Pointwise Estimate for Linear Combinations of Bernstein-Kantorovich Operators

For linear combinations of Bernstein-Kantorovich operators K_n, r(f, x), we give an equivalent theorem with ω^2r_?^λ(f, t). The theorem unites the corresponding results of classical and Ditzian-Totik moduli of smoothness.     

A novel approach for the preparation of organic-siloxane oligomers and the creation of hydrophobic surface

In this paper, poly(acrylate-g-siloxane) with novel comb-like structure was designed and prepared so as to create a strongly hydrophobic polymer surface. In order to achieve this goal, a series of organic-siloxane oligomers with different chain lengths and a double bond were firstly synthesized through the catalytic reforming and hydrosilylation reaction. Then, poly(acrylate-g-siloxane) was prepared by the copolymerization of the resulting oligomers with acrylate via emulsion polymerization. The as-synthesized oligomers were characterized by ¹H NMR and UV spectrometry, and the morphologies and surface chemical compositions of the dried membrane were investigated by FT-IR, XPS, as well as AFM. XPS analysis result shows that the chemical composition of the membrane's surface was rich in polysiloxane segments, which could be responsible for an increase of surface water repellency (the contact angle could reach 115° at a lower content of polysiloxane). A further investigation suggest that the side chain length of siloxane in the poly(acrylate-g-siloxane) was the dominant factor in influencing the hydrophobicity of the membrane’ surface. When the siloxane chain length reaches to eight, the membrane's surface could exhibit the strongest hydrophobicity.     

Pointwise Estimate for Exponential-Type Operators

The purpose of this paper is to derive the pointwise estimate for three general exponential-type operators by using new Ditzian-Totik modulus.AMS Subject Classification (2000): 41A27, 41A36Supported by the National Science Foundation, Hebei, China.     

Copper(II) Complex of a Urea-functionalized Pyridyl Ligand: Synthesis,Crystal Structure,and Acetate Binding Properties

A copper(II) acetate complex with a urea-functionalized pyridyl ligand, [CuL(OAc)₂]₂ · 2AcOH ( 1 ) [L = N-(3-chlorophenyl)-N'-(3-pyridyl) urea], was synthesized by the reaction of L with Cu(OAc)₂ in methanol. A zigzag-shaped hydrogen bond chain of L is obtained via urea N–H ··· N_pyridyl interactions, and a two-dimensional hydrogen bond network structure is further formed through the C–H ··· O interaction. In the complex 1 , a paddle-wheel structure is generated by Cu ··· O_acetate interactions and Cu ··· N_pyridyl interactions. Furthermore, hydrogen bonding chain structure is extended through weak C–H ··· O hydrogen bond interactions. Through ultraviolet-visible (UV/Vis) spectroscopy, the acetate binding properties of L in solution were also evaluated. Variable temperature magnetic susceptibility measurement indicates that the metal complex 1 displays antiferromagnetic coupling property.     

Nitrogen-Doped and Surface Functionalized CDs: Fluorescent Probe for Cellular Imaging and Environmental Sensing of ClO–

A novel nitrogen doped and surface functionalized fluorescent CDs (T1) was synthesized by one-step and green hydrothermal method, which exhibits a satisfactory fluorescence quantum yield and a series of admirable features such as good aqueous solubility, narrow particle size distribution, resistance to photobleaching as well as excitation-dependent behavior. Benefitting from above merits, T1 can be employed to serve as an outstanding sensing platform for sensitive and accurate detection of ClO^– by remarkable fluorescence “on–off” process with rapid and anti-interference. More notably, the good biocompatibility and photostability can ensure enormous bioimaging potential and successful application of T1 in monitoring of exogenous ClO^– in MG-63 cells. Meanwhile, T1 can also be regarded as a filter paper sensor providing a convenient and efficient analyzing technology for monitoring of free residual chlorine in practical environmental samples. All these results demonstrate that there exists promising possibility for practical applications of T1 in bioimaging systems and environmental monitoring.

Graphical abstract

     

Numerical study of centroid detection accuracy for Shack-Hartmann wavefront sensor

It is crucial for the wavefront sensor to reduce the influence of noise and enhance the detection accuracy of the centroid, which is also an important step for improving the performances of adaptive optics. In this paper, based on the theoretical analysis and by utilizing the Monte-Carlo simulation (MCS) technology, the results obtained by using the centroid algorithms have been compared in detail for the case, in which centroid of the signal is not at the center of the detection area and it also has a relatively large area. It is shown that the size of the signal spot and its centroid position have considerable influences on the centroid detection accuracy. The numerical results agree well with the theoretical predictions and the optimized parameters for each algorithm have been found. The study will be helpful for further optimizing the optical system and improving the centroid measurement accuracy of the wavefront sensor.     

长短桩组合型复合地基优化设计方法研究

在软土地基上建造建(构)筑物需要进行地基处理,复合地基是一种行之有效的地基处理方式。工程上一般对地基浅层土的承载力要求较高,而深层只需满足下卧层强度要求即可。长短桩复合地基可做到浅层置换率高,深部置换率低,这样就合理地满足了软弱地基不同深度对承载力的要求。同时长短桩复合地基浅部置换率高,加固区复合地基模量大,深部置换率低,复合地基模量较低,正好适应浅部附加应力大,深部附加应力小的应力场,这样对减少软弱地基总沉降有利。本文探讨了长短桩复合地基优化设计方法,提出了长短桩复合地基优化设计数学模型,并利用复合形法求解优化设计数学模型,同时给出了优化设计计算算例,计算结果表明,此优化设计方法不仅可有效地保证长短桩复合地基设计方案技术上可靠,还可获得最佳的经济效益。     

Steckin-Marchard-Type Inequalities for Some Durrmeyer Operators

In this paper, we will derive some Steckin-Marchard-type inequalities for Bernstein-Durrmeyer and Szasz-Durrmeyer operators.     

化学驱动的[2]轮烷型分子梭

机械互锁的轮烷型分子梭在分子机器化学领域具有重要的位置,可通过"积小为大"的方法在分子水平进行新材料的自组装.在外界的刺激下,大环分子可以在轴分子的不同识别位点间或态间往复穿梭,从而引起体系物理或化学性质的交替变化,这种变化又构成了一类基本的机械开关,可以用来执行特定的功能,在分子开关、信息储存和处理等领域具有潜在的应用前景,是超分子化学领域的研究热点.本文以[2]轮烷型分子梭的驱动力(外部刺激)为主线,分别从酸碱驱动、离子配位作用驱动和溶剂极性改变引起的疏水驱动等角度,综述了近年来化学驱动的[2]轮烷型分子梭在合成和应用方面的最新研究进展,同时介绍了其他力(如热力学参数熵、互锁体系中修饰基团尺寸大小、外加化学氧化剂或还原剂、得失电子引起的电化学氧化还原以及紫外-可见光照射诱发的偶氮苯顺反光异构化等方式)驱动的轮烷型分子梭的进展,最后对化学驱动的[2]轮烷型分子梭的未来发展趋势进行了展望.