000033   Joshi D C (Mathematics Dep, South Gujarat University, Surat-7) : Ritz' collocation solution of the miscible fluid flow through porous media. Acta Cienc Indica-Math 2003, 29(1), 27-30.

Discusses a general solution, represent the concentration of the miscible fluid flow through porous media in terms of linear function. The mathematical formulation of the miscible fluid flow through porous media gives a non-linear partial differential equation (pde) which descrbies the concentration of the fluid. The pde is transformed into ordinary differential equation (ode) by similarity analysis. An alternative general solution is obtained by Ritz's collocation method. Here the phenomenon of longitudinal dispersion is discussed by regarding the cross-sectional flow velocity as time dependent in a specific form.

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000028   Gorain G C;Bose S K (Dep of Math, J.K. Coll, Purulia-723 101) : Uniform stability of damped nonlinear vibrations of an elastic string. Proc Indian Acad Sci-Mathl Sci 2003, 113(4), 443-9.

Uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends has been considered. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the system.

16 ref

000027   Gopalan M A;Venkatachalapathy M (Mathematics Dep, National College, Tiruchirapalli, T.N.) : Note on the cubic diophantine equation x<. Acta Cienc Indica-Math 2003, 29(1), 115-6.

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000026   Gopalan M A;Devibala S (Mathematics Dep, National College, Trichy, T.N.) : Note on the diophantine equation y(Y=2) = 3 x (X+1). Acta Cienc Indica-Math 2003, 29(2), 273-4.

000025   Gopalan M A;Devibala S (Mathematics Dep, National College, Trichy, T.N.) : Note on the double equations ∑<. Acta Cienc Indica-Math 2003, 29(1), 149-50.

It is well known that if the sum of 3 integers is a multiple of 3 then one can find another set of 3 integers whose sum and sum of squares are respectively equal to the sum and sum of squares of the given set. The converse of this above result namely, the problem of determining two sets of non-zero integers (x₁ + x₂+x₃) and (x₁+X₂+x₃) satisfying the system of equations, x₁+x₂+x₃ = X₁+X₂+X₃ and x₁²+x₂²+x₃² = X₁²+X₂²+X₃³ has been dealt with.

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000024   Gopalan M A;Devibala S (Mathematics Dep, National College, Trichy, T.N.) : Note on the double equations. Acta Cienc Indica-Math 2003, 29(1), 41-2.

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000023   Ghosh M K;Mallikarjuna Rao K S (Dep of Math, Indian Inst of Sci, Bangalore-560 012) : A probabilistic approach to second order variational inequalities with bilateral constraints. Proc Indian Acad Sci-Mathl Sci 2003, 113(4), 431-42.

A class of second order variational inequalities with bilateral constraints has been studied. Under certain conditions the existence of a unique viscosity solution of these variational inequalities has been shown and a stochastic representation to this solution has been given. As an application, a stochastic game with stopping times has been studied and the existence of a saddle point equilibrium has been shown.

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000022   Ghosh K (Dep of Applied Math, University College of Science & Technology, University of Calcutta, 92, APC Road, Calcutta-700 009) : Analytical and numerical models of gliese 229B- A newly detected rotating brown dwarf. Bull Calcutta Mathl Soc 2003, 95(3), 223-8.

The observed radius of the brown dwarf configuration under the consideration of the internal rotation is significantly than the previous estimation while the newly calculated central density, central temperature, effective temperature and luminosity of the model show prominent decrease from their old estimations. Efforts have been made to estimate the present age, present radius present central density, central pressure, central temperature and effective temperature under this new consideration for the newly detected brown dwarf Gliese 229B taking its mass to be 0.03 - 0.055M₀, M₀ being the mass of the sun and its present luminosity to be 6.4 x 10^-6 L₀, L₀ being the luminosity of the sun. Some remarks are placed by the author about the atmosphere of Gliese 229B and also about the recent searches for brown dwarfs after Gliese 229B.

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000021   Garai B;Bandyopadhyay C (Dep of Math, Univ of Burdwan, Burdwan 713104, W.B.) : On Irresolvable spaces. Bull Calcutta Mathl Soc 2003, 95(2), 107-12.

Introduces a topology on the set of reals which is irresolvable having no isolated point.

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000020   Dutta T K;Sardar S K (Dep of Math, Univ of Calcutta, 35, Ballygunge circular road, Calcutta-700 019) : On Levitzki radical of a Γ-semiring. Bull Calcutta Mathl Soc 2003, 95(2), 113-20.

The notion of Levitzki radical of a Γ-semiring has been introduced and it has been studied via operator semirings of the Γ-semiring.

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000019   Dutt P;Tomar S (Dep of Math, Indian Inst of Techno, Kanpur-208 016) : Stability estimates for h-p spectral element methods for general elliptic problems on curvilinear domains. Proc Indian Acad Sci-Mathl Sci 2003, 113(4), 395-429.

It has been shown that the h-p spectral element method applies to elliptic problems in curvilinear polygons with mixed Neumann and Dirichlet boundary conditions provided that the Babuska-Brezzi inf-sup conditions are satisfied. Basic stability estimates for a non-conforming h-p spectral element method have been established which allows for simultaneous mesh refinement and variable polynomial degree. The spectral element functions are non-confirming if the boundary conditions are Dirichlet. For problems with mixed boundary conditions they are continous only at the vertices of the elements. A stability estimate has been examined when the spectral element functions vanish at the vertices of the elements, which is needed for parallelizing the numerical scheme. Finally it has been indicated how the mesh refinement strategy and choice of polynomial degree depends on the regularity of the coefficients of the differential operator, smoothness of the sides of the polygon and the regularity of the data to obtain the maximum accuracy achievable.

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000018   Dheena P;Nandakumar P (Mathematics Dep, Annamalai University, Annamalai Nagar-608 002) : Regular weakly divisible near-rings. Acta Cienc Indica-Math 2003, 29(2), 295-8.

Properties of regular weakly divisible near-rings are obtained. Some characterization of regular weakly divisible near-rings has been given. It has been shown that if N is a left π-duo weakly divisible near-ring and if K is a left invariant of N, then √K is an invariant N-subgroup and is prime of type 2.

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000017   Das N (Mathematics Dep, University of North Bengal, P.O. North Bengal University, Dist. Darjeeling, West Bengal) : Generation of surface waves on a rotating sea by wind stress. Acta Cienc Indica-Math 2003, 29(2), 275-82.

A study has been made on the unsteady motion of the waves in an incompressible, inviscid fluid, rotating with the uniform angular velocity. The assumption is based on the linearization of the dynamical equations of motion referred to the cylindrical polar co-ordinates with symmetry about the Z-axis. The motion is produced by the wind stress distribution specified on the radial velocity component along with the harmonically oscillating time dependent perturbation.

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000016   Chauhan T S;Chauhan I S;Rajendra Kumar (Mathematics Dep, Bareilly College, Bareilly, U.P.) : On recurrent and birecurrent para-Sasakian manifolds. Acta Cienc Indica-Math 2003, 29(1), 145-8.

Defines recurrent and Ricci Recurrent para-Sasakian manifold and establishes a few properties thereof. In the last section Birecurrent para-Sasakian manifold has been dealt with.

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000015   Chauhan T S;Chauhan I S (Mathematics Dep, Bareilly College, Bareilly, U.P.) : Lie derivatives in a special Kawaguchi space. Acta Cienc Indica-Math 2003, 29(2), 345-7.

Delineates the theory of Lie derivatives in a special Kawaguchi Space and establishes a few properties thereof. K-Motion in Special Kawaguchi Space has been studied.

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000014   Chaudhuri P K;Ray S (Dep of Applied Math, University College of Science, 92, APC Road, Kolkata-700 009) : Receding axisymmetric contact between a transversely isotropic layer and a transversely isotropic half-space. Bull Calcutta Mathl Soc 2003, 95(2), 151-64.

A receding axisymmetric contact between a layer and over a half-space, both of transversely isotropic materials has been studied. The solution of the problem has been reduced to the solution of an eigenvalue problem. The problem may be considered as an extension of a class of contact problems in isotropic medium to the field of anisotropy and indicates some important observations, special for anisotropic media. Some numerical computation have also been done for a quick comparison.

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000013   Chalishajar D N (Dep of Appl Math, Sardar Vallabhbhai Patel Inst of Tech, Vasad-388306, Dist. Anand, Gujrat State) : Controllability of singular system using α-times integrated semigorups. Bull Calcutta Mathl Soc 2003, 95(2), 95-100.

Yang has obtained the solution of singular equation in terms of α-times integral (or α-fractional order integral) of semigroup. Sufficient condition for the controllability of singular system using α-times integrated semigroups has been provided.

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000012   Bulut E;Cakalli H (Dep of Math, Istanbul University, Vezneciler, 34459, Istanbul, Turkey) : Lacunary statistical h-regular series methods in Topological groups. Bull Calcutta Mathl Soc 2003, 95(2), 87-94.

The concept of lacunary statistical h-regularity of series methods is introduced in topological groups and some theorems related to series-to-sequence transformations are proved. It has been obtained that a triangular series-to-sequence method is lacunary statistical h-regular if and only if it is lacunary statistically generalized h-multiplicative.

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000011   Bhatt L;Dube K K (Mathematics, Statistics and Computer Science Dep, G.B. Pant University of Agriculture and Technology, Pantnagar-263 145) : Semi-invariant submanifolds of r-Kenmotsu manifolds. Acta Cienc Indica-Math 2003, 29(1), 167-72.

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000010   Bhatt L;Dube K K (Mathematics, Statistics and Computer Science Dep, G.B. Pant University of Agriculture and Technology, Pantnagar-263 145) : On CR-submanifolds of a trans hyperbolic Sasakian manifold. Acta Cienc Indica-Math 2003, 29(1), 91-6.

Bejancu defined and studied CR-submanifolds of a Kaehlerian manifolds. CR-submanifolds of a Sasakian manifold have been studied by Kobayashi. Oubina studied a new class of almost contact Reimannian manifold known as trans-Sasakian manifold, which generalizes both α-Sasakian and β-Kenmotsu structure. Hasan Shahid studied CR-submanifolds of trans-Sasakian manifold. Almost hyperbolic contact manifold have been defined and studied. CR-submanifolds of a trans hyperbolic Sasakian manifolds have been defined and studied.

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000009   Bhatt L;Dube K K (Mathematics, Statistics and Computer Science Dep, G.B. Pant University of Agriculture and Technology, Pantnagar-263 145) : On semi-invariant submanifold of a para Kenmotsu manifold. Acta Cienc Indica-Math 2003, 29(1), 37-40.

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000008   Bayer-Fluckiger E;Parimala R; Queguiner-Mathieu A (Dep de Math, Ecole Polytechnique, Federale de Lausanne, 1015 Lausanne, Switzerland) : Pfister involutions. Proc Indian Acad Sci-Mathl Sci 2003, 113(4), 365-77.

The question of the existence of an analogue, in the framework of central simple algebras with involution, of the notion of Pfister form is raised. In particular, algebras with orthogonal involution which split as a tensor product of quaternion algebras with involution are studied. It is proven that, up to degree 16, over any extension over which the algebra splits, the involution is adjoint to a Pfister form. Moreover, cohomological invariants of those algebras with involution are discussed.

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000007   Banerjee D (Dep of Math, Ramakrishna Mission Vivekananda Centenary College, Rahara Dist. - North 24 Parganas, West Bengal) : Note on maximum term of composite entire functions. Bull Calcutta Mathl Soc 2003, 95(3), 235-40.

Generalize some results of the paper of Lahiri and Sharma (1994) connecting the maximum term of a composite entire function.

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000005   Balasubramanian S (Mathematics Dep, Sri Subbaraya and Narayana College, Narasaraopet-522 601) : Alexander's subbase theorem in weak-and strong-lindelof bitopological spaces-I. Acta Cienc Indica-Math 2003, 29(2), 397-9.

Studied the Alexander's subbase theorem in weak and strong-Lindelof Bitopological spaces.

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000004   Balasubramani M S;Ravindran K T (Mathematics Dep, University of Calicut, Kerala-673 635) : On the Dixmier's approximation theorem. Acta Cienc Indica-Math 2003, 29(2), 409-11.

Proves the Diximier's approximation theorem which involves fixed point algebras of the Von Neumann algebra relative to groups of automorphisms. Diximier's approximation theorem is central to the study of the existence of dimension functions. SAGA property for Von Neumann algebras has been introduced and it has been shown that the intersection of the G-centre of a von Neumann algebra M and norm closure of convex hull of the set {t(a) : t ∈ G} is nonempty, whenever the von Neumann algebra M satisfies the above property.

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000003   Balasubramani M S;Ravindran K T (Math Dep, University of Calicut, Kerala-673 635) : NNG von Neumann algebras and its properties. Acta Cienc Indica-Math 2003, 29(2), 249-50.

The Dixmier's approximation theorem was proved using the SAGA property of von Neumann algebra and whenever the von Neumann algebra is G-finite then the intersection of G^-: CoM(a) and M^G, is a singleton was proved using the existence of linear map T:M→M^G. G^-: CoM(a)∩M^G is a singleton is proved by constructing a suitable functional on the von Neumann algebra.

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000001   Akhter N;Majumdar S (Dep of Math, University of Rajshahi, Rajshahi 6205, Bangladesh) : Determination of the Homology and the Cohomology of Nec groups with non-orientable orbit spaces and no reflexions. Bull Calcutta Mathl Soc 2003, 95(3), 207-18.

A free resolution of Z has been constructed for the integral group ring of the NEC groups G with non-orientable orbit spaces and non reflexions which is suitable for determination of the homology and the cohomology of G with arbitrary coefficient modules. The integral homology and cohomology have been computed explicity. The method depends only on the given presentation and not on any topological or geometrical aspect of the group. The resolution has been obtained only by solving systems of linear equations over the corresponding integral group ring.

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004211   Zhang X H;Wang Y Q;Dudek W A (Math and Computer Sci Dep, Shaanxi Inst of Sci and Technol, Hanzhong 723 001, Shaanxi Province, Peoples Republic of China) : T-ideals in bz-algebras and t-type bz-algebras. Indian J pure appl Math 2003, 34(11), 1559-70.

Notions of T-type BZ-algebra and T-ideal in BZ-algebra have been introduced as the generalizations of one of BCI-algebras. Also the notion of associative ideal in BZ-algebra has been introduced. The properties and characterizations of them have been investigated, and the following results: let <60>X;*,0<62> be a BZ-algebra, (1) X is a quasi-associative which implies that X is a T-type BZ-algebra, and the inverse is not true; (2) If X is a T-type BZ-algebra, then X has a homomorphism with an involution group. (3) An ideal I of X is an T-ideal if and only if (0^* x)^* x I for any x ∈ X. (4) X is a T-type BZ-algebra if and only if for each ideal I of X is a T-ideal or the zero ideal {0} of X is a T-ideal. (5) For any ideal I of X, the quotient algebra X over I (i.e. X /I) is a T-type BZ-algebra if and only if I is a T-ideal of X. (6) an ideal of BZ-algebra is associated if and only if it is anti-grouped ideal and T-ideal. (7) BZ-algebra X is associated if and if each ideal of X (or its zero ideal) is an associative ideal. (8) For any ideal I of X, the quotient algebra X over I (i.e. X /I) is associated if and only if I is an an associative ideal of X.

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004210   Zhang B G;Saker S H (Math Dep, Ocean Univ of Qingdao, Qingdao 266071, People's Republic of China) : Kamenev-type oscillation criteria for nonlinear neutral delay difference equations. Indian J pure appl Math 2003, 34(11), 1571-84.

By means of Reccati transformation techniques some oscillation criteria for second order-superlinear and sublinear neutral delay difference equations have been presented.

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004209   Zayed E M E (Math Dep, Fac of Sci, Zagazig Univ, Zagazig, Egypt) : An inverse problem of the three-dimensional wave equation for a general annual vibrating membrane. Indian J pure appl Math 2003, 34(10), 1407-18.

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004208   Yu-Mei L;Xue-Ping W (Math Dep, Sichuan Normal Univ, Chengdu, Sichuan 6100 066, People's Republic of China) : The solution sets of @-fuzzy relational equations in finite domains and on a complete Brouwerian lattice. Indian J pure appl Math 2003, 34(8), 1249-57.

@-Fuzzy relational equations (where, "@" is the inf - α composie operator) in finite domains and on a complete Brouwerian lattice are discussed by utilizing the good properties of an α-operator. The solution sets of three @-Fuzzy relational equations are given respectively.

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004207   Yousefi B;Kashkuli A I (Dep of Math, Shiraz Univ, 71454 Shiraz, Iran) : Hypercyclic adjoint multipliers on banach spaces of analytic functions. Far East J mathl Sci 2003, 11(1), 113-9.

Some sufficient conditions have been given for the adjoint of a multiplication operator on a reflexive Banach space to be hypercyclic. Also, dense invarient linear manifold of hypercyclic vectors have been investigated for the adjoint of a hypercyclic multiplication operator.

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004206   Yildirim M (Math Dep, Fac of Sci, Cumhuriyet University, Sivas-58140, Turkey) : On the spectrum and fine spectrum of the compact Rhaly operators. Indian J pure appl Math 2003, 34(10), 1443-52.

In 1989, Rhaly determined the spectrum of Rhaly operator R_a regarded as an operator on the Hilbert space l₂ normed by <124><124> x <124><124> = (Σ_n <124> x_n <124>²)^1/2. Determines the spectrum of Rhaly operator R_a as an operator on the spaces bυ_o and b<117.

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004205   Yang Y;Kim D (Dep of Math and Information, Cheju National Univ, Jeju, 690-756, Korea) : On generalized roots of hyponormal operators. Far East J mathl Sci 2003, 11(1), 75-83.

A new class of operators called the n-th roots of hyponormal operators. An operator T ∈ L(H) is the n-th root of a hyponormal operator have been studied if Tⁿ is hyponormal. Also several properties of n-th roots of hyponormal operators have been studied.

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004204   Xu T (Appl Math Dep, Beijing Inst of Technol, Beijing 100081, People's Republic of China) : Covariant completely positive maps. Indian J pure appl Math 2003, 34(8), 1131-40.

Let A, B are unital C^*-algebras, M is a left-cancellative semigroup with unit, θ is a fixed 2-cocycle of M. α: x → α_x is a homomorphism from M into the group Aut (A) or automorphisms of A, W is an isometric projective homomorphism from M to B, J is a closed two-sidedideal of B, τ is a unital *-homomorphism from C_θ(M) to B/J. An abstract convariant version of Stinespring's dilation theorem is given. It is shown that a W-covariant completely positive map ϕ from A to B extends to a completely positive map on the (twisted) crosseed product C^*_θ(A, M, α). These results are used to give necessary and suficient conditions for τ to have a completely positive lifting.

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004203   Xiong W (Dep of Information and Computing Sci, Guangxi Inst of Technol, 545006, Liuzhou Guangxi, P R Chine) : Meromorphic functions that share one finite set CM. J Analysis Applic 2003, 1(3), 163-73.

Gross uniqueness question has been studied and the following results has been proved For nonconstant meromorphic functions ↵(z) and g(z), two nonconstant meromorphic function of finite non-integral lower order ↵(z) and g(z)

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004202   Williams K S (Centre Res in Algebra and Number Theory, Sch of Math and Statists, Carleton Univ, Ottawa, Ontario, Canada K1S 5B6) : n = Δ + Δ - 2(Δ + Δ). Far East J mathl Sci 2003, 11(2), 233-40.

For a nonnegative integer n, an explicity formula is given for the number of quadruples (t_{1, t2, t3, t4) of trianular numbers such that n = 11 =2 +(t3, t4), As a consequence of this formula i has been deduced that every nonnegative integer is of the form t1 + t2 + 2(t3 + t4) for some triangular numbers t1, t2, t3, t4.}

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004201   Vikram;Man Singh (Dep of Math and Statis, CCS Haryana Agric Univ, Hisar) : Steady-state solution of multiple parallel channels in series with impatient customers and balking. J Indian Soc Statist Ops Res 2003, 24(1-4), 25-37.

Queueing models of multiple parallel channels in series with impatient customers where the concepts of both balking and reneging have been introduced. Derives the steady-state solutions of M-serial service phases where the i^th service phase consists of c_i (i = 1, 2, 3, ......,M) identical parallel service channels. The model has direct applications to real life situations.

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004200   Vaganan B M;Kumaran M S (Sch of Math, Madurai Kamaraj Univ, Madurai-625 021) : Direct similarity solutions of the Burgers equation with variable viscosity. Indian J pure appl Math 2003, 34(11), 1645-69.

Direct method of Clarkson and Kruskal is applied to the Burgers equation with variable viscosity, u_t + u u_x = 1/2 Δ (t) u_xx to obtain the similarity solutions Similarity variables are found in terms of an infinite series using perturbation technique.

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004199   Tuteja R K;Taneja G;Malik A (Dep of Statistics, M.D.University, Rohtak-124 001) : Profit evaluation of a two-unit warm standby system with partial failure and waiting time of repairman. J Indian Soc Statist Ops Res 2000, 21(1-4), 39-51.

The profit of a two-unit warm standby system with waiting time of repairman has been analysed. A unit can fail totally either directly from normal state or via partial failure. On the failure of a unit, a repairman is informed immediately about the failure of a unit and he takes some random time to arrive at the system. If both the units fail, the arrival time is assumed to be negligible. Before going back, the repairman repairs all the units which fail during his stay at the system.

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004198   Tripsiannis G A;Papathanasiou A A;Philippou A N (Dep of Med Statist, Fac of Medicine Democritus Univ of Thrace, 68100 Alexandroupolis, Greece) : Multivariate generalized negative binomial distribution of order k, type II. J Indian Soc Statist Ops Res 2003, 24(1-4), 1-15.

Sen and Jain (1996, 1997) derived an order k (or cluster) generalized negative binomial distribution and a multivariate generalized negative binomial one. Philippou et al. (1988, 1990) introduced the study of multivariate distributions of order k, two of which are the type II multivariate negative binomial of order k and the multinomial of the same order. Presently, all four distributions are generalized to a multivariate generalized negative binomial distribution of order k, type II, by means of an approprite sampling scheme and a first passage event. This new distribution includes as special cases several known and new multivariate distributions of order k, type II, and gives rise in the limit to multivariate generalized logarithmic and Borel-Tanner distributions, and, by conpounding to multivariate generalized Polya distribution of the same order and type. Limiting cases are considered and applications are indicated.

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004197   Tripathy B C;Mikail E T;Altin Y (Math Sci Div, Inst of Advanced Study in Sci and Tech, Khanapara, Guwahati-781 022) : Generalized difference sequence spaces defined by orlicz function in a locally convex space. J Analysis Applic 2003, 1(3), 175-92.

The idea of difference sequence spaces was introduced by Kizmaz and this concept was generalized by Et and Colalk. Some new sequence spaces with respect to an Orlicz function and for allq∈Q, where Q is the set of continuous seminorms has been introduced. Some inclusion relations involving these sequence spaces has have been given. It has been show that the spaces.

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004196   Sulaiman W T (NO, Ajman Univ, P.O. Box 346, Ajman, United Arab Emirates) : Inclusion theorems for absolute matrix summability methods of an infinite series (IV). Indian J pure appl Math 2003, 34(11), 1547-57.

New general theorems characterising the relation between the two summabilities <124> T, p_n <124>_k and <124> N_{comp(D), pn<124>k are given. Many other results are deduced.}

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004195   Singh S P (Math Dep, T.D.P.G. Coll, Jaunpur-222 002) : On certain transformation formulae for poly-basic hypergeometric series. Indian J pure appl Math 2003, 34(11), 1539-46.

Certain transformation formulae for poly-basic hypergeometric functions have been established.

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004194   Singh R P;Rajeev Kumar (Dep of Math, Lajpat Rai Coll, Sahibabad (Ghaziabad)) : Weighted J-divergence of order α and type β and its applications. J Indian Soc Statist Ops Res 2000, 21(1-4), 31-8.

Derives non-additive weghted J-divergence of order α and type β, through a generalized functional equation. The generalized functional equation has been solved by the method of substitution. Presents the particular cases. Considering homogeneity of weighted distribution, Euler's theorem has been used to get some important inequalities due to non-homogeneity of the probability distribution.

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004193   Sindhu B S (Dep of Math, Univ Coll, Rohtak-124 001) : Reliability and profit evaluation of a Two-unit cold standby system with regular and visiting repairman. J Indian Soc Statist Ops Res 2002, 23(1-4), 1-17.

Deals with a two-unit cold standby system with two types of repairman-regular and visiting. Regular repairman remains always with the system and while repairing a failed unit, he may need rest then another repairman (known as visiting repairman) is called to complete the repair. Two models are discussed. In Model 1, it is assumed that the repairman repairs all the units which fail during his stay at the system. In Model 2, the regular repairman on his availability takes over the unit from the visiting repairman. System is analysed by making use of semi-Markov processes and regenerative point technique. Comparative study of two models is made through graphs.

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004192   Shu X;Li Y (Math Dep, Zhongshan (Sun Yat-Sen) Univ, Guangzhou, 510275, P.R. China) : Ishikawa iterative process for constucting solutions of k-subaccretive operator equations. Far East J mathl Sci 2003, 11(2), 215-28.

The convergence of Ishikawa iterative sequences with errors is studied for equation x - Tx = ∫ with a l-subaccretive operator in uniformly smooth Banach spaces and general Banach spaces.

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004191   Shoukaku Y;Yoshida N (NO, Toyama Natn Coll of Maritime Technol, Toyama 933-0293 Japan) : Oscillatory properties of solutions of nonlinear parabolic equations with functional arguments. Indian J pure appl Math 2003, 34(10), 1469-78.

The oscillations of nonlinear parabolic equations are studied, and it is shown that every solution of certain boundary value problems is oscillatory or satisfied some limit condition. The approach used is to reduce the multi-dimensional problem to a one-dimensional oscillatio problem by using some integral means of solutions.

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004190   Shirali N (Dep of Math, Chamran Univ, Ahvaz, Iran) : On the cardinality of the minimal generating set of modules with Krull-dimension. Far East J mathl Sci 2003, 11(1), 95-104.

The concept of λ-critical loewy modules has been introduced and studied. Using this concept a nontrivial upper bound for the cardinality of the minimal generating set of modules with krull-dimension has been found. This generalizes the similar result for Artinian modules.

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004189   Sharma A;Sharma A K (Dep of Math, Raj Rishi P.G. College, Alwar-301 001) : A deterministic production inventory model for deteriorating items with inventory level dependent demand rate considering shortages. J Indian Soc Statist Ops Res 2002, 23(1-4), 75-81.

Studies a production Inventory Model for deteriorating items when demand rate depends on inventory level at that time. The Production rate depends on demand rate. The proposed model allows for shortages and excess demand is back logged, as well. Approximate expressions for the production scheduling period, maximum inventory level, unfilled order backlog and total average cost obtained.

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