Sharp bounds for multilinear Hausdorff operators北大核心CSCD

We give the necessary conditions of boundedness of multilinear Hausdorff operators on Lebesgue spaces and λ-central Morrey spaces, respectively, when the kernel functions are nonnegative. Meanwhile, the corresponding operator norms are worked out. ©, 2015, Chinese Academy of Sciences. All right reserved.     

λ-Kantorovich算子的逼近性质

首先在无穷空间上构造了一类新的λ-Szász-Kantorovich算子,通过分析计算得到了该类算子矩的估计及Korovkin型逼近性质;其次,利用连续模和K-泛函的等价关系给出了收敛速度的刻画;最后,借助于Holder不等式建立了Lipschitz连续函数的收敛定理.     

关于满足ACC的*-λ-半环

从满足ACC的任何偏序集是pre-CPO出发,研究了满足ACC的偏序集上的定向集,并由此给出满足ACC的＊-λ-半环的一些性质.证明了S是满足ACC的＊-λ-半环,则S是局部闭＊-半环和连续＊-半环.进一步得到任何满足ACC的＊-λ-半环是对称＊-λ-半环。     

Macrobicyclic triphosphazides and tri-λ-phosphazenes derived from PhC(CH2PPh2)3. Two propeller-shaped diastereoisomers in the crystals

New macrobicyclic cage-compounds composed of two tripodal, propeller-shaped fragments linked by phosphazide and phosphazene units have been synthesized by reaction of PhC(CH₂PPh₂)₃ with tris(m-azidobenzyl)amines. Two diastereoisomers of one of these cages have been characterized in the solid state by X-ray crystallography, one presenting two propellers with the same sense of twist P^∗,P^∗ whereas in the second one the helical sense of both propellers is the opposite, P^∗,M^∗. In contrast, only one species is apparent in CDCl₃ solution.     

Synthesis and structure of supramolecular complexes between 1-alkynyl(phenyl)(tetrafluoroborato)-λ-iodanes and 18-crown-6

Slow evaporation of a solution of 1-decynyl(phenyl)(tetrafluoroborato)-λ³-iodane and 18-crown-6 in dichloromethane-diethyl ether-hexane gave a supramolecular 1:1 complex, while 3,3-dimethyl-1-butynyl- and phenylethynyl(phenyl)(tetrafluoroborato)-λ³-iodanes afforded 2:1 complexes. Complexation with 18-crown-6 increased the thermal stability of the phenylethynyl-λ³-iodane. Solid state and solution structures of these complexes were examined by single crystal X-ray analyses, ¹H and ¹³C NMR spectra, and cold-spray ionization MS. Binding constants were measured by ¹H NMR titrations.     

Reaction of [P3N3Cl4(NH2)2] with [HN(POCl2)2]; The crystal structure of the phosphazenium salt [P3N3HCl4(NH2)2]+[N(POCl2)2]−

The reaction of diaminotetrachloro-cyclotriphosphazene with tetrachloride of μ-imino-diphosphoric acid leads to the formation of the salt-like compound [P₃N₃HCl₄(NH₂)₂]⁺[N(POCl₂)₂]⁻ which identity was unambiguously established by means of X-ray structure analysis. The structure is composed of [P₃N₃HCl₄(NH₂)₂]⁺ cations and [N(POCl₂)₂]⁻ anions joined by a system of H-bonds. As in other phosphazenium salts, the protonation of the ring N atom leads to significant changes in the endocyclic P N bond lengths.     

基于λ/4相移分布反馈半导体激光器四波混频的THz波长转换特性研究

利用耦合模方程，分析了基于λ/4相移分布反馈半导体激光器四波混频的波长转换特性.数值模拟表明：增大偏置电流、减小失谐量有利于扩展转换效率及消光比的动态范围，同时恶化了频率啁啾的动态范围; 受激射效应影响，消光比及频率啁啾在弛豫振荡频率处达到极大值.通过合理选择系统参量，可以获得较理想的波长转换效果.该方案无需抽运光输入，可实现高速、宽带波长转换，在光通信系统中有一定的应用前景. 关键词： λ/4相移分布反馈半导体激光器')" href="#">λ/4相移分布反馈半导体激光器 四波混频 波长转换     

Landau Wavefunction Immediately Derived by Virtue of the <λ| Representation

We show that by virtue of the <λ| representation (Hong-Yi Fan, Phys. Lett. A 126 (1987) 150) the Landau wavefunctions of an electron in a uniform magnetic field can be immediately derived without solving the corresponding Schrödinger equation. It turns out that the differential operation form of the electron's dynamic Hamiltonian, adopted in standard quantum mechanics textbooks, is actually expressed in <λ| representation.     

Electrowetting — From statics to dynamics

More than one century ago, Lippmann found that capillary forces can be effectively controlled by external electrostatic forces. As a simple example, by applying a voltage between a conducting liquid droplet and the surface it is sitting on we are able to adjust the wetting angle of the drop. Since Lippmann's findings, electrocapillary phenomena – or electrowetting – have developed into a series of tools for manipulating microdroplets on solid surfaces, or small amounts of liquids in capillaries for microfluidic applications. In this article, we briefly review some recent progress of fundamental understanding of electrowetting and address some still unsolved issues. Specifically, we focus on static and dynamic electrowetting. In static electrowetting, we discuss some basic phenomena found in DC and AC electrowetting, and some theories about the origin of contact angle saturation. In dynamic electrowetting, we introduce some studies about this rather recent area. At last, we address some other capillary phenomena governed by electrostatics and we give an outlook that might stimulate further investigations on electrowetting.     

New approach to λ-phosphinines

A novel approach to λ⁵-phosphinines has been discovered. Phosphonium salts bearing an alkyl group and the residue of β-dialkylaminocrotonic acid react with DMADMF affording λ⁵-phosphinines. A plausible mechanism of the reaction is offered.