Stable hysteretic reflection of light at a nonlinear interface

We have observed a hysteretic (bistable) reflection of a Gaussian laser beam at the interface between glass and a liquid solution of polystyrene microspheres as nonlinear medium with both branches of the hysteretic curve being stable, in contrast to the results of previous experiments.     

On hermitian polynomial optimization

We compare three levels of algebraic certificates for evaluating the maximum modulus of a complex analytic polynomial, on a compact semi-algebraic set. They are obtained as translations of some recently discovered inequalities in operator theory. Although they can be stated in purely algebraic terms, the only known proofs for these decompositions have a transcendental character. Received: 27 June 2005     

The condition on the stability of stationary lines in a curvature flow in the whole plane

The long time behavior of a curve in the whole plane moving by a curvature flow is studied. Studying the Cauchy problem, we deal with moving curves represented by entire graphs on the x-axis. Here the initial curves are given by bounded functions on the x-axis. It is proved that the solution converges uniformly to the solution of the Cauchy problem of the heat equation with the same initial value. The difference is of order O(t−1/2) as time goes to infinity. The proof is based on the decay estimates for the derivatives of the solution. By virtue of the stability results for the heat equation, our result gives the sufficient and necessary condition on the stability of constant solutions that represent stationary lines of the curvature flow in the whole plane.     

The Micro-Theory of Ultra-Short Pulse Propagating in Nonlinear Fiber

The modified quantum nonlinear Schrodinger equation of ultra-short pulse propagating in fiber is derived using dispersion relation and the Hamiltonian of the transmission system. The derived equation is solved with linearization approximation, and modulation instability is analyzed. The equation is also solved with Hartree approximation. The results indicate that pulse power, loss and self-steeping effect change the critical frequency, the maximum gain and the gain spectrum range, but the third order dispersion has no effect on modulation instability. The expectation value of optical field is average of a set of modified classical solitons, and higher order terms change the amplitude, pulse position and phase of soliton.     

Heat “polynomials” for a singular differential operator on (0, ∞)

We generalize the theory of the heat polynomials introduced by P. V. Rosenbloom and D. V. Widder for a more general class of singular differential operator on (0, ). The heat polynomials associated with the Bessel operator and studied by D. T. Haimo appear as a particular case in this paper. In the special cases of second derivative and Bessel operators the heat polynomials are in fact polynomials inx andt, however, this property does not hold in general.Communicated by Tom. H. Koornwinder.     

Algorithms for non-linear huber estimation

The Huber criterion for data fitting is a combination of thel ₁ and thel ₂ criteria which is robust in the sense that the influence of wild data points can be reduced. We present a trust region and a Marquardt algorithm for Huber estimation in the case where the functions used in the fit are non-linear. It is demonstrated that the algorithms converge under the usual conditions.     

The absorption of pulsed CO2-laser radiation by ethylene at total pressures from 25 to 3000 Torr

The absorption of pulsed CO₂-laser radiation by ethylene has been measured at total pressures from 25 to 3000 Torr, using the P(12) and P(14) lines in the 10.6 m band, with incident fluences from 0.1 to 0.7 J/cm². Marked deviations from the Beer-Lambert absorption law were observed, with the effective absorption coefficient varying with pressure, fluence, absorption path-length and the addition of non-absorbing gas. Pressure broadening of the rotational lines of the ethylene absorption spectrum was shown to be the major cause of these deviations, together with lesser effects which can be attributed to the rise in temperature of the absorbing gas during the laser pulse.     

Accurate determination of wavenumbers for iodine molecular lines in the red spectral region

The hyperfine structure of various absorption lines of molecular iodine with wavenumbers between 12980 and 13890 cm^–1 has been resolved using Doppler-free polarization spectroscopy. The wavenumbers of theo-component of 17 rovibrational lines of I₂ due to the transitionB ³ _ou ⁺ –X¹ _g ⁺ with even rotational quantum numbers have been determined with an accuracy of 0.001 cm^–1. A comparison of the centers of gravity of these 17 lines with the values of the iodine atlas of Gerstenkorn et al. yields a difference of thus corroborating the data of the iodine atlas in the red region within limits of error.     

云南山竹子中的一个新奇的苯甲酮类化合物

多异戊烯基取代的苯甲酮类化合物存在于多种藤黄科植物中, 具有多种显著的生物活性. 为了进一步发现生物活性成分, 对藤黄科藤黄属植物云南山竹子的枝条和果实进行了研究, 从中分离得到了两个多异戊烯基取代的苯甲酮类化合物, 其中一个为新化合物. 经多种波谱方法确定了两个化合物的化学结构, 一个新化合物命名为藤黄酮K, 另一个化合物为Cambogin.     

Optimization of sucrose ethanol fermentation for K,Na, Ca,and cu metal contents

The effect of the trace metals Cu, K, Na, and Ca, separately or in mixture, on fermentation time, ethanol production rate, and cell growth in the fermentation of synthetic media containing sucrose is discussed. The results are related to the range of contents found in raw materials, molasses and raisins, in order to determine their optimum concentrations for alcohol production.