A Cheeger-Müller Theorem for Symmetric Bilinear Torsions

The authors establish a Cheeger-Müller type theorem for the complex valued analytic torsion introduced by Burghelea and Hailer for fiat vector bundles carrying non- degenerate symmetric bilinear forms. As a consequence, they prove the Burghelea-Haller conjecture in full generality, which gives an analytic interpretation of (the square of) the Turaev torsion.     

强Prüfer环的同调刻画

设R是环,R的小finitistic维数定义为fPD(R)=sup{pd_RM|M∈FPR}.本文证明了:若R是连通的强Prüfer环,则fPD(R)≤1.也证明了若R是强Prufer环,M∈FPR,且M是Q-挠模,则pd_RM≤1.     

关于一类Müntz有理逼近的点态估计

给定M〉0,设A={λn}∞n=1是一非负实数序列,满足λn＋1-λn≥Mn In n对所有的n≥1成立,本文给出了Müntz系统{x^λn）的有理逼近在区间[0,1]之右端点1处的点态估计．     

VIBRATION AND STABILITY OF RING-STIFFENED THIN-WALLED CYLINDRICAL SHELLS CONVEYING FLUID

Based on the Flügge shell theory,equations of motion of ring-stiffened thin-walled cylindrical shells conveying fluid are developed with the aid of the Hamilton's principle.Analysis is carried out on t...     

球坐标系下多介质混合物模型的数值模拟

利用多介质混合模型在求解球坐标系下的Riemann问题时,需要考虑界面处压力平衡性弱、奇点处理、状态方程复杂等多个难点。本文将原始基于体积分数的Mie-Grüneisen多介质混合模型扩展到球坐标系下,并对多个细节进行了修正和改进,包括:在界面处对热力学参数进行修正、采用质量分数导出新输送方程、利用质量分数加权计算偏导数、采用相邻网格点的物理量定义奇点等。经过改进后的计算模型,可以得到无振荡的数值解,而且可以准确捕捉到冲击波和界面的位置。另外,使用改进后的质量分数模型比原始的体积分数模型得到的计算结果更准确。     

Grünwald插值算子的加权L1收敛速度

给出了以第一类Chebyshev多项式的零点为插值结点组的Grünwald插值多项式在加权L1下收敛速度的一个估计.     

Grünwald插值算子的L2收敛性

证明了以Legendre多项式的极值点为插值结点组的Grünwald插值多项式在L2范数下是收敛的.     

Magnetocaloric Effect in Anisotropic Mixed Spin ½—1 System: Pair Approximation Method

We use the Pair Approximation method to analyze the magnetic and magnetocaloric behaviors of diluted mixed spin ${\rm S_A}$=1 and spin ${\rm S_B}$=1/2 with the anisotropic Heisenberg model, on a cubic lattice with coordination number $z$=6. Our system is described in presence of an external magnetic field; the phase diagram and thermodynamic properties related to the concentration of magnetic atom (A or B) and the single ion anisotropy are constructed and discussed. Special attention is paid to magnetocaloric properties provided by isothermal entropy change as well as the cooling capacity. These cooling power keys are plotted and discussed as a function of interaction anisotropy and magnetic component concentration of two sublattices ions A and B. Numerical results show a double peak structure in the entropy change curve and the inverse magnetocaloric effect related to the presence of the negative single-ion anisotropy.     

贵金属金的状态方程

 提出了一个热压强的计算公式,从而获得金的状态方程。并结合实验数据与文献中常用的其它两个状态方程进行了比较。结果发现,修正后的状态方程与实验数据吻合很好,略优于其它两个状态方程。     

压缩变形对C20富勒烯分子电子传输特性的影响

The geometry,electronic structure and electronic transmission of Au electrode-compressed C20 fullerene Au electrode systems are investigated systemically,and some interesting results are obtained by use of molecular dynamics,Extend Hückel method of the first principle,and Green's function based method. The analytical results show that,due to intervention of Au electrodes,the electronic structure of compressed C20 fullerene is changed significantly,the coalescent between C20 fullerene and Au electrodes is intervenient of covalent bond and electrovalent bond,and the compressed C20 fullerenes are better conductors of electricity than those uncompressed or slightly compressed ones. The methods and the relative conclusions are beneficial to go further deep into electronic transmission of carbon fullerenes.