基于薄板样条插值法的MEMS陀螺仪温度补偿模型辨识

MEMS陀螺仪以其优异的性能及廉价的成本,被广泛地应用于水下航行器中;然而传感器的温度变化严重影响测量精度,因此,对其温度补偿模型准确辨识具有重要意义。本文利用基于可持续激励准则的快速标定算法获取标定参数,然后利用薄板样条插值方法建立MEMS陀螺仪温度补偿模型,并将该方法辨识结果与多项式拟合算法的辨识结果进行对比,实验验证,利用本文所提出算法辨识得到的传感器温度补偿模型,有效改善了MEMS陀螺仪测进精度。     

关于最小二乘QR分解算法(LSQR)的一个注记

本文从最小多项式出发,通过寻找包含奇异线性系统Ax=b最小范数解的一个解空间,获得了一个更简单的求解广义逆的计算公式.并从理论上对最小二乘QR分解算法（LSQR）收敛性进行了简单分析,分析表明LSQR的收敛性与矩阵A的非零奇异值密切相关,并用A的非零奇异值以及所寻找到的最小范数解空间将最小范数解线性表出.     

岩盐结构氧化锌物态方程的分子动力学模拟

利用分子动力学方法和有效经验对势模型对ZnO岩盐结构高温高压下的物态方程进行了研究， 发现分子动力学方法得到的ZnO岩盐结构的摩尔体积(300?1273 K，3.2?10.4 GPa)和实验结果吻合；另外，基于经验势模型的可靠性预测了1373?2273 K和0? 50 GPa的ZnO岩盐结构的P-V -T关系，并利用相应的热力学公式拟合得到了ZnO岩盐结构常态下的线性热膨胀系数、等温体模量及其对压力的一阶导数等重要的热力学参量．     

Polynomial integrability of the Hamiltonian systems with homogeneous potential of degree − 3

In this paper, we study the polynomial integrability of natural Hamiltonian systems with two degrees of freedom having a homogeneous potential of degree k given either by a polynomial, or by an inverse of a polynomial. For k=−2,−1,…,3,4, their polynomial integrability has been characterized. Here, we have two main results. First, we characterize the polynomial integrability of those Hamiltonian systems with homogeneous potential of degree −3. Second, we extend a relation between the nontrivial eigenvalues of the Hessian of the potential calculated at a Darboux point to a family of Hamiltonian systems with potentials given by an inverse of a homogeneous polynomial. This relation was known for such Hamiltonian systems with homogeneous polynomial potentials. Finally, we present three open problems related with the polynomial integrability of Hamiltonian systems with a rational potential.     

General construction of mean-field potential and its application to the multiphase equations of state of tin

The mean-field potential (MFP) approach is an efficient way to evaluate the free energy contribution of ion motions for both solid and liquid states. In this paper the MFP is generally constructed with a volume-dependent term and a shape function. The former is derived in accordance with quasi-harmonic approximation. The latter is given semi-empirically. Application to multiphase equations of state for β-, γ- and liquid-tin has been examined. The theoretical phase diagram and thermodynamic properties of isotherm, thermal expansion, heat capacity, Hugoniot states as well as phase transitions are all in excellent agreement with experiments.     

一种显示器投影成象系统的彩色图象几何畸变校正方法

显示器投影成象系统是解决数字图象输出的一种设备,它可将显示器荧屏上的图象(可来自数码相机、光盘、计算机等)扩印在普通彩色相纸上.由于光学镜头会产生几何畸变,加之显示器表面有一定弧度,因此成象在相纸上的图象存在着非线性的畸变.本文主要介绍了如何用数字图象处理的方法对显示器投影成象系统的图象进行几何畸变校正,并对其软件实现进行了简单的讨论.     

A proof of Markov's theorem for polynomials on Banach spaces

Our object is to present an independent proof of the extension of V.A. Markov's theorem to Gâteaux derivatives of arbitrary order for continuous polynomials on any real normed linear space. The statement of this theorem differs little from the classical case for the real line except that absolute values are replaced by norms. Our proof depends only on elementary computations and explicit formulas and gives a new proof of the classical theorem as a special case. Our approach makes no use of the classical polynomial inequalities usually associated with Markov's theorem. Instead, the essential ingredients are a Lagrange interpolation formula for the Chebyshev nodes and a Christoffel-Darboux identity for the corresponding bivariate Lagrange polynomials. We use these tools to extend a single variable inequality of Rogosinski to the case of two real variables. The general Markov theorem is an easy consequence of this.