Real-world systems that involve some non-smooth change are often well-modeled by piecewise-smooth systems. However there still remain many gaps in the mathematical theory of such systems. This doctoral thesis presents new results regarding bifurcations of piecewise-smooth, continuous, autonomous systems of ordinary differential equations and maps. Various codimension-two, discontinuity induced bifurcations are unfolded in a rigorous manner. Several of these unfoldings are applied to a mathematical model of the growth of Saccharomyces cerevisiae (a common yeast). The nature of resonance near border-collision bifurcations is described; in particular, the curious geometry of resonance tongues in piecewise-smooth continuous maps is explained in detail. Neimark-Sacker-like border-collision bifurcations are both numerically and theoretically investigated. A comprehensive background section is conveniently provided for those with little or no experience in piecewise-smooth systems.
This book documents the United States Coast Guard career of Herbert E. Nolda, from his enlistment in April 1942 to his discharge in December 1945. The book also encompasses his early life before the war and his life after the war as it relates to veterans' matters. On the morning of December 7, 1941, Herbert was living in Santa Monica, California, where he was employed at the huge Douglas Aircraft factory. He arrived at a boarding house for lunch to find the landlady hysterical with the news of the bombing of Pearl Harbor. Several other young men were there too. Within minutes one of the young men stood up and announced: "Our country's in trouble and needs our help. I'm going down to enlist. Is anyone else coming with me?" "I am," Herbert replied. His time in the service was varied, from patrols on the East Coast, to four major invasions in North Africa and Europe. On June 6, 1944, D-Day, he was manning the #1 gun on his ship, LCI(L) #92 as she plowed into the maelstrom of Omaha Beach. Her sister ship, LCI(L) #91 had hit the beach a half hour earlier. She had been Herbert's home until a month before D-Day. The two small ships became famous in the annuals of D-Day. Later, in mid-August 1945, Herbert was aboard the troop transport, USS Admiral H.T. Mayo anchored at Ulithi Atoll in the South Pacific when the guns of the neighboring ships started firing, but there were no enemy planes in sight. . . This book is filled with the grim and the humorous incidents of war as experienced by a young sailor from landlocked Nebraska. Also interwoven are shorter biographies of some of Herbert's crewmembers. It is richly illustrated with 185 photographs and other historical documents.
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