Direct high-power laser acceleration of ions for medical applications

Theoretical investigations show that linearly and radially polarized multiterawatt and petawatt laser beams, focused to subwavelength waist radii, can directly accelerate protons and carbon nuclei, over micron-size distances, to the energies required for hadron cancer therapy. Ions accelerated by radially polarized lasers have generally a more favorable energy spread than those accelerated by linearly polarized lasers of the same intensity.     

Michael addition reactions with eta2-coordinated anisoles: controlling the stereochemistry of the para and benzylic carbons

Several eta(2)-coordinated anisole complexes were treated with various Michael acceptors in the presence of a Lewis or Bronsted acid to generate stable 4H-anisolium complexes. These reactions were found to proceed with high stereochemical control with predictable outcomes, provided that the moderate acid (NH(2)Ph(2))OTf was used and the complex was dissolved in an acidic solution. The stereochemistry is shown to originate from an unexpectedly high preference for one coordination diastereomer of the anisole complex in the solid state and a Diels-Alder like transition state for the Michael reaction.     

Solid-state induced control of kinetically unstable stereoisomers

Arene complexes of the form TpM(pi-acid)(L)(eta2-arene) (Tp = hydridotris(pyrazolyl)borate, M = Re, Mo, or W, pi-acid = CO or NO, L = 1-alkylimidazole, pyridine, PMe3, arene is prochiral) exist as a dynamic equilibrium of coordination diastereomers in solution. In both crystalline and amorphous solid states, however, only one diastereomer is present. Reactions on the bound arenes in these complexes have been performed stereoselectively, by exploiting the homomorphic nature of the solid phase.     

Dihapto coordination of carboxylic acid derivatives with an asymmetric rhenium pi-base: a new mechanism for amide isomerization?

The asymmetric pi basic metal fragment [TpRe(CO)(MeIm)] (Tp = hydridotris(pyrazolyl)borate, MeIm = 1-methylimidazole) forms thermally stable complexes with ethyl acetate, acetic anhydride, N-methylsuccinimide, N-acetylpyrrole, and N-methylmaleimide in which the metal binds a carbonyl group in a pi fashion. In all cases a single diastereomer is observed, indicating that one enantioface of the carbonyl is selectively coordinated. X-ray and NMR data for the compound TpRe(CO)(MeIm)(eta(2)-N-methylsuccinimide) indicate that metal coordination effectively removes the pi interaction between the bound carbonyl and the nitrogen of the succinimide ring.     

Approximate D-optimal designs of experiments on the convex hull of a finite set of information matrices

In the paper we solve the problem of D _ℋ-optimal design on a discrete experimental domain, which is formally equivalent to maximizing determinant on the convex hull of a finite set of positive semidefinite matrices. The problem of D _ℋ-optimality covers many special design settings, e.g., the D-optimal experimental design for multivariate regression models. For D _ℋ-optimal designs we prove several theorems generalizing known properties of standard D-optimality. Moreover, we show that D _ℋ-optimal designs can be numerically computed using a multiplicative algorithm, for which we give a proof of convergence. We illustrate the results on the problem of D-optimal augmentation of independent regression trials for the quadratic model on a rectangular grid of points in the plane.     

Applications of Kalman filtering to real-time trace gas concentration measurements

A Kalman filtering technique is applied to the simultaneous detection of NH₃ and CO₂ with a diode-laser-based sensor operating at 1.53 μm. This technique is developed for improving the sensitivity and precision of trace gas concentration levels based on direct overtone laser absorption spectroscopy in the presence of various sensor noise sources. Filter performance is demonstrated to be adaptive to real-time noise and data statistics. Additionally, filter operation is successfully performed with dynamic ranges differing by three orders of magnitude. Details of Kalman filter theory applied to the acquired spectroscopic data are discussed. The effectiveness of this technique is evaluated by performing NH₃ and CO₂ concentration measurements and utilizing it to monitor varying ammonia and carbon dioxide levels in a bioreactor for water reprocessing, located at the NASA–Johnson Space Center. Results indicate a sensitivity enhancement of six times, in terms of improved minimum detectable absorption by the gas sensor. Received: 13 July 2001 / Revised version: 11 October 2001 / Published online: 29 November 2001     

Metrical Theorems on Prime Values of the Integer Parts of Real Sequences II

Let [ ] denote the integer part. Among other results in [3]we gave a complete solution to the following problem. PROBLEM. Given an increasing sequence a_n R⁺, n = 1, 2, ...,where a_n as n , are there infinitely many primes in the sequence[a_n] for almost all ?     

On values of n 2 + 1 free of large prime factors

Let P ⁺(m) denote the greatest prime factor of the positive integer m. Improving and simplifying work of Dartyge [3] we show that

Reversible H2 addition across a nickel-borane unit as a promising strategy for catalysis

We report the synthesis and characterization of a series of nickel complexes of the chelating diphosphine-borane ligands ArB(o-Ph(2)PC(6)H(4))(2) ([(Ar)DPB(Ph)]; Ar = Ph, Mes). The [(Ar)DPB(Ph)] framework supports pseudo-tetrahedral nickel complexes featuring η(2)-B,C coordination from the ligand backbone. For the B-phenyl derivative, the THF adduct [(Ph)DPB(Ph)]Ni(THF) has been characterized by X-ray diffraction and features a very short interaction between nickel and the η(2)-B,C ligand. For the B-mesityl derivative, the reduced nickel complex [(Mes)DPB(Ph)]Ni is isolated as a pseudo-three-coordinate "naked" species that undergoes reversible, nearly thermoneutral oxidative addition of dihydrogen to give a borohydrido-hydride complex of nickel(II) which has been characterized in solution by multinuclear NMR. Furthermore, [(Mes)DPB(Ph)]Ni is an efficient catalyst for the hydrogenation of olefin substrates under mild conditions.