Theoretical investigations of magnetic properties of ferromagnetic single-walled nanotubes

The magnetic behaviors of ferromagnetic single-walled nanotubes are systematically investigated by use of the many-body Green's function method of quantum statistical theory. The spontaneous magnetization, absolute value of ferromagnetic energy, area of hysteresis loop and coercivity increase with diameter of the tubes and spin quantum number, and decrease with temperature. Curie temperature increases with diameter and spin quantum number. As the diameter of the tube tends to infinity, all the numerical results approach to those of a two-dimensional monolayer. The dependences of initial susceptibility on temperature and diameter below and above Curie point are contrary. The calculated results are compared with experimental results where possible, and are qualitatively in agreement with the latter. The Curie temperature is determined by the tube diameter and independent of rolling helicities.     

Thermally tunable THz filter made of semiconductors

By using the finite-difference time domain method, the transmission properties of terahertz wave passing through two different periodic subwavelength structures on InSb semiconductor slabs under different temperatures have been investigated. The results show that the peak transmittance increases and the transmittance peak has a blue shift when the temperature is increasing. It is extremely versatile to control the tunable THz filter by varying the temperature.     

Terahertz spectroscopic investigations of caffeine and 3-acetylmorphine

Experimental and theoretical investigations of THz spectral features of caffeine and 3-acetylmorphine in the region of 0.2-2.6 THz have been presented. The refractive indices and absorption coefficients of the two drugs were obtained by a terahertz time-domain spectroscopy (THz-TDS) technique. The simulated absorption spectra using the density functional theory (DFT) and Hartree-Fork (HF) are in agreement with the experimental data. The observed spectral absorption features were assigned based on DFT and HF calculation.     

Representation of elliptic Ding-Iohara algebra

We define a vector representation V(u)of elliptic Ding-Iohara algebra u(q,t,p).Furthermore,we construct the tensor products of the vector representations and the Fock modulesF(u)by taking the inductive limit of certain subspaces in the finite tensor products of vector representations.     

2-Arc-transitive cyclic covers of $$K_{n,n}$$

In this paper, a complete classification is achieved of all the regular covers of the complete bipartite graphs \(K_{n,n}\) with cyclic covering transformation group, whose fibre-preserving automorphism group acts 2-arc-transitively. All these covers consist of one threefold covers of \(K_{6,6}\), one twofold cover of \(K_{12, 12}\) and one infinite family X(r, p) of p-fold covers of \(K_{p^r,p^r}\) with p a prime and r an integer such that \(p^r\ge 3\). This infinite family X(r, p) can be derived by a very simple and nice voltage assignment f as follows: \(X(r, p)=K_{p^r, p^r}\times _f \mathbb {Z}_p\), where \(K_{p^r, p^r}\) is a complete bipartite graph with the bipartition \(V=\{ \alpha \bigm |\alpha \in V(r,p)\}\cup \{ \alpha '\bigm |\alpha \in V(r,p)\}\) for the r-dimensional vector space V(r, p) over the field of order p and \(f_{\alpha ,\beta '}=\sum _{i=1}^ra_ib_i,\,\, \mathrm{for\,\,all}\,\,\alpha =(a_i)_r, \beta =(b_i)_r\in V(r,p)\).     

Dynamical behaviors for 1D compressible Navier-Stokes equations with density-dependent viscosity

The dynamical behaviors of vacuum states for one-dimensional compressible Navier-Stokes equations with density-dependent viscosity coefficient are considered. It is first shown that a unique strong solution to the free boundary value problem exists globally in time, the free boundary expands outwards at an algebraic rate in time, and the density is strictly positive in any finite time but decays pointwise to zero time-asymptotically. Then, it is proved that there exists a unique global weak solution to the initial boundary value problem when the initial data contains discontinuously a piece of continuous vacuum and is regular away from the vacuum. The solution is piecewise regular and contains a piece of continuous vacuum before the time T_∗>0, which is compressed at an algebraic rate and vanishes at the time T_∗, meanwhile the weak solution becomes either a strong solution or a piecewise strong one and tends to the equilibrium state exponentially.     

Elliptic equations with indefinite concave nonlinearities near the origin

In this note existence of infinitely many solutions is proved for an elliptic equation with indefinite concave nonlinearities.     

Morse index and stability of elliptic Lagrangian solutions in the planar three-body problem

We illustrate a new way to study the stability problem in celestial mechanics. In this paper, using the variational nature of elliptic Lagrangian solutions in the planar three-body problem, we study the relation between Morse index and its stability via Maslov-type index theory of periodic solutions of Hamiltonian system. For elliptic Lagrangian solutions we get an estimate of the algebraic multiplicity of unit eigenvalues of its monodromy matrix in terms of the Morse index, which is the key to understand the stability problem. As a special case, we provide a criterion to spectral stability of relative equilibrium.     

Homeomorphism classification of complex projective complete intersections of dimensions 5, 6 and 7

In this paper we prove that two complete intersections X_n(d){X_n(\underline{d})} and X_n(d￠){X_n(\underline{d}^\prime)} are homeomorphic if and only if they have the same total degree, Pontrjagin classes and Euler characteristics, provided n = 5, 6, 7. This extends earlier result of Fang and Klaus (Manuscr Math 90:139–147, 1996).     

三维Boussinesq方程组大解的全局L~2稳定性

对三维有界及无界区域上的Boussinesq方程的全局L~2稳定性进行了讨论.在解满足适当的条件下,证明了此解为稳定的,并得出此稳定性条件的等价性条件,最后得出了二维Boussinesq方程组在三维扰动下的解的全局存在性和稳定性.