Minimum selections and fixed points of set-valued operators in Banach spaces with some uniform convexity

A new continuity theorem of minimum selection is presented for a continuous set-valued operator from a topological space into a Banach space with some uniform convexity. As applications, some problems concerning minimum right inverses for linear operators and minimum fixed points for condensing set-valued nonlinear operators are discussed. Also, the existence of minimum solutions for an integral inclusion is proved.     

Convergence analysis for finite family of relatively quasi nonexpansive mappings and systems of equilibrium problems

In this paper, a new iterative scheme by hybrid method is constructed. Strong convergence of the scheme to a common element of the set of common fixed points of finite family of relatively quasi-nonexpansive mappings and set of common solutions of a system of equilibrium problems in a uniformly convex and uniformly smooth real Banach space is proved using the properties of generalized f-projection operator. Our results extend important recent results.     

包含$l^{\beta}(0<\beta<1)$渐近等距翻版的有界线性算子空间

Assume X is a normed space,every x ＊ ∈ S（X＊） can reach its norm at some point in B（X）,and Y is a β-normed space.If there is a quotient space of Y which is asymptotically isometric to l β,then L（X,Y） contains an asymptotically isometric copy of l β.Some sufficient conditions are given under which L（X,Y） fails to have the fixed point property for nonexpansive mappings on closed bounded β-convex subsets of L（X,Y）.     

Air‐Stable Oxyallyl Patterns and a Switchable N‐Heterocyclic Carbene

Oxyallyl derivatives are typically elusive compounds. Even recently reported “stabilized” 1,3‐diaminooxyallyl species are still highly reactive and have short lifetimes at room temperature. Herein, we report the synthesis and preliminary study of mesoionic pyrimidine derivatives that feature 1,3‐bis(dimethylamino)oxyallyl patterns with an unprecedented level of stabilization. The latter are not only insensitive towards air and moisture, but they are also compatible with the formation of an ancillary stable N‐heterocyclic carbene moiety. As the oxyallyl pattern is proton‐responsive, it allows the reversible switching of the electronic properties of the carbene, as a ligand.     

Aromatic 19F–13C TROSY—[19F, 13C]‐Pyrimidine Labeling for NMR Spectroscopy of RNA

We present the access to [5‐¹⁹F, 5‐¹³C]‐uridine and ‐cytidine phosphoramidites for the production of site‐specifically modified RNAs up to 65 nucleotides (nts). The amidites were used to introduce [5‐¹⁹F, 5‐¹³C]‐pyrimidine labels into five RNAs—the 30 nt human immunodeficiency virus trans activation response (HIV TAR) 2 RNA, the 61 nt human hepatitis B virus ? (hHBV ?) RNA, the 49 nt SAM VI riboswitch aptamer domain from B. angulatum, the 29 nt apical stem loop of the pre‐microRNA (miRNA) 21 and the 59 nt full length pre‐miRNA 21. The main stimulus to introduce the aromatic ¹⁹F–¹³C‐spin topology into RNA comes from a work of Boeszoermenyi et al., in which the dipole‐dipole interaction and the chemical shift anisotropy relaxation mechanisms cancel each other leading to advantageous TROSY properties shown for aromatic protein sidechains. This aromatic ¹³C–¹⁹F labeling scheme is now transferred to RNA. We provide a protocol for the resonance assignment by solid phase synthesis based on diluted [5‐¹⁹F, 5‐¹³C]/[5‐¹⁹F] pyrimidine labeling. For the 61 nt hHBV ? we find a beneficial ¹⁹F–¹³C TROSY enhancement, which should be even more pronounced in larger RNAs and will facilitate the NMR studies of larger RNAs. The [¹⁹F, ¹³C]‐labeling of the SAM VI aptamer domain and the pre‐miRNA 21 further opens the possibility to use the biorthogonal stable isotope reporter nuclei in in vivo NMR to observe ligand binding and microRNA processing in a biological relevant setting.     

Duffing单边碰撞系统的混沌鞍合并激变

以典型的Duffing单边碰撞系统为研究对象,对系统中的混沌鞍进行了细致的分析.研究表明,系统的混沌鞍同样存在合并激变,合并激变是由连接两个混沌鞍的周期鞍的稳定流形与不稳定流形相切所诱发,相切使得边界上的混沌鞍与内部的混沌鞍发生碰撞而突然合并为一个较大的边界混沌鞍.混沌鞍的合并激变行为最终会诱导混沌吸引子的合并激变发生. 关键词： Duffing碰撞系统 混沌鞍 周期鞍 稳定与不稳定流形     

分数阶系统有限时间稳定性理论及分数阶超混沌Lorenz系统有限时间同步

研究了分数阶系统有限时间稳定性理论及分数阶混沌系统的同步问题.根据分数阶微分性质及分数阶系统稳定性理论,建立了分数阶系统有限时间稳定性理论并进行了证明.根据该理论设计控制器实现了分数阶超混沌Lorenz系统有限时间同步并运用数值仿真进行了验证. 关键词： 分数阶 超混沌Lorenz系统 稳定 有限时间同步     

应用级联倍频方法提高倍频系统输出稳定性研究

提出应用级联倍频方法提高倍频系统输出稳定性,并就该方法的有效性进行了理论分析和模拟计算.分析和计算结果不但证明级联倍频方法能实现倍频系统稳定输出,而且还表明可以通过仔细调节第一块倍频晶体中波矢方向 k 与光轴间夹角、两块倍频晶体间的间隔,能调节改变实现倍频系统最稳输出时所需第二块晶体的理论计算长度,使之与第二块倍频晶体的实际加工长度一致,最终实现系统稳定倍频输出.级联倍频方法在实现高输出稳定性的同时能实现高的倍频转换效率,对应用于光参量啁啾脉冲放大系统的高稳定抽运源系统的设计建造具有重要参考意义. 关键词： 级联倍频 稳定倍频输出 光参量啁啾脉冲放大     

Stable aqueous dispersion of magnetic iron oxide core–shell nanoparticles prepared by biocompatible maleate polymers

A new method is applied to prepare stable aqueous dispersion of magnetic iron oxide nanoparticles (MNPs) by biocompatible maleate polymers. Fe₃O₄ magnetic core–shell nanoparticles are obtained via forming an inclusion complex between carboxylic acid groups of maleated biocompatible polymers shell and Fe₃O₄ MNPs core surface. Maleate polymers are synthesized via esterification of poly(ethylene glycol), poly(vinyl alcohol) and starch with maleic anhydride (MA). The Fe₃O₄ magnetic core–shell nanoparticles are characterized by Fourier transform infrared spectroscopy, X‐ray diffraction, transmission electron microscopy and vibrating sample magnetometer. The obtained magnetic core–shell nanoparticles exhibit superparamagnetic property and reveal long‐term aqueous stability. This work represents a valid methodology to produce highly stable aqueous dispersion of Fe₃O₄ MNPs ferrofluids which can be expected to have great potential as contrast agent for magnetic resonance imaging. Furthermore, the shell composition of biocompatible maleate polymers with double bond of MA as crosslinker agent allows the polymerization with other monomers to design preferred drug delivery systems. Copyright © 2014 John Wiley & Sons, Ltd.