Use of a sonogashira-acetylide coupling strategy for the synthesis of the aromatic spiroketal skeleton of gamma-rubromycin

[reaction: see text] The synthesis of the fused aromatic spiroketal core of gamma-rubromycin is described via addition of an aryl acetylide fragment to an aryl acetaldehyde fragment. In turn, the aryl acetylene precursor was readily prepared with use of a Sonogashira reaction.     

Counting Lattice Points in The Sphere

We consider the error term which occurs in the counting of lattice points in a sphere ofradius R. By considering second and third power moments, weprove that . An upper bound for the gap between the sign changes of P₃(R) is also proved.1991 Mathematics Subject Classification 11P21.     

Demonstration of highly efficient photon echoes

Highly efficient two-pulse and stimulated photon echoes are experimentally demonstrated in an absorbing medium. Recall efficiencies of 235% and 150% with excellent signal contrast are measured for two-pulse and stimulated photon echoes, respectively, in a Tm:YAG crystal with an absorption length of 3.8. The reported efficiencies do not include any correction for decay or beam profile. We believe that this is the first demonstration of an uncorrected echo efficiency greater than 100% with good signal fidelity in an optically thick medium.     

高斯光束非线性“热像”效应研究

高功率激光系统中非线性“热像”强度可能达到光学元件损伤阀值，从而对系统的安全运行造成威胁.以往的非线性“热像”现象研究都是基于无限大平面光波背景，但实际系统中传输的是有限束宽光束.本文以高斯光束为例，基于无像差自聚焦理论分析了有限束宽光束的“热像”形成规律.结果表明，高斯光束“热像”的强度与位置在光束腰斑较小时与平面光波情况有明显不同，但光束腰斑较衍射物大得多时，高斯光束可以近似当作平面光波处理.     

Embedding polynomial matrices of one variable

A non square matrix with coefficients in K[z] can (if a condition on its minors is satisfied) be embedded into a square matrix with determinant 1. Finding theoretically and in an algorithmic way an embedding of small degree is solved by a construction with vector bundles on the projective line over K.     

Numerical experiments with several variant WENO schemes for the Euler equations

Numerical experiments with several variants of the original weighted essentially non‐oscillatory (WENO) schemes (J. Comput. Phys. 1996; 126 :202–228) including anti‐diffusive flux corrections, the mapped WENO scheme, and modified smoothness indicator are tested for the Euler equations. The TVD Runge–Kutta explicit time‐integrating scheme is adopted for unsteady flow computations and lower–upper symmetric‐Gauss–Seidel (LU‐SGS) implicit method is employed for the computation of steady‐state solutions. A numerical flux of the variant WENO scheme in flux limiter form is presented, which consists of first‐order and high‐order fluxes and allows for a more flexible choice of low‐order schemes. Computations of unsteady oblique shock wave diffraction over a wedge and steady transonic flows over NACA 0012 and RAE 2822 airfoils are presented to test and compare the methods. Various aspects of the variant WENO methods including contact discontinuity sharpening and steady‐state convergence rate are examined. By using the WENO scheme with anti‐diffusive flux corrections, the present solutions indicate that good convergence rate can be achieved and high‐order accuracy is maintained and contact discontinuities are sharpened markedly as compared with the original WENO schemes on the same meshes. Copyright © 2008 John Wiley & Sons, Ltd.     

A moving finite element method for the population balance equation

A moving finite element algorithm has been compared against the upwind-differencing and Smolarkiewicz methods for the population balance equation of multicomponent particle growth processes. Analytical solutions and an error function have been used to test the numerical methods. The moving finite elements technique is much more accurate than other methods for a wide range of parameters. Since this method uses moving grids, it is able to model very narrow particle size distributions. It is also shown that the method can be extended to solve condensational growth problems which include particle curvature and non-continuum mass transfer effects.     

The effect of Reynolds number on a turbulent far-wake

The turbulent far-waked generated by a circular cylinder is investigated for two values (1350 and 4600) of the Reynolds number Re _θ (based on the free stream velocity and the momentum thickness). Two arrays of sixteen X-wires, eight in the (x,?y)-plane and eight in the (x,?z)-plane, are used to capture the main features of the large-scale motion in two orthogonal planes. Both the magnitude of the measured Reynolds stresses and the size of the two-point velocity and vorticity correlation contours increase with Reynolds number. The probability density function and spectra of the velocity signals also exhibit differences with Re _θ. A comparison of centerline turbulence intensities with those in the literature suggests that the Reynolds number dependence may disappear for Re _θ?5000.