Bum simulations have been carried out for the DT ignitor/DD fuel pellet model by using a hydrodynamic code including neutron transport. The results showed that neutron heating has large effects on the bum performance, for instance the fusion yield and the internal tritium breeding ratio. The DD burning could be sustained by neutron heating and thus sufficient tritium could be bred by using one of the branches of the DD reaction, D + D -• p + T. Furthermore, several treatments for neutron transport were compared. It was found that the treatment of the anisotropy of neutron scattering has a larger influence on the bum performance than the treatment of the time dependence of neutron transport. Finally a compressed state of the pellet was proposed as a candidate for the advanced fuel ICF reactor TAKANAWA-I.

We introduce a new algorithm for computing comprehensive Gröbner systems. There exists the Suzuki-Sato algorithm for computing comprehensive Gröbner systems. The Suzuki-Sato algorithm often creates overmuch cells of the parameter space for comprehensive Gröbner systems. Therefore the computation becomes heavy. However, by using inequations ("not equal zero"), we can obtain different cells. In many cases, this number of cells of parameter space is smaller than that of SuzukiSato's. Therefore, our new algorithm is more efficient than Suzuki-Sato's one, and outputs a nice comprehensive Gröbner system. Our new algorithm has been implemented in the computer algebra system Risa/Asir. We compare the runtime of our implementation with the Suzuki-Sato algorithm and find our algorithm superior in many cases.

No abstract

A computation method of algebraic local cohomology with parameters, associated with zerodimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the structure of algebraic local cohomology classes. This decomposition informs us several properties of input ideals and the output of our algorithm completely describes the multiplicity structure of input ideals. An efficient algorithm for computing a parametric standard basis of a given zero-dimensional ideal, with respect to an arbitrary local term order, is also described as an application of the computation method. The algorithm can always output "reduced" standard basis of a given zero-dimensional ideal, even if the zero-dimensional ideal has parameters.

A new algorithm is given for computing parametric local cohomology classes associated with semi-quasihomogeneous singularities. The essential point of the proposed algorithm involves Poincaré polynomials and weighted degrees. The proposed algorithm gives a suitable decomposition of the parameter space depending on the structure of the parametric local cohomology classes. As an application, an algorithm for computing parametric standard bases of zerodimensional ideals, is given. These algorithms work for nonparametric cases, too.