A new graphical coding of DNA sequence and its similarity calculation

The DNA primary sequence is translated into “structure graph” based on classification of its four bases. Then the invariants, such as topological indices, are extracted from those graphic representations of DNA primary sequences, and used to calculate the similarities among the eleven species. From these similarities/dissimilarities the homologies can be revealed that they are in agreement with evolutionary relation satisfactorily.     

The effect of 3-aminopropyltrimethoxysilane on the formation of NiFe2O4/SiO2 nanocomposites

NiFe₂O₄/SiO₂ nanocomposites were prepared using a sol–gel method with the addition of 3-aminopropyltrimethoxysilane (APS). Different phases and morphologies of NiFe₂O₄/SiO₂ nanocomposites were obtained when different amounts of APS were used. The structural properties of the products were examined by X-ray diffraction (XRD) and transmission electron microscopy (TEM). Sheet-like morphology was observed at higher molar ratio of APS to NiFe₂O₄, while spherical NiFe₂O₄/SiO₂ nanoparticles separated from each other were formed at lower molar ratio of APS to NiFe₂O₄. The magnetic properties of the nanocomposites were also investigated, indicating that the interparticle interactions exhibit strong dependence on the molar ratio of APS to NiFe₂O₄.     

Multistability and multiperiodicity of delayed Cohen-Grossberg neural networks with a general class of activation functions

In this paper, by using analysis approach and decomposition of state space, the multistability and multiperiodicity issues are discussed for Cohen-Grossberg neural networks (CGNNs) with time-varying delays and a general class of activation functions, where the general class of activation functions consist of nondecreasing functions with saturation’s including piecewise linear functions with two corner points and standard activation functions as its special case. Based on the Cauchy convergence principle, some sufficient conditions are obtained for checking the existence and uniqueness of equilibrium points of the n-neuron CGNNs. It is shown that the n-neuron CGNNs can have 2ⁿ locally exponentially stable equilibrium points located in saturation regions. Also, some conditions are derived for ascertaining equilibrium points to be locally exponentially stable or globally exponentially attractive and to be located in any designated region. As an extension of multistability, some similar results are presented for ascertaining multiple periodic orbits when external inputs of the n-neuron CGNNs are periodic. Finally, three examples are given to illustrate the effectiveness of the obtained results.     

Adiabatic approximation in PT-symmetric quantum mechanics

In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics, which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.     

Raman spectra of samarium-fullerene intercalation compounds

Samarium-fullerene intercalation compounds of nominal composition Sm_xC₆₀ (x=1,2,…,6) have been synthesized by a solid-state reaction method. We obtain a Sm_2.75C₆₀ superconducting phase with orthogonal structure and a Sm₆C₆₀ phase with body-centered cubic structure. The broadening and weakening of Raman peaks of the Sm_xC₆₀ compounds are due to the distortion of C₆₀ and electron-phonon interaction. The Raman measurements reveal that the distortion of C₆₀ decrease in Sm_xC₆₀ (x=3,4,5) exposed to air, although the fulleride solids have transformed into an amorphous state. The Raman results also show that the distortion of C₆₀ is still very large in the Sm₆C₆₀ exposed to air, or the C₆₀ molecules have been destroyed and become some amorphous carbide.     

Local discrimination scheme for some unitary operations

It has been shown that for two different multipartite unitary operations U_1 and U_2, when tr(U_1~?U_2) = 0, they can always be perfectly distinguished by local operations and classical communication in the single-run scenario. However, how to find the detailed scheme to complete the local discrimination is still a fascinating problem. In this paper, aiming at some U_1 and U_2 acting on the bipartite and tripartite space respectively, especially for U_1~?U_2 locally unitary equivalent to the high dimensional X-type hermitian unitary matrix V with trV = 0, we put forward the explicit local distinguishing schemes in the single-run scenario.     

带非线性源项的Riesz回火分数阶扩散方程的预估校正方法

本文针对带非线性源项的Riesz回火分数阶扩散方程,利用预估校正方法离散时间偏导数,并用修正的二阶Lubich回火差分算子逼近Riesz空间回火的分数阶偏导数,构造出一类新的数值格式.给出了数值格式在一定条件下的稳定性与收敛性分析,且该格式的时间与空间收敛阶均为二阶.数值试验表明数值方法是有效的.     

SUPERSYMMETRIC SU(1|2) GAUDIN MODEL

In this paper, we propose a supersymmetric SU(1|2) Gaudin model and have derived its eigenvalues. We also present the well-defined eigenstates through the quasi-classical limit of the eigenstates in the supersymmetric t-J model.     

线性分段折射率分布多量子阱波导色散关系的精确分析

本文从标量Helmholtz方程出发,采用转移矩阵技术,求出了线性分段折射率分布多量子阶波导TE模色散关系的精确解,数值计算结果显示出该波导的色散特性以及与波导结构的关系,为实际制作该量子阶波导进行参数选择提供了理论依据。