一类次线性三点边值问题正解的存在性

利用Krasnosel’skii不动点定理研究了一类次线性二阶非线性常微分方程三点边值问题正解的存在性问题,得到了正解存在的一个充分条件。     

留数定理在一类定积分中的计算

应用复变函数的思想可以求解多种形式的定积分。本文通过留数定理求出一类复杂函数的定积分。     

Algorithm for adaptively smoothing the log-periodogram

We use the principle of minimum cross entropy (MCE) to build a non-parametric adaptive algorithm for smoothing the log-transformed periodogram, and construct an optimal estimate for the spectral density function of a process. We show that this estimate minimizes the cross-entropy with the log-transformed spectral density function of the process. The method is non-parametric and performs very well for the case of processes having rapidly changing spectra that exhibits a variable order of smoothness. The algorithm is locally based on linearly approximating the information present in the process, and uses this approximation to allow the bandwidth of the spectral window in the smoothed log-periodogram to vary. We extend the algorithm empirically for better application to processes having mixed, narrow-band spectra. Comparisons with other currently used procedures are performed through the means of simulated examples.     

对人民币均衡汇率探讨

本文首先对当前人民币基本均衡汇率的研究成果给出了综述,然后对动态购买力平价理论做出分析和研究,指出动态购买力平价理论均衡汇率是符合中国国情的。最后对人民币均衡汇率给出估算。     

Connecting Science and Mathematics: The Nature of Proof and Disproof in Science and Mathematics

Disagreements exist among textbook authors, curriculum developers, and even among science and mathematics educators/researchers regarding the meanings and roles of several key nature-of-science (NOS) and nature-of-mathematics (NOM) terms such as proof, disproof, hypotheses, predictions, theories, laws, conjectures, axioms, theorems, and postulates. To assess the extent to which these disagreements may exist among high school science and mathematics teachers, a 14-item survey of the meanings and roles of the above terms was constructed and administered to a sample of science and mathematics teachers. As expected, the science teachers performed better than the mathematics teachers on the NOS items (44.1 versus 24.7%, respectively) and the mathematics teachers performed better than the science teachers on the NOM items (59.0 versus 26.1%, respectively). Nevertheless, responses indicated considerable disagreement and/or lack of understanding among both groups of teachers concerning the meanings/roles of proof and disproof and several other key terms. Therefore it appears that these teachers are poorly equipped to help students gain understanding of these key terms. Classroom use of the If/and/then/Therefore pattern of argumentation, which is employed in this paper to explicate the hypothesis/conjecture testing process, might be a first step toward rectifying this situation.     

正线性周期卷积算子在Lp_2π^p空间中的饱和等价定理

利用Holder不等式和Minkovski不等式得到一个不等式,利用得到的不等式得到了正线性周期卷积算子在L^p2π中的饱和等价定理,推广了谢庭藩和陈文忠的一些结果。     

EPR佯谬的正-反粒子对阐释

试图通过运用粒子-反粒子对重新阐释EPR佯谬.不同于D.Bohm所给出的工作于离散自旋空间的模型,这里仍然如同Einstein等人在他们的原始论文中一样考虑连续的坐标和动量变量.这里给出的阐释将有助于消除EPR模型中形式上的困惑.     

弱非完整系统相对于非惯性系的Noether定理

首先建立了弱非完整系统相对于非惯性系的Ｊｏｕｒｄａｉｎ型变分原理，然后给出了弱非完整系统相对于非惯性系在一阶近似情况下的广义Ｎｏｅｔｈｅｒ定理。     

状态依赖时滞型微分方程正周期解的存在性

本文利用Krasnoselskii不动点定理,考虑了状态依赖时滞性微分方程x′(t) = &;#8722;A(t, x(t))x(t) + B(x(t))F(x(t &;#8722;  (t, x(t))))正周期解的存在性, 得到了该方程存在与不存在正周期解的充分条件.     

浅谈蝴蝶定理的再推广及其应用

本文以高等几何的相关理论为背景,充分利用射影几何的交比,从二次曲线定弦BC上的任意一点、二次曲线内或外的任意一定点A、正方形、变态的二次曲线等四个方面对蝴蝶定理进行了再推广,并给出推广后命题的一些简单应用。