Investigation of the Emission Cross-sections and the Spectra of (Cr~(4 ), Yb~(3 ) ): YAG Crystal

l introductionIn recent years, Cr4 --doped crystals have attracted a great deal of attention aspassive Q--,wit,h.,[l~4]. These Cr4 --dOPed crystals include Cr4 : YAG[l'21 ) Cr4 :GSGG[s], Cr4 : YSO['] etc. They have a large absorption cross section and lOwsaturable intensity at the laser wavelength. In comparison with previously usedsaturable absorbers such as dyes['] and LiF: FZ-- [6] cOlor center crystals, Cr4 -dopedcrystals are more photO--chemically and thermally stable and h…     

Pole Dynamics for Elliptic Solutions of the Korteweg-deVries Equation

The real, nonsingular elliptic solutions of the Korteweg-de Vries equation are studied through the time dynamics of their poles in the complex plane. The dynamics of these poles is governed by a dynamical system with a constraint. This constraint is solvable for any finite number of poles located in the fundamental domain of the elliptic function, often in many different ways. Special consideration is given to those elliptic solutions that have a real nonsingular soliton limit. This revised version was published online in July 2006 with corrections to the Cover Date.     

ON INDEFINITE SUBLINEAR ELLIPTIC EQUATIONS

The existence, uniqueness, multiplicity and asymptotic behavior of the solutions to the equation are studied by means of variational and sub-sup-solution methods, where 0 ＜ q ＜ p ＜1, Ω RN with N ＞ 3 is a smooth bounded domain, a, b ∈ L∞(Ω) and λ ∈ R1 is aparameter.     

几乎临界增长的半线性椭圆方程正解的存在性

该文讨论一个几乎临界增长的半线性椭圆方程 .证明了对相应的格林函数的每个严格的局部极小点 x0 ,所考虑的问题有一个正解集中在 x0 .     

The behavior of bounded solutions to the equation Δu−c(x)u=0 on riemannian manifolds of special type

In the paper we consider solutions of the equation Δu−c(x)u=0,c(x)≥0, on complete Riemannian manifolds constituted as follows: the exterior of some compact set is isometric to the direct product of the semiaxis by some compact manifold with the metricds ²=h ²(r)dr ²+g ²(r)dθ². Necessary and sufficient conditions under which bounded solutions of the equation have a limit independent of θ asr→∞ are obtained and also conditions under which the two-sided Liouville theorem is valid. Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 215–221, February, 1999.     

Interface Problems for Elliptic Systems

Interface problems for elliptic systems of second order partial differential equations are studied. The main result is that the solution in the neighborhood of the singular point can be divided into two parts one of which is a solution to the homogeneous system with constant coefficients, and the other one possesses higher regularity.     

半群与弱椭圆算子(英)

设ｉＡｊ（１≤ｊ≤）是有界Ｃ_０群的可交换生成元,Ｐ（Ａ）＝∑_｜μ｜≤２ａ_μＡ~μ（Ａ~μ＝Ａ_１~μ…Ａ_ｎ~μｎ）如果Ｐ是弱椭圆的且其实部是上有界的,则我们证明Ｐ（Ａ）生成一个Ｃ_０半群．     

First order spectrum for elliptic system and nonresonance problem

In this paper we will study the first order spectrum for elliptic systems and the existence of solutions for a quasilinear elliptic system under the condition of nonresonance below the first eigensurface. This revised version was published online in June 2006 with corrections to the Cover Date.     

Modulation instability analysis,optical and other solutions to the modified nonlinear Schrödinger equation

This paper studies the new families of exact traveling wave solutions with the modified nonlinear Schrödinger equation, which models the propagation of rogue waves in ocean engineering. The extended Fan sub-equation method with five parameters is used to find exact traveling wave solutions. It has been observed that the equation exhibits a collection of traveling wave solutions for limiting values of parameters. This method is beneficial for solving nonlinear partial differential equations, because it is not only useful for finding the new exact traveling wave solutions, but also gives us the solutions obtained previously by the usage of other techniques (Riccati equation, or first-kind elliptic equation, or the generalized Riccati equation as mapping equation, or auxiliary ordinary differential equation method) in a combined approach. Moreover, by means of the concept of linear stability, we prove that the governing model is stable. 3D figures are plotted for showing the physical behavior of the obtained solutions for the different values of unknown parameters with constraint conditions.     

一个新的具有大的吸收截面的双光子引发剂的合成和非线性光学性质

E,E-1,4-Bis（4＇-N,N-diphenylaminostyryl）-2,5-dimethoxybenzene （DPAMOB） has been synthesized by a simple and effective solid phase Wittig reaction and characterized by 1^H NMR spectra and elemental analysis, Linear absorption, single-photon induced fluorescence and two-photon induced fluorescence spectra were experimentally studied. The new dye has a large two-photon absorption （TPA） cross-section of σr= 1007,2 GM [1 GM= 1 × 10^-50 cm^4·s/（photon molecule）] at 800 nm measured by the two-photon induced fluorescence method. The experimental results confirm that DPAMOB is a good TPA chromophore and can successfully initiate two-photon photopolymerization of ethoxylated trimethylolpropane triacrylate esters （SR454）. Finally, a microstructure has been fabricated by use of DPAMOB as initiator.