• Volume 105, Issue 4

November 1995,   pages  371-469

• The Hodge conjecture for certain moduli varieties

For smooth projective varietiesX over ℂ, the Hodge Conjecture states that every rational Cohomology class of type (p, p) comes from an algebraic cycle. In this paper, we prove the Hodge conjecture for some moduli spaces of vector bundles on compact Riemann surfaces of genus 2 and 3.

• Equivariant cobordism of Grassmann and flag manifolds

We consider certain natural (ℤ2)n actions on real Grassmann and flag manifolds andS1 actions on complex Grassmann manifolds with finite stationary point sets and determine completely which of them bound equivariantly.

• Local behaviour of the first derivative of a deficient cubic spline interpolator

Considering a given functionfC4 and its unique deficient cubic spline interpolant, which match the given function and its derivative at mid point between the successive mesh point, we have obtained in the present paper asymptotically precise estimate fors′ -f′.

• On the partial sums, Cesáro and de la Valleé Poussin means of convex and starlike functions of order 1/2

In this paper we study certain properties of partial sums, cesáro and de la valleé Poussin means of convex and starlike functions.

• Uniqueness of the uniform norm and adjoining identity in Banach algebras

LetAe be the algebra obtained by adjoining identity to a non-unital Banach algebra (A, ∥ · ∥). Unlike the case for aC*-norm on a Banach *-algebra,Ae admits exactly one uniform norm (not necessarily complete) if so doesA. This is used to show that the spectral extension property carries over fromA to Ae. Norms onAe that extend the given complete norm ∥ · ∥ onA are investigated. The operator seminorm ∥ · ∥op onAe defined by ∥ · ∥ is a norm (resp. a complete norm) iffA has trivial left annihilator (resp. ∥ · ∥op restricted toA is equivalent to ∥ · ∥).

• Weakly prime sets for function spaces

We define and study weakly prime sets for a function space and show that it coincides with the known concept of weakly prime sets for function algebras and spaces of affine functions.

• Oscillation of higher order delay differential equations

A sufficient condition was obtained for oscillation of all solutions of theodd-order delay differential equation$$x^{(n)} (t) + \sum\limits_{i = 1}^m {p_i (t)} x(t - \sigma _{_i } ) = 0,$$ wherepi(t) are non-negative real valued continuous function in [T ∞] for someT≥0 and σi,∈(0, ∞)(i = 1,2,…,m). In particular, forpi(t) =pi∈(0, ∞) andn &gt; 1 the result reduces to$$\frac{1}{m}\left( {\sum\limits_{i = 1}^m {(p_i \sigma _i^m )^{1/2} } } \right)^2 &gt; (n - 2)!\frac{{(n)^n }}{e},$$ implies that every solution of (*) oscillates. This result supplements forn &gt; 1 to a similar result proved by Ladaset al [J. Diff. Equn.,42 (1982) 134–152] which was proved for the casen = 1.

• Nontrivial solution of a quasilinear elliptic equation with critical growth in ℝn

Suppose Δnu = div (¦ ∇u ¦n-2∇u) denotes then-Laplacian. We prove the existence of a nontrivial solution for the problem$$\left\{ \begin{gathered} - \Delta _n u + \left| u \right|^{n - 2} u = \int {(x,u)u^{n - 2} in \mathbb{R}^n } \hfill \\ u \in W^{1,n} (\mathbb{R}^n ) \hfill \\ \end{gathered} \right.$$ wheref(x, t) =o(t) ast → 0 and ¦f(x, t)¦ ≤C exp(αn¦t¦n/(n-1)) for some constantC &gt; 0 and for allx∈ℝ;t∈ℝ with αn =nωn1/(n-1), ωn = surface measure ofSn-1.

• An axisymmetric steady-state thermoelastic problem of an external circular crack in an isotropic thick plate

A steady state thermoelastic mixed boundary value problem for an isotropic thick plate is considered in this paper. The faces of an external circular crack situated in the mid-plane of the plate are opened up by the application of temperature while the bounding surface of the plate are maintained at a constant zero temperature. Solution valid for large values of the ratio of the plate thickness to the diameter of the crack has been obtained. Expressions for various quantities of physical interest are derived by finding iterative solutions of the equations and the results are shown graphically.

• Some characterization theorems in rotatory magneto thermohaline convection

The present paper extends the results of Banerjeeet al [2] for the hydromagnetic thermohaline convection problems of Veronis’ [9] and Stern’s [8] types to include the effect of a uniform vertical rotation.

• Proceedings – Mathematical Sciences

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