一类非线性共形分数阶微分方程的边值问题和脉冲初值问题（英文）

本文研究一类非线性共形分数阶微分方程的边值问题和脉冲初值问题,利用基于锥理论的和型算子不动点定理和混合单调算子不动点定理,获得共形分数阶微分方程边值问题和脉冲初值问题正解的存在性和唯一性定理,并且得到一组可以逼近唯一正解的单调迭代序列,最后给出一个实例用来验证结论的有效性.     

全景环形透镜原理与特点剖析

本文从分析传统中心投影法入手，介绍了平面圆柱投影（ＦＣＰ）的基本概念、主要特点，深入地探讨了实现ＦＣＰ的一种光学器件——全景环形透镜（ＰＡＬ）的工作原理。ＰＡＬ具有线性投影关系、方向选择性、景深无限远等重要特性。优化设计了一个口径为３４ｍｍ的ＰＡＬ，模拟计算进一步证实了ＰＡＬ的上述特性。     

对高考数学命题的几点建议

1 要严格执行《数学科考试说明》(以下简称《说明》)的各项条款,维护《说明》的权威性。国家教委考试中心制定并颁布的《说明》,是高考数学命题的法定性文性,也是迎考师生教学与总复习的依据,应该维护它的权威性。     

New localized excitations in a (2+1)-dimensional Broer—Kaup system

Starting with the extended homogeneous balance method and a variable separation approach, a general variable separation solution of the Broer—Kaup system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakon and fractal localized solutions, some new types of localized excitations, such as compacton and folded excitations, are obtained by introducing appropriate lower-dimensional piecewise smooth functions and multiple-valued functions, and some interesting novel features of these structures are revealed.     

具转向点常微分方程混合边值问题的一致收敛差分格式

本文得到了具转向点的二阶常微分方程混合边值问题解的导数估计,提出了Il′in型差分格式,证明了此差分格式按L~1模关于小参数ε的一阶一致收敛性。最后,给出了一个数值例子,计算结果与理论分析一致。     

固态硫酸锂—水合物脱水过程的非等温动力学

采用TG-DTG技术研究了固态硫酸锂-水合物脱水过程，运用Malek等提出的热分析动力学数据处理方法，确定了脱水过程的动力学机理模式f(a)为n(1-a)[-ln(1-a)]^1-1/a或为a^n(1-a)^n，并求得相应动力学参数。     

数学之神——阿基米德

近代数学史家倍尔说,任何一张列出有史以来三个最伟大的数学家的名单中,必定会包括阿基米德,另外两位通常是牛顿和高斯.其实,早在公元1世纪就有人称阿基米德为“数学之神”.阿基米德到底是怎样的一尊“神”呢? 阿基米德,公元前287年生于意大利半岛南端西西里岛的叙拉古城,他有一位当天文学家的父亲,他从小就受到了良好的家庭教育.后来,阿基米德的亲戚当上了叙拉古国王,又使他有机会飘洋过海,到号称“智慧之都”的亚历山大城学习.在那里,阿基米德受到了良好的数学教育,结交了不少著名学者.返回叙拉古后,阿基米德毕生从事研究工作.     

关于等比数列定义的探讨

本文将讨论有关等比数列的几个关系式的等价性,从而深入地探讨等比数列的种种定义,同时兼论一些数学书籍和资料中关于等比数列问题解答上的失误。(一) 在不少数学书籍、刊物和资料中,常见到有这样的结论:     

NETS IN MULTISYSTEMS OF n 3 AND n 4 PHASES

From the free energy surfaces in G-p-T space a series of basic characteristics have beensummarized. For the reactions of most systems with phases of constant composition, eachof the surfaces should be approximate to a plane. After they meet, the points, curves andsurfaces possess distinct stability levels. Across the intersecting curves and points, the freeenergy surfaces and curves will change their stability levels. Linking invariant points ofdistinct stability levels, we can get various univariant curves differing in structure. Theangular extent between two univariant curves around the invariant points is less than 180°.The surfaces meeting in space and projecting onto the p-T section will give rise to partiallyclosed or open, rather than completely closed nets. Finally, based upon the basic characteristicsand criteria, we have derived the partially closed nets of n 3 and n 4 phases with maxi-mum closure by using geometrical and analytical methods. From the free energy surfaces in G-p-T space a series of basic characteristics have beensummarized. For the reactions of most systems with phases of constant composition, eachof the surfaces should be approximate to a plane. After they meet, the points, curves andsurfaces possess distinct stability levels. Across the intersecting curves and points, the freeenergy surfaces and curves will change their stability levels. Linking invariant points ofdistinct stability levels, we can get various univariant curves differing in structure. Theangular extent between two univariant curves around the invariant points is less than 180°.The surfaces meeting in space and projecting onto the p-T section will give rise to partiallyclosed or open, rather than completely closed nets. Finally, based upon the basic characteristicsand criteria, we have derived the partially closed nets of n 3 and n 4 phases with maxi-mum closure by using geometrical and analytical methods.