• Volume 98, Issue 1

June 1988,   pages  1-99

• Cohomology of certain moduli spaces of vector bundles

LetX be a smooth irreducible projective curve of genusg over the field of complex numbers. LetM0 be the moduli space of semi-stable vector bundles onX of rank two and trivial determinant. A canonical desingularizationNo ofMo has been constructed by Seshadri [17]. In this paper we compute the third and fourth cohomology groups ofNo. In particular we give a different proof of the theorem due to Nitsure [12], that the third cohomology group ofNo is torsion-free.

• On a class of slowly changing functions

We study the slowly changing functions and use them in the study of entire functions.

• Zeta functions of orders in quadratic fields

The zeta function of a lattice over an order in a semisimpleQ-algebra introduced by L Solomon, is a generalization of Dedekind zeta function and has an Euler product in terms of local zeta functions. In this paper, the local zeta functions of localized orders in quadratic fields and hence the global ones are computed first by using Solomon's combinatorial method. Next the same formulae are obtained by considering orders in algebras (overp-adic fields) obtained by completing quadratic fields. In the complete case, the methods of integration initiated by Bushnell and Reiner to study Solomon's zeta functions are used.

• Absolute matrix summability of the allied series of a Fourier series

In this paper we have proved a theorem for infinite triangular matrix using new techniques.

• On the$$|\bar N,p_n |$$ summability factors of infinite seriessummability factors of infinite series

In this paper a theorem of Chen [1] on$$|\bar N,p_n |$$ summability factors of infinite series has been proved under weaker conditions.

• On the bilateral generating functions of simple Bessel polynomial

In this note the bilateral generating relation of simple Bessel polynomial derived by Das, Chongdar and Chatterjea has been extended by using the group-theoretic method. An application of our result is also pointed out.

• Nonlinear random elliptic boundary value problem

In this paper we obtain a solvability result for random elliptic boundary value problem. Our result extends Browder's [2] main theorem to the random case. We use author's [4] fixed point theorem for this purpose.

• Unsteady state heat flow in epidermis and dermis of a human body

We investigate the unsteady state temperature distribution in human skin where subcutaneous tissues are not present. The mathematical model is employed for a onedimensional unsteady state case, taking the blood mass flow rate and metabolic heat generation variable with respect to the position in the dermis. The metabolic heat generation depends on the tissue temperature. The thermal conductivity is taken constant but different in two layers. The problem has been solved using Laplace transform and Bessel functions. Numerical results for a simple case are discussed.

• A class of exact solutions and physical behaviour of magnetic field lines in plasma column

Using hodograph and Legendre transformation functions the basic equations are recast in terms of this function, and the conditions which this function should satisfy are stated. Several applications of this method are considered, and the geometry of magnetic field lines is discussed.

• Propagation of waves in a micropolar elastic layer with stretch immersed in an infinite liquid

The effect of liquid on the propagation of waves in a micropolar elastic layer with stretch has been investigated. The frequency and wave velocity equations for symmetric and antisymmetric vibrations are derived. Propagation of monochromatic waves in a micropolar elastic layer with stretch is discussed. Results of this analysis reduce to those without stretch.

• # Proceedings – Mathematical Sciences

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