形如1/3(2~p+1)的孤立数

设p是奇素数.X_p=1/3(2~p+1),证明了:X_p都是孤立数.     

Lax Pair and Darboux Transformation for a Variable-Coefficient Fifth-Order Korteweg-de Vries Equation with Symbolic Computation

In this paper, we put our focus on a variable-coe~cient fifth-order Korteweg-de Vries （fKdV） equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out.     

Salt effects and the mechanism of electrophilic mercuration of unsaturated compounds

The reaction of Hg(OAc)₂ with bornylene in THF-H₂O and CH₃CN-H₂O mixed solvents (75 25, v/v) was studied. The effects of the addition of NaOAc on the reaction rate and the composition of products were investigated. In the CH₃CN-H₂O mixture, the addition of NaOAc decreases the amount of the rearranged product, fundamentally changes the ratio between the regioisomeric solvoadducts, and promotes the formation of products of Hg(OAc)₂ addition. The reaction proceedsvia an ion pair and free mercurinium ion; the cation of the ion pair and the free mercurinium ion have dissimilar structures.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 544–548, March, 1995.     

Tensor logarithmic norm and its applications

Matrix logarithmic norm is an important quantity, which characterize the stability of linear dynamical systems. We propose the logarithmic norms for tensors and tensor pairs, and extend some classical results from the matrix case. Moreover, the explicit forms of several tensor logarithmic norms and semi‐norms are also derived. Employing the tensor logarithmic norms, we bound the real parts of all the eigenvalues of a complex tensor and study the stability of a class of nonlinear dynamical systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Doping and temperature dependence of electronic Raman response in cuprate superconductors

The doping and temperature dependence of the electronic Raman response in cuprate superconductors is studied within the kinetic energy driven superconducting mechanism. It is shown that the temperature dependent depletion at low-energy shifts is faster in the B1g symmetry than in the B2g symmetry. In analogy to the domelike shape of the doping dependent superconducting transition temperature, the maximal peak energy in the B2g channel occurs around the optimal doping, and then decreases in both underdoped and overdoped regimes. Moreover, the overall density of Cooper pairs increases with increasing doping in the underdoped regime.     

The essentially tame local Langlands correspondence, I

Let be a non-Archimedean local field (of characteristic or ) with finite residue field of characteristic . An irreducible smooth representation of the Weil group of is called essentially tame if its restriction to wild inertia is a sum of characters. The set of isomorphism classes of irreducible, essentially tame representations of dimension is denoted . The Langlands correspondence induces a bijection of with a certain set of irreducible supercuspidal representations of . We consider the set of isomorphism classes of certain pairs , called ``admissible', consisting of a tamely ramified field extension of degree and a quasicharacter of . There is an obvious bijection of with . Using the classification of supercuspidal representations and tame lifting, we construct directly a canonical bijection of with , generalizing and simplifying a construction of Howe (1977). Together, these maps give a canonical bijection of with . We show that one obtains the Langlands correspondence by composing the map with a permutation of of the form , where is a tamely ramified character of depending on . This answers a question of Moy (1986). We calculate the character in the case where is totally ramified of odd degree.

     

Lax Pairs for Integrable Six-Vertex Model with Color Parameters

Using the colored Yang-Baxter equation, the Lax pairs for the system with color parameters and periodic boundary conditions are derived. The explicit expressions of the Lax pairs for the six-vertex standard R matrices of both the Baxter and free-Fermion types are given.     

q变形对相干态的相位概率分布特性

通过推广Pegg和Barnett的相位算符和相位态到q变形的双模情况, 应用数值计算 研究了q变形对相干态的相位概率分布特性. 结果表明, q变形对相干态的相位概率分布受到相位参数、q参数和参数│ξ│的调节, 从而反映出不同的量子相干特性.     

新型感可见光的光引发体系乙基曙红碘■盐的研究

合成并研究了新型感可见光的光引发体系乙基曙红碘盐。结果表明，该引发剂的物理化学性质和光敏引发效率受其结构、介质性质和浓度等诸多因素影响。在可见光照射下，发生由乙基曙红阴离子向二苯基碘阳离子的电子转移反应，产生具有引发活性的苯自由基和非活性的乙基曙红自由基。测定了光聚合的动力学方程以及聚合物的分子量和分子量分布。比较了曙红单碘盐和双碘盐的各种不同性质     

分子光化学贮存太阳能 Ⅲ.双环[2,2,1]-2,5-庚二烯的光诱导电子转移敏化异构化反应

以N,N,N′,N′-四甲基联苯二胺、2,6-二甲氧基萘和2,7-二甲氧基萘为光敏剂,在正己烷溶液中实现了双环[2,2,1]-2,5-庚二烯到四环[2,2,1,0^2,6,0^3,5]庚烷的异构化。测定了反应的量子产率。讨论了反应机理。通过激发态的光敏剂与二烯之间的电子转移反应,形成单重态和三重态处于平衡状态的离子自由基对中间体。处于溶剂笼中的三重态离子自由基对经电子反传,产生激发三重态二烯。最后该激发态二烯经分子内[2+2]环合加成反应异构化为四环烷。