投影的约化极小模和空间的夹角

Let M and N be nonzero subspaces of a Hilbert space H, and PM and PN denote the orthogonal projections on M and N, respectively. In this note, an exact representation of the angle and the minimum gap of M and N is obtained. In addition, we study relations between the angle, the minimum gap of two subspaces M and N, and the reduced minimum modulus of （I - PN）PM,     

全函数空间和置换空间的一些性质

In this paper, an equivalent relation among the reflexivity, weak sequential completeness and bounded completeness in full function space is given. Some results on weakly sequential compactness of subset and the property （u） in substitution spaces are obtained.     

非Lipschitz条件Hilbert空间上扩散过程的短时间大偏差原理

Under the non-Lipschitzian condition, a small time large deviation principle of diffusion processes on Hilbert spaces is established. The operator theory and Gronwall inequality play an important role.     

关于Newton级数的符号算子方法

In this paper, we present several expansions of the symbolic operator （1 ＋E）^x. Moreover, we derive some series transforms formulas and the Newton generating functions of {f（k）}.     

Physalis method for heterogeneous mixtures of dielectrics and conductors: Accurately simulating one million particles using a PC

Prosperetti’s seminal Physalis method, an Immersed Boundary/spectral method, had been used extensively to investigate fluid flows with suspended solid particles. Its underlying idea of creating a cage and using a spectral general analytical solution around a discontinuity in a surrounding field as a computational mechanism to enable the accommodation of physical and geometric discontinuities is a general concept, and can be applied to other problems of importance to physics, mechanics, and chemistry. In this paper we provide a foundation for the application of this approach to the determination of the distribution of electric charge in heterogeneous mixtures of dielectrics and conductors. The proposed Physalis method is remarkably accurate and efficient. In the method, a spectral analytical solution is used to tackle the discontinuity and thus the discontinuous boundary conditions at the interface of two media are satisfied exactly. Owing to the hybrid finite difference and spectral schemes, the method is spectrally accurate if the modes are not sufficiently resolved, while higher than second-order accurate if the modes are sufficiently resolved, for the solved potential field. Because of the features of the analytical solutions, the derivative quantities of importance, such as electric field, charge distribution, and force, have the same order of accuracy as the solved potential field during postprocessing. This is an important advantage of the Physalis method over other numerical methods involving interpolation, differentiation, and integration during postprocessing, which may significantly degrade the accuracy of the derivative quantities of importance. The analytical solutions enable the user to use relatively few mesh points to accurately represent the regions of discontinuity. In addition, the spectral convergence and a linear relationship between the cost of computer memory/computation and particle numbers results in a very efficient method. In the present paper, the accuracy of the method is numerically investigated by example computations using one dielectric particle, one isolated conductor particle, one conductor particle connected to an external source with imposed voltage, and two conductor/dielectric particles with strong interactions. The efficiency of the method is demonstrated with one million particles, which suggests that the method can be used for many important engineering applications of broad interest.     

Influence of deposition pressure on structural, optical and electrical properties of nc-Si:H films deposited by HW-CVD

Hydrogenated nanocrystalline silicon (nc-Si:H) thin films were deposited using HW-CVD technique at various deposition pressures. Characterisation of these films from Raman spectroscopy revealed that nc-Si:H thin films consist of a mixture of two phases, crystalline phase and amorphous phase containing small Si crystals embedded therein. We observed increase in crystallinity in the films with increase in deposition pressure whereas the size of Si nanocrystals was found ∼2 nm over the entire range of deposition pressure studied. The FTIR spectroscopic analysis showed that with increasing deposition pressure the predominant hydrogen bonding in the films shifts from, Si-H to Si-H₂ and (Si-H₂)_n complexes and the hydrogen content in the films was found in the range 6.2-9.3 at% over the entire range of deposition pressure studied. The photo and dark conductivities results also indicate that the films deposited with increasing deposition pressure get structurally modified. It has been found that the optical energy gap range was between 1.72 and 2.1 eV with static refractive index between 2.85 and 3.24. From the present study it has been concluded that the deposition pressure is a key process parameter to induce the crystallinity in the Si:H thin films using HW-CVD.     

The ESR study of single crystal spinel ZnCr2Se4 diluted with Sb and V

The single crystal of Sb³⁺ and V³⁺ doped zinc chromium selenide spinel ZnCr₂Se₄ were prepared by a chemical transport method and characterized by ESR spectroscopy in order to examine the effect of nonmagnetic antimony and magnetic vanadium on properties of the system. For antimony admixtures the Neel temperature is very similar to that of the parent spinel ZnCr₂Se₄ (22 K). However, upon incorporating vanadium ions, the T_N temperature decreases down to 17.5 K, determined for the maximum vanadium content (x=0.06). The temperature dependence of the ESR linewidth over paramagnetic region is interpreted by an occurrence of spin-phonon interaction. The strong broadening linewidth together with its strong temperature dependence for vanadium doped ZnCr₂Se₄ is explained by the complex paramagnetic relaxation model.     

Structural transition of Ti3SiC2 under high hydrostatic pressure: A first-principles study

We theoretically studied the phase transformation, electronic and elastic properties of Ti₃SiC₂ ceramic by using the pseudopotential plane-wave method within the density functional theory. Our results demonstrate that there exists a structural phase transition from α‐Ti₃SiC₂ to β‐Ti₃SiC₂ under pressure up to 384 GPa, and α‐Ti₃SiC₂ is the most stable phase at zero pressure. The calculated electronic band structure and density of states reveal the metallic behavior for the polymorphs of Ti₃SiC₂. The mechanical stability of α‐Ti₃SiC₂ at zero pressure is confirmed by the elastic constants, and is analyzed in terms of electronic level. By analyzing the ratio between bulk and shear moduli, we conclude that α‐Ti₃SiC₂ is brittle in nature.     

CO adsorption on oxygen-modified molybdenum surfaces

Structures of carbon monoxide layers on the oxygen-modified Mo(1 1 0) and Mo(1 1 2) surfaces have been investigated by means of density-functional (DFT) calculations. It is found that CO molecules adsorb at hollow sites on the O/Mo(1 1 0) surface and nearly atop Mo atoms on the O/Mo(1 1 2) surface. The favorable positions for adsorption are shown to be near protrusions of electron density above the Mo surface atoms. The presence of oxygen on the molybdenum surface significantly reduces the binding energy of the CO molecule with the substrate; on the oxygen-saturated Mo(1 1 0) surface, the adsorption of CO is completely blocked. The calculated local densities of states (LDOS) demonstrate that the O 2s peak for O adsorbed on Mo(1 1 0) surface is at −19 eV (with respect to the Fermi level), while for the oxygen atom of an adsorbed CO molecule the related 3σ molecular orbital gives rise to a peak at −23 eV. This difference stems from the bonding of the O atom either with Mo surface for adsorbed O or with C atom in adsorbed CO, and therefore the position of the O 2s peak in photoemission spectra can serve as a convincing argument in favor of either the presence or absence of the CO dissociation on Mo surfaces.     

Synthesis of nanocrystalline and mesoporous zinc sulphide from a single precursor Zn(SOCCH3)2Lut2 complex

We report the formation of mesoporous zinc sulphide, composed by the fine network of nanoparticles, which was formed via a single precursor Zn(SOCCH₃)₂Lut₂ complex. The complex was chemically synthesized using zinc carbonate basic, 3,5-lutidine and thioacetic acid, in air. The metal precursor complex was characterized using different conventional techniques. Thermogravimetric analysis (TGA) result indicates that the decomposition of the complex starts at 100 °C and continues up to 450 °C, finally yielding ZnS. ZnS nanocrystals were characterized by powder X-ray diffraction (XRD) technique, field emission scanning electron microscopy (FESEM), N₂-sorption isotherm, UV-vis spectroscopy and photoluminescence (PL) spectroscopy. The grain diameter of nanocrystals was found to be 4-5 nm. The material followed Type-IV N₂-sorption isotherm, which is the characteristic of mesoporous materials. The band gap energy, as obtained from optical measurements was around 3.8 eV.