002168   Singh K N;Singh K (Dep of Math, S.G.R.P.G. Coll, Dobhi, Jaunpur-222 149) : On uniform matrix summability of a fourier series. Acta Cienc Indica-Math 2005, 31(3), 815-8.

The concept of uniform matrix summability has been introduced. Saxena and Rajagopal established same interesting results on uniform harmonic and No'rlund Summability of Fourier Series. A more general result than those of Saxena and Rajagopal has been obtained so that their results come out as particular cases.

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002167   Singh A P;Nadeem A;Kumar S (NO, , ) : Routing selection criteria in a distributed service network. Acta Cienc Indica-Math 2005, 31(3), 861-6.

A mathematical solution for solving the routing selection problem with the constraints on the travel time has been formulated.

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002166   Sidheshwar Prasad (Germplasm Conserv Div, Natn Bur of Pl Genetic Resour, Pusa Campus, New Delhi-110 012) : New algorithm for accurate conversion of seed research data to uniform moisture level base. Seed Res 2005, 33(2), 211-2.

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002165   Sharma Y (Math Dep, Jodhpur Engng Coll & Res Cent, Jodhpur) : Generalized stieltjes transform of matrix variable. J Indian Acad Math 2005, 27(2), 289-93.

A generalization of the Stieltjes transform of matrix variable has been presented by taking the iteration of laplace transform.

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002164   Sharma P R;Chawla S (Math Dep, Univ of Raj, Jaipur-302 004) : Effect of slip velocity on MHD flow through inclined channel : upper wall is moving with constant velocity and lower wall is lying on the surface of two porous media of different permeabilities. J Indian Acad Math 2005, 27(2), 339-47.

The effect of slip velocity on MHD flow of an incompressible viscous electrically conducting fluid through inclined porous channel of non-conducting walls when upper wall is moving with constant velocity and lower wall is resting on two porous media of different permeabilities are investigated. The fluid flow regions are divided into three zones, e.g., Zone I : free fluid region, Zone II : high permeability region and Zone III : low permeability region. The velocity distributions are derived usig N-S equations, Darcy's law and Brinkman equation for slip boundary conditions for the above zones, respectively. The effects of croos-flow Reynolds number, permeability parameters, slip parameter and the Hartmann number on the velocity field are discussed numerically and presented through Figures. The expression of skin-friction coefficient at the upper wall is derived, discussed numerically and it's numerical values for various values are presented through table.

2 illus, 1 table, 12 ref

002163   Sharma D;Gupta D (Dep of Math, N.A.S. Coll, Meerut (U.P)) : Stochastic behaviour of standby redundant parallel system. Acta Cienc Indica-Math 2005, 31(3), 867-47.

The authors have considered a complex system consists of two identical subsystems in standby redundancy. The authors idea is to take standby system can be put into the operation, after failure of original, through an imperfect switch. The whole system can fail either due to the failure of switch or due to the failure of both subsystem. Availability and cost function have obtained at the end. Complex system, exponential and general time distribution, ergodic, behaviour, Abel's lemma, and some particular cases have been considerd.

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002162   Sharma D;Gupta D (Dep of Math, N.A.S. Coll, Meerut (U.P)) : Measures of different reliability paramaters for a complex redundant system under head-of-line repair. Acta Cienc Indica-Math 2005, 31(3), 844-53.

A complex system having two subsystems A and B connected in series have been considerd. The subsystem A consists of N non-identical units in series, while subsystem B consists of three identical units in parallel. Head-of-line repiar policy is being adopted. The whole system can fail either due to its normal working or due to environmental effects. Availability and cost function have been obtained in the end.

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002161   Saxena R K;Ram J;Chandak S (Dep of Math and Statist, Jai Narain Vyas Univ, Jodhpur-342 005) : Integral formulas for the H-function generalized fractional calculus associated with erdelyl-kober operator of weyl type. Acta Cienc Indica-Math 2005, 31(3), 761-6.

The object of this article is to derive the images of the product of the H-function, in which its argument contains a factor zt^h (t^k + c^μ)^-p, and a general class of polynomials defined by Srivastava under the multiple Erdelyi-Kober operator due to Galue et al. The results obtained are general in character and includes, as special cases, the results for Riemann-Liouville operator, Erdelyi-Kober operator, Saigo operator and the operator defined by Kalla and Kiryakova.

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002160   Sarsak M S (Math Dep Fac of Sci and Arts, The Hashemite Univ, P.O. Box 150 459, Zarqa-13115, Jordan, Email: sarsak@hu.edu.jo) : Quasi continuous functions. J Indian Acad Math 2005, 27(2), 407-14.

A new class of functions on a bitopological space called quasi continuous functions is introduced and studied; a decomposition of quasi continuous functions is given; it is shown that a function is quasi continuous if, and only if, it is quasi λ-continuous and quasi g-continuous. Also the class of quasi homoeomorphisms is introduced and a group of quasi homeomorphisms on a bitopological space is investigated.

6 ref

002159   Sao G S;Sahu D P;Patel R N;Dasgupta M;Patel T (Dep of Math, K.G. Arts and Sci Coll, Raigarh-496 001) : (NULL). Acta Cienc Indica-Math 2005, 31(3), 891-2.

Common fixed point theorem using compatability in 2-Metric space has been established

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002158   Sao G S;Sahu D P;Patel R N;Dasgupta M;Patel T (Dep Math, K.G. Arts & Sci Coll, Raigarh-496 001) : Common fixed point theorem under weak compatability of type (A) in fuzzy 2-metric space. Acta Cienc Indica-Math 2005, 31(3), 893-6.

Common fixed point theorem using compatability in fuzzy 2-Metric space has been established.

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002157   Sao G S;Sahu D P;Patel R N;Dasgupta M;Patel T (Dep of Math, K.G. Arts and Sci Coll, Raigarh-496 001) : Common fixed point theorem under weak compatability of type (A) in L. space. Acta Cienc Indica-Math 2005, 31(3), 889-90.

Common fixed point theorem using weak compatability of type (A) in L-space has been established.

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002156   Sao G S;Sahu D P;Patel R N;Dasgupta M;Patel T (Dep of Maths & Res Cent, K.G. Arts & Sci Coll, Raigarh-496 001) : Common fixed point throrem for generalized asymtotically regular mapping in 2-metric space. Acta Cienc Indica-Math 2005, 31(3), 887-8.

Common fixed point theorem using Asymptotically Regular in 2-Metric space has been established.

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002155   Santosh Ksumar;Imdad M (Appl Math Dep, Coll of Engng, Roorkee, U.A.-202 002) : General common fixed point theorem without continuity. J Indian Acad Math 2005, 27(2), 215-29.

A common fixed point theorem for eight non-continuous pairwise coincidentally commuting mappings satisfying a functional inequality in proved which generalizes earlier results.

28 ref

002154   Santhakumaran A P;Athisayanathan S (Dep of Math, ST. Xavier's Coll (Autonomous), Palayamkottai-627 002) : Average degree, deficiency, sufficiency and density of a graph. Acta Cienc Indica-Math 2005, 31(3), 717-24.

The concepts of average deficiency and average sufficiency of a graph have been introduced and their relationships with average degree and density of a graph have been discussed and results regarding these parameters. Necessary and sufficient conditions for the average degree have been analysed to realize certain values and also for the existence of a graph with a given number as its average degree. Graphs for which the deficiency is equal to, greater than or less than the sufficiency and also graphs for which the average degree and density are equal have been characterised. Further Nordhaus-Gaddum type results on all these parameters are derived.

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002153   Santhakumaran A P (Dep of Math, ST. Xavier's Coll (Autonomous), Palayamottai-627 002) : Median with respect to cliques. Acta Cienc Indica-Math 2005, 31(3), 633-42.

The concepts of vertex-to-clique distance sum, clique-to-vertex distance sum and clique-to-clique distance sum have been introduced in a connected graph. Using these concepts the corresponding medians and peripheries have been defined and the properties of these centrality concepts have been investigated. A self clique-to-clique median graph have been chracterized in terms of its clique graph.

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002152   Sallam R H;Adeb A N;Manna A H (Math Dep Fac of Scinence, Helwan Univ, Cairo, Egypt) : On quasi-frobenius rings a strongly right johns which is quasi-frobenius. J Indian Acad Math 2005, 27(2), 295-8.

A ring R is called right johns if R is right noetherian ring such that every right ideal A of R is an annihilator (i.e. rl (A) = A for all right ideals A of R). R is called strongly right johns if every matrix ring over R is right johns. It is shown by Carl Faith and Pere Menal that a right R is strongly right johns if, and only if, R is right noetherian left FP-injective ring. It is shown that strongly right johns ring is quasi-frobenius without any extra condition.

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002151   Reddy K J (Dep of Math, L.B.R. Coll of Engng, Maylavaram, Krishna Dist (A.P.)) : Flow of a viscous incompressible fluid of variable viscosity through a Porous medium between two parallel planes in the presence of suction/injection. Acta Cienc Indica-Math 2005, 31(3), 751-6.

The steady flow of a viscous incompressible fluid between parallel infinitely long horizontal planes is considered. A layer of porous medium occupies the region adjacent to the upper plane. The two planes are kept at different constant temperatures and the viscosity of the fluid is assumed to vary exponentially with the temperature. The fluid motion is also subjected to a uniform suction and injection at the upper and lower planes respectively. The horizontal upper porous layer moves along with a constant velocity U. The lower plane is at rest. The Brinkman's law is modified for the flow through a moving porous medium. The vertical velocity is a constant. The horizontal velocity and temperature are functions of the vertical coordinate. The matching conditions are obtained using the law of conservation of momentum across the interface. The steady non-linear problem is solved subject to the boundary conditions at the two horizontal planes and the matching conditions at the interface. A shooting method known as the method of Adjoints is used to obtain the numerical solution. The effect of the presence of the porous layer is investigated in comparison with the case of a free fluid.

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002150   Rawat R S;Silswal G P (Dep of Math, H.N.B. Garhwal Univ Campus, Badshahithaul Tehri (Garhwal)-249 199) : Decomposition of recurrent curvature tensor fields in a kaehlerian recurrent space. Acta Cienc Indica-Math 2005, 31(3), 795-9.

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002149   Rastogi S C (Dep of Math, Saroj Inst of Technol and management Ahimamau, Sultanpur Road, Lucknow-226 006) : Generalised bi-recurrent and semi recurrent riemannian spaces. Acta Cienc Indica-Math 2005, 31(3), 617-24.

Defined generalized bi-recurrent and generalized semi-recurrent Riemannian spaces and studied their properties vis-a-vis other well known recurrent spaces, studied by Ruse, Walker, De and Biswas, Lichnerowicz and Rastogi.

8 ref

002148   Rao P S R C (Math Dep, Kakatiya Inst of Technol and Sci, Warangal-506 015, Email: patibanda20@yahoo.co.in) : Solution of the fourth order boundary value problems using spline functions. Indian J Math mathl Sci 2006, 2(1), 47-56.

The conventional approach due to Ahlberg. et' al. for the construction of a fifth order spline function has been used and applied the albesiny and Hoskin method to solve the fourth order differential equation y ^IV (x) + g (x) y (x) = r (x), where g (x) r (x) are given functions, with the two sets of boundary conditions has been applied. Examples are solved to demonstrate the application of the methods discussed.

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002147   Ramaraj T;Nirmala G (NO, A.V.V.M. Sri Pushpam Coll (Autonomous), Poondi-613 503) : Genetic algcorithm to formulate quadratic steiner tree problem of optimal neuro fuzzy network. Acta Cienc Indica-Math 2005, 31(3), 897-902.

With the advent of computers, optimization has became a part of Computer aided design activities. Optimization is an esoteric technique used only in the History of Mathematics and Operations research activities. Genetic algorithms are stochastic in nature with statistical probabilistic transition rules. Genetic Algorithm and its operators have been applied to the 0-1-2 Steiner problem seeks a minimum weight subgraph. Wide-band technology has the capability to carry many services such as voice, video and other web-site technology on one-link Corresponding networks thus differ significantly from traditionally dense copper based networks. Wide-band networks are sparse and tree-like, with few disjoint paths between any pair of nodes. Therefore connectivity has become a very important issue for these networks. A genetic algorithm generates Topology of decomposition tree sub-graphs of networks. A study on minimal graphs has been initiated to construct 0-2 problems.

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002146   Ramaraj T;Komahan G (A.V.V.M.Sri Pushpam Coll, (Autonomous), Poondi-613 503) : Fuzzy scalar and vector median filters based on fuzzy distances. Acta Cienc Indica-Math 2005, 31(3), 745-9.

Fuzzy scalar median (FSM) is proposed defined by using ordering of fuzzy numbers based on fuzzy minimum and maximum operations defined by using the extension principle. Alternatively, the FSM is defined from the minimization of fuzzy distance measure, and the equivalence of the two definitions is proven. Then, the fuzzy vector median (FVM) is proposed as an extension of vector median, based on a novel distance definition of fuzzy vectors, which satisfy the property of angle decomposition. By defining properly the fuzziness of a value, the combination of the basic properties of the classical scalar and vector median (VM) filter with other desirable characteristics can be succeeded.

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002145   Ramaraj T;Kannappa N (Dep of Math, A.V.V.M. Sri Pushpam Coll (Autonomous), Poondi (T.N)) : On bi-ideals of Smarandache-near-rings. Acta Cienc Indica-Math 2005, 31(3), 731-3.

Smarandache-near-ring through bi-ideals with idempotents have been studied. Smarandache-bi-ideal and some properties have been obtained.

8 ref

002144   Pradhan P;Sharma G (Dep of Math and Statist GKVV, , Hardwar (Uttaranchal)) : Some queueing theoretic solution methods for parallel and distributed systems. Acta Cienc Indica-Math 2005, 31(3), 911-16.

32 ref

002143   Pescar V (Math Dep Fac of Sci, Transilvania Univ of Brasov, 2200 Brasov, Romania) : On the univalence of some integral operators. J Indian Acad Math 2005, 27(2), 239-43.

Some integral operators are studied and conditions for the univalence of these integral operators have been determined.

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002142   Patel R N;Sahu D P;Sao G S;Dasgupta M;Patel T (Dep of Maths & Res Cent, K.G. Arts & Sci Coll, Raigarh-496 001) : Common fixed point theorem for generalized asymptotically regular mapping in fuzzy 2-metric spaces. Acta Cienc Indica-Math 2005, 31(3), 841-3.

Common fixed point theorem using Asymptotically Regular in 2-Fuzzy Metric space has been established.

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002141   Pal R B;Gupta I C;Sharma R K (Dep of Math, Govt. Raza P.G. Coll, Rampur (U.P)) : Semi-Symmetric metric (F-T) connection in an almost norden contact metric manifolds. Acta Cienc Indica-Math 2005, 31(3), 829-830.

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002140   Navlekar A;Khobragade N W (Dep of Math, MJP Educ Campus Nagpur Univ, Nagpur-440 010) : Unsteady-state thermoelastic problems of a thin annualar disc. Acta Cienc Indica-Math 2005, 31(3), 691-6.

Direct steady-state thermoelastic problem to determine the temperature, displacement and stress functions of a thin annular disc occupying the space D: a ≤ r ≤ b, 0 ≤ z ≤ h with the stated boundary conditions has been considerd. The finite Hankel transform and Laplace transform techniques have been used.

7 ref

002139   Narayanan R (NO, , 127, Nehru Nagar, Thrissur-680 006) : Infinite family of generalized fibonacci polynomials. J Indian Acad Math 2005, 27(2), 415-20.

Fibonacci Polynomials are generalized by : H₀ (x) = 0, H₁ (x) = 1, H₂(x) = a_ξ-2 x, H₃ (x) = a_ξ-3 x,..., H_{ξ-1 (x) = a1 x and for n ≥ 0 Hn+ξ (x) = a1 x Hn+ξ-1 (x) + a2 x Hn+ξ-2 (x) + ... + ξ-3 x Hn+3 )x) + aξ-2 x Hn+2 (x) + aξ-1 Hn+1 (x) + aξ Hn (x). where, a1, a2, a3... aξ-1, aξ are arbitrary algebraic integers and ξ = 2, 3, ... ∞. One should note this notation Hn (x) where ξ may be called the level of the Generalized fibonacci polynomials.}

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002138   Najafzadeh S;Kulkarni S R (Dep of Math, Fergusson Coll, Pune-411 004) : Some inequalities on multivalent functions Defined by hypergeometric and exponential function in terms of ruscheweyh derivative. Acta Cienc Indica-Math 2005, 31(3), 789-94.

By using hypergeometric and exponential functions a p-valent function of the from f(z)= mz^p- Σ^2p_k=p+1 t_k-p-1 z^k-p-1 + (e^z+2F₁ (a,b;c,z) k=p+1 has been defined. Some theorems involving inequalities on this function in terms of Ruscheweyh derivative have been found.

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002137   Murugesan N (Dep of Math, Sri Ramakrishna Engng Coll, Coimbatore-641 0022) : Utilization of distorted rays in the discrete geometric space. Acta Cienc Indica-Math 2005, 31(3), 647-50.

Discrete analytic continuation is the standard process of defining analytic functions in all the discrete function theories. It is the process of continuing the given function defined on a suitably chosen subset of the space to the whole space under consideration. q-analytic functions studied by Harman in 1972 defined in such a way from the points of coordinate axes. That is from the set of limit points. The utilization of distorted rays in the discrete geometric space defined by Harmon for analytic continuation of q-analytic functions from a set of interior points have been discussed.

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002136   Murty M S N;Appa Rao B V (Appl Math Dep, A.N.U.P.G. Cent, Nuzvid-521 201) : On three-point boundary value problems for quasi-linear systems. J Indian Acad Math 2005, 27(2), 245-51.

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002135   Mohd Rafi;Mohd Salmi (NO, Natn Univ of Malaysia, 43600 UKM, Bangi, Selangor D.E., Mlaysia, Email: mdratzi@yahoo.com) : Generalized fixed point of asymptotically regular multivalued mappings in PM spaces. Indian J Math mathl Sci 2006, 2(1), 57-67.

Some results on generalized fixed point of asymptotically regular multivalued mapping are obtained in PM spaces. The structure of common fixed points and coincidence points of a pair of compatible multivalued mapping in PM spaces have been discussed. The work generalizes the work done by Ismat Beg and Akbar Azam from metric spaces to PM spaces.

11 ref

002134   Mittal P K;Dhasmana V;Bijalwan M (Dep of Math, Govt. P.G. Coll, Rishikesh, Dehradun (Uttaranchal)) : A Note on vorticity for surface flow through a porous medium in an inclined channel. Acta Cienc Indica-Math 2005, 31(3), 675--80.

Vorticity of steady laminar flow of viscous in-compressible fluid through a porous medium bounded by an open inclined channel. The free surface of the fluid is exposed to the atmospheric pressure. Fourier transform technique has been used to solve the problem. Analytical expression for velocity and vorticity of the flow has been obtained and the effects of permeability parameter, K on the vorticity of fluid flow has been represented graphically and interpreted thereof.

12 ref

002133   Mittal P K;Bijalwan M (Dep of Math, Govt. P.G. Coll, Rishikesh-249 201) : A Study of vorticity of fluctuating flow of an visco-elastic fluid past an infinite plate with variable suction in slip flow regime. Acta Cienc Indica-Math 2005, 31(3), 903-10.

The vorticity of the two-dimensional flow of an incompressible viscoelastic (Kuvshinski type) fluid past an infinite porous wall with variable suction in slip-flow regime is investigated under the following conditions : the suction velocity normal to the plate oscillates in magnitude but not in direction about non-zero mean and the free stream velocity oscillate in time about a constant mean. Analytical expression for the vorticity has been obtained from the expression of velocity of given fluid flow. To see the quantitative effects of different physical parameters such as elasticity parameter, λ suction parameter, A and rarefaction parameter, h₁ on the vorticity of given fluid, the changes in vorticity profile have been obtained mumerically and shown graphically followed by a discussion.

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002132   Mittal P K;Bijalwan M (Dep of Math, Govt. P.G Coll, Rishikesh, Dehradun (Uttranchal)) : A Note on vorticity of unsteady flow of an electrically conducting dusty viscous liquid between two parallel plates. Acta Cienc Indica-Math 2005, 31(3), 874-86.

This paper investigates the vorticity of two dimensional laminar flow of an electrically conducting viscous incompressible fluid with embedded non-conducting indentical spherical particles between two parallel flat plates under the influence of a uniform magnetic field and a time varying pressure gradient taking the fluid and dust particles to be initially at rest. Laplace transform technique has been used to solve the problem analytically and expression for vorticity of the flow has been obtained for two particular cases when both plates are at rest. The changes in vorticity profiles for liquid and dust panicles have been obtained numerically and the effect of magnetic field on vorticity profiles have been shown graphically and interpreted thereof.

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002131   Metkar A M;Chirade V R;Deshmukh A G (Dep of Math, Govt. Vidarbha Inst of Sci & Humanities, Amravati-444 604) : The coordinate system in which gaalfa = 0, for the plane gravitational waves for Z= (z-t) and Z = (t/z) types in six dimension. Acta Cienc Indica-Math 2005, 31(3), 855-60.

Coordinate system in which g_aα = 0; a = 1, 2, 3, 4, α = 5, 6 has been obtained.

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002130   Metha R D;Modi H B (Dep of Math, Sardar Patel Univ, Vallabh Vidyanagar-388 120) : Equivalent conditions for normal and relativity regular element in the C-algebra. Acta Cienc Indica-Math 2005, 31(3), 819-22.

The equivalent conditions for normal and relatively regular elements in the C*-algebra have been found.

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002129   Mehta D A;Shah D V (NO, , ) : p-th Order (a, d)-cut-off numbers. J Indian Acad Math 2005, 27(2), 231-7.

p-th order (a, d)-Cut off Numbers' are introduced. Using the theory the theory of Pell's equation, it has been proved that for any given positive integers a and d (and fixed p), there always exist infinitely many such numbers. Complete characterization of such numbers is performed and the formula for these numbers is described. Also the estimation of such numbers not exceeding some large real number Z has been obtained. Finally, the recurrence relation for these numbers is obtained.

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002128   Maragathawalli S;John M S (Dep of Math, Sree Saraswati Thyagaraja Coll, Pollachi-642 108) : Strongly alfag -closed sets in topological spaces. Acta Cienc Indica-Math 2005, 31(3), 805-21.

A new class of sets namely strongly α-closed sets, which is a proper subset of g* closed sets. Applying these sets author introduce five new spaces s*T_es *T*_g, αgT_s; gsT_s* and gT_s* spaces. Paper also investigated several properties of strongly αg* closed sets and the above five spaces.

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002127   Linga Raju T;Murty P S R (Engng Math Dep, Andhra Univ, Visakhapatnam-530 003, Email: tlraju45@yahoo.com) : Quasi-steady state solutions of unsteady ionized hydromagnetic flow between two parallel porous walls in a rotating system. J Indian Acad Math 2005, 27(2), 391-406.

An attempt has been made to present the quasi-steady state solutions for an unsteady MHD ionized flow with Hall currents between two parallel porous walls subject to the action of uniform transverse magnetic field in a rotating frame of reference. It is assumed that the induced magnetic field is negligible in comparison with applied magnetic field under an assumption that the magnetic Reynolds number is small. The exact solutions for both primary and secondary velocity distributions, their corresponding mean velocities are also obtained for two cases such as when the walls are made up of non-conducting and conducting porous materials. The velocity profiles have been drawn after obtaining the computational values for various sets of values of the governing parameters involved. In case of non-conducting porous walls, the solutions are independent of `s' (ratio of electron pressure to the total pressure) while these are depending on it for conducting porous walls. The primary velocity distribution increases in the upper half of the channel and decreases in the lower half of the channel, whereas the secondary velocity distribution increases except near the upper wall as the suction number increases.

12 illus, 31 ref

002126   Krishna D V;Rao P N (Dep of Math, S.K. Univ, Anantapur-515 003) : Magneto hydrodynamic unsteady flow through a rectangular duct with a prescribed discharge. Acta Cienc Indica-Math 2005, 31(3), 917-32.

Transient MHD flow through a rectangular duct with insulated walls using Galerkin Weighted residual method has been investigated. The unsteadiness in the flow is due to the time dependent prescribed discharge. A uniform magnetic field is imposed normal to one of the channel walls and assuming that the Magnetic Reynolds number smaller than unity, the induced magnetic field is neglected compared to the applied field. An initial-value problem is formulated and the Galerkin method is used to obtain the approximate solution of the transformed equation. The pressure gradient and the velocity field are evaluated using Laplace inversion method and their behaviour is discussed numerically for different forms of the discharge as well as variations in the governing parameters.

14 illus, 3 table, 28 ref

002125   Khobragade N W;Wankhede P C (Dep of Math, MJP Educ Campus Nagpur Univ, Nagpur-440 010) : An inverse steady-state problem of thermoelastic deformation of a finite length hollow cylinder -VIII. Acta Cienc Indica-Math 2005, 31(3), 665-74.

This paper is concerned with the inverse steady-state thermoelastic problem to determine the temperature, displacement and stress functions on the outer curved surface in the finite isotropic hollow cylinder of length 2h occupying the space D : a ≤ r ≤ b, - h≤z≤h by applying finite Marchi-Fasulo integral transform technique. The third kind boundary condition [T(r,z)+ ϑT(r,z)/ϑr]_r=ξ = f(z) for a fixed value of ξ a <60> ξ <60> b is a known function of z and homogeneous boundary condition of the third kind is maintained on the plane surfaces while on inner curved surface the third kind boundary condition is maintained at u(z), which is a known function of z.

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002124   Khobragade N W;Khot P G (Dep of Math, MJP Educ Campus Nagpur Univ, Nagpur-440 010) : Alternative approach to the simplex method - II. Acta Cienc Indica-Math 2005, 31(3), 651-6.

An alternative approach to the simplex method of linear programming is suggested. The method sometimes involves less iterations than in the simplex method or at the most an equal number. This powerful technique is better understood by resolving a cycling problem.

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002123   Khobragade N W (Dep of Math, MJP Educ Campus Nagpur Univ, Nagpur-440 010) : Steady-state direct thermoelastic problems of a thin rectangular plate. Acta Cienc Indica-Math 2005, 31(3), 697-702.

Direct steady-state thermoelastic problem to determine the temperature, displacement and stress functions of a thin rectangular plate occupying the space D: 0 ≤ x ≤ a, -b ≤ y ≤ b with the stated boundary conditions has been considerd by applying finite Marchi-Fasulo transform technique. The results are illustrated graphically.

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002122   Khobragade K W;Khobragade N W (Math Dep, MJP Educ Campus Nagpur Univ, Nagpur-440 010) : Inverse steady-state thermoelastic problem of a finite length hollow cylinder-II. J Indian Acad Math 2005, 27(2), 261-88.

An attempt has been made to solve two inverse problems of thermoelasticity. In the first proble, an attempt has been made to determine the unknown temperature, displacement and stress functions on the upper plane surface in the finite isotropic hollow cylinder of length h occupying the space D: a ≤ r ≤ b, O ≤ z ≤ h by applying finite Hankel Transform technique. In the third king boundary condition [T(r,z) + ∂T/∂Z (r,z)] z = ζ + f(r) for a fixed value of ζ, 0 <60> ∂ <60> h is a known function of r and the temperature is maintained of the third kind is maintained on lower plane surface of the cylinder. The second problem, an attempt has been made to determine the unknown temperature, displacement and stress functions on the upper plane surface in the finite isotropic hollow cylinder of length h occupying the space D: a ≤ r ≤ b, O ≤ z ≤ h by applying finite Hankel Transform technique. The third kind boundary condition [T (r,z) + ∂T/∂Z (r,z)] z=ζ = f(r) for a fixed value of ζ, O <60> ζ <60> h is a known function of r with the temperature is maintained at zero on the curved surfaces and on lower plane surface, the on lower plane surface, the third..

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002121   Khadekar G S;Sam Durkar S (Math Dep, Nagpur Univ, Mahatma Jyotiba Phule Educational Campus, Amravati Road, Nagpur-440 010) : Cosmological models with variable cosmological term in Kaluza-Klein theory of gravitation. J Indian Acad Math 2005, 27(2), 307-15.

Five-dimensional Kaluza-Klein type variable Λ-cosmological models have been constructed with perfect fluid. Further, it is shown that the field equations are solvable for any arbitrary cosmic scale function B(t) or C(t). Some physical and geometrical features of ther models are discussed.

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002120   Kalpana;Gajendra Singh (Math Dep, Mahila Mahavidyalaya B.H.U., Varanasi-221 005) : Cr-submanifolds of a special quadratic Kahler manifold-I. J Indian Acad Math 2005, 27(2), 329-38.

Holomorphic sectional curvature and the scalar curvature of CR-submanifolds of an AQ-Kahler manifold have been obtained. Some results on totally geodesic and minimal CR-submanifolds of an SQ-Kahler manifold of constant holomorphic sectional curvature have also been discussed.

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002119   Hazarika M (Math Sci Dep, Tezpur Univ, Napaam-784 028, Email: munmun@tezuernet.in) : Unitary equivalence and reducibility of unilateral operator weighted shifts. J Indian Acad Math 2005, 27(2), 361-72.

The class of unilateral weighted shifts on H² (K) with quasi invertible weights has been considered. For an operator S in this class, a matrical description of the commutant of S is established and it is shown that S is unitarily equivalent to a weighted shift with positive weights. A criteria for reducibility of S is also established. Hence, it is shown that the lattice of reducing subspaces of S is isomorphic to the lattice of invariant subspaces of the weakly closed algebra generated by the weight sequence of S.

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