Topological photonic states in gyromagnetic photonic crystals: Physics,properties, and applications

Topological photonic states (TPSs) as a new type of waveguide state with one-way transport property can resist backscattering and are impervious to defects, disorders and metallic obstacles. Gyromagnetic photonic crystal (GPC) is the first artificial microstructure to implement TPSs, and it is also one of the most important platforms for generating truly one-way TPSs and exploring their novel physical properties, transport phenomena, and advanced applications. Herein, we present a brief review of the fundamental physics, novel properties, and practical applications of TPSs based on GPCs. We first examine chiral one-way edge states existing in uniformly magnetized GPCs of ordered and disordered lattices, antichiral one-way edge states in cross magnetized GPCs, and robust one-way bulk states in heterogeneously magnetized GPCs. Then, we discuss the strongly coupling effect between two co-propagating (or counter-propagating) TPSs and the resulting physical phenomena and device applications. Finally, we analyze the key issues and prospect the future development trends for TPSs in GPCs. The purpose of this brief review is to provide an overview of the main features of TPSs in GPC systems and offer a useful guidance and motivation for interested scientists and engineers working in related scientific and technological areas.     

Topological Phase Transition and Phase Diagrams in a Two-Leg Kitaev Ladder System

A scheme to investigate the topological properties in a two-leg Kitaev ladder system composed of two Kitaev chains is proposed. In the case of two identical Kitaev chains, it is found that the interchain hopping amplitude plays a significant role in the separation of the energy spectrum and in inducing a topologically nontrivial phase, while the interchain pairing strength only affects the size of the energy gap. Moreover, another situation that the system consists of two non-identical Kitaev chains is also investigated and the corresponding phase diagram is calculated. It is found that two pairs of degenerate nonzero edge modes will, respectively, appear in the upper and lower energy gaps when the interchain hopping amplitude or the interchain pairing strength is large enough. Furthermore, it is pointed out that the winding number is quantitatively equivalent to half of the number of zero energy edge modes in our system.     

DNA 环化时间的半经验计算方法

DNA 分子是生命遗传信息的主要物质载体。DNA 环化是DNA 不同位置所携带信息的一种协同实现方式。典型的例子是转录调控,增强子通过DNA 环化与启动子相互作用,从而实现了对基因表达水平的调控。因此,破译DNA 的环化动力学是解读基础生命过程的重要课题。本文在介绍DNA 结构和力学性质的基础上,综述DNA 环化时间的计算方法。在生理条件下,DNA 的主要性质特点是弯折柔性强,而扭转和拉伸刚性强;据此,DNA 环化可视作自发的熵减过程。运用热力学统计理论,可获得计算DNA 环化时间的半经验公式。公式中的参数可由单分子光谱共聚焦技术测得的数据确定。该公式表明,空间拓扑决定了环化概率,DNA 长度决定了环化时间。该公式适用于计算DNA 上的顺式元件之间、顺式元件与启动子之间的相互作用。其优点在于避开了DNA 结构和细胞核环境的复杂性。     

Quality transitivity of Danhong Huayu Koufuye: A study on chemical profiles of medicinal herbs,compound preparation and dosed rat plasma using ultra-performance liquid chromatography–quadrupole time-of-flight mass spectrometry

Danhong Huayu Koufuye (DHK), an effective Chinese medicine preparation, is mainly used for the treatment of blurred vision and sudden blindness caused by qi stagnation and blood stasis, as well as the absorption period of central retinal vein occlusion. However, the current quality standard is relatively low, only stipulating the content of protocatechualdehyde. Chemical transitivity is the basis for discovering quality markers and is used in quality process control of Chinese medicines. Herein, the chemical profiles of seven medicinal herbs, DHK and dosed rat plasma were comprehensively analyzed using ultra-performance liquid chromatography–quadrupole time-of-flight mass spectrometry. As a result, 134 chemical constituents were identified in seven medicinal herbs, including salvianolic acids, diterpene quinones, phenolic acids, phthalides, cyanogenic glycosides, flavonoids and triterpenoid saponins. Among them, 55 chemical constituents were transferred to DHK along with extraction and preparation, and 26 were further absorbed into blood and metabolized to produce 11 metabolites after oral administration. The transitivity of DHK from medicinal herbs to compound preparation and into blood was analyzed for the first time. This article will be valuable to ascertain the quality markers for quality process control and further pharmacokinetic studies.     

On Some Functional Equations and Representations of Topological Semigroups

Let a representation T of a semigroup G on a linear space X be given. We call x ∈ X a finite vector if its orbit T(G) is contained in a finite-dimensional subspace. In this paper, some statements about finite vectors are applied to the following problem. For a given positive integer n > 1, describe all continuous functions f : G → ? such that the function (x₁,..., x _n ) ? f(x₁ + ? + x _n ) can be polynomially expressed via functions of sums of fewer variables.     

Cartesian Closed Topological Categories and Tensor Products

The projective tensor product in a category of topological R-modules (where R is a topological ring) can be defined in Top, the category of topological spaces, by the same universal property used to define the tensor product of R-modules in Set. In this article, we extend this definition to an arbitrary topological category X and study how the Cartesian closedness of X is related to the monoidal closedness of the category of R-module objects in X. Mathematics Subject Classifications (2000) 18D15, 18D35, 18A40.     

Countably compact groups from a selective ultrafilter

We prove that the existence of a selective ultrafilter on implies the existence of a countably compact group without non-trivial convergent sequences all of whose powers are countably compact. Hence, by using a selective ultrafilter on , it is possible to construct two countably compact groups without non-trivial convergent sequences whose product is not countably compact.