Checking robust nonsingularity of tridiagonal matrices in linear time

In this paper we present a linear time algorithm for checking whether a tridiagonal matrix will become singular under certain perturbations of its coefficients. The problem is known to be NP-hard for general matrices. Our algorithm can be used to get perturbation bounds on the solutions to tridiagonal systems.Research produced with the help of the Cooperation Agreement CNR-MOSA.     

Creation of quaternary stereocenters in carbonyl allylation reactions

Despite the advances in stereoselective carbonyl allylation reactions, the creation of quaternary stereocenters in the addition of 3,3'-disubstituted allylmetals to aldehydes is still a challenging issue. This feature article describes the most powerful approaches that have been devised to address this problem.     

Solute rotational dynamics at the water liquid/vapor interface

The rotational dynamics of a number of diatomic molecules adsorbed at different locations at the interface between water and its own vapors are studied using classical molecular dynamics computer simulations. Both equilibrium orientational and energy correlations and nonequilibrium orientational and energy relaxation correlations are calculated. By varying the dipole moment of the molecule and its location, and by comparing the results with those in bulk water, the effects of dielectric and mechanical frictions on reorientation dynamics and on rotational energy relaxation can be studied. It is shown that for nonpolar and weekly polar solutes, the equilibrium orientational relaxation is much slower in the bulk than at the interface. As the solute becomes more polar, the rotation slows down and the surface and bulk dynamics become similar. The energy relaxation (both equilibrium and nonequilibrium) has the opposite trend with the solute dipole (larger dipoles relax faster), but here again the bulk and surface results converge as the solute dipole is increased. It is shown that these behaviors correlate with the peak value of the solvent-solute radial distribution function, which demonstrates the importance of the first hydration shell structure in determining the rotational dynamics and dependence of these dynamics on the solute dipole and location.     

Testing of matrix-poset properties

Combinatorial property testing, initiated by Rubinfeld and Sudan [23] and formally defined by Goldreich, Goldwasser and Ron in [18], deals with the following relaxation of decision problems: Given a fixed property P and an input f, distinguish between the case that f satisfies P, and the case that no input that differs from f in less than some fixed fraction of the places satisfies P. An (ε, q)-test for P is a randomized algorithm that queries at most q places of an input f and distinguishes with probability 2/3 between the case that f has the property and the case that at least an ε-fraction of the places of f need to be changed in order for it to have the property. Here we concentrate on labeled, d-dimensional grids, where the grid is viewed as a partially ordered set (poset) in the standard way (i.e. as a product order of total orders). The main result here presents an (ε, poly(1/ε))-test for every property of 0/1 labeled, d-dimensional grids that is characterized by a finite collection of forbidden induced posets. Such properties include the “monotonicity” property studied in [9,8,13], other more complicated forbidden chain patterns, and general forbidden poset patterns. We also present a (less efficient) test for such properties of labeled grids with larger fixed size alphabets. All the above tests have in addition a 1-sided error probability. This class of properties is related to properties that are defined by certain first order formulae with no quantifier alternation over the syntax containing the grid order relations. We also show that with one quantifier alternation, a certain property can be defined, for which no test with query complexity of O(n ^1/4) (for a small enough fixed ε) exists. The above results identify new classes of properties that are defined by means of restricted logics, and that are efficiently testable. They also lay out a platform that bridges some previous results. A preliminary version of these results formed part of [14]. Research supported in part by grant 55/03 from the Israel Science Foundation.     

Regio- and stereoselective copper-catalyzed carbozincation reactions of alkynyl sulfoximines and sulfones

[structure: see text]. Stereochemically pure polysubstituted vinyl sulfoximines and sulfones are easily prepared by a copper-catalyzed syn carbozincation reaction of the corresponding alkynyl derivatives.     

Heat load of a GaAs photocathode in an SRF electron gun

A great deal of effort has been made over the last decades to develop a better polarized electron source for high energy physics. Several laboratories operate DC guns with a gallium arsenide photocathode, which yield a highly polarized electron beam. However, the beam's emittance might well be improved by using a superconducting radio frequency (SRF) electron gun, which delivers beams of a higher brightness than that from DC guns because the field gradient at the cathode is higher. SRF guns with metal and CsTe cathodes have been tested successfully. To produce polarized electrons, a Gallium-Arsenide photo-cathode must be used: an experiment to do so in a superconducting RF gun is under way at BNL. Since a bulk gallium arsenide (GaAs) photocathode is normal conducting, a problem arises from the heat load stemming from the cathode. We present our measurements of the electrical resistance of GaAs at cryogenic temperatures, a prediction of the heat load and verification by measuring the quality factor of the gun with and without the cathode at 2 K. We simulate heat generation and flow from the GaAs cathode using the ANSYS program. By following the findings with the heat load model, we designed and fabricated a new cathode holder (plug) to decrease the heat load from GaAs.     

A quantitative approach to soliton instability

We present an approach for instabilities of solitons that is based on the spectrum of a fourth-order linearized operator. Unlike the standard approach which is based on the slope (Vakhitov-Kolokolov) condition, this approach provides the quantitative value of the instability rate and the qualitative nature of the instability dynamics.     

A shift in retrosynthetic paradigm

The current state-of-the-art synthesis for the formation of enantiomerically enriched all-carbon quaternary stereocenters in acyclic system relies on the formation of a single carbon-carbon bond per chemical step by asymmetric catalysis. These extraordinary sophisticated methods were logically classified among the most powerful and innovative ones. In this concept article, we are proposing a new retrosynthetic paradigm to solve differently such challenging problems. These new synthetic pathways lead to the diastereo- and enantiomerically pure formation of three new carbon-carbon bonds in acyclic system, in a one-pot reaction, including the formation of all-carbon quaternary stereocenters by using classical reagents and experimental conditions and from common starting materials.