Temperature-dependent chemical shift and relaxation times of (23)Na in Na(4)HTm[DOTP

We describe the characterization of a (23)Na temperature-dependent chemical shift and relaxation rates in the complex, Na(4)HTm[DOTP]. This is the first characterization of a (23)Na temperature-dependent chemical shift in a nonmetallic sample. The (23)Na temperature-dependent chemical shift coefficient is approximately -0. 5 PPM/ degrees C for both an aqueous solution and a 6% agarose gel of this compound. This is 50 times the magnitude of the temperature-dependent chemical shift coefficient of water protons. The relaxation times, T(1), T(2f), and T(2s) increased by 0.1, 0.01, and 0.05 ms/ degrees C, respectively. Applications of these unique properties for designing an MRI technique for monitoring heat deposition in tissue and tissue phantoms are discussed.     

Nonlinear resonances free of field and doppler broadenings

For the case where the Rabi frequencies of the guiding fields are much larger than the relaxation constants but much smaller than the Doppler broadening, it is shown that resonances which are neither field nor Doppler broadened can appear in the absorption (or gain) spectrum of the probe field. A classification of four-level systems according to the number of resonances is made for cases where two strong fields interact either with opposite or adjoining transitions. The conditions under which the number of resonances reaches eight, while for stationary atoms the maximum number is four, are found. A method is proposed for calculating the number of resonances in a multilevel system with several strong fields using analysis of the extremum points of the frequency branches in the velocity-frequency plane.     

A note on the vorticity downstream of a curved shock

Zusammenfassung Es wird ein expliziter Ausdruck für die Wirbelst?rkeω hinter einem gekrümmten Verdichtungsstoss für den Fall der zweidimensionalen Str?mung eines idealen Gases in Termen der Geschwindigkeit der ungest?rten Str?mungV _∞, ihrer Mach-ZahlM _∞, des Stosswinkelsσ und des Krümmungsradiusr _s des Verdichtungsstosses im betrachteten Punkt aufgestellt. Die dimensionslose Wirbelst?rkeω r _s /V _∞ h?ngt nur vonM _∞ undσ ab. Bei festgehaltenemM _∞ treten bei einem Stosswinkel von 90° (senkrechter Verdichtungsstoss) und auch dann, wenn der Stosswinkel dem Mach-Winkel der ungest?rten Str?mung gleich ist (Verdichtungsstoss der Intensit?t Null), keine Wirbel auf. Für einen dazwischenliegenden Winkel, der von 68° fürM _∞=1,5 bis zu 36° fürM _∞=10 variiert, wird die Wirbelst?rke ein Maximum.      

The empirical behavior of sampling methods for stochastic programming

We investigate the quality of solutions obtained from sample-average approximations to two-stage stochastic linear programs with recourse. We use a recently developed software tool executing on a computational grid to solve many large instances of these problems, allowing us to obtain high-quality solutions and to verify optimality and near-optimality of the computed solutions in various ways. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grant 9726385. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grant DMS-0073770. Research supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, U.S. Department of Energy, under Contract W-31-109-Eng-38, and by the National Science Foundation under Grants 9726385 and 0082065.     

On the Π-operator in hyperholomorphic function theory

We consider a class of generalizations of the complex one-dimensional II-operator in spaces of quaternion-valued functions depending on four real variables and study some of its basic properties.     

Antiferromagnetic resonance in Bi2CuO4

Magnetic resonance of the low-frequency spin-wave branch in the Bi₂CuO₄ antiferromagnet with an easy-plane anisotropy has been studied. Angular, frequency, and temperature dependences of the position and width of the antiferromagnetic resonance (AFMR) line have been measured. Our measurements combined with earlier data [H. Ochta, K. Yoshida, T. Matsuya, T. Nanba, M. Motokawa, K. Yamada, Y. Endon, and S. Hosoya, J. Phys. Soc. Jpn. 61, 2921 (1992); E. W. Ong, G. H. Kwei, R. A. Robinson, B. L. Ramakrishna, and R. B. von Dreele, Phys. Rev. B 42, 4255 (1990) [ have allowed us to determine anisotropy constants of this material and to account for the unusual character of its static susceptibility anisotropy. The AFMR line shifts to the high-field side and broadens in a temperature range of 10–15 K, and the cause of this has remained unclear. In the low-temperature range the line shows a hysteresis corresponding to a static field magnitude several times as large as the spin-flop field. The position and width of the AFMR line depend sensitively on the sample preparation technique. Zh. éksp. Teor. Fiz. 113, 2244–2255 (June 1998)     

Extending Solutions of Holomorphic Partial Differential Equations Across Real Hypersurfaces

The main result in this paper, Theorem 1.2, generalizes a theoremof Zerner [26] concerning sufficient conditions for the holomorphiccontinuability of a solution of a linear holomorphic partialdifferential equation across a point of a hypersurface, on oneside of which it is holomorphic. The point of the new theoremis, roughly speaking, that it applies also to regular solutionsof partial differential equations whose coefficients may havecertain kinds of singularities. This enables us to deduce somenew results (see 2) on elliptic partial differential equationsin R²:Theorem 2.1 extends a result of Vekua on the size of thedomain of holomorphy of solutions to elliptic equations, inthe case where singularities are permitted in the coefficients;Theorem 2.2 is of an apparently novel type, showing (roughly)that under certain conditions the solution to Cauchy's problemis real-analytic in a domain whose size depends only on theprincipal part of the operator, which is assumed to be the Laplacian,and the Cauchy data on the real axis. (Results of this kindare very delicate, as we shall illustrate in 4 with a simplecounterexample.) Theorem 2.2 is new and non-trivial even forequations with analytic coefficients, in which case though,Theorem 1.2 is not needed for the proof.