四阶方程两点边值问题Hermite有限元解的渐近展式与外推

1引言有限元解的渐近展式是提高微分方程数值解精度的重要工具,比如亏量校正和外推就是建立在有限元解的渐近展式的基础之上．许多作者对此进行了大量的研究(见[1]-[4]),特别是文[1],提出了在研究有限元解的渐近展式中十分有用的能量嵌入技巧．本文利用能量嵌入定理得到了四阶方程两点边值问题Hermite有限元解及其二阶平均导数的渐近展式,进一步我们还讨论了它们的Richardson外推公式．考虑四阶方程两点边值问题     

Nanoparticle composites: FePt with wide-band-gap semiconductor

We present a simple way to synthesize FePt and ZnO (wide-band-gap semiconductor) nanoparticle composites. The FePt nanoparticles were fabricated using the method reported by Sun et al. By controlling the heating rate, 3 nm FePt nanoparticles were synthesized. Well-dispersed FePt and ZnO nanoparticle composites were prepared by further adding zinc acetate and oleyl amine into the 3 nm FePt nanoparticle dispersion. By controlling the molar ratio of the FePt and zinc acetate, FePt and ZnO nanoparticle composites with different FePt particle fractions were obtained. The intensity of photo luminescence spectra of the nanoparticle composites increases very much with decreasing FePt particle fraction, whereas the peak position shifts a little. After annealing at 550 °C for half an hour, the nanoparticle composites become magnetically hard or semi-hard with coercivity much dependent on the FePt particle volume fraction. The coercivity of the composites increases with annealing temperature. The composites hold the promise of applications in new generation recording and/or optical devices.     

Phosphonate electrochemical recognition by molecularly imprinted deposited film

In this paper, thin films of titanium oxide imprinted with O,O-dimethyl-(2,4-dichlorophenoxyacetoxyl)(3′-nitrobenyl) methinephosphonate (Phi-NO₂) were prepared via liquid phase deposition (LPD) method on a glassy carbon electrode. The imprinted molecular in the films was removed by treatment with immersion in CH₂Cl₂. X-ray diffraction (XRD) and electrochemical methods were introduced to show the evidence of the molecular imprinting phenomenon. It was also found that the recognition ability of the sensor depended on the substituents associated with tridimensional structures of the nitro-compounds. Under the optimized condition, the sensor showed better sensitivity, selectivity and reproducibility to the imprinted molecule and the linear relationship between the current and the concentration of analyte in the range of 0.1-50 μM was obtained. LPD proved to be a powerful method for imprinting titanium oxide thin sense films.     

On the persistence of elliptic lower-dimensional tori in Hamiltonian systems under the first Melnikov condition and Rüssmann’s non-degeneracy condition

In this paper we formulate a theorem on the persistence of elliptic lower-dimensional invariant tori for nearly integrable analytic Hamiltonian systems under the first Melnikov condition and Rüssmann’s non-degeneracy condition, and give the measure estimates of parameters for the non-resonance conditions under Rüssmann’s non-degeneracy condition, which is essential for the proof of our result.     

An Extension Landau-Lifshitz Model in Studying Soft Ferromagnetic Films

In this paper, we propose a model in studying soft ferromagnetic films, which is readily accessible experimentally. By using penalty approximation and compensated compactness, we prove that the dynamical equation in thin film has a local weak solution. Moreover, the corresponding linear equation is also dealt with in great detail.     

Stagnation flow on a cylinder with partial slip--an exact solution of the Navier-Stokes equations

The stagnation slip flow on an axially moving cylinder is studied.The Navier–Stokes and energy equations reduce to nonlinearordinary differential equations under a similarity transform.For large slip, the flow field decays exponentially into potentialflow. The heat transfer can be expressed as an incomplete gammafunction. In general, the heat transfer increases with slip,Prandtl number and Reynolds number.     

Studies on the method of total synthesis of koumine: I. 4-Substituted 1,2-dihydropyridine derivatives and their function as a conjugated diene in Diels-Alder reaction

A route to the total synthesis of koumine has been suggested. Five 4-substituted 1, 2-d hydropyridine derivatives, which are supposed to be a conjugated diene of Diels-Alder reaction to produce the isoquinuclidine ring of koumine, have been synthesized. Only two of them were found to be able to undergo the Diels-Alder reaction. The stereochemistry of the reaction product has also been examined.     

Cathodoluminescence study of extended defects in hydrothermal ZnO crystals

Understanding the luminescence of ZnO is very important for some applications. In spite of the many studies carried out, there are still some points concerning the origin of some of the luminescence emissions in ZnO crystals that require additional study; in particular, the role of extended defects remains to be a matter of controversy. We present here a cathodoluminescence analysis of the defects generated by Vickers indentation in hydrothermal HTT crystals. Special emphasis was paid to the luminescence band peaking around 3.3 eV. The origin of this band is a matter of controversy, since it has been related to different causes, extended defects being one of the candidates for this emission. The CL images were acquired around crystal defects. It is observed that the 3.3 eV emission is enhanced around the crystal defects; though it is also observed, but weaker, out of the defect regions, which suggests that there exist two luminescence emissions peaking very close to 3.3 eV. The two emissions, one related to structural defects and the other to the LO phonon replica of the free excitonic band, appear very close each other and their relative intensity should determine the shape of the spectrum.     

Generation of red light at 660 nm by frequency doubling a Nd:YAG laser with periodically-poled stoichiometric LiTaO<Subscript>3</Subscript>

High power red light was generated from a periodically-poled stoichiometric LiTaO₃ (PPSLT) by single-pass frequency doubling of a diode-side-pumped, Q-switched Nd:YAG laser at 1319 nm. An average power of 2.4 W of the 660 nm red light was obtained at the fundamental power of ∼5.4 W with the conversion efficiency up to 44.4% and with low fluctuation down to 2%. The high efficiency and stability at the red output indicate that it is a practical method to construct a reliable compact red laser. PACS 42.70.Mp; 42.79.Nv; 42.55.Xi