Fate of Grafenberg Rings

Age and Fate of Saturn's Rings

When Saturn was the only known ringed planet, the rings were believed to be as old as the solar system, some 4.5 billion years old in the conventional chronology. The existence of the rings to the present day was taken as evidence of this chronology. In the 1970s and 1980s, other planets were found to have shortlived, rapidly dissipating rings with life times of the order of millennia. Subseque...

Chiral rings, Mirror Symmetry and the Fate of Localized Tachyons

We study the localized tachyon condensation of non-supersymmetric orbifold backgrounds in their mirror Landau-Ginzburg picture. We first show that the R-charges of chiral primaries increase under the process of condensing the tachyon in the same chiral ring. Then, utilizing the existence of four copies of (2,2) worldsheet supersymmetry, we show that the minimal tachyon mass in twisted sectors i...

Differential Polynomial Rings of Triangular Matrix Rings

Retinoic Acid Determines the Fate of Spermatogonia

In this review, we aim to examine the effect of extrinsic and intrinsic factors on spermatogenesis process taking into account a complex signaling pathway. Primarily, it is suggested that retinoic acid (RA) has a vital function in spermatogenesis process and it is considered to be essential for completion of spermatogonia into mature spermatozoa. In the present review, the key effects of retino...

Rings of Singularities

This paper is a slightly revised version of an introduction into singularity theory corresponding to a series of lectures given at the ``Advanced School and Conference on homological and geometrical methods in representation theory'' at the International Centre for Theoretical Physics (ICTP), Miramare - Trieste, Italy, 11-29 January 2010. We show how to associate to a triple of posit...