Signal enhancement in 5QMAS spectra of spin-5/2 quadrupolar nuclei

5QMAS experiments on spin-5/2 systems display a low sensitivity compared with their 3QMAS counterparts. Nevertheless, the superior resolution of 5QMAS over 3QMAS makes these experiments a favorable choice for many materials. We report an enhancement scheme for the 5QMAS experiment, using an improved five-quantum excitation pulse scheme combined with a FAM-II conversion pulse. The results are verified experimentally on a polycrystalline sample of gamma-(27)Al(2)O(3), showing an enhancement factor of 2.4 over the simple two-pulse (CW) 5QMAS scheme. Numerical computations of the efficiency parameter epsilon support these results.     

Joint quasimodes,positive entropy,and quantum unique ergodicity

We study joint quasimodes of the Laplacian and one Hecke operator on compact congruence surfaces, and give conditions on the orders of the quasimodes that guarantee positive entropy on almost every ergodic component of the corresponding semiclassical measures. Together with the measure classification result of (Lindenstrauss, Ann Math (2) 163(1):165–219, 2006), this implies Quantum Unique Ergodicity for such functions. Our result is optimal with respect to the dimension of the space from which the quasi-mode is constructed. We also study equidistribution for sequences of joint quasimodes of the two partial Laplacians on compact irreducible quotients of \({\mathbb {H}}\times {\mathbb {H}}\) .     

Diagram groups and directed 2-complexes: Homotopy and homology

We show that diagram groups can be viewed as fundamental groups of spaces of positive paths on directed 2-complexes (these spaces of paths turn out to be classifying spaces). Thus diagram groups are analogs of second homotopy groups, although diagram groups are as a rule non-Abelian. Part of the paper is a review of the previous results from this point of view. In particular, we show that the so-called rigidity of the R. Thompson's group F and some other groups is similar to the flat torus theorem. We find several finitely presented diagram groups (even of type F_∞) each of which contains all countable diagram groups. We show how to compute minimal presentations and homology groups of a large class of diagram groups. We show that the Poincaré series of these groups are rational functions. We prove that all integer homology groups of all diagram groups are free Abelian.     

Optimization of Adiabatic Selective Pulses

Adiabatic RF pulses play an important role in spin inversion due to their robust behavior in presence of inhomogeneous RF fields. These pulses are characterized by the trajectory swept by the tip of theB_effvector and the rate of motion upon it. In this paper, a method is described for optimizing adiabatic inversion pulses to achieve a frequency-selective magnetization inversion over a given bandwidth in a shorter time and to improve slice profile. An efficient adiabatic pulse is used as an initial condition. This pulse allows for flexibility in choosing its parameters; in particular, the transition sharpness may be traded off against the inverted bandwidth. The considerations for selecting the parameters of the pulse according to the requirements of the design are discussed. The optimization process then improves the slice profile by optimizing the rate of motion along the trajectory of the pulse while preserving the trajectory itself. The adiabatic behavior of the optimized pulses is fully preserved over a twofold range of variation in the RF amplitude which is sufficient for imaging applications in commercial high-field MRI machines. Design examples demonstrate the superiority of the optimized pulses over the conventional sech/tanh pulse.     

Interactions between inorganic salts and polyacrylamide in aqueous solutions and gels

The swelling of poly(acrylamide) (PAAm) gels and the osmotic pressure of linear PAAm in aqueous solutions were predominantly affected by anion type and increased according to the lyotropic series ranking of sodium halide anions: F^? < (H₂O) < Cl^? < Br^? < I^?. The osmotic pressure of PAAm in all examined salt solutions followed the scaling theory, with an exponent of 2.3 ± 0.1. In solutions of a sodium halide series, the value of the pre‐exponential factor seemed to depend on salt concentration, anion radius, and the apparent “anionic‐portion radius” of the water molecule. This radius, extracted from the literature data, marks a transition point of the anion radius effect. Larger anions increase the osmotic pressure of PAAm more significantly as their concentration increases and vice versa. The effects of the anions on the osmotic pressure of PAAm are related to their preferential interactions with the polymer. Iodide, which increased the osmotic pressure of PAAm with respect to its value in pure water, seemed to preferentially adsorb onto the polymer with a binding constant of K_b = 9.7 ± 2.0 M^?1 determined by isothermal titration microcalorimetry. However, fluoride, which decreased the osmotic pressure, was preferentially repulsed. The mechanisms of attraction and repulsion were attributed to ion‐water‐polymer interactions and the solvent quality of the hydrated ions. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 508–519, 2003     

SL(2,C) Gauge Theory of Gravitation and the Quantization of the Gravitational Field

A new approach to quantize the gavitationalfield is presented. It is based on the observation thatthe quantum character of matter becomes more significantas one gets closer to the big bang. As the metric loses its meaning, it makes sense to considerSchrodinger's three generic types of manifolds —unconnected differentiable, affinely connected, andmetrically connected — as a temporal sequencefollowing the big bang. Hence one should quantize thegravitational field on general differentiable manifoldsor on affinely connected manifolds. The SL(2,C) gaugetheory of gravitation is employed to explore thispossibility. Within this framework, the quantization itselfmay well be canonical.     

Anomaly constraints on nonlinear sigma models

Anomalies in nonlinear sigma models can sometimes be cancelled by local counterterms. We show that these counterterms have a simple topological interpretation, and that the requirements for anomaly cancellation can be easily understood in terms of 't Hooft's anomaly matching conditions. We exhibit the anomaly cancellation on homogeneous spaces $\text{G}\text{H}$ and on general riemannian manifolds $\text{M}$. We include external gauge fields on the manifolds and derive the generalized anomaly-cancellation conditions. Finally, we discuss the implications of this work for superstring theories.     

α-Chlor-nitrone V: Substitutionsreaktionen an Olefin- und Benzolderivaten. Eine Methode zur Darstellung von β,γ-un-gesättigten und β- arylsubstituierten Aldehyden. Stereospezifische Bildung von tetra-alkylsubstituierten Olefindoppelbindungen. Über synthetische Methoden, 9. (vorläufige) Mitteilung

The Ag⁺-induced α-chloro-aldonitrone/olefin reaction in polar solvents can proceed by substitution, thereby providing a method for the preparation of β, γ-unsaturated aldehydes. Positional as well as configurational retention of the olefinic double bond are mechanistically significant and preparatively useful characteristics of this process. Substitution also occurs with great ease at nucleophilic aromatic nuclei; this offers a simple preparative route to certain β-aryl-aldehydes. The results illustrate a general aspect of the chemistry of α-chloro-aldonitrones: the N-alkenyl-N-alkyl-nitrosonium-ions derived from them can serve as preparative equivalents of the elusive corresponding α-acyl-carbonium-ions.     

Rhodium complexes with chiral counterions: achiral catalysts in chiral matrices

The neutral complexes [Rh(I)(NBD)((1S)-10-camphorsulfonate)] (2) and [Rh(I)((R)-N-acetylphenylalanate)] (4) reacted with bis-(diphenylphosphino)ethane (dppe) to form the cationic Rh(I)(NBD)(dppe) complexes, 5 and 6, respectively, accompanied by their corresponding chiral counteranions. Analogously, 4 reacted with 4,4^′-dimethylbipyridine to yield complex 7. Complexes 5 and 6 disproportionated in aprotic solvents to form the corresponding bis-diphosphine complexes 8 and 9, respectively. 8 was characterized by an X-ray crystal structure analysis. In order to form achiral Rh(I) complexes bearing chiral countercations new sulfonated monophosphines 13-16 with chiral ammonium cations were synthesized. Tris-triphenylphosphinosulfonic acid (H₃TPPS, 11) was used to protonate chiral amines to yield chiral ammonium phosphines 14-16. Thallium-tris-triphenylphosphinosulfonate (Tl₃TPPS, 12) underwent metathesis with a chiral quartenary ammonium iodide to yield the proton free chiral ammonium phosphine 13. Phosphines 15 and 16 reacted with [Rh(NBD)₂]BF₄ to afford the highly charged chiral zwitterionic complexes [Rh(NBD)(TPPS)₂][(R)-N,N-dimethyl-1-(naphtyl)ethylammonium]₅ (17) and [Rh(NBD)(TPPS)₂][BF₄][(R)-N,N-dimethyl-phenethylammonium]₆ (18), respectively. Complexes 5, 6, and 18 were tested as precatalysts for the hydrogenation of de-hydro-N-acetylphenylalanine (19) and methyl-(Z)-(α)-acetoamidocinnamate (MAC, 20) under homogeneous and heterogeneous (silica-supported and self-supported) conditions. None of the reactions was enantioselective.