EXISTENCE OF ALMOST PERIODIC SOLUTIONS FOR DIFFERENCE SYSTEMS

1IntroductionAsisknown,therehavebeenquiteafewresu1tsontheexistenceofalrilostperiodicsolutionsforordinaryanddelaydifferentialstystems.However,tothebestofourknowledge,therehavenotappearedanycorrespondingresu1tsfOrevenordinarydifferencesystemssofar.Todealwithsuchproblems,wewilldefinethenotionoftheso-calleduni-formlyalmostperiodicsequencesbesidesthealmostsequencesandasymptoti-callyalmostsequences.Thenweprovidethecriteriaandthebasicpropertiesofuniformlyalmostperiodicsequenceswhichareneededinestabl…     

一类非线性系统周期解的存在唯一性及其渐近性态

利用Liapunov函数方法,研究了一类一般的非线性系统周期解的存在唯一性与渐近稳定性,得到了存在唯一渐近稳定周期解的充分条件。     

横观各向同性半无限空间表面典型荷载作用下的地基附加应力系数

在胡海昌和Lekhnitskii解的基础上,求得了地基表面作用竖直载荷时的附加应力系数的统一表达式,它可同时适用于各向同性和横观各向同性地基材料。详细讨论了5种典型载荷工况:圆形均布荷载、矩形均布荷载、矩形三角形分布荷载、均布线性和条形荷载。解的最终结果可由初等函数表示。文中同时也通过数值例子图示了材料各向异性对附加应力系数的影响。     

四阶微分方程解的渐近稳定性

本利用Ｌｉａｐｕｎｏｖ函数方法,研究了一类四阶非线性微分方程解的渐近稳定性及有界性。     

一类非线性变系数差分方程平衡点的全局吸引性

本利用相关的差分方程的全局吸引性研究了一类具时滞的非线性变系数差分方程ｘｎ＋１＝ｘｎｅｘｐ（ｒｎ１－ｘｎ－ｋ１－ｃｘｎ－ｋ）的正平衡点ｘ＾－＝１的全局吸引性,获得了一个好的充分条件。     

香草醛晶体光学非线性系数的有限场方法研究

采用有限场方法计算了有机非线性材料3-甲氧基-4-羟基-苯甲醛(分子式C~8H~8O~3,简称MHBA)的二阶非线性光学系数d~2~1,d~2~2,d~2~3,d~2~5。研究结果表明在MP2近似和6-31G+(p,d)基组水平上理论值能较好地与实验值符合,同时也表明拉电子基团HC＝O和推电子基团HO对MHBA分子的光学非线性性能的影响很大,而晶体中分子间的氢键作用对d值的贡献很小。     

具有正负系数中立型微分方程的正解

本文研究具有正负系数的中立型微分方程[X（t）-R（t）x（t-r）]'+P（t）x（t-r）-Q（t）x（t-δ）=0.在允许R（t）＋Q（s）ds1不成立的条件下,获得方程（*）存在正解的两个充分条件．     

关于四阶和五阶非线性系统不稳定性的新结果

本文运用Ｌｉａｐｕｎｏｖ直接方法研究了一类四阶五非线性系统的不稳定性问题,解决了文「１」中遗留的问题,得到了较 结果,文章最后给出了几个具体例子。     

Improvement of absolute band gaps in 2D photonic crystals by anisotropy in dielectricity

Two-dimensional (2D) photonic band gaps (PBG) structure fabricated from anisotropic dielectric is studied by solving Maxwell's equations with use of plane-wave expansion method. Numerical simulations show that absolute photonic band gaps can be substantially improved in two dimensional square and triangular lattices of cylinders by introducing anisotropy in material dielectricity. Owing to different refractive indices for electromagnetic waves with E- and H-polarization, the quasi-independent adjustment of band gaps for the E- and H-polarization modes can be implemented by uniaxial crystals with their extraordinary axis parallel to the cylinders. Large absolute band gaps can be created for uniaxial cylinders in air with a positive anisotropy. In the case of air holes in background uniaxial dielectric with even a weak negative anisotropy, the absolute band gap can be increased 2-3 times. Large absolute band gap can also be obtained in other complex configurations of uniaxial and biaxial materials and this enables a full exploitation of potential utilization for anisotropic materials available in nature. Such a mechanism of band gap adjustment should open up a new scope for designing band gaps in 2D PBG structures. Received 26 January 1999     

腔耦合漂移管结构等长化腔列设计

质子直线加速器中使用的脏耦合漂移管加速结构,如采用等长化腔列,可以简化加速腔的制造和调试,降低成本.文中引入粒子动力学系数的新定义,探讨了等长化腔耦合漂移管结构设计方法,并给出部分计算结果.