离散大系统在结构扰动下周期解的存在性

对于离散系统稳定性的研究,近年来受到人们的重视,但对于周期解的研究,在文献中还很少看到。本文首先讨论了离散系统解的有界性,并且得到了若一个具有周期系数的差分方程的解为最终有界的,则存在周期解的结果。然后利用李雅普诺夫函数方法研究了离散大系统在结构扰动之下周期解的存在性和离散大系统的平稳振荡。     

Co-induced nano-structures on Si(1 1 1) surface

The interaction of cobalt atoms with silicon (1 1 1) surface has been investigated by means of scanning tunneling microscopy (STM) and low-energy electron diffraction (LEED). Besides the Co silicide islands, we have successfully distinguished two inequivalent Co-induced reconstructions on Si(1 1 1) surface. Our high-resolution STM images provide some structural properties of the two different derived phases. Both of the two phases seem to form islands with single domain. The new findings will help us to understand the early stage of Co silicide formations.     

Directional terahertz radiation through groove-assisted hole array

The authors theoretically demonstrate the terahertz beam shaping with metallic subwavelength holes array surrounded by concentric periodic grooves. High transmission and directional radiation can be obtained simultaneously for the resonant excitation of the surface wave in the combined structure. Finite-difference time-domain simulation results shows that the transmission mainly depends on the lattice constant of hole array and the features of incident surface around it, while the far-field angle distribution is dominated by the details of the output surface. This compact beam shaping structure is hoped to serve as a basic device for future terahertz systems.     

Convergence of generalized AOR iterative method for linear systems with strictly diagonally dominant matrices

In this paper, some improvements on Darvishi and Hessari [On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices, Appl. Math. Comput. 176 (2006) 128–133] are presented for bounds of the spectral radius of _lω,r$l_{\omega ,r}$, which is the iterative matrix of the generalized AOR (GAOR) method. Subsequently, some new sufficient conditions for convergence of GAOR method will be given, which improve some results of Darvishi and Hessari [On convergence of the generalized AOR method for linear systems with diagonally dominant coefficient matrices, Appl. Math. Comput. 176 (2006) 128–133].     

Synthesis of indoles via domino reaction of N-aryl amides and ethyl diazoacetate

A general and concise synthesis of functionalized indoles via domino reaction of N-aryl amides and ethyl diazoacetate has been developed. The methodology offers a great potential for the synthesis of biologically active and naturally occurring indole derivatives.     

TiIV-mediated reactions between primary amines and secondary carboxamides: amidine formation versus transamidation

Titanium(IV)-mediated reactions between primary amines and secondary carboxamides exhibit different outcomes, amidine formation versus transamidation, depending on the identity of the TiIV complex used and the reaction conditions employed. The present study probes the origin of this divergent behavior. We find that stoichiometric TiIV, either Cp*TiIV complexes or Ti(NMe2)4, promotes formation of amidine and oxotitanium products. Under catalytic conditions, however, the outcome depends on the identity of the TiIV complex. Competitive amidine formation and transamidation are observed with Cp*TiIV complexes, generally favoring amidine formation. In contrast, the use of catalytic Ti(NMe2)4 (< or =20 mol %) results in highly selective transamidation. The ability of TiIV to avoid irreversible formation of oxotitanium products under the latter conditions has important implications for the use of TiIV in catalytic reactions.     

Mechanical and electrical properties of CdTe tetrapods studied by atomic force microscopy

The mechanical and electrical properties of CdTe tetrapod-shaped nanocrystals have been studied with atomic force microscopy. Tapping mode images of tetrapods deposited on silicon wafers revealed that they contact the surface with three of its arms. The length of these arms was found to be 130+/-10 nm. A large fraction of the tetrapods had a shortened vertical arm as a result of fracture during sample preparation. Fracture also occurs when the applied load is a few nanonewtons. Compression experiments with the atomic force microscope tip indicate that tetrapods with the shortened vertical arm deform elastically when the applied force was less than 50 nN. Above 90 nN additional fracture events occurred that further shortened the vertical arm. Loads above 130 nN produced irreversible damage to the other arms as well. Current-voltage characteristics of tetrapods deposited on gold revealed a semiconducting behavior with a current gap of approximately 2 eV at low loads (<50 nN) and a narrowing to about 1 eV at loads between 60 and 110 nN. Atomistic force field calculations of the deformation suggest that the ends of the tetrapod arms are stuck during compression so that the deformations are due to bending modes. Empirical pseudopotential calculation of the electron states indicates that the reduction of the current gap is due to electrostatic effects, rather than strain deformation effects inside the tetrapod.     

Copper-catalyzed multicomponent reaction: facile access to functionalized 5-arylidene-2-imino-3-pyrrolines

The synthesis of a novel class of 2-imino-5-arylidene-3-pyrrolines via a copper-catalyzed multicomponent reaction of sulfonyl azides with alkynes and aziridines is described. The protocol is efficient and general.