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Some filtrations of the tensor product of a highest weight module and a lowest weight module over quantum group Uq(g)are constructed in[1]and one can use them to define a two-sided ideal of the modified quantized enveloping algebra. It is shown that the quotient algebra inherits a canonical basis from the modified quantized enveloping algebra and is dual to the quantum coordinate algebra defined by Kashiwara for a symmetrizable Kac–Moody algebra g.

We consider the numerical solution of the time-fractional diffusion-wave equation on two-dimensional and three-dimensional unbounded spatial domains. Introduce an artificial boundary and find the exact and approximate artificial boundary conditions for the given problem, which lead to a bounded computational domain. Using the exact or approximating boundary conditions on the artificial boundary, the original problem is reduced to an initial-boundary-value problem on the bounded computational domain which is respectively equivalent to or approximates the original problem. Finite difference methods are used to solve the reduced problems on the bounded computational domain and the stability of these finite difference methods are proved. The numerical results demonstrate that the method given in this paper is effective and feasible.

In this paper, we construct some unirational Calabi–Yau threefolds in characteristic 3. We adopt the method by Schoen, but we use quasi-elliptic surfaces instead of elliptic surfaces. We find new examples which do not admit a lifting to characteristic zero.

This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits. We also propose a kinetic formulation for the Hall-MHD equations which contains as fluid closure different variants of the Hall-MHD model. Then, we prove the existence of global weak solutions for the incompressible viscous resistive Hall-MHD model. We use the particular structure of the Hall term which has zero contribution to the energy identity. Finally, we discuss particular solutions in the form of axisymmetric purely swirling magnetic fields and propose some regularization of the Hall equation.