Generalized spherical and simplicial coordinates

Elementary trigonometric quantities are defined in l2,p analogously to that in l2,2, the sine and cosine functions are generalized for each p>0 as functions sinp and cosp such that they satisfy the basic equation p|cosp(φ)|+p|sinp(φ)|=1. The p-generalized radius coordinate of a point ξ∈Rn is defined for each p>0 as . On combining these quantities, ln,p-spherical coordinates are defined. It is shown that these coordinates are nearly related to ln,p-simplicial coordinates. The Jacobians of these generalized coordinate transformations are derived. Applications and interpretations from analysis deal especially with the definition of a generalized surface content on ln,p-spheres which is nearly related to a modified co-area formula and an extension of Cavalieri's and Torricelli's indivisibeln method, and with differential equations. Applications from probability theory deal especially with a geometric interpretation of the uniform probability distribution on the ln,p-sphere and with the derivation of certain generalized statistical distributions.     

χ-Fe_5C_2：结构，合成与催化性质调控

铁碳化物,特别是χ-Fe_5C_2,因在多个不同领域的应用长期以来受到研究者的密切关注。事实上,χ-Fe_5C_2已经被认定为铁基费托合成催化剂的活性相。除了作为催化剂外,χ-Fe_5C_2在电化学、磁成像和治疗等方面也有应用价值。自发现以来,人们对χ-Fe_5C_2的结构、稳定性、催化性能等物理化学性质开展了研究。χ-Fe_5C_2的C2/c结构在上世纪60年代初次得到解析,但是受限于样品中常常混合其他氧化铁和碳化铁,在结构方面还存在争议。研究者仍致力于结合先进表征技术和理论方法,利用高纯度的样品来建立更加准确的模型。作为一种亚稳态结构,传统合成方法很难制备高纯度的χ-Fe_5C_2。经过对合成方法的不断探索,物相单一和尺寸形貌可控的合成已经实现。多种铁和碳的前驱体可以用来合成χ-Fe_5C_2,而固-固、固-气和固-液相的碳化过程均能够用来制备不同粒度和形貌的χ-Fe_5C_2。合成方法方面的成果来了对χ-Fe_5C_2物相形成机理的新认识。利用原位表征方法,研究者已经揭示了气固相和液固相制备过程中物相形成的一些细节。无定形的Fe-C复合物的形成与晶化有可能是关键步骤。在新的制备方法基础上,出现了多种调控χ-Fe_5C_2催化活性的新手段。低钴含量的有钴纳米粒子和χ-Fe_5C_2组成的复合体具有非常高的低温费托合成活性。通过第二组分的修饰后可以使χ-Fe_5C_2突破传统的费托合成反应的局限,成为制备低碳烯烃、长链α烯烃、芳烃和含氧化物的新型催化剂。在这篇综述中,我们将回顾自上世纪中期以来对χ-Fe_5C_2物相的研究成果,聚焦于对结构解析,制备方法,生成机制以及在催化性能调控等方面的进展。我们总结了一系列用于制备χ-Fe_5C_2的方法以及控制催化性质的路径。合成方法的突破是更好认识χ-Fe_5C_2物理化学的关键。     

拓扑指数与烷烃色谱保留指数的定量相关研究

基于分子图论, 计算了64个链烷烃的一阶连接性指数(¹χ)和奇偶指数(OEI), 并对气相色谱保留指数进行定量结构-性质相关(QSPR)研究, 得到多元线性回归模型RI＝55.7631＋25.7317OEI＋111.4508¹χ (R²＝0.9960, RMS＝9.36, ARD＝1.02%). 交叉验证和预测结果表明, 所建立的QSPR模型具有良好的稳定性和预测能力. 与文献结果比较, 本文所用的参数少, 且计算简便.     

A simple scheme to generate χ-type four-charge entangled states in circuit QED

We propose a simple scheme to generate χ-type four-charge entangled states by using SQUID-based charge qubits capacitively coupled to a transmission line resonator (TLR). The coupling between the superconducting qubit and the TLR can be effectively controlled by properly adjusting the control parameters of the charge qubit. The experimental feasibility of our scheme is also shown.     

Maximal independent sets in minimum colorings

Every graph G contains a minimum vertex-coloring with the property that at least one color class of the coloring is a maximal independent set (equivalently, a dominating set) in G. Among all such minimum vertex-colorings of the vertices of G, a coloring with the maximum number of color classes that are dominating sets in G is called a dominating-χ-coloring of G. The number of color classes that are dominating sets in a dominating-χ-coloring of G is defined to be the dominating-χ-color number of G. In this paper, we continue to investigate the dominating-χ-color number of a graph first defined and studied in [1].     

A survey of χ-boundedness

If a graph has bounded clique number and sufficiently large chromatic number, what can we say about its induced subgraphs? András Gyárfás made a number of challenging conjectures about this in the early 1980s, which have remained open until recently; but in the last few years there has been substantial progress. This is a survey of where we are now.     

Secure four-site distribution and quantum communication of χ−type entangled states

The research of multi-particle entanglement is a hot topic because of its important applications and far-reaching effects on vast aspects of quantum information. The article is devoted to the χ − type entangled state, a peculiar four-particle entangled state, which is different from a four-particle GHZ or W state under stochastic local operations and classical communication (SLOCC). Secure four-site distribution using decoy particles is proposed. Moreover, applying it, several communication protocols are presented, including four-party hierarchical quantum secret sharing, supervisory three-party asymmetric deterministic secure quantum communication, etc. The security of the four-site distribution and the communication protocols are also analyzed.     

χ3+χ5介质中非束缚态空间亮孤子的传输行为

本文从理论上研究了主克尔型介质中非束缚态空间亮孤子的传输行为。数值计算结果表明:在主克尔型χ⁽³⁾+χ⁽⁵⁾介质中可以传输非束缚态空间亮孤子。传输稳定性与其背景平面波的横向渐近传播常数q和χ⁽³⁾,χ⁽⁵⁾系数有关,非平凡相位因子在三、五阶效应竞争中的平衡作用,是获得非束缚态空间亮孤子稳定传输的关键。