2 0 Se p 19 99 Completion of Linear Differential Systems to Involution ⋆

ar X iv : m at h / 99 09 11 4 v 2 [ m at h . A P ] 6 D ec 1 99 9 Completion of Linear Differential Systems to Involution

In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic differential field. Given a ranking of derivative terms and an involutive division, we formulate the involutivity conditions which form a basis of involutiv...

Se p 19 99 Bethe Equation at q = 0 , Möbius Inversion Formula , and Weight Multiplicities : I . sl (

The Uq(ˆ sl(2)) Bethe equation is studied at q = 0. A linear congruence equation is proposed related to the string solutions. The number of its off-diagonal solutions is expressed in terms of an explicit combinatorial formula and coincides with the weight multiplicities of the quantum space.

X iv : h ep - p h / 99 09 20 5 v 2 2 6 Se p 19 99 On the direct evidence of time - reversal non - invariance in the K 0 − K̄ 0 system

Numerical method for solving optimal control problem of the linear differential systems with inequality constraints

In this paper, an efficient method for solving optimal control problems of the linear differential systems with inequality constraint is proposed. By using new adjustment of hat basis functions and their operational matrices of integration, optimal control problem is reduced to an optimization problem. Also, the error analysis of the proposed method is nvestigated and it is proved that the orde...

ar X iv : h ep - p h / 99 09 31 7 v 1 1 0 Se p 19 99 LAL 99 - 45 July 1999 AFTER SITGES F . RICHARD