KUNIAKI NAKANISHI,1 FUMIKO TAJIMA,2 HIROSHI ITOH,3 YASUKO NAKATA,2 NORIO HAMA,3 OSAMU NAKAGAWA,3 KAZUWA NAKAO,3 TOSHIAKI KAWAI,4 CHIKAO TORIKATA,4 TATSUKO SUGA,5 KUNIO TAKISHIMA,5 TAKASHI AURUES,1 AND TOMOSUMI IKEDA1 1Division of Environmental Medicine, National Defense Medical College Research Institute, and Departments of 4Pathology and 5Biochemistry, National Defense Medical College, Tokoroz...

Many commonly used time–frequency distributions are members of the Cohen class. This class is defined for continuous signals, and since time–frequency distributions in the Cohen class are quadratic, the formulation for discrete signals is not straightforward. The Cohen class can be derived as the class of all quadratic time–frequency distributions that are covariant to time shifts and frequency...

R.G. and Perez proved that under certain conditions the test ideal of a module closure agrees with trace closure. We use this fact to compute ideals various rings respect closures coming from their indecomposable maximal Cohen–Macaulay modules. also give an easier way hypersurface ring in three variables particular type matrix factorization.