Exact solutions of the generalized K(m, m) equations

Family of equations, which is the generalization of the K(m, m) equation, is considered. Periodic wave solutions for the family of nonlinear equations are constructed.     

Attractive singularity problems for superlinear Liénard equation

Positivity - In this paper, we consider the following quasilinear Liénard equation with a singularity $$\begin{aligned} (\phi _p(x'(t)))'+f(x(t))x'(t)+g(t,x(t))=e(t),...     

Guided Waves in the Multilayered One-Dimensional Hexagonal Quasi-crystal Plates

Guided waves in the multilayered one-dimensional quasi-crystal plates are,respectively,investigated in the context of the Bak and elasto-hydrodynamic models.Dispersion curves and phonon and phason displacements are calculated using the Legendre polynomial method.Wave characteristics in the context of these two models are analyzed in detail.Results show that the phonon-phason coupling effects on the first two layers are the same at low frequencies;but,they are more significant on the first layer than those on the second layer at high frequencies.These obtained results lay the theoretical basis of guided-wave nondestructive test on multilayered quasi-crystal plates.     

Sharp inequalities related to the functional $$U_j$$ U j and some applications

Geometriae Dedicata - Sharp inequalities of the parameterized functional $$U_j$$ for Borel measures on the unit sphere in $${\mathbb {R}}^n$$ are established. As two applications, some inequalities...     

13C chemical-shift anisotropy of alkyl-substituted aromatic carbon in anthracene derivatives

The ¹³C chemical-shift anisotropy in anthracene derivatives (9,10-dimethylanthracene, 9,10-dihydroanthracene, dianthracene, and triptycene) has been measured by the 2D FIREMAT timed pulse sequence and the corresponding set of principal values has been determined by the TIGER processing method. These molecules expand the data base of ¹³C CSA measurements of fused aromatic rings some bridged by sp³ carbon resulting in an unusual bonding configuration, which leads to distinctive aromatic ¹³C CSA values. Crystal lattice distortions to the CSA were observed to change the isotropic shift by 2.5 to 3.3 ppm and changes as large as 8.3 ppm in principal components. Modeling of the CSA data by GIPAW DFT (GGA-PBE/ultrafine) shielding calculations resulted in an rms chemical-shift distance of 2.8 ppm after lattice including geometry optimization of the diffraction structures by the GIPAW method at GGA-PBE/ultrafine level. Attention is given to the substituted aromatic carbon in the phenyl groups (here forth referred to as the α-carbon) with respect to CSA modeling with electronic methods. The ¹³C CSA of this position is accurately determined due to its spectral isolation of the isotropic shift that limits overlap in the FIREMAT spectrum. In cases where the bridging ring is sp³ carbon, the current density is reduced from extending beyond the peripheral phenyl groups; this plays a significant role in the magnetic shielding of the α-position. Nuclear independent chemical-shift calculations based on GIAO DFT (B3LYP/6-31G(d)) shielding calculations were used to model the intramolecular π-interactions in dianthracene and triptycene. These NICS results estimate the isotropic shift of the α-position in dianthracene to be insignificantly affected by the presence of the neighboring aromatic rings. However, a notable change in isotropic shielding, Δσ_iso=−2.1 ppm, is predicted for the α- position of triptycene. Experimentally, the δ₂₂ principal component at the α-position for both dianthracene and triptycene increases by at least 12 ppm compared to 9,10-dihydroanthracene. To rationalize this change, shielding calculations in idealized structures are explored. The spatial position of the bicyclic scaffolding of the bridging ring plays a key role in the large increase in δ₂₂ for the α-carbon.     

The Cauchy Problems and Global Solutions to the Deybe System and Burgers＇ Equations in Pseudomeasure Spaces

In this paper we consider the Cauchy problems of Burgers＇ equations and the Deybe system. Their existence and uniqueness of the time-global solutions for small initial data in some pseudomeasure spaces are obtained. The asymptotic stability of small solutions is proved. As an immediate result the existence and uniqueness of the self-similar solutions are also obtained provided the initial data satisfy the self-similar structures.     

The best bounds in Wallis' inequality

For all natural numbers , let denote a double factorial. Then

The constants and are the best possible. From this, the well-known Wallis' inequality is improved.

     

新型MOLEDs的光学性能

将负折射率介质层(NRIDL)引入到微腔有机电致发光器件(MOLEDs)中,设计了新型的微腔器件。利用传输矩阵法对此器件的反射率大小、器件厚度对发射峰的影响以及电致发光(EL)光谱性质进行了分析和讨论。结果表明:与普通微腔器件相比,新型微腔器件的谱线宽度显著窄化,峰值强度明显增强,并且受腔体长度的影响较小。这些结果为进一步提高微腔器件的发光色纯度、薄化器件厚度提供了新方法。     

PROPERTIES OF TENSOR COMPLEMENTARITY PROBLEM AND SOME CLASSES OF STRUCTURED TENSORS

This paper deals with the class of Q-tensors, that is, a Q-tensor is a real tensor A such that the tensor complementarity problem(q, A):finding an x ∈ R~n such that x ≥ 0, q+Ax~(m-1)≥ 0, and x~T(q+Ax~(m-1)) = 0,has a solution for each vector q ∈ R~n. Several subclasses of Q-tensors are given: P-tensors, R-tensors, strictly semi-positive tensors and semi-positive R_0-tensors. We prove that a nonnegative tensor is a Q-tensor if and only if all of its principal diagonal entries are positive, and so the equivalence of Q-tensor,R-tensors, strictly semi-positive tensors was showed if they are nonnegative tensors. We also show that a tensor is an R_0-tensor if and only if the tensor complementarity problem(0, A) has no non-zero vector solution, and a tensor is a R-tensor if and only if it is an R_0-tensor and the tensor complementarity problem(e, A) has no non-zero vector solution, where e =(1, 1 ···, 1)~T.     

Mg-Al-Ca合金中三元Laves相的稳定性和电子结构

采用基于密度泛函理论的第一性原理方法,应用VASP (Vienna Ab-initio Simulation Package) 计算软件,研究了Mg-Al-Ca合金中三元Laves相,即Ca(Mg1-x,Alx)2和Al2(Ca1-x,Mgx) (x=0, 0.25, 0.50, 0.75, 1)在不同形态结构(C14, C15和C36)下的相稳定性及电子结构。计算所得的晶格常数和实验值吻合很好,形成能和相关能的计算用来研究三元Laves相的合金化能力和稳定性,结果表明：C14-Ca(Mg0.25,Al0.75)2具有很好的合金化能力,而C15- CaAl2具有很好的结构稳定性。态密度和电荷密度的计算用来研究Mg-Al-Ca合金中三元Laves相稳定性的内在微观机制。