• Volume 110, Issue 3

      August 2000,   pages  233-345

    • Poincaré Polynomial of the Moduli Spaces of Parabolic Bundles

      Yogish I Holla

      More Details Abstract Fulltext PDF

      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 Harder-Narasimhan 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.

    • The Algebra of 𝐺-relations

      Vijay Kodiyalam R Srinivasan V S Sunder

      More Details Abstract Fulltext PDF

      In this paper, we study a tower $\{A^G_n(d):n≥ 1\}$ of finite-dimensional algebras; here, 𝐺 represents an arbitrary finite group, 𝑑 denotes a complex parameter, and the algebra $A^G_n(d)$ has a basis indexed by `𝐺-stable equivalence relations' on a set where 𝐺 acts freely and has 2𝑛 orbits.

      We show that the algebra $A^G_n(d)$ is semi-simple for all but a finite set of values of 𝑑, 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 $\{A^G_n(d): n≥ 1\}$ (in the generic case).

    • On the Generalized Hankel-Clifford Transformation of Arbitrary Order

      S P Malgonde S R Bandewar

      More Details Abstract Fulltext PDF

      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).

    • 𝐶2-rational Cubic Spline Involving Tension Parameters

      M Shrivastava J Joseph

      More Details Abstract Fulltext PDF

      In the present paper, 𝐶1-piecewise rational cubic spline function involving tension parameters is considered which produces a monotonic interpolant to a given monotonic 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 𝐶2-rational cubic spline interpolant are established. The error analysis of the spline interpolant is also given.

    • Coin Tossing and Laplace Inversion

      J C Gupta

      More Details Abstract Fulltext PDF

      An analysis of exchangeable sequences of coin tossings leads to inversion formulae for Laplace transforms of probability measures.

    • Differential Equations Related to the Williams-Bjerknes Tumour Model

      F Martinez A R Villena

      More Details Abstract Fulltext PDF

      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 on 𝐼 ⊂ 𝑍2. The solution of this problem is a family 𝑝=(𝑝𝑖(𝑡)), where each 𝑝𝑖(𝑡) could be considered as an approximation to the probability that the cell situated at 𝑖 is cancerous at time 𝑡. We prove that this problem has a unique solution, it is defined on [0, + ∞], and, for some relevant situations, lim𝑡 → ∞ 𝑝𝑖(𝑡)=1 for all 𝑖 ∈ 𝐼. Moreover, we study the expected number of cancerous cells at time 𝑡.

    • Suppression of Instability in Rotatory Hydromagnetic Convection

      Joginder S Dhiman

      More Details Abstract Fulltext PDF

      Recently discovered hydrodynamic instability [1], in a simple Bénard configuration in the parameter regime 𝑇0𝛼2 > 1 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 $(\mathscr{Q}𝜎_1/𝜋^2+\mathscr{J}/𝜋^4) > 1$ and the effective Rayleigh number $\mathcal{R}$(1-𝑇0𝛼2) is dominated by either 27𝜋4(1 + 1/𝜎1)/4 or 27𝜋4/2 according as 𝜎1 ≥ 1 or 𝜎1 ≤ 1 respectively. Here 𝑇0 is the temperature of the lower boundary while 𝛼2 is the coefficient of specific heat at constant volume due to temperature variation and 𝜎1, $\mathcal{R}, \mathscr{Q}$ and $\mathscr{T}$ respectively denote the magnetic Prandtl number, the Rayleigh number, the Chandrasekhar number and the Taylor number.

  • Proceedings – Mathematical Sciences | News

© 2017 Indian Academy of Sciences, Bengaluru.