First principles study on electronic structure of β-Ga2O3

We have studied the electronic structure of β-Ga₂O₃ using the first principles full-potential linearized augmented plane wave method. It is found that β-Ga₂O₃ has an indirect band gap with a conduction band minimum (CBM) at Γ point and a valence band maximum on the E line. The anisotropic optical properties are explained by the selection rule of the band-to-band transitions. On the other hand, the shape of the CBM is almost isotropic and, therefore, the observed electronic anisotropy in the n-type semiconducting state should not be attributed to the properties of a perfect lattice. The Burstein-Moss shift is discussed using the effect of several allowed transitions between the levels of the valence band and the CBM.     

Electronic structure calculations for BaSxSe1−x alloys

A series of first principles calculations have been carried out to study structural, electronic properties of BaS_xSe_1−x alloys. We have used the local density as well as the generalized gradient approximations for the exchange-correlation potential. The structural properties of these materials, in particular the composition dependence to the lattice constant and bulk modulus, are found to be linear. It is also found linear relationship between theoretical band gaps and 1/a² (where a is lattice constant).     

内蕴平方函数交换子在加权弱Hardy空间上的端点估计

证明了由BMO函数与α阶内蕴面积函数S_α和内蕴g_(λ,α)*函数生成的交换子都是由加权弱Hardy空间WH_(b,ω)~1到加权弱L1空间WL_ω~1上的有界算子.     

Weighted boundedness of parametric Marcinkiewicz integral and higher order commutator

In this paper, the weighted boundedness of parametric Marcinkiewicz integral and its commutator with rough kernels are considered. In addition, the weak type norm inequalities for parametric Marcinkiewicz integral and its commutator with different weight functions and Dini kernel are also discussed.     

Investigation on Guided-Mode Characteristics of Hollow-Core Photonic Crystal Fibre at Near-Infrared Wavelengths

Guided-mode characteristics of hollow-core photonic crystal fibre （HC-PCF） are experimentally and theoretically investigated. The transmission spectrum in the range from 755 to 845nm is observed and the loss is measured to be 0.12dB/m at 800nm by cut-back method. Based on the full-vector beam propagation method and the full-vector plane-wave method, the characteristics of mode field over propagation distance 1 m are simulated, and the results show that the propagation efficiency can be above 80%. Compared with the fundamental guided mode well confined in air core within shorter propagation distance, the second-order guided mode leaks into the cladding region and gradually attenuates due to larger refractive index difference. The primary loss factors in HC-PCF and the corresponding solutions are elementarily discussed.     

Weighted endpoint estimates for commutators of Marcinkiewicz integrals

Let μΩ^mb be the commutator generalized by μΩ, the n-dimensional Marcinkiewicz integral, and b ∈ BMO（R^n）. The author establishes the weighted weak LlogL-type estimates for μΩ^mb when Ω satisfies a kind of Dini conditions, which improves the known result essentially.     

Sharp multi-weighted bounds for multilinear fractional rough operators and Cohen–Gosselin type commutators

In the article, we consider the multilinear fraction maximal operators and the multilinear fraction integrals with rough kernels, we introduce a new class for $(m+1)$-weights tuple $(u,\vec{\omega })$, and prove the optimal constant estimates of the sharp multi-weighted bounds for both operators. We also show the sharp multi-weighted bounds for the Cohen–Gosselin type multi-commutator of the both operators.     

INTERIOR ESTIMATES IN MORREY SPACES FOR SOLUTIONS OF ELLIPTIC EQUATIONS AND WEIGHTED BOUNDEDNESS FOR COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

It is proved that, for the nondivergence elliptic equations ∑in, j=1 aijuxixj = f,if f belongs to the generalized Morrey spaces Lp,ψ(ω), then uxixj ∈ Lp,ψ(ω), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp,ψ (ω).     

First principles study of structural, elastic, electronic and optical properties of the cubic perovskite BaHfO3

First principles study of structural, elastic, electronic and optical properties of the cubic perovskite-type BaHfO₃ has been reported using the pseudo-potential plane wave method within the local density approximation. The calculated equilibrium lattice is in a reasonable agreement with the available experimental data. The elastic constants and their pressure dependence are calculated using the static finite strain technique. A linear pressure dependence of the elastic stiffnesses is found. Band structures show that BaHfO₃ is a direct band gap between the occupied O 2p and unoccupied Hf d states. The variation of the gap versus pressure is well fitted to a quadratic function. Furthermore, in order to understand the optical properties of BaHfO₃, the dielectric function, absorption coefficient, optical reflectivity, refractive index, extinction coefficient, and electron energy loss are calculated for radiation up to 30 eV. We have found that O 2p states and Hf 5d states play a major role in the optical transitions as initial and final states, respectively. This is the first quantitative theoretical prediction of the elastic, electronic and optical properties of BaHfO₃ compound, and it still awaits experimental confirmation.