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51.
52.
Ilya Kapovich Gilbert Levitt Paul Schupp Vladimir Shpilrain 《Transactions of the American Mathematical Society》2007,359(4):1527-1546
Motivated by the work of Leininger on hyperbolic equivalence of homotopy classes of closed curves on surfaces, we investigate a similar phenomenon for free groups. Namely, we study the situation when two elements in a free group have the property that for every free isometric action of on an -tree the translation lengths of and on are equal.
53.
Gabriele Stevanato Dr. Joseph T. Hill‐Cousins Dr. Pär Håkansson Dr. Soumya Singha Roy Dr. Lynda J. Brown Prof. Dr. Richard C. D. Brown Dr. Giuseppe Pileio Prof. Dr. Malcolm H. Levitt 《Angewandte Chemie (International ed. in English)》2015,54(12):3740-3743
Nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) are supremely important techniques with numerous applications in almost all branches of science. However, until recently, NMR methodology was limited by the time constant T1 for the decay of nuclear spin magnetization through contact with the thermal molecular environment. Long‐lived states, which are correlated quantum states of multiple nuclei, have decay time constants that may exceed T1 by large factors. Here we demonstrate a nuclear long‐lived state comprising two 13C nuclei with a lifetime exceeding one hour in room‐temperature solution, which is around 50 times longer than T1. This behavior is well‐predicted by a combination of quantum theory, molecular dynamics, and quantum chemistry. Such ultra‐long‐lived states are expected to be useful for the transport and application of nuclear hyperpolarization, which leads to NMR and MRI signals enhanced by up to five orders of magnitude. 相似文献
54.
Salvatore Mamone Judy Y.-C. Chen Rangeet Bhattacharyya Malcolm H. Levitt Ronald G. Lawler Anthony J. Horsewill Toomas Rõõm Zlatko Bačić Nicholas J. Turro 《Coordination chemistry reviews》2011,255(7-8):938-948
The supramolecular complex, H2@C60, represents a model of a quantum rotor in a nearly spherical box. In providing a real example of a quantum particle entrapped in a small space, the system cuts to the heart of many important and fundamental quantum mechanical issues. This review compares the predictions of theory of the quantum behaviour of H2 incarcerated in C60 with the results of infrared spectroscopy, inelastic neutron scattering and nuclear magnetic resonance. For H2@C60, each of these methods supports the quantization of translational motion of H2 and the coupling of the translational motion with rotational motion and provides insights to the factors leading to breaking of the degeneracies of states expected for a purely spherical potential. Infrared spectroscopy and inelastic neutron scattering experiments at cryogenic temperatures provide direct evidence of a profound quantum mechanical feature of H2 predicted by Heisenberg based on the Pauli principle: the existence of two nuclear spin isomers, a nuclear spin singlet (para-H2) and a nuclear triplet (ortho-H2). Nuclear magnetic resonance is capable of probing the local lattice environment of H2@C60 through analysis of the H2 motional effects on the ortho-H2 spin dynamics (para-H2, the nuclear singlet state, is NMR silent). In this review we will show how the information obtained by three different forms of spectroscopy join together with quantum theory to create a complementary and consistent picture which strikingly shows the intrinsically quantum nature of H2@C60. 相似文献
55.
Ge M Nagel U Hüvonen D Rõõm T Mamone S Levitt MH Carravetta M Murata Y Komatsu K Lei X Turro NJ 《The Journal of chemical physics》2011,135(11):114511
We report on the dynamics of two hydrogen isotopomers, D(2) and HD, trapped in the molecular cages of a fullerene C(60) molecule. We measured the infrared spectra and analyzed them using a spherical potential for a vibrating rotor. The potential, vibration-rotation Hamiltonian, and dipole moment parameters are compared with previously studied H(2)@C(60) parameters [M. Ge, U. Nagel, D. Hüvonen, T. R??m, S. Mamone, M. H. Levitt, M. Carravetta, Y. Murata, K. Komatsu, J. Y.-C. Chen, and N. J. Turro, J. Chem. Phys. 134, 054507 (2011)]. The isotropic part of the potential is similar for all three isotopomers. In HD@C(60), we observe mixing of the rotational states and an interference effect of the dipole moment terms due to the displacement of the HD rotation center from the fullerene cage center. 相似文献
56.
Thureau P Sauerwein AC Concistrè M Levitt MH 《Physical chemistry chemical physics : PCCP》2011,13(1):93-96
A new solid-state NMR method is presented for estimating homonuclear dipole-dipole couplings for selected groups of nuclear spins in a multiple-spin coupled network. The methodology combines off-magic-angle spinning, frequency selective spin echoes, and multiple quantum filtering. The new method is insensitive to incoherent relaxation effects and may be used to estimate weak couplings. Internuclear (13)C-(13)C couplings are estimated in uniformly (13)C-labelled l-Histidine·HCl·H(2)O. Weak intermolecular couplings between (13)C nuclei separated by distances exceeding 6 ? are estimated. 相似文献
57.
Abbasi YA Shahida S. Ali A. Khan MH Khan MI 《Journal of Radioanalytical and Nuclear Chemistry》2019,320(2):273-282
The extraction behavior of Nd(III) and Eu(III) with 0.05 mol dm−3 furosemide in benzyl alcohol as single acidic extractant and then with equimolar (0.05 mol dm−3) synergic mixture of furosemide as acidic extractant and tribenzylamine as neutral donor in benzyl alcohol has been studied from aqueous solutions of pH 1 to 6. The effect of various parameters and of various cations and anions on the extraction of these metal ions was investigated. The composition of the extracted adducts was determined by slope analysis method that came out to be [(M(FS)2)+ (CH3COO)−] and [M(FS)3·3TBA] where M = Nd(III) and Eu(III).
相似文献58.
David G. Levitt 《Journal of statistical physics》1973,7(4):329-336
A new derivation of two important one-dimensional time-dependent distributions for an infinite system of hard rods is presented. This derivation is simpler than previous derivations and it provides a direct physical interpretation of the individual terms in the final expressions. A new, more unusual distribution is also presented and discussed. Finally, an exact expression for the diffusion of a Brownian particle is obtained and compared with the exact expression for the self-diffusion coefficient. 相似文献
59.
Norman Levitt 《Discrete and Computational Geometry》1992,7(1):59-67
If a numerical homotopy invariant of finite simplicial complexes has a local formula, then, up to multiplication by an obvious constant, the invariant is the Euler characteristic. Moreover, the Euler characteristic itself has a unique local formula. 相似文献
60.
The purpose of this study was to quantify the effect of timing errors on the intelligibility of deaf children's speech. Deviant timing patterns were corrected in the recorded speech samples of six deaf children using digital speech processing techniques. The speech waveform was modified to correct timing errors only, leaving all other aspects of the speech unchanged. The following six-stage approximation procedure was used to correct the deviant timing patterns: (1) original, unaltered utterances, (2) correction of pauses only, (3) correction of relative timing, (4) correction of absolute syllable duration, (5) correction of relative timing and pauses, and (6) correction of absolute syllable duration and pauses. Measures of speech intelligibility were obtained for the original and the computer-modified utterances. On the average, the highest intelligibility score was obtained when relative timing errors only were corrected. The correction of this type of error improved the intelligibility of both stressed and unstressed words within a phrase. Improvements in word intelligibility, which occurred when relative timing was corrected, appeared to be closely related to the number of phonemic errors present within a word. The second highest intelligibility score was obtained for the original, unaltered sentences. On the average, the intelligibility scores obtained for the other four forms of timing modification were poorer than those obtained for the original sentences. Thus, the data show that intelligibility improved, on the average, when only one type of error, relative timing, was corrected. 相似文献