Symmetry and “Magic” Numbers or from the pythagoreans to Eugene Wigner

I trace the evolution of the scientific world view in general and of the variational approach specifically, including transformation groups I then review the impact of these ideas at the atomic, nuclear and particle levels.     

Comparison of location models of Weibull type samples and extreme value processes

Summary Four different location parameter models are compared within the sufficiency and deficiency concept. The starting is a location model of a Weibull type sample with shape parameter -1<a<1. Here our basic inequality concerns the approximate sufficiency of the k lower extremes. In addition, the lower extremes are approximately equal, in distribution, to where S _m is the sum of m i.i.d. standard exponential random variables and t is the location parameter. The final step leads us to the model of extreme value processes ...     

EVALUATION OF PORPHYRIN CHARACTERISTICS REQUIRED FOR PHOTODYNAMIC THERAPY

The cytotoxicity (in the dark), phototoxicity (red light) and subcellular localization (using confocal laser scanning microscopy) were determined for 15 porphyrins (1-15) in C6 glioma cells. The partition coefficient in 2-octanol was also determined for each porphyrin at pH 7.4. The cytotoxicity increased with pi (log of partition coefficient) up to pi values of +2. The 7 porphyrins with cationic side chains exhibited a classical parabolic correlation between phototoxicity and pi, with maximal activity at a pi value of approximately 1.0. There was also a significant correlation between subcellular localization and degree of phototoxicity, with the three most photosensitive porphyrins all possessing cationic side chains, and all three localizing in mitochondria.     

The double salt tris(diisopropylammonium) tetrachloridoferrate(III) dichloride: Synthesis, crystal structure, and vibrational spectra

Tris(diisopropylammonium)tetrachloridoferrate(III) dichloride crystallizes in the monoclinic space group P2₁/c (a = 7.6685(2) ?, b = 17.6079(3) ?, c = 23.3217(4) ?, β = 91.396(2)°, V = 3148.1(1) ?³, Z = 4, T = 113 K) with three diisopropylammonium cations (dip), one tetrachloridoferrate(III) anion, and two chloride anions in the asymmetric unit. The dip cations and the chloride anions form hydrogen bonded one-dimensional polymers along [010]. The tetrachloridoferrate(III) anion, habituated in between these chains, is not involved in any hydrogen bonding. The structural characterization is supported by infrared and Raman spectroscopic data.     

Trees and Markov Convexity

We show that an infinite weighted tree admits a bi-Lipschitz embedding into Hilbert space if and only if it does not contain arbitrarily large complete binary trees with uniformly bounded distortion. We also introduce a new metric invariant called Markov convexity, and show how it can be used to compute the Euclidean distortion of any metric tree up to universal factors. The research of the first author was conducted while he was at U. C. Berkeley and the Institute for Advanced Study.     

Limits on tunneling theories of strong-field ionization

It is shown that tunneling theories of ionization by lasers are subject to upper and lower bounds on the Keldysh parameter gamma. The tunneling limit, gamma-->0, applies to ionization by quasistatic electric fields, but not by laser fields. For lasers, the gamma-->0 limit requires a relativistic treatment. Bounds on the applicability of tunneling theories depend on parameters other than gamma, confirming the rule that strong-field phenomena require more than one dimensionless parameter for scaling.