弱Lp空间的Marcienkiewicz型内插定理及其应用

在弱$L_p$空间之间建立一类Marcienkiewicz型内插定理并且给出它在现代调和分析理论中的某些应用.     

非完整约束奇异广义力学系统的Poincaré-Cartan积分

对受高阶微商非完整约束并用奇异Lagrange量描述的广义力学系 统，基于广义Apell-Четаев约束条件，并考虑到系统的内在约束，导出了该非完整 约 束奇异广义力学系统的广义Poincaré-Cartan积分不变量. 并证明了该不变量与非完整约束 奇异广义力学系统的广义正则方程等价.     

解弹性力学第二类边界积分方程的求积法与分裂外推

利用Sidi奇异求积公式,提出了解曲边多角形域上线性弹性力学第二类边界积分方程的求积法,即离散矩阵的每个元素的生成只需赋值不需计算任何奇异积分.通过估计离散矩阵的特征值和利用Anselone聚紧收敛理论,证明了近似解的收敛性;同时得到了误差的多参数渐近展开式;通过并行地解粗网格上的离散方程,利用分裂外推获得了高精度近似解和后验误差.     

Tomographic analysis of the central magnetohydrodynamic oscillations on the HT-7 tokamak

Multi-channel soft x-ray (SX) detectors are applied to generate images of magnetohydrodynamic (MHD) oscillation on the HT-7 tokamak, and the data from SX cameras are analysed by using the Fourier--Bessel harmonic reconstruction method and the singular value decomposition. The image reconstruction of SX emissivity is obtained on the assumption of plasma rigid rotation. One of the important phenomena in the HT-7 discharge is the transition from the sawtooth oscillations to the MHD oscillations when the plasma density grows higher. The MHD structure observed in the SX tomography is featured as follows: the magnetic surface of MHD structure is made up of the crescent-shaped ``hot core' and the circular ``cold bubble'. The structure of the magnetic surface is relatively stable. It rotates in the direction of the electron diamagnetic drift at a frequency being the oscillation frequency of the MHD oscillations.     

A nonlocal multi-point singular fractional integro-differential problem of Lane–Emden type

In this paper, using Riemann–Liouville integral and Caputo derivative, we study a nonlinear singular integro-differential equation of Lane–Emden type with nonlocal multi-point integral conditions. We prove the existence and uniqueness of solutions by application of Banach contraction principle. Also, we prove an existence result using Schaefer fixed point theorem. Then, we present some examples to show the applicability of the main results.     

四阶微分方程奇异边值问题的正解

本文利用锥上的不动点指数理论,在更一般的边界条件下讨论了一类四阶奇异边值问题正解的存在性并给出了应用．     

奇异一阶周期系统的多重正解

主要建立了奇异一阶周期系统的多重正解,证明了在适当的条件下这个问题至少存在两个解.第一个正解的存在性是利用非线性L eray-Schauder抉择定理得到的,第二个解是利用K rasnoselsk ii锥不动点定理得到的.     

Infinite horizon quadratic control of linear singularly perturbed systems with small state delays: an asymptotic solution of Riccati-type equations

Email: valery{at}techunix.technion.ac.il Received on January 31, 2006; Accepted on October 5, 2006 An infinite horizon linear-quadratic optimal control problemfor a singularly perturbed system with multiple point-wise anddistributed small delays in the state variable is considered.The set of Riccati-type equations, associated with this problemby the control optimality conditions, is studied. Since thesystem in the control problem is singularly perturbed, the equationsof this set are also perturbed by a small parameter of the singularperturbations. The zero-order asymptotic solution to this setof equations is constructed and justified. Based on this asymptoticsolution, parameter-free sufficient conditions for the existenceand uniqueness of solution to the original optimal control problemare established.