• Volume 93, Issue 1

      November 1984,   pages  1-66

    • Semistable sheaves on homogeneous spaces and abelian varieties

      V B Mehta M V Nori

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      In this paper we prove that semistable sheaves with zero Chern classes on homogeneous spaces are trivial and semistable sheaves on abelian varieties with zero Chern classes are filtered by line bundles numerically equivalent to zero. The method consists in reducing modp and then showing that the Frobenius morphism preserves semistability on the above class of varieties. For technical reasons, we have to assume boundedness of semistable sheaves in charp.

    • Thermal instability of a horizontal layer of micropolar fluid with heat source

      S P Bhattacharyya S K Jena

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      The thermal instability of a horizontal layer of micropolar fluid which loses heat throughout its volume at a constant rate has been considered. The influence of the various micropolar fluid parameters on the onset of convection have been analysed. It is found that heat source and heat sink have the same destabilising effect in micropolar fluid. It is observed that the horizontal dimension of the cells remains insensitive to the changes in the micropolar fluid parameters and also to the heat source parameterQ except forQ values near zero, where the change is drastic. Further, it is observed that though the vertical component of velocity and the curl of microrotation do not vanish anywhere between the two boundaries forQ=0, they vanish at a point nearer to the lower boundary even for a small change in theQ value.

    • Couette flow of a stratified fluid with suction varying along a boundary

      S Padmavathi K N Venkatasiva Murthy

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      A viscous incompressible fluid between two plane boundaries is stratified by maintaining the planes at different temperatures. The upper plane moves with a uniform velocity. The suction/injection mechanism with constant injection velocity at the upper plane and suction velocity varying sinusoidally along the lower plane with a wave numberk is introduced at the boundaries. The steady linearised equations are solved using similarity variables for the velocity components. The wave numberk is shown to be effective in controlling the boundary layer thickness.

    • Numerical studies of slow viscous rotating fluid past a sphere

      C V Raghava Rao K Pramadavalli

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      Navier-Stokes equations for steady, viscous rotating fluid, rotating about the zaxis with angular velocity ω are linearized using Stokes approximation. The linearized Navier-Stokes equations governing the axisymmetric flow can be written as three coupled partial differential equations for the stream function, vorticity and rotational velocity component. Only one parameterR=2ωa2/v enters the resulting equations. Even the linearized equations are difficult to solve analytically and the method of matched asymptotic expansions is to be applied. Central differences are applied to the two-dimensional partial differential equations and are solved by the Peaceman-Rachford ADI method. The resulting algebraic equations are solved by successive over relaxation method. Streamlines are plotted for Ψ=0·01, 0·05, and 0·25 andR=0·1, 0·3, 0·5.

    • Cohomology of discontinuous groups

      P Krishna Prasad

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      Prasad (1979) proved that the set of all equivalence classes of representationsp of a Fuchsian group Γ whose restrictions to the cyclic subgroups Γi-(ci) corresponding to the parabolic and elliptic elements of Γ occurring in the structure of Γ, are given, is a complex analytic manifold. In the process the author has proved thatH1(X,A)≈P1(Γ,ρ) and with suitable notation.

      This paper gives the corresponding results to the two above mentioned results, when in place of Γ we consider any discontinuous group of Poincare isometries Δ, and when similar assumptions are made.

    • On residual varieties of groups

      R D Giri

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      The concept of residuation in varieties introduced by Neumann [5] and reoriented and developed by Jónsson is further studied in this paper.

    • A Laurent series expansion formula and its applications

      R K Raina

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      This paper gives a certain Laurent series expansion for a generalized Rodrigues type formula. The main result finds many applications which are enumerated briefly.

    • A note on means and proximate type of entire Dirichlet series

      G S Srivastava H S Kasana

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      Proximate type is defined and constructed with the help of means under certain conditions for an entire Dirichlet series with index pair (p, q).

    • Formula for primes, twinprimes, number of primes and number of twinprimes

      A Venugopalan

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