Refined class number formulas and Kolyvagin systems

We use the theory of Kolyvagin systems to prove (most of) a refined class number formula conjectured by Darmon. We show that for every odd prime $p$, each side of Darmon's conjectured formula (indexed by positive integers $n$) is "almost" a $p$-adic Kolyvagin system as $n$ varies. Using the fact that the space of Kolyvagin systems is free of rank one over $\mathbf{Z}_p$, we show that Darmon's formula for arbitrary $n$ follows from the case $n=1$, which in turn follows from classical formulas

Why Do We Worry about Trace Poisons?

Dr. Mazur relates how protests by the political left against nuclear tests and by the political right against fluoridation set the stage for Silent Spring to move the public toward being concerned about latent risks

Looking Back at Fluoridation

The author reviews the 50-year history of the debate over fluoridating drinking water as a public health measure

Prospects for United States of America-China political and economic relations under Donald Trump's presidency

The purpose of this article was to introduce the possible future relations between China and the United States of America under Donald Trump’s presidency. The paper is divided into five sections: economy, real challenges, trade policy and industry, diplomacy. Each of them is introducing key issues in terms of the main topic. The secondary point of this article was to show the gravity of change after United States of America election results in December 2016 and the impact of this event on American policy toward China. The main conclusion which arised from the article is: USA-China relations during upcoming decade are going to be eminently tensed that it was before. Trade policy, Taiwan, strategic rapprochement of the United States of America with such countries as India and Russia, as well as innovation race across many industries, will remain a point of contention. The future of Sino-US relations will probably depend mostly on the emerging administration of the 45th President of the United States of America

Looking Back: Unneeded X-rays

From the discovery of x-rays in 1896 to the present, Dr. Mazur explores the history of risk management of radiation exposure from x-rays and nuclear fallout