The expected length of the longest probe sequence for bucket searching when the distribution is not uniform

We study the expected value of the maximum number of accesses needed to locate an element in a hashing file constructed by using an order-preserving hashing function and with collision resolution by the method of separate chaining. It is assumed that X₁, …, X_n are independent [0,1]-valued random variables with common density f, and that X_i is hashed to the $\text{nX}{}_{\mathrm{i}}\text{+ 1}\text{st}$ bucket (chain). For all densities that are bounded, the expected value of the maximum number of accesses is shown to be asymptotic to $\text{log}\text{n}\text{log log}\text{n}$, and the dependency of this expected value on f is made explicit by exhibiting the first few terms in the asymptotic expansion. For unbounded f, a tight upper bound is given for the expected value.     

Relativistically covariant Bohm-Bub hidden-variable theory for spin measurement of a single particle

We present a simple first step toward a relativistically covariant generalization of the Bohm-Bub hidden-variable theory. The model is applicable to spin measurement on a single Dirac particle and describes the collapse of the state vector to a spin-up or spin-down state. The essential postulate is that the hidden-variable vector transforms in the same way as the state vector under a Lorentz transformation. This yields a covariant collapse equation, which reduces to the ordinary Bohm-Bub equation for an observer stationary with respect to the particle and shows a time dilated collapse for a moving observer. The model yields the correct quantum transition probabilities for all observers.Deceased.     

La structure des copolyèdres au sens de Stamm

Sans résumé     

A fourfold coordinated point defect in silicon

Vacancies, interstitials, and Frenkel pairs are considered to be the basic point defects in silicon. We challenge this point of view by presenting density functional calculations that show that there is a stable point defect in silicon that has fourfold coordination and is lower in energy than the traditional defects.     

Global optimization by energy landscape paving

We introduce a novel heuristic global optimization method, energy landscape paving (ELP), which combines core ideas from energy surface deformation and tabu search. In appropriate limits, ELP reduces to existing techniques. The approach is very general and flexible and is illustrated here on two protein folding problems. For these examples, the technique gives faster convergence to the global minimum than previous approaches.     

Synthesis and NKT cell stimulating properties of fluorophore- and biotin-appended 6"-amino-6"-deoxy-galactosylceramides

Alpha-galactosylceramides are potent stimulators of human T cells. Stimulation occurs through binding of the glycolipids by CD1d, presentation to T cells, and formation of a CD1d-glycolipid-T cell receptor complex. To facilitate the elucidation of the structural features of glycolipids necessary for T cell stimulation, alpha-galactosylceramides have been prepared with small molecules appended at the C6 position of the sugar. The appended molecules do not significantly influence the abilities of the glycolipids to stimulate T cells. [reaction: see text]     

Favorskii-type rearrangement of α-chloro ketimines

The first examples of the Favorskii-type rearrangement of α-monochloro ketimines are reported. The regiospecific opening of the intermediate cyclopropylideneamines parallels the opening of cyclopropanones under Favorskii-conditions.