On infinite products of positive linear operators reproducing linear functions

Infinite products of positive linear operators (p.l.o.) reproducing linear functions are considered from a quantitative point of view. Refining and generalizing convergence theorems of Gwó?d?-?ukawska, Jachymski, Gavrea, Ivan and the present authors, it is shown that infinite products of certain positive linear operators, all taken from a finite set of mappings reproducing linear functions, weakly converge to the first Bernstein operator. A discussion of products of Meyer-König and Zeller operators is included.     

On an Aitken–Newton type method

We study the solving of nonlinear equations by an iterative method of Aitken type, which has the interpolation nodes controlled by the Newton method. We obtain a local convergence result which shows that the q-convergence order of this method is 6 and its efficiency index is $\sqrt[5]{6},$ which is higher than the efficiency index of the Aitken or Newton methods. Monotone sequences are obtained for initial approximations farther from the solution, if they satisfy the Fourier condition and the nonlinear mapping satisfies monotony and convexity assumptions on the domain.     

ABAB homoleptic bis(phthalocyaninato)lutetium(III) complex: toward the real octupolar cube and giant quadratic hyperpolarizability

The concept of octupolar molecules has considerably enlarged the engineering of second-order nonlinear optical materials by giving access to 2D and 3D architectures. However, if the archetype of octupolar symmetry is a cube with alternating donor and acceptor groups at the corners, no translation of this ideal structure into a real molecule has been realized to date. This may be achieved by designing a bis(phthalocyaninato)lutetium(III) double-decker complex with a crosswise ABAB phthalocyanine bearing alternating electron-donor and electron-acceptor groups. In this communication, we present the first step toward this goal with the synthesis, crystal structure determination, and measurement of the molecular first-order hyperpolarizability β by harmonic light diffusion, of an original lutetium(III) sandwich complex displaying the required ABAB-type alternation for one face of the cube. This structure is characterized by an intense absorption in the near-IR due to an intervalence transition and exhibits the highest quadratic hyperpolarizability ever reported for an octupolar molecule, √<β(2)(HLS)> = 5750 × 10(-30) esu.     

Dependence of avidity on linker length for a bivalent ligand-bivalent receptor model system

This paper describes a synthetic dimer of carbonic anhydrase, and a series of bivalent sulfonamide ligands with different lengths (25 to 69 ? between the ends of the fully extended ligands), as a model system to use in examining the binding of bivalent antibodies to antigens. Assays based on analytical ultracentrifugation and fluorescence binding indicate that this system forms cyclic, noncovalent complexes with a stoichiometry of one bivalent ligand to one dimer. This dimer binds the series of bivalent ligands with low picomolar avidities (K(d)(avidity) = 3-40 pM). A structurally analogous monovalent ligand binds to one active site of the dimer with K(d)(mono) = 16 nM. The bivalent association is thus significantly stronger (K(d)(mono)/K(d)(avidity) ranging from ~500 to 5000 unitless) than the monovalent association. We infer from these results, and by comparison of these results to previous studies, that bivalency in antibodies can lead to associations much tighter than monovalent associations (although the observed bivalent association is much weaker than predicted from the simplest level of theory: predicted K(d)(avidity) of ~0.002 pM and K(d)(mono)/K(d)(avidity) ~ 8 × 10(6) unitless).     

REXS contribution to electronic ordering investigation in solids

Resonant Elastic X-Ray Scattering (REXS) has played a fundamental role in understanding electronic properties and in revealing hidden order, local symmetries and exotic states realized in correlated solids. This article reports on some of the relevant scientific contributions and technical advances over the last 20 years, by providing a list of related publications produced by various groups all around the world. The given perspective is that of a group of young scientists involved at various times in the investigation of the beauty of electronic ordering by the REXS technique.     

YBCO高温超导磁体临界电流密度快速确定方法

基于绘图法基本原理,以及YBCO高温超导带材的临界电流特性,采用有限元电磁场分析软件AnsoftMaxwell建立了空心圆柱磁体模型.根据磁场分布、并考虑到带材的临界电流密度随磁场大小和方向的变化关系,给出了影响磁体工作电流特性的磁场的分布.基于以上工作提出了一种利用Ansoft电磁场分析软件快速确定YB-CO高温超导带材临界电流密度的方法.     

A SASE free electron laser optimization based on new generation in-vacuum undulators

Optimization studies for an accelerator based light source, namely self-amplified spontaneous emission (SASE) free electron laser (FEL), based on new generation in-vacuum hybrid and superconducting undulator configurations, are compared and discussed. It is shown that the FEL wavelength should be down to soft X-rays ($～3\mathrm{nm}$) part of the spectrum while keeping the same linear accelerator (linac) energy about 1 GeV. On the other hand, numerical calculations and simulation results of the main performance parameters for SASE operation (1D gain length, saturation power and saturation length), are optimized. Finally, technological advantages and challenges for both cases, are briefly mentioned.     

Fundamental structure of Fresnel diffraction: longitudinal uniformity with respect to fractional Fourier order

Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. Transverse samples can be taken on these surfaces with separation that increases with propagation distance. Here, we are concerned with the separation of the spherical reference surfaces along the longitudinal direction. We show that these surfaces should be equally spaced with respect to the fractional Fourier transform order, rather than being equally spaced with respect to the distance of propagation along the optical axis. The spacing should be of the order of the reciprocal of the space-bandwidth product of the signals. The space-dependent longitudinal and transverse spacings define a grid that reflects the structure of Fresnel diffraction.     

Deposition of titanium nitride and hydroxyapatite-based biocompatible composite by reactive plasma spraying

Titanium nitride is a bioceramic material successfully used for covering medical implants due to the high hardness meaning good wear resistance. Hydroxyapatite is a bioactive ceramic that contributes to the restoration of bone tissue, which together with titanium nitride may contribute to obtaining a superior composite in terms of mechanical and bone tissue interaction matters.The paper presents the experimental results in obtaining composite layers of titanium nitride and hydroxyapatite by reactive plasma spraying in ambient atmosphere. X-ray diffraction analysis shows that in both cases of powders mixtures used (10% HA + 90% Ti; 25% HA + 75% Ti), hydroxyapatite decomposition occurred; in variant 1 the decomposition is higher compared with the second variant. Microstructure of the deposited layers was investigated using scanning electron microscope, the surfaces presenting a lamellar morphology without defects such as cracks or microcracks. Surface roughness values obtained vary as function of the spraying distance, presenting higher values at lower thermal spraying distances.     

功能染料4,4′-双(4-羧基偶氮苯)二苯并-18-冠-6的制备及其吸收光谱

以二苯并-18-冠-6和对氨基苯甲酸为原料,经重氮化、偶合等多步反应,制备了一种功能染料——4,4’-双(4-羧基偶氮苯)二苯并-18-冠-6.产率68.5%,通过IR、~1H NMR和元素分析等方法对其结构进行表征。研究了不同金属离子对目标化合物紫外一可见吸收光谱的影响,用密度泛函理论对其作用机理进行探讨。结果表明,目标化合物的吸收光谱性能良好,对稀土元素和金属汞离子具有不同作用机理的选择性识别作用。