Urawa Red Diamonds and fixtures between them were known as "Marunouchi derbies", although the term is falling out of use as they are now based in different prefectures and rarely play home games in Tokyo stadiums. Rivals further afield include Kashima Antlers, F.C. Tokyo, Yokohama Marinos, Kawasaki Frontale, and, even farther away, Gamba Osaka. Old JSL championship rivalries with Sanfrecce Hiroshima, Cerezo Osaka and Shonan Bellmare have ebbed down as those clubs had nadirs in the second tier. The club also has women's and amateur teams. Mitsubishi (Amateur era) Urawa Red Diamonds (Professional era) See "Individual Award Winners (Urawa Red Diamonds)" "As of
Hearing the shape of a drum Lester R. Ford Award in 1967 and the Chauvenet Prize in 1968. The frequencies at which a drumhead can vibrate depends on its shape. The Helmholtz equation calculates the frequencies if the shape is known. These frequencies are the eigenvalues of the Laplacian in the space. A central question is whether the shape can be predicted if the frequencies are known; for example a circle-shaped triangle can be recognized in this way. Kac did not know whether it was possible for two different shapes to yield the same set of frequencies; the question was finally answered by the negative in