008756   Nimisha;Gaur A;Upadhye N (Dep of Math, IMS Engng Coll, Ghaziabad, Uttar Pradesh) : Networks of queues and extensions. Acta Cienc Indica-Math 2005, 31(2), 333-40.

The general closed networks of queues and their relationship with cyclic queue model has been developed and has been compared to the job-shop like queuing system.

8 ref

008755   Natrajan R;Vairavan L (Dep of Math, Alagappa Univ, Karaikudi-630 003) : Distributive ideal in a semilattice. Acta Cienc Indica-Math 2005, 31(2), 401-10.

The concept of distributive ideal, standard ideal and neutral ideal in a lattice L have been introduced and studied by Hashimoto, J., Gratzer, G., and Schmidt, E.T. In the paper authors has introduced the concept of distributive ideal, dually distributive ideal in a semilattice S and characterized them.

2 illus, 7 ref

008754   Natrajan R;Punithavathi P (Dep of Math, Alagappa Univ, Karaikudi-630 003) : Characterisation of supermodular join semilattices. Acta Cienc Indica-Math 2005, 31(2), 505-12.

Authors has introduced the concept of supermodularity in join semilattices and characterised supermodular join semilattices in the orems 3.5, 3.6 and 3.7.

5 ref

008753   Murthy N V E S (NO, , 5-4-6/1, Punyapu Veedhi, SBI-6, Srikakulam-532 001) : μ-MODULES. Acta Cienc Indica-Math 2005, 31(2), 379-86.

The aim of the paper is to generalize the existing notion of fuzzy submodule and show that all the existing properties of fuzzy submodules extend in a natural way.

9 ref

008752   Mukherjee M C (Vidyamandir, Netaji Nagar, Kolkata-700 092) : On mixed trilateral generating relations of modified Bessel polynomial. Acta Cienc Indica-Math 2005, 31(2), 447-8.

In the paper a theorem of mixed trilateral generating relation of modified Bessel Polynomial ηr_n^(α-m) (x) has been derived from the Lie-group view point.

3 ref

008751   Modi H B;Ranabhatt G A (Dep of Math, Bhavnagar Univ, Bhavnagar-364 002) : Generalization of a series. Acta Cienc Indica-Math 2005, 31(2), 361-4.

Authors generalized the series F(2) = ∑^∞_k=1 1/2k(2k-1) = log 2 as F(n) = ∑^∞_k=1 1/nk (nk-1) ... (nk-n+1) (n ∈N) and give the exact value of the series F(3) and F(4) and show that the double series ∑^∞_n=2 F(n) is convergent.

2 ref

008750   Mittal S K;Jain S;Mittal C (NO, M.M. Coll, Modinagar, Uttar Pradesh) : Stochastic analysis of an automated teller machine system under wear out failures. Acta Cienc Indica-Math 2005, 31(2), 577-85.

Study deals with the stochastic analysis of an automated teller machine system with three subsystems viz., the ATM stations, the consortium computers and the bank computers connected in series. Concept of wear out failures has been taken and then the mathematical modeling for ATM system is made by using LT technique to obtain various state probabilities and then the reliability, MTSF and profit function have been evaluated by some graphical illustrations to explain the practical utility of the mode.

2 illus, 2 tables, 12 ref

008749   Mishra B K;Panda T C (Dep of Math, Birla Inst of Technol and Sci, Pilani-333 031) : Non-newtonian model of blood flow through an arterial stenosis. Acta Cienc Indica-Math 2005, 31(2), 341-8.

An analysis has been made to study the resistance to flow across mild stenosis situated symmetrically on steady blood flow through arteries with uniform or non-uniform cross-section by assuming the blood as Non-Newtonian, incompressible and homogeneous fluid. Non-new-tonian model of power law have been solved numerically.

2 tables, 9 ref, 2 graphs

008748   Mishra B K (Dep of Math, Srinath Niketan, Matwari, Hazaribag-825 301) : Heat transfer in MHD free convection flow over an infinite vertical plate with time-dependent suction. Acta Cienc Indica-Math 2005, 31(2), 371-4.

The heat transfer in the hydromagnetic unsteady laminar boundary layer flow past an infinite vertical plate with time-dependent suction is studied. Expression for temperature distribution inside the boundary layer is obtained and numerically computed for suction parameter ϖ and Prandtl number Pr.

7 ref

008747   Krishna D V;Rao P N (Dep of Math, S.K. Univ, Anantapur-515 003) : Finite element analysis of magneto-hydrodynamic steady flow through a Reactangular duct. Acta Cienc Indica-Math 2005, 31(2), 545-62.

Paper discuss the steady flow of a conducting fluid through a rectangular duct under transverse magnetic field. The equations for the velocity and induced magnetic field are suitably coupled. The actual flow is due to prescribed pressure gradient. The Galerkin finite element method with rectangular elements is used to obtain the velocity, the shear stresses and the induced magnetic fields. Their behaviour at different horizontal levels is discussed for variation in the governing parameters.

13 illus, 4 tables, 43 ref

008746   Kannamma S;Rangarajan K;Thomas D G (Dep of Math, S.D.N.B. Vaishnav Coll for Women, Chennai-600 044) : Coded petri nets and line pictures. Acta Cienc Indica-Math 2005, 31(2), 497-504.

A class of coded Petri Net languages and study some algebraic properties. Author has employed coded Petri Net over the alphabet π = (l, r, d, u) (where the alphabets respectively represent movements through one unit to the left, right down and up from a specified point) to define coded Petri Net picture language and analyse some of its properties.

2 illus, 14 ref

008745   Goyal A K;Gaur M (Dep of Math, N.A.S. P.G. Coll, Meerut, Uttar Pradesh) : Mathematical modelling of some physical system. Acta Cienc Indica-Math 2005, 31(2), 457-8.

5 illus, 2 ref

008744   Gopalan M A;Somanath M;Vanitha N (Dep of Math, Natn Coll, Trichy, Tamil Nadu) : On double and triple nasty numbers. Acta Cienc Indica-Math 2005, 31(2), 567-9.

Explicit formulas for double and triple nasty numbers are presented.

4 ref

008743   Gopalan M A;Devibala S (Dep of Math, Natn Coll, Trichy, Tamil Nadu) : Integral solutions of the system a(x<. Acta Cienc Indica-Math 2005, 31(2), 325-6.

A method to obtain integral solutions of the system of two binary quadratic equations a(x² - y²) + N₁² = u², b(x² - y²) + N₂² = v² is given, when the product ab is a square-free integer.

1 table, 3 ref

008742   Gopalan M A;Devibala S (Dep of Math, Natn Coll, Trichy, Tamil Nadu) : Integral solutions of the system x<. Acta Cienc Indica-Math 2005, 31(2), 607.

A system of two equations of second degree in two unknowns represented by a(x² - y²) + N₁² = u², b(x² - b²) + N₂² = v² is studied in [1] for its integral solutions. In the communication, authors has proposed to solve in integers the system of binary quadratic double equations given by x² - y² + b=u², a(x² - y²) + c = v² where a is a square free.

1 table, 31 ref

008741   Goel R;Hari Kishan;Aggrawal V K (Dep of Math, D.N. Coll, Meerut, Uttar Pradesh) : Thompson-Chanderasekhar criterion in terrestrial physics. Acta Cienc Indica-Math 2005, 31(2), 597-9.

The paper mathematically and logically proves the correctness for Prof. Chandrasekhar's solution for the vertical velocity w in the overstable case of the magnetohy-drodynamic simple Benard problem with free and perfectly conducting boundaries which was shown incorrect by Banerjee, et al (1988).

9 ref

008740   Goel C K;Singh S B;Jai Kishore (Dep of Math, C.C.S. Univ, Meerut, Uttar Pradesh) : Reliability and MTTF analysis of a standby redundant system with common cause failures. Acta Cienc Indica-Math 2005, 31(2), 365-70.

The paper studies the analysis of a two identical unit standby redundant system with two type of failures namely hardware and common-cause failure. Any unit may fail either partially or completely. The failure and repair follow exponential and general distributions respectively. Supplementary variable technique has been employed to obtain various probability states. The steady state behaviour, special cases and numerical examples have also been taken.

3 illus, 3 ref

008739   Gaur M;Sharma S K (Dep of Math, N.A.S. P.G. Coll, Meerut, Uttar Pradesh) : Some mathematical aspects of nomenclature of chemical compounds. Acta Cienc Indica-Math 2005, 31(2), 461-2.

1 illus, 5 ref

008738   Gaur M;Ajay Kumar (Dep of Math, N.A.S. P.G. Coll, Meerut, Uttar Pradesh) : The bottle neck problems in a network. Acta Cienc Indica-Math 2005, 31(2), 359-60.

Authors discuss about bottle-neck problems in a network for a maximum flow.

2 ref

008737   Dube M (Dep of Math and Computer Sci, R.D. Univ, Jabalpur, Madhya Pradesh) : Interpolation by discrete beta-spline. Acta Cienc Indica-Math 2005, 31(2), 417-20.

The existence uniqueness and convergence properties of discrete cubic Beta spline are pre-sented in the paper. It is the analogue to the result on discrete cubic spline studied by Lyche [6] and cubic splines studied by Alhberg, Nilson and Walsh [1].

8 ref

008736   Chaubey N K;Pandey R (Dep of Math, Govt. Model Sci Coll, Jabalpur-482 001) : A note on interpolating deficient quartic splines. Acta Cienc Indica-Math 2005, 31(2), 375-8.

Authors has established existence and convergence of a deficient quartic spline interpolant matching with the given function at the nodes as well as at the midpoints between successive nodes.

4 ref

008735   Chaturvedi A;Kumar J (Dep of Statist, Univ of Allahabad, Allahabad-211 002) : Bayesian unit root test for time series model with quadratic trend. Univ Allahabad Stud-Sect A 2004, 3(1), 7-12.

Considers the Bayesran analysis of an autoregressive model with quadratic trend. For the model under consideration, under the unit root hypothesis, the quadratic trend component does not vanish completely and its degree reduces by one. The posterior odds ratio for the unit root hypothesis has been derived under appropriate prior assumptions for the parameters of the model.

9 ref

008734   Basak S;Karanjai S (Dep of Math, Kokrajhar Coll, Kokrajhar, B.T.C., Assam-783 370) : Interlocking problem in anisotropically scattering media (Planetary phase function). Acta Cienc Indica-Math 2005, 31(2), 317-24.

The equation of transfer for the interlocked multiplets with planck-function as a linear function of optical depth in anisotropically scattering media with planetary phase functions is solved by the method of discrete-ordinates an attempt has also been made for getting the exact solution by infinite approximation.

10 ref

008733   Ashish Kumar;Saluja S (Dep of Math, N.A.S. P.G. Coll, Meerut, Uttar Pradesh) : Neighbourhood system of the set of graphs. Acta Cienc Indica-Math 2005, 31(2), 459-60.

2 illus, 3 ref

008732   Ali M Z;Shinohara Y;Takeuchi T (Dep of Math, Univ of Rajashahi, Rajshahi-6205, Bangladesh) : Existence and uniqueness of solution of nonlinear systems. Acta Cienc Indica-Math 2005, 31(2), 513-18.

R.E. Moore discussed the computationally verifiable conditions for the existence, uniqueness and convergence of solutions of nonlinear systems by a series of three lemmas and two theorems. M. Urabe also gave a theorem that discussed the error bounds for the approximate solutions of nonlinear systems. An attempt has been made to combine Moore's two theorems into a single one and apply Urabe's theorem to this theorem to find an interval enclosing a real root of a nonlinear equation.

4 tables, 4 ref

007694   Tajuddin M;Narayan Reddy G (Dep Math, Osmania University, Hyderabad-500 007, Email: taj_osmania@yahoo.co.in) : Effect of boundaries on the dynamic interaction of a liquid-filled porous layer and a supporting continuum. Sadhana 2005, 30(4), 527-35.

Transcendental equation is derived relating wave number and phase velocity of propagation of waves in a partially saturated layered half-space under plane strain conditions. The period equation is derived and discussed for two types of boundaries, permeable and impermeable. In the limiting cases, the problem reduces to more simplified forms as discussed by earlier researchers.

1 illus, 1 table, 9 ref

007693   Sunita Rani;Singh S J (Dep Appl Math, Guru Jambheshwar University, Hisar-125 001, Email: s_ b_rani@rediffmail.com) : A note on 2-D lithospheric deformation due to a blind strike-slip fault. J Earth Syst Sci 2005, 114(1), 105-10.

Analytical solution for the problem of a surface-breaking long strike-slip fault in an elastic layer overlying an elastic half-space is well known. The purpose of the note is to obtain the corresponding solution for a blind fault. Since the solution is valid for arbitrary values of the fault-depth and the dip angle, the effects of these two important fault parameters can be studied numerically. The variation of the parallel displacement and shear stress with the distance from the fault is studied numerically for different values of the fault-depth and dip angle.

3 illus, 4 ref

007692   Rajneesh Kumar;Ailawalia P (Dep Math, Kurukshetra University, Kurukshetra-136 119, Email: rajneesh_kuk@rediffmail.com) : Viscous effect at an orthotropic micropolar boundary surface. Sadhana 2005, 30(4), 513-25.

Steady state responses at viscous fluid/orthotropic micropolar solid interfaces to moving point loads have been studied. An eigenvalue approach using the Fourier transform has been employed to solve the problem. The displacement, microrotation and stress components for the orthotropic micropolar solids so obtained in the physical domain are computed numerically by applying numerical inversion technique. Viscosity and anisotropy effects on normal displacement, normal force stress and tangential couple stress have been shown graphically for a particular model.

4 illus, 1 table, 30 ref

007691   Kuldeep Singh;Madan D K;Goel A;Garg N R (Dep Math, Guru Jambheshwar University, Hisar-125 001, Email: nrgmath@rediffmail.com) : Two-dimensional static deformation of an anisotropic medium. Sadhana 2005, 30(4), 565-83.

Problem of two-dimensional static deformation of a monoclinic elastic medium has been studied using the eigenvalue method, following a Fourier transform. Author has obtained expressions for displacements and stresses for the medium in the transformed domain. As an application of the above theory, the particular case of a normal line-load acting inside an orthotropic elastic half-space has been considered in detail and closed form expressions for the displacements and stresses are obtained. Further, the results for the displacements for a transversely isotropic as well as for an isotropic medium have also been derived in the closed form. The use of matrix notation is straightforward and avoids unwieldy mathematical expressions. To examine the effect of anisotropy, variations of dimensionless displacements for an orthotropic, transversely isotropic and isotropic elastic medium have been compared numerically and it is found that anisotropy affects the deformation significantly.

5 illus, 9 ref

007690   Khobragade N L;Deshmukh K C (Dep Math, Dharampeth M P Deo Memorial Science College, Nagpur 440 010, Email: kcdeshmukh2000@rediffmail.com) : Thermal deformation in a thin circular plate due to a partially distributed heat supply. Sadhana 2005, 30(4), 555-63.

Author has developed an integral transform to determine temperature distribution in a thin circular plate, subjected to a partially distributed and axisymmetric heat supply on the curved surface, and study the thermal deformation. The results, obtained in series form in terms of Bessel's functions, are illustrated numerically.

6 illus, 5 ref

007689   Anil Kumar;Sarva Jit Singh;Singh J (Dep Math, Maharshi Dayanand University, Rohtak 124 001, Email: s_j_singh@yahoo.com) : Deformation of two welded elastic half-spaces due to a long inclined tensile fault. J Earth Syst Sci 2005, 114(1), 97-103.

Calculation of the deformation caused by shear and tensile faults is necessary for the investigation of seismic and volcanic sources. The solution of the two-dimensional problem of a long inclined shear fault in two welded half-spaces is well known. The purpose of this note is to present the corresponding solution for a tensile fault. Closed-form analytical expressions for the Airy stress function for a tensile line source in two welded half-spaces are first obtained. These expressions are then integrated analytically to derive the Airy stress function for a long tensile fault of arbitrary dip and finite width. Closed-form analytical expressions for the displacements and stresses follow immediately from the Airy stress function. These expressions are suitable for computing the displacement and stress fields around a long inclined tensile fault near an internal boundary.

1 illus, 13 ref

006597   yang B (Dep Math, Guangdong Educ Coll, Guangzhou, Guangdong-510303, P.R. China, Email: bcyang@pub.guangzhou.gd.cn ) : On the extended Hilbert's integral inequality and applications. Int Rev pure appl Math 2005, 1(1), 1-12.

Gives a new generalization of the extended Hilbert's integral inequality with a best constant factor involving the β function.

8 ref

006596   Xiao Z G;Zhang Z H;Lokesha V;Tang R (Hunan Inst Sci Techonology, , Yueyang, Hunan-414006, Email: xzgzzh@163.com) : Two-parameters the mean of n variables. Int Rev pure appl Math 2005, 1(1), 93-111.

Van der Monde's determinant is generalized, two-parameters mean of n positive numbers is defined, and a class of mean inequalities are obtained.

24 ref

006595   Werner W (Dep de Mathematiques, IUF and Universite Paris-Sud, 91405 Orsay Cedex, France, Email: Wendelin.Werner@math.u-psud fr) : Some mathematical aspects of the scaling limit of critical two-dimensional systems. Pramana J Phys 2005, 64(5), 757-73.

It has been observed long ago that many systems from statistical physics behave randomly on macroscopic level at their critical temperature. In two dimensions, these phenomena have been classified by theoretical physicists thanks to conformal field theory, that led to the derivation of the exact value of various critical exponents that describe their behavior near the critical temperature. In the last couple of years, com bining ideas of complex analysis and probability theory, mathematicians have constructed and studied a family of random fractals (called 'Schramm-Loewner evolutions or SLE) that describe the only possible conformally invariant limits of the interfaces for these models. This gives a concrete construction of these random systems, putsvarious predictions on a rigorous footing, and leads to further understanding of their behavior. The goal of the paper is to survey some of these recent mathematical developments, and to describe a couple of basic underlying ideas. Author has also briefly describe some very recent and ongoing developments relating SLE, Brownian loop soups and conformal field theory.

1 illus, 39 ref

006594   Vijaya K (Dep Math, Vellore Inst of Technol Deemed Univ, Vellore-G32014 Tamil Nadu, Email: kvavit@yahoo.co.in ) : A generalized class of harmonic univalent functions with varying arguments. Int Rev pure appl Math 2005, 1(1), 59-67.

Define a family of complex valued harmonic functions that are orientation preserving and univalent in the open unit disc that are related to uniformly convex functions by introducing a Ruscheweyh type operator. For functions in this new generalized class, coefficient conditions, distortion bounds and extreme points were obtain.

12 ref

006593   Shams S;Kulkarni S R;Jahangiri M J (Dep Math, Fergresson Coll, Pune-411 004, Email: kulkarni_ferg@yahoo.com) : Classes of harmonic univalent starlike functions. Int Rev pure appl Math 2005, 1(1), 123-33.

A class of complex - valued harmonic functions of the form f = h + g<96>, which are univalent and sense preserving in the open unit. Determine sufficient coefficient conditions for these functions to be starlike and show that these coefficient conditions are also necessary if h has negative coefficients and g has positive coefficients. Obtained extreme points, and Ruscheweyh derivatives for the functions in this class.

006592   Ryoo C S (Dep Math, Hannam Univ, Daejeon 306-791, Korea) : Distribution of the zeros of q-bernoulli polynomials. Int Rev pure appl Math 2005, 1(1), 135-41.

Deals with the distribution of the roots of q-Bernoulli Polynomials β_n,q (x) for values of the index n by using computer.

8 illus, 1 table, 5 ref

006591   Ponraj R;Somasundaram S (Dep Math, Manonmaniam Sundaranar Univ, Tirunelveli-627 012) : On the degree splitting graph of a garaph. Natn Acad Sci Lett 2004, 27(7-8), 275-8.

Authors has define degree splitting graph of a graph and has studied some properties of degree splitting graph.

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006590   Navaneetha Kumar V;Manivannan L; Saravanamoorthy P (Dep Math, Shirdi Sai Engng Coll, Anekal, Bangalore, Email: nava_2000@sify.com) : M-N model for finding shortest route between any two points. Int Rev pure appl Math 2005, 1(1), 69-73.

Describes M-N model for finding shortest route between any two points from source node to destination node. This is one of the shortest route finding model of cyclic nature with major application in the areas of transportation and networking. Here the M-N model gives good results and focus towards destination direction. Its presented with example.

006589   Muthucumaraswamy R;Chandrakala P (Dep Inf Technol, Sri Venkateswara Coll of Engng, Sriperumbudur-602 105, Email: msamy@svce.ac.in) : MHD effects on moving vertical plate with homogeneous chemical reaction. Int Rev pure appl Math 2005, 1(1), 47-58.

Laplace transform solution of MHD Stokes problem for the flow of an electrically conducting, incompressible, viscous fluid past an impulsively started infinite vertical in the presence of variable temperature and uniform mass diffusion, taking into account the homogeneous chemical reaction of first-order. The plate temperature is raised linearly with time and the concentration level near the plate are raised to C'_w. The solutions for the velocity and skin-friction are obtained for different magnetic field parameter, Schmidt number and chemical reaction parameter. It is observed that the velocity decreases with increasing magnetic field parameter. It is also observed that the skin-friction increases with decreasing chemical reaction parameter.

3 illus, 5 ref

006588   Mitrovic Z D (Fac Electl Engng, Univ of Banja Luka, 78000 Banja Luka, Patre 5, Bosnia and Herzegovina, Email: zmitrovic@etfbl.net) : Remarks on generalized vector equilibrium problem. Int Rev pure appl Math 2005, 1(1), 35-46.

Proves an existence result for the generalized vector equilibrium problem by using Fan-KKM type theorem. As an application, were derived derive variational inequality theorem and best approximation theorem were derived. The results of this paper generalize some known results in the literature.

36 ref

006587   Karmakar S B (Universal Enterprise, , 33 Shirley Parkway Piscataway, NJ 08854, USA, Email: math235@yahoo.com) : An elementary proof of fermat's last theorem for the first case. Int Rev pure appl Math 2005, 1(1), 83-92.

A simple proof that the equation aⁿ + bⁿ = cⁿ can not have any nonzero integer solutions for the first case is presented. To prove the theorem first an accompanying equation x²ⁿ + y²ⁿ = z²ⁿ where n does not divide xyz is introduced. The roots of these equations are related as a = x², b = y², c = z². The theorem is proved by justifying the statement that if there are no integers x², y², z² so that the accompanying equation is satisfied with (x², y², z²) = 1 then there can not exist integers a, b, c so that the original equation is satisfied with (a, b, c) = 1 and when none of a, b, c is divisible by the exponent n <62> 2.

006586   Kanemitsu M (Dep Math, Aichi Univ of Educ, 1-Hirosawa, Igaya-Cho, Kariya- 448-8542, Japan, Email: mkanemit@auecc.aichi-edu.ac.jp) : On powerful ideals in semigroups. Int Rev pure appl Math 2005, 1(1), 75-82.

Let S be a commutative semigroup with a torsion-free (additive) quotient group q(S), and let I be an ideal of S. We say that/is powerful (strongly prime, strongly primary, respectively) if whenever x, y ∈ q(S) and x + y ∈ I, we have x ∈ S or y ∈ S (x ∈ I or y ∈ I; x ∈ I or ny ∈ / for some n ≥ I, respectively). Show that if S has a powerful ideal I, then S<96> is a PVS, that is, each prime ideal of S is a strongly prime ideal, with maximal ideal N = Rad (I + S<96>) and (N:_q(S) N) is a valuation oversem-igroup of S with maximal ideal N. Also, Study some properties of powerful ideals in semigroups. Give some semigroup version of [1]. A semigroup stands for a commutative cancellation torsion-free additive semigroup, and it is a (non-zero) semigroup with 0. Let S be a semigroup. If we set G = [s-s'<157>s,s'∈S}, then G is a torsion-free abelian group with respect to addition and S is a subsemi-group of G. G is called the quotient group of S and is denoted by q (S). Any semigroup T between S and q(S) is called an oversemigroup of S. From now on, assume that S is a semigroup with quotient group G = q(S). Recall some notation and definitions ([2], [3], [4], [5] and [6]). Therefore (m+n)(x+y)=0 in V. Hence x is a unit in V. This is a contrdiction. Consquently, it is given that x ∉ S<96>. By Corollary 3. N is a powerful ideal. So -x+N ⊂ S<96>, Proposition 1 (1). If -x+N+S<96>, then x ∈N⊂S<96>. This is a contradiction. Hence-x+N⊂N. Thus -x ∈ V= (N:N). Consequently x is a unit of V. Therefore N is the maximal ideal of V=(N:N).

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006585   Dhanasekaran M;Balakrishnan S (Dep Math, Thanthai Periyar Government Inst of Technol, Vellore, Tamil Nadu, Email: dhanskar2000@yahoo.co.in) : Steady state solution of a single server queue with two classes of customers and server vacations. Int Rev pure appl Math 2005, 1(1), 13-34.

It is concerned with the analysis of a single server retrial queue of two classes of customers with Bernoulli scheduled vacations. In case of blocking, the class-I customer leaves the system forever, whereas the class-II leaves the service area and enters the orbit in accordance with an FCFS (First Come First Served) discipline and only the customer at the head of the queue is allowed access to the server. The analytical results for the queue length distribution as well as some performance measures of the system under steady state condition are obtained.

006584   Chandrasekhara Rao K;Nagoor Gani A (Dep Math, Mohamed Sathak Engng Coll, Kilakarai-623 806, Email: kcraoin2002@yahoo.co. in) : On ℑ₁ℑ₂-semi pre open sets and ℑ₁ℑ₂-quasi open sets. Natn Acad Sci Lett 2004, 27(7-8), 279-83.

ℑ₁ℑ₂-semi pre open sets are characterized by conditions. Condition under which a ℑ₁ℑ₂-semi pre open set becomes a ℑ₁ℑ₂ semi open set is given. Also author has defined ℑ₁ℑ₂-quasi open sets in a biological space (X,ℑ₁ℑ₂) and discuss their properties.

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006583   Bougoffa L (Dep Math Fac Sci, King Khalid Univ, P.O. Box-9004, ABHA, Saudi Arabia, Email: abogafah@kku.edu.sa) : A coupled system with integral conditions. Int Rev pure appl Math 2005, 1(1), 113-21.

Proves a result, which governs the separation of a system of two coupled equations, and this separation leads to study boundary value problems with non-local conditions. Using the Riesz representation theorem, existence and uniqueness of generalized solutions were proved.

9 ref

006582   Bhullar B S;Nayyar S (Dep Math Statist Phys, Punjab Agric Univ, Ludhiana) : Determination of requisite sample size for surveys. J Res-Punjab Agric Univ 2004, 41(3), 360-4.

The sample sizes required to estimate population mean with per-specified margins of error were empirically determined. As expected, it was observed that the sample size required depend upon the population standard deviation; and the permissible margin of error. More the population standard deviation, more will be the required sample size; and more the permissible margin of error, less the sample size. Also, the formulae for the estimation of required sample size as proposed by Sukhatme and Sukhatme (1970) and Murthy (1977) were found to be valid for the actual data on farmer's fields.

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006581   Arora P;Tandon P N (191-193, Karmchari Nagar, Bareilly, Email: gopalI960@yahoo.co.uk) : Mathematical model of controlled release of solute-drugs from biodegradable implants. Natn Acad Sci Lett 2004, 27(11-12), 419-23.

In medical sciences, chronical diseases and pathological states require long term doses of tablets, pills, capsules or ointments, creams, aerosols and injectables. These drugs release promptly but with significant fluctuations within various regions of the body. In the communication, author has presented a simple model for an alternative method of drug release through erodible polymeric/ceramic implants of desired geometry which can release the drug at a pre-assigned rate assuring effectiveness at lower end and minimizing adverse effect at the higher end. Such implants need not be removed after drug supply to the site by operating again because the implants are erodible. The model presents a control problem for design parameters for a pre-assigned drug release rate. The effects of various geometric and design parameters have been discussed.

5 illus, 11 ref

005468   Zaman F D;Masood K;Muhiameed Z (Dep of Math Sci, King Fahd Univ of Petrol and Miner, Dhahran 31261, Saudi Arabia, Email: fzaman@kfupm.edu.sa) : Recovery of variation in density and bulk modulus in the presence of damping. Far East J mathl Sci 2005, 17(1), 93-105.

An inverse problem arising from a one dimensional problem in a medium with variable density and bulk modulus in the presence of damping in the medium is discussed. The method is based upon Born's approximation and the assumption that the density, bulk modulus, wave speed and damping are well approximated by the background speed plus a perturbation term. The WKBJ approximation of Green's function for high frequency seismic data is used to derive the inversion formula.

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005467   Xie C (Dep of Math, Arkansas Tech Univ, Russellville, AR 72801, U S A, Email: chunping.xie@atu.edu) : Littlewood-Paley functions and Morrey spaces. Far East J mathl Sci 2005, 17(1), 81-92.

Useful characterizations of Morrey space norm of a function or Rⁿ in terms of the behavior of its Poisson integral. With the Littlewood-Paley functions g(f), S(f), and g*_λ(f), authors has developed several characterizations of Morrey spaces have been developed. Therefore work may give us several new ways to view Morrey spaces.

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