Asymmetric hydrogenation of itaconic acid and enol acetate derivatives with the Rh-TangPhos catalyst

[reaction: see text] The Rh-TangPhos catalyst has been used for asymmetric hydrogenation of itaconic acid and enol acetate derivatives. A variety of chiral 2-substituted succinic acids and chiral acetates have been obtained in excellent ee values (up to 99% ee).     

Oscillations of nonlinear partial difference systems

This paper studies the following two-dimensional nonlinear partial difference systems

     

Symmetric and Rees algebras of Koszul cycles and their Gröbner bases

In this paper we study the symmetric algebra S(E _i ) and Rees algebra R(E _i ) of the modules E _i of i-cycles of the Koszul complex associated with the sequence of indeterminates of a polynomial ring . For i=2 and i=n–2 we show that is a d-sequence on S(E _i ) and R(E _i ) and we determine Gröbner bases and Sagbi bases related to these algebras. Mathematics Subject Classification (2000):13A30, 13D02, 13H10, 13P10The second author is grateful to the National Natural Science Foundation of China for support.Part of this work was made while the third author was visiting the Fachbereich Mathematik und Informatik der Universität Essen, to which he would like to thank for its hospitality.     

Uniqueness of positive radial solutions for Δu−u+u=0 on an annulus

We prove uniqueness of positive radial solutions to the semilinear elliptic equation , subject to the Dirichlet boundary condition on an annulus in . As a by-product, our argument also provides a much simpler, if not the simplest, new proof for the uniqueness of positive solutions to the same problem in a finite ball or in the whole space .     

Vortex sound generation due to a flow impedance discontinuity on a flat surface

The sound generated by the unsteady motion of a vortex filament moving over a flat boundary with a sharp flow impedance discontinuity is studied theoretically. Theoretical results show that the vortex filament undergoes significant accelerating or decelerating motions and radiates sound at the instant when it moves across the plane of impedance discontinuity. The accelerations and decelerations of the vortex filament are shown to be the major mechanisms of sound generation. The sound so produced has a large low-frequency content such that the change in the flow impedance affects only the sound generation process but not the subsequent sound propagation to the far field.     

Asymptotic Normalization Constants in Nuclear Astrophysics

The indirect method of determining astrophysical nuclear reaction rates is discussed. The overall normalization of the astrophysical S-factor for such reactions may be determined from one quantity, the asymptotic normalization coefficient of the overlap function of the bound state wave functions for the initial and final channels. These coefficients can be found also from peripheral transfer reactions whose amplitudes are determined by the same overlap function as the amplitudes of the corresponding astrophysical radiative capture processes. The experimental test of this approach and the last results of S₁₇ measurements are presented.     

Anomalous Vibrational Dependence of the Rotational and Hyperfine Parameters in the B(4)Pi-X(4)Sigma(-) Transition of NbO

The laser excitation spectrum of jet-cooled NbO in the region 16 000-18 000 cm(-1) has been recorded at high resolution, giving rotational and hyperfine constants for the levels v=0-3 of the B(4)Pi state and v=1 of the X(4)Sigma(-) state; zero gaps have also been measured at low resolution for some weaker bands involving higher vibrational levels. Taken together with the laser data for the B-X (0,0) band from Adam et al. (J. Chem. Phys. 94, 6240-6262 (1994)) and the Fourier transform emission data for the doublet manifold from Launila et al. (J. Mol. Spectrosc. 186, 131-143 (1997)), the new data give a very complete picture of the vibrational energy level pattern in this region. Strong irregularities in the vibrational dependences of the B(4)Pi rotational and hyperfine constants can be interpreted in terms of spin-orbit interaction between the B(4)Pi state and the f(2)Pi, e(2)Phi, and d(2)Delta states. The interaction is strong enough that all three doublet states can be seen in absorption from the X(4)Sigma(-) ground state, adding to the complexity of the spectrum. The hitherto unknown sigmadeltasigma* (4)Delta state is estimated to lie near 17 500 cm(-1), from the change of sign in the spin-rotation parameter gamma of the B(4)Pi state between v=2 and 3. Copyright 2001 Academic Press.     

Recording intramolecular mechanics during the manipulation of a large molecule

The technique of single atom manipulation by means of the scanning tunneling microscope (STM) applies to the controlled displacement of large molecules. By a combined experimental and theoretical work, we show that in a constant height mode of manipulation the STM current intensity carries detailed information on the internal mechanics of the molecule when guided by the STM tip. Controlling and time following the intramolecular behavior of a large molecule on a surface is the first step towards the design of molecular tunnel-wired nanorobots.     

Message encoding-decoding at 2.5 Gbits/s through synchronization of chaotic pulsing semiconductor lasers

Chaotic optical communication with fast chaotic pulsing semiconductor lasers is experimentally demonstrated. Both a pulse stream at a 500-MHz repetition rate and a pseudorandom bit sequence at a 2.5-Gbit/s bit rate are successfully transmitted. The quality of synchronization in a chaos-modulation scheme is examined. The quality of message recovery is correlated to the quality of chaos synchronization.     

Three-dimensional density spectra of sandy sediments

Power spectra of density variability for sandy sediments offshore Panama City, Florida, are estimated and modeled using digital x-ray computed tomography images of sediment structure. Spectral analysis reveals that while shell pieces and mud mixtures are the main contributors to density variability at large scales, intrinsic density variability associated with sand grain contacts dominates at small scales. The power spectrum of sandy sediments is modeled by an analytic form that consists of two power-law components, one associated with the shell and mud contributions and the other with the intrinsic density variability of sand. The dominant term has a much higher power-law exponent than previously reported. Implications for the scattering of high-frequency sound in sandy sediments are discussed.