变分法研究半直线上二阶微分方程由边值条件产生的多个解(英文)

本文讨论半直线上的一类具有非线性边值条件的二阶微分方程.利用变分法和B.Ricceri的三临界点定理得到该方程的多个正解.同时建立该方程由边值条件产生的两个解存在的充分条件.最后给出一个例子来阐释本文的结果.     

Finding the response matrix to the external action from a subspace for a discrete linear stochastic dynamical system

For a discrete linear stochastic dynamical system, computation of the response matrix to the external action from a subspace using given observational data is examined. An algorithm is proposed and substantiated that makes it possible to improve the numerical accuracy and to reduce the amount of observational data compared to the general case where an arbitrary external action is allowed. As an illustration, a discrete system arising in the analysis of a linear stochastic dynamical continuous-time system is considered more thoroughly. Some numerical results are presented.     

Boundedness from below of composition operators on the Bloch spaces

This paper proves that a necessary condition for a composition operator on the Bloch space of the unit disk to be bounded below given by Ghatage, Yan and Zheng is also sufficient. Given furthermore are a sufficient condition and a necessary condition of the boundedness from below for a composition operator on the Bloch space of a unit ball with dimensions bigger than one.     

Photoelectrochemical cells using metal-decorated carbon nanotube electrodes

We fabricated the photoelectrochemical (PEC) cells using n-type TiO₂ and metal (Pt, Pd)-decorated carbon nanotubes (CNTs) as an anode and a cathode, respectively. Photovoltaic effects were clearly observed. Compared with conventional PEC cell with Pt cathode, a larger photo-voltage was found in the PEC cells with the metal-decorated CNT cathode due to p-type semiconducting properties of CNTs. Additionally, we connected two PEC cells in series to decompose water into oxygen and hydrogen. Indeed, the connected PEC cells yielded the photo-voltage of about 1.35 V, which is larger than 1.23 V required for water splitting. This result demonstrates the possibility of hydrogen generation using the connected PEC cells without an external bias.     

Novel synthetic approach to alfaprostol key intermediates via Stille coupling with an alkyne

Novel intermediates based on the Corey skeleton for preparation of the ω-chain of non-halogenated unnatural prostaglandin analogues containing a triple bond at position 13–14 (PG numbering) were synthesized. The utilization of a novel synthetic approach towards a new tin intermediate, and subsequent Stille coupling opens up new possibilities for preparing these important pharmaceutical intermediates.     

Multiple scattering investigation of the 1T-TaS2 surface termination

Multiple scattering theory based on a cluster model is used to simulate full hemispherical X-ray photoelectron diffraction measurements on a 1T-TaS₂(0001) surface. Key points to determine the surface termination are discussed. As the commonly applied single scattering simulations do not give satisfying results, a multiple scattering approach has to be used to accurately simulate the full hemispherical photoelectron diffraction patterns. Differences and similarities between calculations of Ta and S terminated surfaces are presented along with experimental results at room temperature using both, the single and the multiple scattering approaches. We find that the surface is S terminated and that the quantitative difference between the calculations for both terminations permits to show the limits of the single scattering approach for solving surface termination problems. Moreover, by generalizing the results obtained using the multiple scattering approach, we discuss the application of this method to other similar systems.     

Long-lasting near-infrared persistent luminescence from β-Ga2O3:Cr nanowire assemblies

Near-infrared (NIR) persistent luminescent β-Ga₂O₃:Cr³⁺ nanowire assemblies were synthesized by a hydrothermal process followed by calcination. The phosphor exhibits more than 4 h afterglow in the wavelength range of 650-850 nm after ceasing the ultraviolet light (280-360 nm) irradiation. The trap structure and persistent luminescence mechanism were revealed by thermoluminescence measurement. The β-Ga₂O₃:Cr³⁺ nanowire assemblies may find applications as identification taggants in security and optical probes in bio-imaging.     

Synthesis, growth, spectral, thermal and photoluminescence properties of a new semiorganic NLO crystal—Thiosemicarbazide lithium chloride [TSLC]

Thiosemicarbazide lithium chloride [TSLC] a new semiorganic nonlinear optical crystal has been synthesized. Single crystals by TSLC have been grown by slow evaporation solution growth technique at room temperature. Chemical composition of the synthesized material was confirmed by elemental analysis. Powder X-ray diffraction (XRD) pattern of the grown crystal has been studied. Functional groups present in the materials were identified by FT IR spectral analysis ranging between 4000 and 450 cm⁻¹. The optical transmission was studied through UV-vis spectrophotometer. Thermal analysis is carried out on the crystal and inferred to be stable at 176 °C. The second harmonic generation (SHG) of the TSLC crystal was confirmed using Nd:YAG laser and also fluorescence spectral analysis is carried out for the TSLC crystal.     

传统光谱变换与连续小波耦合定量反演潮土有机质含量

以北京地区的96个潮土土样的有机质含量为研究对象,以传统光谱变换为参照,研究分析传统光谱变换与连续小波的耦合在估测土壤有机质含量的可行性;首先采用传统光谱变换与连续小波处理土壤光谱数据,然后将处理后的光谱数据与土壤有机质含量进行相关性分析,提取敏感波段,并采用偏最小二乘法构建土壤有机质含量估测模型。结果表明：耦合传统光谱变换技术与连续小波技术可大幅提升光谱对有机质含量的敏感性,其相关系数R2最高可达0.714,这表明耦合传统光谱变换技术与连续小波技术可深入挖掘光谱内的有益信息;与传统光谱变换技术相比,基于耦合传统光谱变换技术与连续小波技术构建的模型精度更高,稳定性更好,其中以微分变换构建的模型最优,其R2=0.772,RMSE=0.223,这表明耦合传统光谱变换技术与连续小波技术可有效压制噪声的负面影响,提升光谱的稳定性。     

Energy transfer in hyperthermal Xe-graphite surface scattering

The scattering of a hyperthermal Xe from a graphite (0001) surface has been studied using a molecular beam-surface scattering technique and molecular dynamics (MD) simulations. The angular and velocity distributions of scattered Xe atoms were measured at incidence energies from 0.45 to 3.5 eV, three incidence angles of 15°, 35° and 60° and the surface temperatures of 300 K and 550 K. The observed time-of-flight spectra exhibit a sharp velocity distribution with only one velocity component, which is ascribed to the direct inelastic scattering process. The angle-resolved energy ratios of the mean final translational energy over the mean incidence energy E_f/E_i agree well with those predicted based on the assumption of the conservation of the momentum parallel to the surface. The Hard-Cube model, where the mass of the cube is approximately 310 u, has reproduced the angle-resolved flux distributions of scattered Xe atoms. In the Hard-Cube model almost 80% of the normal component of the incidence translational energy is found to be lost in collision. The MD simulations reproduce well the experimental results by using the Brenner potential for intralayer C atoms and a Lennard-Jones potential for interlayer C–C pair interactions.