让学材成为学生数学核心素养发展的有力推手

学习材料简称学材,是驱动学生学习的情感源泉,是学生实践探究的辅助工具。数学学材的选择与运用对教学产生重要影响。

Properties of defect mode and optical enhancement of 1Dphotonic crystals with a defect layer of negative refractiveindex material

The band gap properties of one-dimensional photonic crystals with a defect layer of negative refractive index materials are studied.The defect mode width is bigger than that of conventional one-dimensional photonic crystals with a defect layer of positive refractive index materials.The defect mode of the former is different from that of the latter,shifts towards the direction of high frequency (short wavelength),and has a bigger shifting velocity.Furthermore the effects on the transmission properties of the former photonic crystals caused by change in the position of the defect layer of negative refractive index are investigated.Finally the optical enhancement of the former photonic crystals is also investigated.

Simulating the particle size distribution of rockfill materials based on its statistical regularity

The particle size distribution of rockfill is studied by using granular mechanics, mesomechanics and probability statistics to reveal the relationship of the distribution of particle size to that of the potential energy intensity before fragmentation, which finds out that the potential energy density has a linear relation to the logarithm of particle size and deduces that the distribution of the logarithm of particle size conforms to normal distribution because the distribution of the potential energy density does so. Based on this finding and by including the energy principle of rock fragmentation, the logarithm distribution model of particle size is formulated, which uncovers the natural characteristics of particle sizes on statistical distribution. Exploring the properties of the average value, the expectation, and the unbiased variance of particle size indicates that the expectation does notequal to the average value, but increases with increasing particle size and its ununiformity, and is always larger than the average value, and the unbiased variance increases as the ununiformity and geometric average value increase. A case study proves that the simulated results by the proposed logarithm distribution model accord with the actual data. It is concluded that the logarithm distribution model and Kuz-Ram model can be used to forecast the particle-size distribution of inartificial rockfill while for blasted rockfill, Kuz-Ram model is an option, and in combined application of the two models, it is necessary to do field tests to adjust some parameters of the model.

Mathematical Model of Dynamics of Micropolar Orthotropic Elastic Thin Bars with Free Fields of Displacements and Rotations

In the present paper, initial-boundary value problem of plane stress state of micropolar theory of elasticity is considered for orthotropic material in the domain of thin rectangle. General hypotheses are formulated, which are the qualitative results of the asymptotic method of integration of the stated initial-boundary value problem. On the basis of the accepted hypotheses general applied one-dimensional models of dynamics of bending deformation of micropolar orthotropic elastic thin bars with free fields of displacements and rotations are constructed with and without consideration of shear deformations. With the help of the constructed models different dynamic problems of micropolar bars can be studied. Here concrete problems of free and forced vibrations of hinged supported micropolar orthotropic elastic thin bar are studied. Numerical analysis is done and specific features of dynamic characteristics of micropolar material are revealed. Particularly, it is shown that there is a frequency of vibrations of the micropolar bar that does not depend on bar sizes.

Poles of L-Functions on Quaternion Groups

The author shows that the(partial) standard Langlands L-functions on quarternion groups have at most simple poles at certain positive integers.

Thermodynamic functions of ZrW_2O_8 from its heat capacity

It is interesting to maximize the amount of information we can obtain from one experiment on a single sample. In obtaining all the thermodynamic properties of some materials from their experimental heat capacity data only, we aim to get the tempera- ture-independent energy spectrum. However, all the practical measured energy spectra depend on the temperature of experi- ments. One promising method to obtain the temperature-independent energy spectrum is to solve the so-called specific heat-phonon spectrum inversion （SPI） problem. Here we show, by developing a new practical solution method of SPI, the phonon spectrum of the negative thermal expansion material ZrW208 is obtained. This phonon spectrum is tempera- ture-independent and almost method independent. Hence all the thermodynamic properties of ZrW208, such as thermodynamic potential, entropy, Helmholtz free energy, etc. are obtained by heat capacity only.