Numerical treatment of second kind Fredholm integral equations systems on bounded intervals

In this paper the authors propose numerical methods to approximate the solutions of systems of second kind Fredholm integral equations. They prove that such methods are stable and convergent. Error estimates in weighted L^p$L^p$ norm, 1?p?+∞$1?p?+\infty$, are given and some numerical tests are shown.     

A weighted L q -approach to Stokes flow around a rotating body

Considering time-periodic Stokes flow around a rotating body in or we prove weighted a priori estimates in L ^q -spaces for the whole space problem. After a time-dependent change of coordinates the problem is reduced to a stationary Stokes equation with the additional term in the equation of momentum, where ω denotes the angular velocity. In cylindrical coordinates attached to the rotating body we allow for Muckenhoupt weights which may be anisotropic or even depend on the angular variable and prove weighted L ^q -estimates using the weighted theory of Littlewood-Paley decomposition and of maximal operators. The research was supported by the Academy of Sciences of the Czech Republic, Institutional Research Plan no. AV0Z10190503, by the Grant Agency of the Academy of Sciences No. IAA100190505, and by the joint research project of DAAD (D/04/25763) and the Academy of Sciences of the Czech Republic (D-CZ 3/05-06).     

基于多块模式决策的边信息生成方法

分布式视频编码中边信息的质量决定了系统的率失真性能,边信息质量越高,则率失真性能越好。针对视频序列中对象运动的不均匀特性,结合MCTI技术,本文提出了一种新的边信息生成算法。其基本思想是在编码端利用多块模式算法对帧中宏块进行划分,将宏块分为运动缓慢块和运动剧烈块;在解码端,对运动缓慢块直接由MCTI算法生成边信息,而运动剧烈块的边信息要经过后处理进行优化得到。仿真实验表明与直接由MCTI生成边信息方法相比,本文算法可以使生成边信息的峰值信噪比(PSNR)比原有的算法提高0.8dB-1.2dB左右,有效提高了边信息的质量。     

基于绝对节点坐标法的大变形柔性梁几种动力学模型研究

对在平面内大范围转动的大变形柔性梁动力学进行了研究, 基于绝对节点坐标法建立了一种新的大变形柔性梁的非线性动力学模型. 该动力学模型中考虑了柔性梁的轴向拉伸变形和横向弯曲变形, 利用Green-Lagrangian应变张量计算柔性梁的轴向应变及应变能, 利用曲率的精确表达式计算柔性梁的横向弯曲变形能. 运用拉格朗日恒等式给出了柔性梁横向弯曲变形能新的表达式, 该变形能表达式更加简洁, 通过新的变形能表达式得到了新的弹性力模型, 由此得到的动力学方程可以精确地描述柔性梁的几何大变形问题. 通过与高次耦合模型以及ANSYS中BEAM188非线性梁单元模型的比较, 验证了本模型在计算大变形时的正确性以及高次耦合模型在处理大变形问题时的不足. 进一步研究发现, 新的广义弹性力模型可以适当地简化, 给出了两种简化模型, 根据不同模型的计算效率以及计算精度的比较确定了不同模型的适用范围.     

振荡超奇性Hilbert变换的Sobolev有界性

主要研究R~n上沿曲线Γ(t)=(t~(p_1),t~(p_2),…,t~(p_n))的振荡超奇性Hilbert变换H_(n,α,β)=∫_0~1 f(x-Γ(t))e~(it-β)t~(-1-α),在Sobolev空间上的有界性,其中0p_1P_2…P_n,αβ0.证明了对于0γ(nα)/((n+1))(p_1+α),当|1/p-1/2|(β-(n+1)[α-(β+p_1)γ])/(2β)时,H_(n,α,β)是从L_γ~2(R~n))到L~2(R~n)的有界算子.特别地,当β≥(α-γp_1)/(γ+1/(n+1))等时,H_(n,α,β)是从L_γ~2(R~n)到L~2(R~n)的有界算子·     

数控加工刀具运动的优化控制

数控加工的精准性与高速性主要体现在加工路径的插补与加工过程中刀具的速度控制.首先针对数控加工过程中常见的折线轨迹进行分析,提出了折线加工转角处的速度平滑过渡方案,保证加工精度的同时提高加工效率.进一步,得出了转角处的最大加工速度与加工误差关系.针对圆弧类曲线插补问题,在折线模型的基础上拓展了内接和外切两种插补方案.计算结果表明,采用折线平滑过渡时,外切插补方案可以保证更高的精度.     

QK空间的插值序列

本文研究了Q_K空间的插值问题.利用复分析和调和分析的方法,获得了单位圆盘上的一个序列{z_n}是Q_K∩H^∞空间的插值序列的一个充分必要条件,推广了Q_p空间的部分结果.     

Indefinite integrals involving the incomplete elliptic integral of the third kind

A substantial number of new indefinite integrals involving the incomplete elliptic integral of the third kind are presented, together with a few integrals for the other two kinds of incomplete elliptic integral. These have been derived using a Lagrangian method which is based on the differential equations which these functions satisfy. Techniques for obtaining new integrals are discussed, together with transformations of the governing differential equations. Integrals involving products combining elliptic integrals of different kinds are also presented.     

A Nonlinear Lagrange Algorithm for Minimax Problems with General Constraints

This article presents a novel nonlinear Lagrange algorithm for solving minimax optimization problems with both inequality and equality constraints, which eliminates the nonsmoothness of the considered problems and the numerical difficulty of the penalty method. The convergence of the proposed algorithm is analyzed under some mild assumptions, in which the sequence of the generated solutions converges locally to a Karush-Kuhn-Tucker solution at a linear rate when the penalty parameter is less than a threshold and the error bound of the solutions is also obtained. Finally, the detailed numerical results for several typical testproblems are given in order to show the performance of the proposed algorithm.     

Stable strong Fenchel and Lagrange duality for evenly convex optimization problems

By means of a conjugation scheme based on generalized convex conjugation theory instead of Fenchel conjugation, we build an alternative dual problem, using the perturbational approach, for a general optimization one defined on a separated locally convex topological space. Conditions guaranteeing strong duality for primal problems which are perturbed by continuous linear functionals and their respective dual problems, which is named stable strong duality, are established. In these conditions, the fact that the perturbation function is evenly convex will play a fundamental role. Stable strong duality will also be studied in particular for Fenchel and Lagrange primal–dual problems, obtaining a characterization for Fenchel case.