一般无约束优化问题的广义拟牛顿法

对一般目标函数极小化问题的拟牛顿法及其全局收敛性的研究,已经成为拟牛顿法理论中最基本的开问题之一．本文对这个问题做了进一步的研究,对无约束优化问题提出一类新的广义拟牛顿算法,并结合Goldstein线搜索证明了算法对一般非凸目标函数极小化问题的全局收敛性．     

The rate of convergence of q-Bernstein polynomials for

In the note, we obtain the estimates for the rate of convergence for a sequence of q-Bernstein polynomials {B_n,q(f)} for 0<q<1 by the modulus of continuity of f, and the estimates are sharp with respect to the order for Lipschitz continuous functions. We also get the exact orders of convergence for a family of functions , and the orders do not depend on α, unlike the classical case.     

一类李代数的结构

本文给出了复数域Ｃ上具有有限多个理想的有限维非可解李代数的结构为Ｌ＝Ｃｒ○＋Ｎ○＋Ｓ，其中Ｓ是Ｌ的Ｌｅｖｉ因子，Ｎ是Ｌ的幂零根基，Ｃｒ○＋Ｎ是Ｌ的根基，ａｄｒ是Ｎ的半单纯线性变换，［ｒ，Ｓ］＝０；还给出了这类李代数的一些重要性质．     

非定常的热传导-对流问题的非线性Galerkin混合元法(Ⅲ):时间二阶精度的全离散格式

In this paper, a fully discrete format of nonlinear Galerkin mixed element method with two-step discretization of time for the non stationary conduction-convection problems is presented. The existence and the convergence of the fully discrete mixed element solution are shown. On the basis of [9] and [10], we have proved that the schemes have second-order convergence accuracy for the time discretization.     

C~*-代数的实完全等距映射

C*-代数的*-同构一定是(完全)等距映射,反之不然.本文证明了C*-代数的实完全等距映射能够完全决定C*-代数*-同构的结论.     

Nanoscaled surface structures of ionic crystals by spinodal decomposition

Self-organised periodic surface structures are prepared by spinodal decomposition of AgCl–NaCl single crystals and subsequent ex-solution of the alkali-rich component. While the kinetics of decomposition was studied previously by time-resolved neutron scattering, in the present paper, the etching process is studied in some detail and the surface structures are characterised by atomic force microscopy. It is shown that the duration of both, the demixing process as well as the etching process, determines the characteristic length scale of the periodic pattern. Under well controlled conditions, relief structures with wavelengths of some 100 nm are obtained that are uniform over areas of some mm². These patterns can possibly be used as templates for the decoration with metals, macromolecules, etc.     

Multiplication formulas and isomorphism theorem of ıSchur superalgebras

We introduce the notion of ?Schur superalgebra, which can be regarded as a type B/C counterpart of the q-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed q-permutation modules over Hecke algebras. Some multiplication formulas for ?Schur superalgebra are obtained to construct their canonical bases. Furthermore, we established an isomorphism theorem between the ?Scuhr superalgebras and the q-Schur superalgebras of type A, which helps us derive semisimplicity criteria of the ?Schur superalgebras.     

Quantum entanglement generation on magnons assisted with microwave cavities coupled to a superconducting qubit

We present protocols to generate quantum entanglement on nonlocal magnons in hybrid systems composed of yttrium iron garnet (YIG) spheres, microwave cavities and a superconducting (SC) qubit. In the schemes, the YIGs are coupled to respective microwave cavities in resonant way, and the SC qubit is placed at the center of the cavities, which interacts with the cavities simultaneously. By exchanging the virtual photon, the cavities can indirectly interact in the far-detuning regime. Detailed protocols are presented to establish entanglement for two, three and arbitrary N magnons with reasonable fidelities.     

Structures and Fluorescent Properties of Cadmium(II) Complexes with 1D and 2D Structures Based on Tridentate Benzimidazole Ligands

The cadmium(II) complexes [CdL1(m‐nba)₂] ( 1 ), [CdL1(p‐nba)₂] · C₂H₅OH ( 2 ), [CdL2(p‐nba)₂] · CH₃OH ( 3 ), and [CdL2(p‐nbat)₂] ( 4 ) containing the ligands L1 and L2 [L1 = 2,6‐bis(benzimidazol‐2‐yl)pyridine, L2 = bis(2‐benzimidazolylmethyl)amine] were synthesized and characterized (m‐nba, p‐nba, and p‐nbat are the anions of p‐nitrobenzoic acid, m‐nitrobenzoic acid, and p‐nitrobenzeneacetic acid, respectively). The complexes were investigated by X‐ray single crystal diffraction, elemental analysis as well as IR and fluorescence spectroscopy. Compounds 1 – 3 contain a distorted pentagonal bipyramidal coordination sphere with Cd^II coordinated by two carboxylate ligands in bidentate‐chelating mode, whereas complex 4 exhibits a distorted octahedral arrangement with one carboxylate ligand in bidentate‐chelating and the other in monodentate coordination mode. 1 and 2 form a 1D chain interplayed by hydrogen bonding and strong π–π stacking interactions. 3 and 4 vary from 1D chain into 2D single‐layer and double‐layer networks because of more extensive hydrogen bonding interactions. The complexes show emission maxima in the blue region in the solid state and emission bands are red‐shifted compared to those of the free ligands.