Sum rules in multiphoton coincidence rates

We show that sums of carefully chosen coincidence rates in a multiphoton interferometry experiment can be simplified by replacing the original unitary scattering matrix with a coset matrix containing 0s. The number and placement of these 0s reduces the complexity of each term in the sum without affecting the original sum of rates. In particular, the evaluation of sums of modulus squared of permanents is shown to turn in some cases into a sum of modulus squared of determinants. The sums of rates are shown to be equivalent to the removal of some optical elements in the interferometer.     

Effects of hydroxyl groups and hydrogen passivation on the structure,electrical and optical properties of silicon carbide nanowires

The effects of hydrogen and hydroxyl passivation on the structure, electrical and optical properties of SiCNWs were investigated. The passivation performance of different atoms (groups) were discussed by analyzing the distribution of electronic states and the polarity of chemical bonds. The results show that passivation can improve the stability of SiCNWs structure, and the effect of hydroxyl is better than hydrogen passivation. And hydrogen and hydroxyl passivation both increase the band gap of SiCNWs, and the changing trend of band gap is relevant to the polarity of the covalent bond formed by the passivation of surface atoms. Moreover, passivation enhances the stability of the optical properties of SiCNWs, resulting in narrowing of light absorption, photoconductivity and other spectra, and the response peak shifts to the deep ultraviolet region, which means that hydrogen or hydroxyl passivation of SiCNWs is likely to be a candidate material for deep ultraviolet micro-nano optoelectronic devices.     

Janus Face All-cis 1,2,4,5-tetrakis(trifluoromethyl)- and All-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)- Cyclohexanes

We report the synthesis of all-cis 1,2,4,5-tetrakis (trifluoromethyl)- and all-cis 1,2,3,4,5,6-hexakis (trifluoromethyl)- cyclohexanes by direct hydrogenation of precursor tetrakis- or hexakis- (trifluoromethyl)benzenes. The resultant cyclohexanes have a stereochemistry such that all the CF₃ groups are on the same face of the cyclohexyl ring. All-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)cyclohexane is the most sterically demanding of the all-cis hexakis substituted cyclohexanes prepared to date, with a barrier (ΔG) to ring inversion calculated at 27 kcal mol⁻¹. The X-ray structure of all-cis 1,2,3,4,5,6-hexakis(trifluoromethyl)cyclohexane displays a flattened chair conformation and the electrostatic profile of this compound reveals a large diffuse negative density on the fluorine face and a focused positive density on the hydrogen face. The electropositive hydrogen face can co-ordinate chloride (K≈10³) and to a lesser extent fluoride and iodide ions. Dehydrofluorination promoted decomposition occurs with fluoride ion acting as a base.     

On a certain class of locally conformal symplectic structures of the second kind

We study locally conformal symplectic (LCS) structures of the second kind on a Lie algebra. We show a method to construct new examples of Lie algebras admitting LCS structures of the second kind starting with a lower dimensional Lie algebra endowed with a LCS structure and a suitable extension. Moreover, we characterize all LCS Lie algebras obtained with our construction. Finally, we study the existence of lattices in the associated simply connected Lie groups in order to obtain compact examples of manifolds admitting this kind of structure.     

Leibniz Conformal Algebras of Rank Two

We classify all Leibniz conformal algebras of rank two.     

LIE SYMMETRY ANALYSIS AND PAINLEVE ANALYSIS OF THE NEW （2＋1）-DIMENSIONAL KdV EQUATION

Lie point symmetries associated with the new （2＋1）-dimensional KdV equation ut ＋ 3uxuy ＋ uxxy = 0 are investigated. Some similarity reductions are derived by solving the corresponding characteristic equations. Painlevé analysis for this equation is also presented and the soliton solution is obtained directly from the Bǎcklund transformation.     

关于群胚作用和李双代数胚态射

在这篇文章中，我们讨论了李双代数胚之间的态射，得到了一些李双代数胚之间态射的性质．研究了泊松群胚在泊松流形上的泊松作用，以及这个泊松作用与被作用流形的切李双代数胚到作用泊松群胚的切李双代数胚之间的态射的关系，得到了一些有用的结论。     

S~1 × S~1-Borsuk-Ulam Theorem on Product Spaces

Ｓ~１×Ｓ~１－Ｂｏｒｓｕｋ－ＵｌａｍＴｈｅｏｒｅｍｏｎＰｒｏｄｕｃｔＳｐａｃｅｓＺｈｏｎｇＣｈｅｎｇｋｕｉ（钟承奎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＬａｎｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｚｈｏｕ，７３００００）Ａｂｓｔｒａｃｔ：...     

Block （or Hamiltonian） Lie Symmetry of Dispersionless D-Type Drinfeld-Sokolov Hierarchy

In this paper, the dispersionless D-type Drinfeld-Sokolov hierarchy, i.e. a reduction of the dispersionless two-component BKP hierarchy, is studied. The additional symmetry flows of this hierarchy are presented. These flows form an infinite-dimensional Lie algebra of Block type as well as a Lie algebra of Hamiltonian type.