5(1), 271-82.

Analyses a transshipment problem whose objective function is fractional where the demand consider is uncertain. The objective here is to maximize the net expected revenue per unit transportation cost, i.e., the total expected revenue minus the transportation and transshipments cost. The stochastic transshipment problem is converted to an equivalent deterministic transportation problem. An algorithm is developed for the deterministic transportation problem and is numerically illustrated.

6 ref

023483   Gupta P K;Tyagi V K (Statistics Dep, DAV College, Muzaffarnagar-251 001, Email: vikastyagi101@yahoo.co.in) : Reliability estimation of sugar plant by employing boolean function expansion algorithm. Int J agric statist Sci 2009, 5(1), 261-9.

Deals with the reliability estimation of a sugar plant by employing Boolean function expansion algorithm. Mathematical formulation of the system has done by using algebra of logics. This mathematical model has been solved by employing Boolean function expansion algorithm. Reliability of the system has been computed. Reliability functions have been obtained in two different cases, when failures follow weibull and exponential time distributions. An important reliability parameter, viz. mean time to failure of the system has also been computed to improve practical utility of the model. Graphical illustration followed by a numerical computation has been appended in the end to highlight important results of the study.

3 illus, 1 table

023482   Govindarajan A;Ramamurthy V;Kesavan S (Mathematics Dep, S.R.M. Univ, Kattankulathur-603 203, Email: ramayamam@yahoo.co.in) : Steady laminar free convection flow of an electrically conducting dusty fluid along a porous hot vertical plate in the presence of heat source / sink. J Indian Acad Math 2008, 30(2), 587-601.

Steady laminar free convection flow of an electrically conducting dusty fluid along a porous hot vertical plate in the presence of heat source / sink is investigated. The governing equations of motion are solved by a regular perturbation technique. The skin-friction coefficient and Nusselt number are derived and tabulated. The velocity and temperature distributions of both the fluid and dust are shown graphically taking two cases namely, case I: when Gr > 0. (i.e. flow on a cooled plate) and Case II: Gr < 0 (i.e. flow on a heated plate). The velocity profiles of both the fluid and dust increase due to an increase in the mass concentration of the dust particles when Gr > 0 (flow on cooled plate) and reverse effect is seen when Gr < 0 (flow on heated plate). The temperature decreases when Gr > 0 (flow on a cooled plate) and opposite trend is maintained when Gr < 0 (flow on a heated plate). Skin friction coefficient decreases with an increase in mass concentration parameter and Nusselt number increases due to an increase in mass concentration of the dust particles when Gr > 0 (flow on a cooled plate), but both behave in opposite manner when Gr < 0 (flow on a heated plate).

4 illus, 2 tables, 15 ref

023481   Garg D K (Statistics Dep, , Punjabi University, Email: dkgarg_state@yahoo.co.in) : New method of construction of EL₂ designs. Int J agric statist Sci 2009, 5(1), 289-95.

New method of construction of Extended L₂ (EL₂) designs defined by Singla (1976) is presented in this paper. The method consists of constructing EL₂ designs by substituting the association matrices of L₂ association scheme defined by Bose and Shimamoto (1952) in the incidence matrix of a symmetric balanced incomplete block (BIB) design. Singla (1976) constructed EL₂ designs by the method of differences alone. New construction method results in constructing some new PBIB designs following EL2 association scheme. Some new block structure properties of EL₂ designs have also been provided.

11 ref

023480   Das K;Saha G C (Mathematics Dep, Kalyani Govt. Engg. College Kalyani, Nadia-741 235) : Two layered model for hemodialyser. J Indian Acad Math 2008, 30(2), 389-402.

A two-layered mode! of blood flow between two infinite permeable parallel plates in the presence of constant suction and uniform magnetic field has been studied. The analytical solutions for the velocity profiles in the core region and peripheral plasma layer (PPL) with flow rate, effective viscosity and effective Reynolds number have been derived and their natures are also represented graphically for different values of encountered parameters. Some important observations regarding dialysis time, the blockage of membrane pores by red cells etc. are obtained leading to medical interest.

19 illus, 12 ref

023479   Chakrabatry D (Statistics Dep, Handique Girl's College, Guwahati-781 001, Email: dhritikesh.c@rediffmail.com) : Probability: chakrabarty's definition from its classical definition. Int J agric statist Sci 2009, 5(1), 181-7.

It has been established by Chakrabarty in 2008 (i) that the classical definition of probability introduced by Bernoulli in 1713, is a consequence of its theoretical definition, constructed by Chakrabarty in 2004, when the elementary events are equally likely and (ii) that the converse of this is not true. In this paper, it has been shown that the classical definition of probability and the definition of mathematical together imply the Chakrabarty's definition of probability.

20 ref

023478   Bhushan S;Pandey A;Karan Singh (Statistics Dep, PUC-Campus, Mizoram University, Aizawl-796 001, Email: Shashi.py@gmail.com) : Improved classes of regression type estimators. Int J agric statist Sci 2009, 5(1), 73-84.

In order to estimate the mean of a finite population, a linear regression type estimator with known mean and variance of auxiliary variable proposed by Bhushan (2007) is reconsidered by using assuming the knowledge of coefficient of variation and the bias and the mean square error of the proposed estimator is obtained. Further, a Jack-knife estimator is proposed which is unbiased and the mean square error of the proposed Jack-knife estimator is obtained along with the optimum value of the parameter. Also, a class of linear regression type estimators is proposed under the estimated value of the parameters involved and its mean square error is found to be equally efficient as compared to the classes mentioned above. A comparative study of the proposed estimator is made with some commonly used estimators shows that the proposed Jack-knife estimator, with known auxiliary mean, variance and coefficient of variation, is better in the sense of unbiasedness and minimum mean square error under optimum value of parameter involved.

11 ref