2D sheet-like architectures constructed from main-group metal ions, 4,4'-bpno and 1,2-alternate p-sulfonatothiacalix[4]arene

Two novel 2D sheet-like complexes 1 and 2 have been prepared by reaction of p-sulfonatothiacalix[4]arene (TC4AS) with main-group metal ions (lead(II) or barium(II)) and 4,4'-bipyridine-N,N'-dioxide (4,4'-bpno). In both complexes 1 and 2, TC4AS molecules prefer 1,2-alternate conformation, forming 2D sheet-like layers in the presence of divalent ions and 4,4'-bpno ligand. The layers extend to 3D architectures via strong hydrogen bonding interactions. In addition, complexes 1 and 2 are thermally stable up to ca. 335 and 305 °C, respectively. It seems that the strong hydrogen bonds between the sheet-like layers impart the extraordinarily high degrees of stability to the structures. Further analysis indicates that complexes 1 and 2 are significantly different: (a) the divalent ions have different coordination environments due to the nature of the different ions; (b) TC4AS within complexes 1 and 2 connects to four Pb(II) or six Ba(II) ions, respectively; (c) 4,4'-bpno shows different connection modes; (d) in the solid state, complex 1 exhibits intense orange luminescence with triexponential decays, while complex 2 does not exhibit any obvious luminescence at cryogenic temperatures.     

Novel iso-reticular Zn(II) metal-organic frameworks constructed by trinuclear-triangular and paddle-wheel units: synthesis, structure and gas adsorption

Two novel Zn(II) metal-organic frameworks (MOFs) constructed by trinuclear-triangular and paddle-wheel units, namely {[Zn(5)(dmtrz)(3)(IPA)(3)(OH)]·DMF·H(2)O}(n) (MAC-4, Hdmtrz = 3,5-dimethyl-1H-1,2,4-triazole, H(2)IPA = isophthalic acid, DMF = dimethyl formamide) and {[Zn(5)(dmtrz)(3)(OH-IPA)(3)(OH)]·DMF·5H(2)O}(n) (MAC-4-OH, OH-H(2)IPA = 5-hydroxyisophthalic acid), were solvothermally synthesized. Single-crystal analyses reveal that MAC-4-OH is an iso-reticular framework of MAC-4 with channels functionalized by hydroxyl groups. Gas adsorption reveals that MAC-4-OH shows a significant enhancement for CO(2) uptake compared with that of MAC-4 due to the existence of electrostatic attractive interactions, though its surface area is lower than that of MAC-4.     

Three novel organic-inorganic complexes based on decavanadate [V10O28]6- units: special water layers, open 3D frameworks and yellow/blue luminescences

Three unusual polyoxovanadate-based inorganic-organic hybrid complexes, [Zn(Im)(2)(DMF)(2)](2)[H(2)V(10)O(28)]·Im·DMF (1), [Zn(3)(Htrz)(6)(H(2)O)(6)][V(10)O(28)]·10H(2)O·Htrz (2) and {[Zn(3)(trz)(3)(H(2)O)(4)(DMF)](2)[V(10)O(28)]·4H(2)O}(n) (3) (Im = imidazole, Htrz = 1,2,4-triazole, DMF = N,N'-dimethylammonium) have been synthesized at room temperature via evaporative crystallization, and characterized by single-crystal X-ray diffraction. Complex 1 shows the structure of a discrete [V(10)O(28)](6-) cluster grafted by two [Zn(Im)(2)(DMF)(2)](2+) fragments through two bridged oxygen atoms, representing a rarely observed coordination mode. Complex 2 consists of a linear trinuclear Zn(II) unit bridging six Htrz ligands and a [V(10)O(28)](6-) cluster as the counter anion, where the extensive hydrogen-bonding interactions lead to {Zn(3)-V(10)}(SMF) and a special water layer involving (H(2)O)(36) rings, and consequently forms a unique 3D metal-organic-water supramolecular network. Complex 3 can be described as a 3,4-connected fsc-type network, and is the first example of open coordination 3D framework based on [V(10)O(28)](6-) and the other two different secondary building units, involving mononuclear and binuclear Zn(II)-Htrz motifs. The optical properties of complexes 1-3 in the solid state are investigated at room temperature. The results show that complexes 1 and 3 emit intense blue luminescences attributed to the ligands, while complex 2 exhibits an infrequent fluorescent property, emitting both blue and yellow luminescences at 472 and 603 nm simultaneously. Furthermore, powder X-ray diffraction and thermogravimetric analyses of 1-3 are also investigated, which demonstrate their high purities and thermal stabilities.     

基于单光弹调制器的米勒矩阵测量技术

针对已有米勒矩阵测量方法的不足,提出了一种基于单光弹调制器的米勒矩阵测量技术,给出了米勒矩阵测量优化算法及系统参数两步校准法。该技术通过两步校准法对系统参数进行校准测量,利用优化算法计算得到待测样品的米勒矩阵。实验结果表明,待测1/4波片相位延迟量测量值为90.4185°,误差在标称偏差λ/300以内,快轴方位角测量值为0.2348°,误差在最大旋转误差0.4°以内。同快轴方位角为0°的1/4波片标准米勒矩阵相比,待测1/4波片米勒矩阵各元素最大相对误差的直接测量值和间接测量值分别为1.97%和0.83%,均小于最大相对误差的模拟仿真值2.11%。通过提高旋转台的读数精度和减小相位延迟量的标称偏差,可以进一步减小米勒矩阵各元素的最大相对误差。     

A convergence rate for approximate solutions of Fredholm integral equations of the first kind

We study the convergence rate for solving Fredholm integral equations of the first kind by using the well known collocation method. By constructing an approximate interpolation neural network, we deduce the convergence rate of the approximate solution by only using continuous functions as basis functions for the Fredholm integral equations of the first kind. This convergence rate is bounded in terms of a modulus of smoothness.     

Cubature Formula for Spherical Basis Function Networks

Some mathematical models in geophysics and graphic processing need to compute integrals with scattered data on the sphere. Thus cubature formula plays an important role in computing these spherical integrals. This paper is devoted to establishing an exact positive cubature formula for spherical basis function networks. The authors give an existence proof of the exact positive cubature formula for spherical basis function networks, and prove that the cubature points needed in the cubature formula are not larger than the number of the scattered data.     

MULTIVARIATE WEIGHTED BERNSTEIN-TYPE INEQUALITY AND ITS APPLICATIONS

Bernstein inequality played an important role in approximation theory and Fourier analysis.This article first introduces a general system of functions and the socalled multivariate weighted Bernstein,N...     

膦酰基离子液体铕配合物的合成、结构与荧光性质

合成了两种膦酰基离子液体,1-丁基-3-(3-二苯基膦酰基)丙基咪唑六氟磷酸盐（[BIMC3P(O)Ph2]PF6）(IL-1)和(3-二苯基膦酰基)-丙基三乙胺六氟磷酸盐（[TEAC3P(O)Ph2]PF6）(IL-2),通过核磁共振和红外光谱确认了它们的结构,并合成了两种离子液体的稀土铕配合物Eu(IL-1)3(NO3)3和Eu(IL-2)3(NO3)3,对其进行了热稳定性和光谱性质的表征。 热重分析表明,离子液体的热稳定性均高于其稀土配合物,相比之下,离子液体IL-1和Eu(IL-1)3(NO3)3具有更好的热稳定性。 从红外光谱中可以看出,形成配合物后,两种离子液体中的P=O吸收峰均向低波数方向移动,同时两种配合物的紫外吸收强度均大于各自游离的离子液体,说明Eu3+和离子液体中的磷酰基发生了配位。 稀土铕配合物Eu(IL-1)3(NO3)3和Eu(IL-2)3(NO3)3的荧光光谱均表现出Eu3+的特征红光,峰形尖锐,单色性好,可作为潜在的红色发光材料。     

An oracle inequality for regularized risk minimizers with strongly mixing observations

We establish a general oracle inequality for regularized risk minimizers with strongly mixing observations, and apply this inequality to support vector machine (SVM) type algorithms. The obtained main results extend the previous known results for independent and identically distributed samples to the case of exponentially strongly mixing observations.     

Lp APPROXIMATION BY GENERAL BERNSTEIN-DURRMEYER OPERATOR DEFINED ON SIMPLEX

As a generalization of the Bernstein-Durrmeyer operatora defined on the simplex, a class of general Bernstein-Durrmeyer operators is introduced. With the weighted moduli of smoothness as a metric, we prove a strong direct theorem and an inverse theorem of weak type for these operators by using a decom-position way. From the theorems the characterization of Lp approximation behavior is derived.