Strong Convergence of an Iterative Method with Perturbed Mappings for Nonexpansive and Accretive Operators

A new iterative method for finding a zero of m-accretive operators is proposed. This method, involving a so-called perturbed mapping, provides a way to construct sunny nonexpansive retractions. Several strong convergence theorems for this method are established in a Banach space that is either uniformly smooth or reflexive with a weakly continuous duality map.     

Nest代数上的在零点广义可导映射

设A为B（H）的子代数,　是A到B（H）的线性映射,我们说　在0点广义可导（广义双边可导）,如果对任意的S,T∈A且ST=0（ST=0或TS=0）,有　（ST）=　（S）T+S　（T）-S　（I）T.本文主要得到如下结果:（1）有限Nest代数上的每个范数拓扑连续的在0点广义可导的线性映射是广义内导子;（2）若N是完备Nest且H_　 H,则algN上的每个范数拓扑连续的在0点广义双边可导的线性映射是广义内导子.     

带约束条件集值优化问题近似Henig有效解集的连通性

研究了带约束条件集值优化问题近似Henig有效解集的连通性.在实局部凸Hausdorff空间中,讨论了可行域为弧连通紧的,目标函数为C-弧连通的条件下,带约束条件集值优化问题近似Henig有效解集的存在性和连通性.并给出了带约束条件集值优化问题近似Henig有效解集的连通性定理.     

离轴三反测绘相机调焦机构的设计

针对测绘相机对相机成像质量和内方位元素稳定性的要求,在分析3种调焦方式特点的基础上,确定了符合离轴三反测绘相机需要的调焦方式。设计了滚珠丝杠驱动的直线导轨式调焦机构,计算得到调焦机构的灵敏度为0.2μm。对该调焦机构进行了精度检测和试验验证,结果显示其指向精度〈2″,定位精度〈3μm。得到的结果表明：该空间调焦机构具有结构紧凑、刚度高、位移精度好等特点,能够满足离轴三反测绘相机的调焦要求。     

On bifurcation points of a complex polynomial

Let be a polynomial of degree . Assume that the set there is a sequence s.t. and is finite. We prove that the set of generalized critical values of (hence in particular the set of bifurcation points of ) has at most points. Moreover, We also compute the set effectively.

     

一致凸Banach空间中渐近非扩张映象的几乎轨道的渐近行为

设Ｘ是有Ｆｒéｃｈｅｔ可微范数的一致凸Ｂａｎａｃｈ空间，Ｃ是Ｘ的有界闭凸子集，Ｔ：Ｃ→Ｃ是一个渐近非扩张映象．证明了，如果｛ｘ_ｎ：ｎ≥１｝是Ｔ的几乎轨道，则序列｛ｘ０｝弱几乎收敛到集合∩from∞to(ｎ＝１)ｃｏ｛ｘ_i：ｉ≥ｎ｝∩Ｆ（Ｔ）的唯一点，其中，Ｆ（Ｔ）是Ｔ的不动点集．     

高维空间中的有界凸域

证明n维空间中的有界凸域D能被拟共形映射到n维单位球B~n(0,1),即D是拟球,从而说明拟共形映射中的黎曼定理在n维空间中的有界凸域类中是成立的．     

RECENT PROGRESS OF NANO-MECHANICAL MAPPING

 Nano-mechanical mapping by atomic force microscopy has been developed as an useful application to measure mechanical properties of soft materials at nanometer scale. To date, the Hertzian theory was used for analyzing force-distance curves as the simplest model among several contact mechanics between elastic bodies. However, the preexisting methods based on this theory do not consider the adhesive interaction in principle, which cannot be neglected in the ambient condition. A new analytical method was introduced to estimate the elasticity and the adhesive energy simultaneously by means of the JKR theory, describing adhesive contact between elastic materials. Poly(dimethylsiloxane) (PDMS) and isobutylene-co-isoprene rubber (IIR) were analyzed to verify the applicable limit of the JKR analysis. For elastic samples such as PDMS, the force-deformation plots obtained experimentally were consistent with JKR theoretical curves. Meanwhile, for viscoelastic samples, especially for IIR, the experimental plots revealed large deviations from JKR curves depending on scanning velocity and maximum loading force. Some nano-rheological arguments were employed based on the difference between these specimens.     

Magnetic resonance imaging in laboratory petrophysical core analysis

Magnetic resonance imaging (MRI) is a well-known technique in medical diagnosis and materials science. In the more specialized arena of laboratory-scale petrophysical rock core analysis, the role of MRI has undergone a substantial change in focus over the last three decades. Initially, alongside the continual drive to exploit higher magnetic field strengths in MRI applications for medicine and chemistry, the same trend was followed in core analysis. However, the spatial resolution achievable in heterogeneous porous media is inherently limited due to the magnetic susceptibility contrast between solid and fluid. As a result, imaging resolution at the length-scale of typical pore diameters is not practical and so MRI of core-plugs has often been viewed as an inappropriate use of expensive magnetic resonance facilities. Recently, there has been a paradigm shift in the use of MRI in laboratory-scale core analysis. The focus is now on acquiring data in the laboratory that are directly comparable to data obtained from magnetic resonance well-logging tools (i.e., a common physics of measurement). To maintain consistency with well-logging instrumentation, it is desirable to measure distributions of transverse (_T2$T_2$) relaxation time–the industry-standard metric in well-logging–at the laboratory-scale. These _T2$T_2$ distributions can be spatially resolved over the length of a core-plug. The use of low-field magnets in the laboratory environment is optimal for core analysis not only because the magnetic field strength is closer to that of well-logging tools, but also because the magnetic susceptibility contrast is minimized, allowing the acquisition of quantitative image voxel (or pixel) intensities that are directly scalable to liquid volume. Beyond simple determination of macroscopic rock heterogeneity, it is possible to utilize the spatial resolution for monitoring forced displacement of oil by water or chemical agents, determining capillary pressure curves, and estimating wettability. The history of MRI in petrophysics is reviewed and future directions considered, including advanced data processing techniques such as compressed sensing reconstruction and Bayesian inference analysis of under-sampled data. Although this review focuses on rock core analysis, the techniques described are applicable in a wider context to porous media in general, such as cements, soils, ceramics, and catalytic materials.     

Bounded holomorphic functions and maps with some boundary behavior

Let Ω be a domain of . As a study of boundary behavior of functions and maps in Ω, we consider “the linear cluster set,” which is the cluster set along segment terminating at a boundary point of Ω. We prove that there exist bounded holomorphic functions and maps defined in Ω which have the linear cluster sets of positive measure at every point of a discrete subset of the boundary of Ω under some conditions.