Synthesis of 3,4-diarylsubstituted hexahydro-1H-indoles

Efficient syntheses of 3,4-diarylsubstituted hexahydro-1H-indoles in good yields with excellent diastereoselectivities were achieved with a two-step protocol comprising an allylic cation mediated nucleophilic addition and an intramolecular cyclization reaction. The N-aryl sulfonyl protecting groups of cyclization products were readily removed to furnish free amines with retention of halogen substitutions and CC double bonds.     

Layer and Cavity Structures of Manganese(II) Diphenate Coordination Polymers

Two novel metal‐organic coordination polymers, [Mn₂(dpa)₂(4,4′‐bipy)₂(H₂O)₂]_n ( 1 ) and [Mn(Hdpa)₂(bpe)(H₂O)₂]_n ( 2 ) (H₂dpa = diphenic acid, 4,4′‐bipy = 4,4′‐dipyridine, bpe = 1,2‐bis(4‐pyridyl)ethene), have been hydrothermally synthesized. Single crystal X‐ray diffraction analyses reveal the two‐dimensional and three‐dimensional structures for complexes 1 and 2 , respectively. In 1 , the dpa ligands link metal ions with different modes into one‐dimensional chains, and the 4,4′‐bipy terminally coordinate to the metal ions extending the chains into a layer. Whereas in 2 , the flexible bpe ligands link the structure motifs into chains, and the hydrogen bonding interactions between the chains lead to the formation of cavity structure.     

含新结构单元[Co3(SS)3(PR3)3]的钴化合物的磁性研究

通过含新结构单元钴化合物:Co₃(bdt)₃(PBu₃)₃(Ⅰ),Co₃(tdt)₃(PBu₃)₃(Ⅱ),[Co₃(bdt)₃(PPh₃)₃][CoBr₃(dmf)](Ⅲ)和[Co₃(edt)₃(PEtB)₃]₂[Co₂Cl₄(Et₂SO₂)₂](Ⅳ)(bdt=1,2-S₂C₆H₄^2-,tdt=4-Me-1,2-S₂C₆H₃^2-,edt=SCH₂CH₂S^2-)的磁极矩和¹H NMR等研究表明:它们均具顺磁性,钴原子之间存在着反铁磁偶合作用,同时还讨论了它们的磁学性质和分子结构之间关系。     

d维Bernstein算子加Jacobi权的收敛阶

１．引 言 设Ｓ＝Ｓｄ（ｄ＝１,２,…）是 Ｒｄ中的单纯形,即记ｋ＝（ｋ１,ｋ２,……,ｋｄ）∈Ｒｄ,ｋｉ为非负整数, ,则Ｓ上定义的函数ｆ所对应的ｄ维Ｂｅｒｎｓｔｅｉｎ算子定义为其中 Ｐｎ,ｋ（ｘ）＝是 Ｂｅｒｎｓｔｅｉｎ基函数．引进多维Ｊａｃｏｂｉ权函数, 这里 ．定义Ｂｅｒｎｓｔｅｉｎ权函数 表示微分算子． 记 是单位向量,即第ｉ个分量为１,其余ｄ－１个分量为０, ．定义函数ｆ在方向ｅ上的ｒ阶对称差分为Ｃ（Ｓ）中的加权Ｓｏｂｏｌｅｖ空间为其中Ｓ为Ｓ的内部．定义加权Ｋ－泛函及加权光滑模其中 为加权范数． …     

A general radial quasi-interpolation operator on the sphere

Geodetic and meteorological data, collected via satellites for example, are genuinely scattered and not confined to any special set of points. In order to learn geodetic and meteorological rules, one needs to use these scattered data only to construct an approximant or interpolant. In this paper, we introduce a general distance generated from the scattered data, and, using this, construct a general radial quasi-interpolation operator on the sphere, and we study the convergence rate of this operator. We also show some potential applications of the results obtained here in satellite geodesy.     

Extending the Structures of the p-Sulfonatothiacalix[4]arene Dimers Through Second-sphere Coordination and π…π Stacking Interactions

Reactions of cobalt(II) nitrate or zinc(II) nitrate, tetrasodium p-sulfonatothiacalix[4]arene (Na₄H₄TCAS), and methylviologen dihexafluorophosphate (MV(PF₆)₂) afforded two isomorphous complexes, {[M(H₂O)₆]^2 + [MV]^2 + [(MV)₂M₂(H₂O)₄(H₂TCAS)₂]^4 ? }·14H₂O (M = Co, 1; Zn, 2). In these two complexes, each two thiacalixarenes form a dimer with C _i symmetry through the coordination of sulfonate groups, and the above dimers further extend their structures through second-sphere coordination and π…π stacking interactions into three-dimension nets.     

Approximation theorems by positive linear operators in weighted spaces

In this study, we obtain some Korovkin type approximation theorems by positive linear operators on the weighted space of all real valued functions defined on the real two-dimensional Euclidean space \mathbbR²{\mathbb{R}^2}. This paper is mainly consisted of two parts: a Korovkin type approximation theorem via the concept of A-statistical convergence and a Korovkin type approximation theorem via A{\mathcal {A}}-summability.     

Controllable Coordination Self‐Assembly Based on Flexible Tripodal Ligands: From Finite Metallocages to Infinite Polycatenanes Step by Step

This article describes the developments in coordination self‐assembly based on flexible tripodal ligands with different metal species. Various finite metallocages such as M₃L₂, M₆L₈, M₆L₄, M₄L₄ and different catenanes based on discrete metallocages constructed from flexible tripodal ligands with suitable metal species are presented here. Many M₃L₂ metallocages based on ligands L¹–L¹² and different two‐coordinated metal species have been prepared, in which various Ag(I) salts and other metal species that have been protected by suitable groups, such as Zn(OAc)₂, ZnBr₂, and PdBr₂, have been used as effective acceptors. All of the M₆L₈‐type metallocages are constructed from ligands L² or L¹²–L²⁰ and different four‐coordinated metal species, such as various palladium(II) salts or NiCl₂, and have similar topological structures. Only a few discrete M₆L₄‐type metallocages, based on ligands L²¹–L²⁴, have been reported, using different strategies such as protecting groups and steric hindrance. All of the M₄L₄‐type cages have similar topological structures and are constructed from ligands L²⁵–L²⁹ with multiple donor sites. More intriguing interlocking ensembles constructed from discrete metallocages are also described here in detail, namely, three [2]catenanes based on ligands L³⁰–L³² and four polycatenanes based on ligands L³³–L³⁴.     

The estimate for approximation error of spherical neural networks

Compared with planar hyperplane, fitting data on the sphere has been an important and an active issue in geoscience, metrology, brain imaging, and so on. In this paper, with the help of the Jackson‐type theorem of polynomial approximation on the sphere, we construct spherical feed‐forward neural networks to approximate the continuous function defined on the sphere. As a metric, the modulus of smoothness of spherical function is used to measure the error of the approximation, and a Jackson‐type theorem on the approximation is established. Copyright © 2011 John Wiley & Sons, Ltd.     

From discrete octahedral nanocages to 1D coordination polymer: coordination-driven a single-crystal-to-single-crystal transformation via anion exchange

A discrete octahedral nano-cage has been synthesized by using a C(3)-symmetry semi-rigid pyridine-based ligand tppa. X-ray structure study reveals that the cage has a big inner cavity, flexible windows and all P=O moieties of tppa ligands are inside positions. By anion exchange the 0D nano-cages can transform to infinite chain without noticeable loss of their crystallinity.