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61.
N. Euler W. -H. Steeb L. G. S. Duarte I. C. Moreira 《International Journal of Theoretical Physics》1991,30(9):1267-1271
The techniques of invertible point transformations and the Painlevé analysis can be used to construct integrable ordinary differential equations. We compare both techniques for the second Painlevé transcendent. 相似文献
62.
We describe a new algorithm which uses the trajectories of a discrete dynamical system to sample the domain of an unconstrained objective function in search of global minima. The algorithm is unusually adept at avoiding nonoptimal local minima and successfully converging to a global minimum. Trajectories generated by the algorithm for objective functions with many local minima exhibit chaotic behavior, in the sense that they are extremely sensitive to changes in initial conditions and system parameters. In this context, chaos seems to have a beneficial effect: failure to converge to a global minimum from a given initial point can often be rectified by making arbitrarily small changes in the system parameters. 相似文献
63.
Steven D. Bull Simon W. Epstein Nadeam Mujtaba Edward D. Savory Juan A. Tamayo 《Tetrahedron》2006,62(33):7911-7925
Enolates of (S)-N,N′-bis-(p-methoxybenzyl)-3-iso-propylpiperazine-2,5-dione exhibit high levels of enantiodiscrimination in alkylations with (RS)-1-aryl-1-bromoethanes and (RS)-2-bromoesters, affording substituted diketopiperazines containing two new stereogenic centres in high de. Deprotection and hydrolysis of the resultant substituted diketopiperazines provides a route to the asymmetric synthesis of homochiral methyl 2-amino-3-aryl-butanoates and 3-methyl-aspartates in high de and ee. 相似文献
64.
A novel technique to overcome the long-term drift and hysteresis of a scanning Fabry–Perot filter was developed and applied to wavelength and power monitoring of DWDM system. By using the comb peaks generated by a temperature-stabilized, near threshold-biased Fabry–Perot diode laser as wavelength reference for the scanning Fabry–Perot filter, wavelength and power measurement accuracy of better than ±10 pm and 0.2 dB, respectively, were achieved. 相似文献
65.
66.
67.
We call a one-way infinite word w over a finite alphabet (ρ,l)-repetitive if all long enough prefixes of w contain as a suffix a ρth power (or more generally a repetition of order ρ) of a word of length at most l. We show that each (2,4)-repetitive word is ultimately periodic, as well as that there exist continuum many, and hence also nonultimately periodic, (2,5)-repetitive words. Further, we characterize nonultimately periodic (2,5)-repetitive words both structurally and algebraically. 相似文献
68.
D.W. Mueller JrA.L. Crosbie 《Journal of Quantitative Spectroscopy & Radiative Transfer》2002,74(1):43-68
Three-dimensional radiative transfer in an anisotropic scattering medium exposed to spatially varying, collimated radiation is studied. The generalized reflection function for a semi-infinite medium with a very general scattering phase function is the focus of this investigation. An integral transform is used to reduce the three-dimensional transport equation to a one-dimensional form, and a modified Ambarzumian's method is applied to formulate a nonlinear integral equation for the generalized reflection function. The integration is over both the polar and azimuthal angles; hence, the integral equation is said to be in the double-integral form. The double-integral, reflection function formulation can handle a variety of anisotropic phase functions and does not require an expansion of the phase function in a Legendre polynomial series. Complicated kernel transformations of previous single-integral studies are eliminated. Single and double scattering approximations are developed. Numerical results are presented for a Rayleigh phase function to illustrate the computational characteristics of the method and are compared to results obtained with the single-integral method. Agreement between the two approaches is excellent; however, as the transform variable increases beyond five the number of quadrature points required for the double-integral method to produce accurate solutions significantly increases. A new interpolation scheme produces accurate results when the transform variable is large. 相似文献
69.
A. P. Vink E. van der Kolk P. Dorenbos C. W. E. van Eijk 《Optics Communications》2002,210(3-6):277-284
The optical properties of Ce3+ in CaSO4, SrSO4 and BaSO4 are reported. The Ce3+ ion shows 4f05d1→2F5/2,2F7/2 luminescence in all three sulphates. Co-doping with Na+ does not change the local surrounding of the Ce3+ ion, but enhances the amount of Ce3+ ions built in. Under optical excitation, besides the typical Ce3+ doublet emission in the ultraviolet spectral region, band emission around 445 nm was observed. This band emission was not assigned to emission from a Ce3+ centre, but to emission from an impurity-trapped exciton. Under X-ray excitation, both Ce3+ emission and an emission band around 380 nm was observed. This band was assigned to emission from a self-trapped exciton. 相似文献
70.
A comprehensive study of the long pulse Nd:YAG laser drilling of multi-layer carbon fibre composites 总被引:2,自引:0,他引:2
W. S. O. Rodden S. S. Kudesia D. P. Hand J. D. C. Jones 《Optics Communications》2002,210(3-6):319-328
The results of an extensive experimental study of the free running Nd:YAG laser drilling of a multi-layer carbon fibre composite, where adjacent layers have differently orientated fibres, are reported. For holes drilled with the laser operating in fixed-Q mode at 1064 nm, parallel sections of blind holes illustrating discontinuities in the hole size along a given section direction will be shown to occur at the interface between adjacent layers. An explanation for this effect is proposed. Detailed single pulse drilling characteristics will be presented illustrating the exit hole diameter as a function of pulse energy and material thickness. These characteristics illustrate a ‘stable' drilling regime in which the exit hole diameters are least sensitive to changes in pulse energy or material thickness and a less ‘stable' regime in which they are more strongly dependent on these parameters. Drilling characteristics will be given for two different beam qualities, illustrating the greater drilling depth and reduced hole size achievable with an improved beam quality. Finally holes drilled through a 2 mm thick sample of material with multiple pulses are considered. Size distribution curves for entrance and exit holes will be presented. The total energy required (number of pulses × pulse energy) to drill through 2 mm thick material will be reported as a function of pulse energy in stationary air and argon atmospheres and in a partial vacuum, illustrating a threshold energy which is dependent upon the drilling atmosphere. The threshold energies will be discussed with reference to plasma formation and the reactivity of the drilling atmosphere. 相似文献