扇形域上高阶Schwarz边值问题

本文主要讨论一类角度为θ=π/α,α≥1/2的扇形域上高阶多解析方程的Schwarz边值问题.通过构造适当的高阶-Schwarz算子和Pompeiu算子,我们给出了详细的解表达式.本文把边值问题进一步推广到高阶情形,丰富了扇形域上边值问题的发展.     

Calculation of Metric for Gaussian Weave State

Using the recoupling theorem and graph calculation in loop quantum gravity, it is demonstrated that the action of metric matrix operator on Gaussian weave state is an eigenaction, the representation matrix elements of the metric operator and their expectation values are calculated. The values of length of tangent vectors of edges adjacent to the vertex of Gaussian weave state, as well as the angles between them are also obtained in the cases of k=0 and k=2.     

双曲正弦、余弦算符与奇偶相干态

利用Fock空间的平移算符引入了双曲正弦和余弦算符,该算符作用在真空态上给出奇相干态和偶相干态的一种新表示形式,并讨论了奇、偶相干态的准概率分布函数和非经典特性．     

Effect of Al3+ substitution on structural,cation distribution,electrical and magnetic properties of CoFe2O4

We present the structural, cation distribution, electrical and magnetic studies of CoAl_xFe_2−xO₄ (x = 0.0, 0.2, 0.4, 0.6, 0.8) ferrites. The Rietveld-fitted X-ray diffraction (XRD) patterns confirm the formation of single-phase cubic spinel structures with $Fd\overline{3}m$ space group for all the samples. A comprehensive analysis of XRD-based cation distribution has been performed to see the effect of Al³⁺ ions substitution on various structural parameters such as site ionic radii, edge length, bond length and interionic distances. The dielectric constant and direct current (DC) conductivity decreases with increasing Al³⁺ substitution up to x = 0.4. However, with further increase in Al³⁺ substitution, both the dielectric constant and the DC conductivity increase. The presentation of dielectric data in the complex electric modulus form reveals the presence of a non-Debye-type relaxation behaviour in the considered ferrites. The power law behaviour of alternating current (AC) conductivity indicates a strong correlation among electrons in these systems. The isothermal magnetisation versus applied field curves with high-field slope and significant coercivity suggest that the studied materials are highly anisotropic with canted spin structures. The samples exhibit ferrimagnetic behaviour at 300 K and the magnetisation decreases with increasing Al³⁺ concentration. The as-prepared samples are promising candidates for various industrial applications.     

Microstructure and high-temperature corrosion behaviors of aluminide coatings by low-temperature pack aluminizing process

Aluminide coatings were produced on carbon steel and Fe-5Cr-Mo alloy at a relatively lower temperature below 600 °C in shorter treatment time by a combination of surface refinement process and pack aluminizing process. Repetitive ball impact, generated by mechanical vibration, caused the top-layer refinement of substrates in a conventional pack aluminizing process. The effects of temperature and treatment time on the formation of aluminide coatings were analyzed. The microstructure of the coatings was investigated by SEM, AFM and XRD. The aluminide coatings were one-layer, compacted structure with ultrafine grains and uniform elemental distribution. High-temperature oxidation and sulphidation tests were carried out at 600 °C in air for 200 h and 10% SO₂ + Ar gas mixture atmosphere for 50 h, respectively. The mass gains and spallation indicated that the aluminide coatings significantly improved the high-temperature oxidation and sulphidation resistance.     

Quantum Hadamard Operators and Their Decomposition Derived by Virtue of IWOP Technique

We introduce the quantum Hadamard operator in continuum state vector space and find that it can be decomposed into a single-mode squeezing operator and a position-momentum mutual transform operator. The two-mode Hadamard operator in bipartite entangled state representation is also introduced, which involves the two-mode squeezing operator and [η〉 ←→｜ξ〉 mutual transformation operator, where [η〉 and ｜ξ〉 are mutual conjugate entangled states. All the discussions are proceeded by virtue of the IWOP technique.     

Husimi Function of Excited Squeezed Vacuum State

The q-p phase-space distribution function is a popular tool to study semiclassical physics and to describe the quantum aspects of a system. In this paper by using the pure state density operator formula of the Husimi operator Δ_h(q,p;κ)=|p,q〉_κκ〈p,q| we deduce the Husimi function of the excited squeezed vacuum state. Then we study the behavior of Husimi distribution graphically.     

Towards a black‐box for biological EXAFS data analysis. II. Automatic BioXAS Refinement and Analysis (ABRA)

In biological systems, X‐ray absorption spectroscopy (XAS) can determine structural details of metal binding sites with high resolution. Here a method enabling an automated analysis of the corresponding EXAFS data is presented, utilizing in addition to least‐squares refinement the prior knowledge about structural details and important fit parameters. A metal binding motif is characterized by the type of donor atoms and their bond lengths. These fit results are compared by bond valance sum analysis and target distances with established structures of metal binding sites. Other parameters such as the Debye–Waller factor and shift of the Fermi energy provide further insights into the quality of a fit. The introduction of mathematical criteria, their combination and calibration allows an automated analysis of XAS data as demonstrated for a number of examples. This presents a starting point for future applications to all kinds of systems studied by XAS and allows the algorithm to be transferred to data analysis in other fields.     

Detection and analysis of new bands of O3 by CRDS between 6500 and 7300 cm

The absorption spectrum of the ¹⁶O₃ isotopologue of ozone has been recorded in the 7000-7920 cm⁻¹ region by high sensitivity CW-Cavity Ring Down Spectroscopy. This report is devoted to the analyses of the 7065-7300 cm⁻¹ region dominated by the ν₁ + 2ν₂ + 5ν₃ and ν₁ + 5ν₂ + 3ν₃ A-type bands at 7130.8 and 7286.8 cm⁻¹ respectively. 289 transitions were assigned to the ν₁ + 2ν₂ + 5ν₃ band. The corresponding line positions were modeled with an effective Hamiltonian involving Coriolis resonance interactions between the (1 2 5) upper state and the (4 4 0), (0 2 6) and (6 1 0) dark states, and an anharmonic resonance interaction with the (2 0 5) state. The very strong interaction (up to 50% mixing of the wavefunctions) between the (1 2 5) and (6 1 0) states leads to the observation of two extra lines of the 6ν₁ + ν₂ band due to a resonance intensity transfer. 213 transitions of the ν₁ + 5ν₂ + 3ν₃ band were assigned and modeled taking into account a Coriolis resonance interaction with the (3 6 0) state.We take the opportunity of the present work to report the analysis of the very weak 4ν₂ + 4ν₃ B-type band at 6506.1 cm⁻¹ which was assigned from previously recorded CRDS spectra. 286 transitions were modeled using the effective Hamiltonian approach.The dipole transition moment parameters of the three analyzed bands were determined by a least-squares fit to the measured line intensities. For the three studied band systems, the effective Hamiltonian and transition moment operator parameters were used to generate line lists provided as Supplementary Materials.