Let K be a field and X an m×n matrix of indeterminates over K. Let K[X] denote the polynomial ring generated by all the indeterminates Xij . For a given positive integer r ≤ min{m, n}, we consider the determinantal ideal Ir+1 = Ir+1(X) generated by all r + 1 minors of X if r < min{m, n} and Ir+1 = (0) otherwise. Let Rr+1 = Rr+1(X) be the determinantal ring K[X]/Ir+1. Determinantal ideals and ri...

Domestic developments since the start of the w a r in Korea now m a k e it plain that w a r t i m e economy wil l be in effect until the threat of communis t aggress ion disappears. A d j u s t m e n t s wil l be essential in the Amer i c an w a y of life. Regard less of part isan political maneuve r ing taxes a r e go ing to rise In prevent ing r u n a w a y inflation. Mate r i a l s and labor...

Naphthalene is an ubiquitous pollutant of the environment and the biodegradation of this pollutant has been receiving constant scientific consideration. The aim of this study was to isolate and identify bacteria that could degrade naphthalene from three regions of the Gol Gohar Mine at Sirjan, Iran. In this study, the total naphthalene degrading bacteria were quantified with the most probable n...

Durante o ano de 2019 um lance polêmico entre dois times do futebol brasileiro dividiu opiniões. Neste jogador, aparentemente em posição impedimento, marcou gol, que foi validado com uma nova tecnologia digital presente nos jogos futebol: VAR (Video Assistant Referee). No artigo abordamos este utilizando matemática para explicar porquê a decisão final ter sido correta. Em seguida, apresentamos ...