Second order parabolic equations in Banach spaces with dynamic boundary conditions

In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications.

     

Modeling of the Kinetics of Intramolecular Processes and Transient Spectra with Allowance for Nonradiative Transitions

It has been shown that the kinetics of intramolecular processes and time-resolved spectra with allowance for the quantum beats of the resonant states of isomers or isolated subsystems of levels of one isomeric form can be described with the use of a molecular model interpreting the effect of beats as a nonradiative transition. We have obtained an expression for the nonradiative transition probability, which is directly proportional to the beat frequency and depends oscillatorily on time, thus modeling the effect of beats. The parameter of the molecular system model is the beat frequency directly related to the parameter characterizing the intramolecular interisomeric interactions (the corresponding nondiagonal element of the energy matrix) rather than the value of the nonradiative transition probability. The character of the change in the level populations and, accordingly, in the band intensities in the spectra in the proposed model is in good agreement with the experiment, including the fine structure of the time dependences — oscillations of the line intensities. In analyzing the temporal experiment with a high resolution, it is necessary to take into account the instrument function leading to quantitative and qualitative changes in the time dependences. The traditional model of nonradiative transitions with a constant probability value has a very limited range of applicability — very high beat frequencies compared to the probability of optical transitions.     

Rational Functions with Prescribed Global and Local Minimizers

A family of multivariate rational functions is constructed. It has strong local minimizers with prescribed function values at prescribed positions. While there might be additional local minima, such minima cannot be global. A second family of multivariate rational functions is given, having prescribed global minimizers and prescribed interpolating data.     

异方差回归中的广义方差比检验

在同方差假设之下,线性模型在回归分析的理论与应用方面起着突出的作用,很受许多研究工作者的青睐.然而,回归模型中同方差性这一标准假设不一定总是成立的.因此我们考虑了用一类基于似残差的方法来检验异方差情形下线性模型拟合观测数据的情况.本文既给出了大量的模拟,又给出了实际数据作为应用的例子.效果都很好.     

风冷热泵冷热水机组动态过程仿真

本文给出了风冷热泵冷热水机组动态过程模型。系统的高、低压段被分成制冷剂侧、管壁、以及水或空气侧三个控制容积。针对每个控制容积建立了质量和能量平衡的微分方程。由于压缩机、热力膨胀阀阀体、以及四通换向阀具有较小的热惯性,因而采用稳态模型描述压缩过程、膨胀过程、以及内泄露过程。膨胀阀感温包中的制冷剂温度对于蒸发器出口温度的延迟用一阶惯性环节来描述。通过“预测-校正”和“自适应步长”方法实现系统仿真。仿真结果与测试数据吻合良好。     

高压沿面放电烟气脱硫技术动态实验研究

本文针对高压沿面放电活化气体的烟气脱硫技术,在静态实验研究的基础上进行了实验室冷态动态的实验研究。设计了便于反应和测量的动态实验装置。实验解释了电子束法脱硫技术中导致氨气泄漏的部分原因,验证了高压沿面放电脱硫技术可以在较低的运行电压下,达到提高脱硫效率,减少氨气泄漏的作用。     

Hille and Nehari type criteria for third-order dynamic equations

In this paper, we extend the oscillation criteria that have been established by Hille [E. Hille, Non-oscillation theorems, Trans. Amer. Math. Soc. 64 (1948) 234-252] and Nehari [Z. Nehari, Oscillation criteria for second-order linear differential equations, Trans. Amer. Math. Soc. 85 (1957) 428-445] for second-order differential equations to third-order dynamic equations on an arbitrary time scale T, which is unbounded above. Our results are essentially new even for third-order differential and difference equations, i.e., when T=R and T=N. We consider several examples to illustrate our results.     

An example of a two-sided Wilcoxon signed rank test which is not unbiased

Although the theory of rank tests is rather complete in the one-sided case, it was not even known in 1959, whether the Wilcoxon two-sample test and other similar tests are unbiased against the two-sided alternatives (Lehmann (1959,Testing Statistical Hypotheses, p. 240, Wiley, New York)). A partial answer to this question was given by Sugiura in 1965, who found, that the test named above may be biased (Sugiura (1965,Ann. Inst. Statist. Math.,17, 261–263)). According to Lehmann (1986,Testing Statistical Hypotheses, 2nd ed., pp. 322–324, Wiley, New York) it seems to be still open, whether the same is true for the WILCOXON one-sample test, which is also known as WILCOXON signed rank test. This will be shown in the present paper.     

Testing for additivity with B-splines

Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance.     

Endoscopic Observation of Tissue by Narrowband Illumination

We propose a new illumination method for a medical endoscope: narrow band imaging (NBI), in which the spectral bandwidth of the filtered light is narrowed. To confirm how the spectral specifications of the filtered light influence a reproduced image, an experiment was conducted observing the endoscopic images of the back mucosa of a human tongue. In addition, the effect of NBI on endoscopic images was investigated through preliminary clinical tests in colonoscopy and upper gastrointestinal endoscopy. It has been shown that NBI can enhance the capillary pattern and the crypt pattern on the mucosa. These patterns are useful features for diagnosing an early cancer.