Finiteness of the number of compatibly-split subvarieties

We show that for a Frobenius split variety, there are only finitely many closed subvarieties which are compatibly-split.Comment: 3 page

ETP-Mine: An Efficient Method for Mining Transitional Patterns

A Transaction database contains a set of transactions along with items and their associated timestamps. Transitional patterns are the patterns which specify the dynamic behavior of frequent patterns in a transaction database. To discover transitional patterns and their significant milestones, first we have to extract all frequent patterns and their supports using any frequent pattern generation algorithm. These frequent patterns are used in the generation of transitional patterns. The existing algorithm (TP-Mine) generates frequent patterns, some of which cannot be used in generation of transitional patterns. In this paper, we propose a modification to the existing algorithm, which prunes the candidate items to be used in the generation of frequent patterns. This method drastically reduces the number of frequent patterns which are used in discovering transitional patterns. Extensive simulation test is done to evaluate the proposed method.Comment: 11 page

Algorithms based on DQM with new sets of base functions for solving parabolic partial differential equations in (2+1)(2+1) dimension

This paper deals with the numerical computations of two space dimensional time dependent parabolic partial differential equations by adopting adopting an optimal five stage fourth-order strong stability preserving Runge Kutta (SSP-RK54) scheme for time discretization, and three methods of differential quadrature with different sets of modified B-splines as base functions, for space discretization: namely i) mECDQM: (DQM with modified extended cubic B-splines); ii) mExp-DQM: DQM with modified exponential cubic B-splines, and iii) MTB-DQM: DQM with modified trigonometric cubic B-splines. Specially, we implement these methods on convection-diffusion equation to convert them into a system of first order ordinary differential equations,in time which can be solved using any time integration method, while we prefer SSP-RK54 scheme. All the three methods are found stable for two space convection-diffusion equation by employing matrix stability analysis method. The accuracy and validity of the methods are confirmed by three test problems of two dimensional convection-diffusion equation, which shows that the proposed approximate solutions by any of the method are in good agreement with the exact solutions

SrCu2(BO3)2Sr Cu_2 (BO_3)_2: A Unique Mott Hubbard Insulator

We discuss the recently discovered system $Sr Cu_2 (BO_3)_2$, a realization of an exactly solvable model proposed two decades earlier. We propose its interpretation as a Mott Hubbard insulator. The possible superconducting phase arising from doping is explored, and its nature as well as its importance for testing the RVB theory of superconductivity are discussed.Comment: 18 pages,7 figures, Based on Invited Talk at 16th Nishinomiya Yukawa memorial symposium, Nov 13-14, Nishinomiya. To appear in Progress in Theoretical Physics, Suppliment 145(2002