On an Inequality of Pual Turan Concerning Polynomials-Ⅱ

Let P(z) be a polynomial of degree n and for any complex number α, let D_αP(z) = nP(z)+(α- z) P′(z) denote the polar derivative of the polynomial P(z) with respect to α. In this paper, we obtain inequalities for the polar derivative of a polynomial having all zeros inside a circle. Our results shall generalize and sharpen some well-known results of Turan, Govil, Dewan et al. and others.     

Quantum-corrected finite entropy of noncommutative acoustic black holes

In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton–Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2+1$2+1$-dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.     

Correlation functions from a unified variational principle: Trial Lie groups

Time-dependent expectation values and correlation functions for many-body quantum systems are evaluated by means of a unified variational principle. It optimizes a generating functional depending on sources associated with the observables of interest. It is built by imposing through Lagrange multipliers constraints that account for the initial state (at equilibrium or off equilibrium) and for the backward Heisenberg evolution of the observables. The trial objects are respectively akin to a density operator and to an operator involving the observables of interest and the sources. We work out here the case where trial spaces constitute Lie groups. This choice reduces the original degrees of freedom to those of the underlying Lie algebra, consisting of simple observables; the resulting objects are labeled by the indices of a basis of this algebra. Explicit results are obtained by expanding in powers of the sources. Zeroth and first orders provide thermodynamic quantities and expectation values in the form of mean-field approximations, with dynamical equations having a classical Lie–Poisson structure. At second order, the variational expression for two-time correlation functions separates–as does its exact counterpart–the approximate dynamics of the observables from the approximate correlations in the initial state. Two building blocks are involved: (i) a commutation matrix which stems from the structure constants of the Lie algebra; and (ii) the second-derivative matrix of a free-energy function. The diagonalization of both matrices, required for practical calculations, is worked out, in a way analogous to the standard RPA. The ensuing structure of the variational formulae is the same as for a system of non-interacting bosons (or of harmonic oscillators) plus, at non-zero temperature, classical Gaussian variables. This property is explained by mapping the original Lie algebra onto a simpler Lie algebra. The results, valid for any trial Lie group, fulfill consistency properties and encompass several special cases: linear responses, static and time-dependent fluctuations, zero- and high-temperature limits, static and dynamic stability of small deviations.     

相机位姿估计的加速正交迭代算法

面对需要实时计算的相机位姿估计问题,针对经典的广泛应用的正交迭代算法,提出了一种加速正交迭代算法。其关键思想是将每一次迭代过程规整化,从而提炼出每一次迭代的重复计算,若将此重复计算在迭代开始前提前计算,则可以大幅度的减少迭代过程中的计算量,使得每一次迭代的计算复杂度从O(n)降低为O(1)。因此,可以在更短的时间内迭代更多的次数,从而获得更高的精度。进行了对比实验,结果显示本加速算法计算精度更高,速度更快。并通过实验提出了选择稳健n点透视(RPn P)计算初值,再使用加速正交迭代算法进行迭代运算的方法,在控制点不多的情况下,是一种精度接近最大似然估计,计算速度最快的算法。     

N,Fe, La三掺杂锐钛矿型TiO2能带调节的理论与实验研究

采用基于密度泛函理论(DFT)的平面波超软赝势方法(PWPP), 利用Material studio 计算N, Fe, La三种元素掺杂引起的锐钛矿TiO₂晶体结构、能带结构和态密度变化. 并通过溶胶-凝胶法制得锐钛矿型本征TiO₂, N, Fe共掺杂TiO₂和N, Fe, La共掺杂TiO₂; 用X射线衍射和扫描电镜表征结构; 紫外-可见分光光度计检测TiO₂对甲基橙的降解效率变化. 计算结果表明, 由于N, Fe, La三掺杂TiO₂的晶格体积、键长等发生变化, 导致晶体对称性下降, 光生电子-空穴对有效分离, 同时在导带底和价带顶形成杂质能级, TiO₂禁带宽度由1.78 eV变为1.35 eV, 减小25%, 光吸收带边红移, 态密度数增加, 电子跃迁概率提升, 光催化能力增加. 实验结果表明: 离子掺杂使颗粒变小, 粒径大小: 本征TiO₂>N/Fe_TiO₂>N/Fe/La_TiO₂, 并测得N/Fe/La_TiO₂发光峰425 nm, 能隙减小, 光催化能力比N/Fe_TiO₂强, 增强原因是杂质能级和电子态数量增加引起.     

Al_2O_3薄层修饰SiN_x绝缘层的IGZO-TFTs器件的性能研究

采用原子层沉积工艺(ALD)生长均匀致密的三氧化二铝(Al2O3)薄层对氮化硅(Si Nx)绝缘层进行修饰,研究了铟镓锌氧薄膜晶体管(IGZO-TFTs)器件的性能。当Al2O3修饰层厚度为4 nm时,绝缘层-有源层界面的最大缺陷态密度相比于未修饰器件降低了17.2%,器件性能得到显著改善。场效应迁移率由1.19 cm2/(V·s)提高到7.11 cm2/(V·s),阈值电压由39.70 V降低到25.37 V,1 h正向偏压应力下的阈值电压漂移量由2.19 V减小到1.41 V。     

氩原子基态波函数和能量的解析计算

以第一性原理和变分原理为基础,给出了氩原子基态波函数的一种解析表达式,计算了基态氩原子(含类氩离子)的能量,导出了所涉及的所有积分的解析表达式.对氩原子,所得到的能量理论值与实验值的相对误差为0.22%.     

自然弯扭梁的非线性分析

研究了两端边界均为完全约束的自然弯扭梁在小应变，大位移和大转动情况下的非线性性质，并考虑了横向剪切变形和扭转翘曲变形的影响，分析中还包括了拉伸，弯曲和扭转的各种弹性耦合。由最小势能原理可以导出所给问题的平衡方程。这里欧拉角可以用来表示任意大的转动。该方法还可方便地推广到其他各种不完全约束边界的情况。此外，利用上述结果还可以得到该梁在小位移理论中的基本方程和有关公式。     

Parameter identification for viscoelastic materials

Starting from the general stress-strain relation for a linear Boltzmann-Volterra material, which is in agreement with the principle of inertia, a new identification procedure is proposed. Instead of running one long-range relaxation experiment, following asingle suitably specified deformation history, material characterization is done using the data ofn short relaxation experiments followingn different deformation histories. To interpret these data a direct non-iterative algorithm has been developed. Compared with other methods, for example curve fitting by using Gauss' method, this direct method is numerically stable and allows a simple direct evaluation of the error due to the scattering of experimental data. The method has been applied to the determination of the relaxation times of an unsaturated polyester material.     

缺口疲劳门槛值的实验研究

本文报告了对常用高强材料３０ＣｒＭｎＳｉＡ的双边Ｖ型缺口疲劳门槛值进行的实验测量。通过测试结果分析，证实了对不同缺口半径的试样（△Ｋ１／√Ｐ）ｔｈ基本一致的结论。