- We find that Ramanujan-type congruences for Hurwitz class numbers can be sustained on nonholomorphic generating series, in contrast to all other known Ramanujan-type congruences.
- For such nonholomorphic congruences of Hurwitz class numbers, we demonstrate a divisibility conclusion.
- The holomorphic projection of theta series products with a Hurwitz class number generating series and a Serre theorem.
The National Academy of Sciences is how esteemed?
- The American National Academy of Sciences (NAS) is thought to be the nation's most esteemed honorary scientific society.
- But it also has a track record for being male, old, and white. By extending an invitation to a younger, more diverse group of scientists to join them, its members today made a significant step in changing their reputation.
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Rumored by contemporaries that he had made a pact with the devil for his musical abilities, Paganini refused to publish his own work, which he alone would perform.
<span>They believed that part of strengthening his rule was to force everyone to simply obey and not speak out against him and by decreeing even how people could write, what they could believe, and what they should do. He succeeded in molding the people to become more similar, to build massively, and to conquer more territory, but people grew to hate him and he became paranoid about assassination and death, and his family and court ended in killings and death.
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Islands form an arc when two oceanic plates converge (come together, approach) creating a row of islands above the overriding plate. The older, heaver plate gets forced below the lighter plate. That old plate heats up and descends into the lithosphere. The edge of that plate begins to melt as it gets deeper into the earth. The melting plate feeds magma chambers that supply volcanic islands that forms an arc <span>when the molten rock erupts onto the ocean floor of the overriding plate.</span>
