Volume 110, Issue 3
August 2000, pages 233-345
pp 233-261 August 2000
Poincaré polynomial of the moduli spaces of parabolic bundles
In this paper we use Weil conjectures (Deligne’s theorem) to calculate the Betti numbers of the moduli spaces of semi-stable parabolic bundles on a curve. The quasi parabolic analogue of the Siegel formula, together with the method of HarderNarasimhan filtration gives us a recursive formula for the Poincaré polynomials of the moduli. We solve the recursive formula by the method of Zagier, to give the Poincaré polynomial in a closed form. We also give explicit tables of Betti numbers in small rank, and genera.
pp 263-292 August 2000
Vijay Kodiyalam R Srinivasan V S Sunder
In this paper, we study a tower {A_{n}^{G}: n} ≥ 1 of finite-dimensional algebras; here, G represents an arbitrary finite group,d denotes a complex parameter, and the algebraA_{n}^{G}(d) has a basis indexed by ‘G-stable equivalence relations’ on a set whereG acts freely and has 2n orbits. We show that the algebraA_{n}^{G}(d) is semi-simple for all but a finite set of values ofd, and determine the representation theory (or, equivalently, the decomposition into simple summands) of this algebra in the ‘generic case’. Finally we determine the Bratteli diagram of the tower {A_{n}^{G}(d): n} ≥ 1 (in the generic case).
pp 293-304 August 2000
On the generalized Hankel-Clifford transformation of arbitrary order
Two generalized Hankel-Clifford integral transformations verifying a mixed Parseval relation are investigated on certain spaces of generalized functions for any real value of their orders (α-β).
pp 305-314 August 2000
C^{2}-rational cubic spline involving tension parameters
In the present paper, C^{1}-piecewise rational cubic spline function involving tension parameters is considered which produces a monotonie interpolant to a given monotonie data set. It is observed that under certain conditions the interpolant preserves the convexity property of the data set. The existence and uniqueness of a C^{2}-rational cubic spline interpolant are established. The error analysis of the spline interpolant is also given.
pp 315-322 August 2000
Coin tossing and Laplace inversion
An analysis of exchangeable sequences of coin tossings leads to inversion formulae for Laplace transforms of probability measures.
pp 323-334 August 2000
Differential equations related to the Williams-Bjerknes tumour model
We investigate an initial value problem which is closely related to the Williams-Bjerknes tumour model for a cancer which spreads through an epithelial basal layer modeled onI ⊂ Z^{2}. The solution of this problem is a familyp = (p_{i}(t)), where eachp_{i}(t)could be considered as an approximation to the probability that the cell situated ati is cancerous at timet. We prove that this problem has a unique solution, it is defined on [0, +∞[, and, for some relevant situations, lim_{t→∞}P_{i}(t) = 1 for alli ∈ I. Moreover, we study the expected number of cancerous cells at timet.
pp 335-345 August 2000
Suppression of instability in rotatory hydromagnetic convection
Recently discovered hydrodynamic instability [1], in a simple Bénard configuration in the parameter regime$$T_0 \alpha _2 $$ under the action of a nonadverse temperature gradient, is shown to be suppressed by the simultaneous action of a uniform rotation and a uniform magnetic field both acting parallel to gravity for oscillatory perturbations whenever (Qσ_{1}/π^{2} + J/π^{4}) > 1 and the effective Rayleigh numberR(1 -T_{0}α_{2}) is dominated by either 27π^{4}(1 + l/σ_{1}/4 or 27π^{4}/2 according as σ_{1} ≥1 or σ_{1}≤ 1 respectively. HereT_{0}is the temperature of the lower boundary while α_{2} is the coefficient of specific heat at constant volume due to temperature variation and σ_{1},R,Q andJ respectively denote the magnetic Prandtl number, the Rayleigh number, the Chandrasekhar number and the Taylor number.
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