Higher Degrees of Distributivity in MV-Algebras

In this paper we deal with the (, )-distributivity of an MV-algebra , where and are nonzero cardinals. It is proved that if is singular and (, 2)-distributive, then it is (, )-distributive. We show that if is complete then it can be represented as a direct product of MV-algebras which are homogeneous with respect to higher degrees of distributivity.     

Multiple symmetric positive solutions of a class of boundary value problems for higher order ordinary differential equations

In this paper, the authors consider the boundary value problem

and give sufficient conditions for the existence of any number of symmetric positive solutions of (E)-(B). The relationships between the results in this paper and some recent work by Henderson and Thompson (Proc. Amer. Math. Soc. 128 (2000), 2373-2379) are discussed.

     

Optimal design of broadband long period grating-based LP01↔LP02 mode converters for dispersion compensation

Dispersion compensation with higher order mode is emerging as a promising technique that can provide full dispersion and dispersion slope compensation for a long distance high bit rate system. Long period grating-based LP₀₁LP₀₂ mode converters are designed in the wavelength region of 1550 nm for this purpose. The simulated mode converters have large bandwidth with conversion efficiencies of over 99% and the estimated figure of merit is 309 ps/(nm dB). The negative dispersion of –124 ps/(nm km) is obtained over a bandwidth (@20 dB) of 58 nm with relative dispersion slope of 0.008/nm.     

Noether＇s and Poisson＇s methods for solving differential equation xs^（m） = Fs（t,xk^（m-2） , xk（m-1）

This paper studies integration of a higher-order differential equation which can be reduced to a second-order ordinary differential equation. The solution of the second-order equation can be obtained by the Noether method and the Poisson method. Then the solution of the higher-order equation can be obtained by integrating the solution of the second-order equation.     

Studies on high order mode of bell-shaped prototype cavities

Aluminium and copper prototype cavities were designed to study higher order modes(HOM).An automatic field mapping system was developed with LabVIEW to measure the adiofrequency(RF)charac teristics,such as resonant frequency,Q-value,shunt impedance and electromagnetic field distribution of the higher-order modes in a model RF cavity.Two kinds of the bell-shaped cavities were measured using the field mapping system,their frequencies are 1.5 GHz and 800 MHz respectively.The fields' distributions of the monopole modes and dipole modes,as well the R/Q values,were measured.     

Embedding of non-simple Lie groups,coupling constant relations and non-uniqueness of models of unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU _L (2) ⇔ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU _L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU _L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin²ϑ=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons likeE ₆, while addition of extra charged fermion singlets can reduce the value of sin² ϑ to 1/4. We point out that at the present time the models of grand unification are far from unique.     

On the Diophantine equation

Let be an odd prime. In this paper, using some theorems of Adachi and the author, we prove that if and , then the equation , and the equation , have no integral solutions respectively. Here is th Bernoulli number.

     

县域“高中化学名师发展基地项目”的探索与实践

为落实《国家中长期教育改革和发展规划纲要》,提升教师专业素养,肥城市教体局与北京师范大学化学学院签订“高中化学名师发展基地项目”,围绕高中教师特别关注的教材教法、课程衔接、科普教育、教研与论文写作、高考指导等主题,形成了“教学研训立体化”的高中化学教师培训体系,提升了高中化学教师的整体教育教学水平,培养出一批教学名师,催生出县域高中与优质高师教育共建教师研训共同体新样态。     

基于移动端虚实结合的高职药学专业有机化学实验教学*

将一种基于移动端的虚拟仿真软件应用于高职院校有机化学实验教学。以“乙酸异戊酯的制备”实验教学为例,通过引入虚拟仿真实验操作,帮助学生了解实验操作的细节,熟悉实验步骤。结果表明,虚拟仿真实验提升了学生的自主学习兴趣,增强了实验信心,提高了实验操作能力。