A short historical account of period doublings in the pre-renormalization era

I will shortly review the history of experimental and theoretical findings on period doubling until the discovery of the quantitative universal properties of the infinite period-doubling cascade.     

Modulated Pulse Generations in a Laser-diode-pumped Passively Q-switched Intracavity-frequency-doubling Nd∶YVO4 Laser

The investigative results of modulated pulse output from an LD end-pumped passively Q-switched intracavity-frequency-doubling Nd∶YVO4/KTP laser with Cr4+∶YAG saturable absorber are presented. The numerical stimulations of these modulated pulses are carried out basing on the rate equations. It indicated that the modulations are attribute to the frequency beating of two eigenstates of the resonant polarized modes. The theoretical calculations are in good agreement with the experimental observations.     

On the Patterson–Sullivan Measure for Geometrically Finite Groups Acting on Complex or Quaternionic Hyperbolic Space

The goal of this paper is to provide a tool, the Global Measure Formula, that will facilitate the study of the limit set of discrete geometrically finite groups of isometries of the rank one symmetric spaces. We consider the shadow of a ball from a fixed reference point onto the boundary, and prove a formula that describes the measure of the shadow in terms of the center of the shadowed ball, generalizing a result from real hyperbolic geometry.     

用激活性非线性介质Nd：MgO：LiNbO3产生二次谐波

以Nd:MgO:LiNbO_3同时兼作激活介质和非线性光学材料,研究自倍频激光器。用小型氙灯泵浦,在室温下获得二次谐波激光(0.547μm) 阈值小于4.8'J,最大输出400μJ/shot,工作温度范围大于20℃～45℃,无光损伤。     

Parabolic Harnack inequality for divergence form second order differential operators

Old and recent results concerning Harnack inequalities for divergence form operators are reviewed. In particular, the characterization of the parabolic Harnack principle by simple geometric properties -Poincaré inequality and doubling property- is discussed at length. It is shown that these two properties suffice to apply Moser's iterative technique.     

Mindlin板几何非线性分析的附加内部剪应变法

本文在几何非线性分析的Ｍｉｎｄｌｉｎ板元中引入单元附加内部剪应变，有效地解决了薄板情况下的剪切自锁问题．文中导出了相应的能量相容条件，给出了有限元非线性列式的全过程及有关簿板及中厚板大挠度问题的数值结果．     

A compact autocorrelator for the wavelength range between 4 and 10 μm

A compact autocorrelator suitable for the measurement of the optical pulse length of the infrared free electron laser (IR-FEL) at the S-DALINAC is described. It allows to investigate the energy transfer process from the electrons into the laser light within the undulator of the FEL. The autocorrelator utilizes the second harmonic generation (SHG) and it provides the possibility of a background-free measurement at wavelengths between 4 and 10 μm. Simulations for three different crystals used for SHG show that the largest efficiency for SHG and the best temporal resolution is achieved with a ZnGeP₂ crystal at a length of 2 mm. A test experiment at the free electron laser for infrared experiments confirmed the expected high efficiency of about 7.5% of SHG for the ZnGeP₂ crystal as well as the easy handling and fast adjustment of the system.     

A two-stage approach to automatic determination of 1H NMR coupling constants

(1)H NMR scalar coupling constants are a rich source of information on molecular structure, but their extraction from spectra can be less than straightforward. Previous approaches to J extraction include methods proposed by Hoye, Golotvin, and the 'modified J-doubling' method. Here we describe the ACCA method, currently implemented in the NMR package MestReC, which allows a high degree of automation in the extraction of coupling patterns even in the case of complex multiplets with sublinewidth splitting. The new approach is illustrated by application to strychnine, for which it has detected previously unreported couplings.     

Resonance Rayleigh scattering, frequency doubling scattering and second-order scattering spectra of the heparin-crystal violet system and their analytical application

In pH 6.0-11.2 Britton-Robinson buffer solution, binding of heparin with crystal violet (CV) can result in a significant enhancement of resonance Rayleigh scattering (RRS) and resonance non-linear scattering, such as frequency doubling scattering (FDS) and second-order scattering (SOS). Their maximum scattering wavelengths, λ_ex/λ_em, appear at 492 nm/492 nm for RRS, 984 nm/492 nm for FDS and 492 nm/984 nm for SOS, respectively. The optimum conditions of the reaction, the influencing factors and the relationship between the three scattering intensities and the concentration of heparin have been investigated. New methods for the determination of trace amounts of heparin based on the RRS, FDS and SOS methods have been developed. The methods exhibit high sensitivities, the detection limit for heparin is 2.9 ng ml⁻¹ for the RRS method, 3.5 ng ml⁻¹ for the FDS method and 3.3 ng ml⁻¹ for the SOS method. The methods have good selectivity and were applied to the determination of heparin in heparin sodium injection samples with satisfactory results.