基于二重网格的动网格松弛法改进

相比传统的弹簧法等方法,基于球松弛算法的动网格松弛法在复杂边界大变形条件下可以得到质量更高的边界网格以及更大的极限变形量,但该方法在时间效率上还有提升的空间.引入二重网格,采用动网格松弛法进行稀疏网格的网格变形,将边界位移传递到整个网格计算域;再利用二重网格映射,将稀疏网格位移映射到原有计算网格的节点上.算例表明,改进...     

The relation between atomic shape and crystal structure illustrated by metallic elements

A new look at the relation between the shape of the atoms and the crystal structure of the elements is made. As a result it was possible to describe the variety of crystal structures (Cu‐, W‐, Mg‐type of structure) of pure metallic elements using a consistent principle. The guiding rule of the principle is the dense arrangement of atoms in the form of a hexagon with a central atom. Different atomic shapes and stacking arrangements lead to different unit cells. The shape of an atom is a more useful visualisation construct than the complicated charge density distribution. The consequences of the proposed model on various aspects of crystallography are discussed. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Metal‐assisted regioselectivity in nucleophilic substitutions: a study by Raman spectroscopy and density functional theory calculations

A series of complexes (Fe^II, Cu^II and Ni^II) of the N,O bidentate ligand 6,7‐dichloroquinoline‐5,8‐dione in water was investigated by using Raman spectroscopy, and the experimental peaks were assigned with the help of computed spectra by density functional theory (DFT) calculations. A strong shift to lower wavenumbers was observed for the vibration of the CO group involved in chelation, depending on the type of metal ion. When each complex was used in the substitution reaction by the nucleophilic reagent piperidine, two products having the same molecular composition but showing the substituent in different regions of the molecule were obtained, and moreover their regioselective formation was in agreement with the size of the Raman shifts previously observed for the complexes. This example confirms the potential of the approach involving Raman spectroscopy combined with DFT calculations in the characterization of metal complexes as key intermediates in organic reactions, with the possibility of predicting the metal system capable to achieve the highest selectivity. Copyright © 2010 John Wiley & Sons, Ltd.     

Study on the surface erosion route to the fabrication of TiO2 hollow spheres

Three-dimensional (3D) architecture of TiO₂ hollow sphere has many excellent and interesting performances that attract significant attention nowadays. In this paper, a simple surface erosion approach to the fabrication of TiO₂ hollow spheres via the hydrothermal process has been developed. The morphologies and the phase were characterized by scanning electron microscopy (SEM) and X-ray diffractometer (XRD). The results indicate that the anatase-type TiO₂ hollow spheres with a diameter of ∼1 μm are successfully synthesized. The shell thickness of TiO₂ hollow spheres is ∼150 nm and the size of hollow cavity is ∼600 nm. By the control experiments, the influence of ammonium fluoride and hydrogen peroxide on the hollow spherical structures was studied. Hydrogen peroxide acts as both the oxidant and the bubble generator, ammonium fluoride is crucial for the erosion and dissolution of titanium, the detailed dissolution-crystallization mechanism for the formation of TiO₂ hollow spheres was also proposed.     

Ultradistributional boundary values of harmonic functions on the sphere

We present a theory of ultradistributional boundary values for harmonic functions defined on the Euclidean unit ball. We also give a characterization of ultradifferentiable functions and ultradistributions on the sphere in terms of their spherical harmonic expansions. To this end, we obtain explicit estimates for partial derivatives of spherical harmonics, which are of independent interest and refine earlier estimates by Calderón and Zygmund. We apply our results to characterize the support of ultradistributions on the sphere via Abel summability of their spherical harmonic expansions.     

Biharmonic Maps from Tori into a 2-Sphere

Biharmonic maps are generalizations of harmonic maps. A well-known result on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere(whatever the metrics chosen) in the homotopy class of maps of Brower degree±1. It would be interesting to know if there exists any biharmonic map in that homotopy class of maps. The authors obtain some classifications on biharmonic maps from a torus into a sphere, where the torus is provided with a flat or a class of non-flat metrics whilst the sphere is provided with the standard metric. The results in this paper show that there exists no proper biharmonic maps of degree±1 in a large family of maps from a torus into a sphere.     

A Nontrivial Homotopy Element of Order p2 Detected by the Classical Adams Spectral Sequence

Let p be an odd prime. The authors detect a nontrivial element ã _p of order p² in the stable homotopy groups of spheres by the classical Adams spectral sequence. It is represented by \(a_0^{p - 2} h_1 \in Ext_A^{p - 1,pq + p - 2} (\mathbb{Z}/p,\mathbb{Z}/p)\) in the E₂-term of the ASS and meanwhile p · ã ^p is the first periodic element α ^p .     

Face numbers of Engström representations of matroids

A classic problem in the theory of matroids is to find a subspace arrangement, such as a hyperplane or pseudosphere arrangement, whose intersection poset is isomorphic to a prescribed geometric lattice. Engström gave an explicit construction for an infinite family of such arrangements, indexed by the set of finite regular CW complexes. In this paper, we compute the face numbers of these topological representations in terms of the face numbers of the indexing complexes and give upper bounds on the total number of faces in these objects. Moreover, for a fixed rank, we show that the total number of faces in the Engström representation corresponding to a codimension one homotopy sphere arrangement is bounded above by a polynomial in the number of elements of the matroid, whose degree is one less than the matroid’s rank.     

Elementary inductive dichotomy: Separation of open and clopen determinacies with infinite alternatives

We introduce a new axiom called inductive dichotomy, a weak variant of the axiom of inductive definition, and analyze the relationships with other variants of inductive definition and with related axioms, in the general second order framework, including second order arithmetic, second order set theory and higher order arithmetic. By applying these results to the investigations on the determinacy axioms, we show the following. (i) Clopen determinacy is consistency-wise strictly weaker than open determinacy in these frameworks, except second order arithmetic; this is an enhancement of Schweber–Hachtman separation of open and clopen determinacy into the consistency-wise separation. (ii) Hausdorff–Kuratowski hierarchy of differences of opens is faithfully reflected by the hierarchy of consistency strengths of corresponding parameter-free determinacies in the aforementioned frameworks; this result is valid also in second order arithmetic only except clopen determinacy.     

Submanifolds in Cauchy Riemann Geometry

In this paper I would like to make a report on the results about hypersurfaces in the Heisenberg group and invariant curves and surfaces in CR geometry. The results are contained in the papers [8, 9, 16] and [14]. Besides, I would also report on the results about the strong maximum principle for a class of mean curvature type operators in [10].