Travelling wave solutions for the nonlinear dispersion Drinfel’d–Sokolov () system

In this paper, travelling wave solutions for the nonlinear dispersion Drinfel’d–Sokolov system (called D(m,n) system) are studied by using the Weierstrass elliptic function method. As a result, more new exact travelling wave solutions to the D(m,n) system are obtained including not only all the known solutions found by Xie and Yan but also other more general solutions for different parameters m,n. Moreover, it is also shown that the D(m,1) system with linear dispersion possess compacton and solitary pattern solutions. Besides that, it should be pointed out that the approach is direct and easily carried out without the aid of mathematical software if compared with other traditional methods. We believe that the method can be widely applied to other similar types of nonlinear partial differential equations (PDEs) or systems in mathematical physics.     

On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group

The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order $H^m(\mathbb {H}^n), m\in \mathbb {N}^n,$ under the heat kernel transform on $\mathbb {H}^n,$ using direct sum and direct integral of Bergmann spaces and certain unitary representations of $\mathbb {H}^n$ which can be realized on the Hilbert space of Hilbert‐Schmidt operators on $L^2(\mathbb {R}^n).$ We also show that the image of Sobolev space of negative order $H^{-s}(\mathbb {H}^n), s(>0) \in \mathbb {R}$ is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on $\mathbb {H}^n$ under the heat kernel transform.     

Integral geometry for \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {D}}$\end{document}‐modules on dual flag manifolds and generalized Verma modules

Given a pair of dual generalized flag manifolds of a semisimple algebraic group, we show that the integral transform between them given by the open orbit in their product is an equivalence. We also describe the links of this problem with the structure of generalized Verma modules, and how the above construction can be applied to the representation theory of real forms of the group.     

A predictable decomposition in an infinite assets model with jumps. Application to hedging and optimal investment

Motivated by the theory of bond markets, we consider an infinite assets model driven by marked point process and Wiener process. The self-financed wealth processes are defined by using measure-valued strategies. Going further on the works of Bjork et al. [“Bond market structure in the presence of marked point processes”, Mathematical Finance, 7 (1997a) pp. 211–239; “Towards a general theory of bond markets”, Finance and Stochastics, 1 (1997b) pp. 141–174] who focus on the existence of martingale measures and market completeness questions, we study here the incompleteness case. Our main result is a predictable decomposition theorem for supermartingales in this infinite assets model context. The concept of approximate wealth processes is introduced, and we show in an example that the space of measure-valued strategies is not complete with respect to the semimartingale topology. As in the case of stock markets, one can then derive a dual representation of the super-replication cost and study the problem of utility maximization by duality methods.     

The central limit theorem for stationary Markov processes with normal generator—with applications to hypergroups

We extend the central limit theorem for additive functionals of a stationary, ergodic Markov chain with normal transition operator due to Gordin and Lif?ic, 1981 [A remark about a Markov process with normal transition operator, In: Third Vilnius Conference on Probability and Statistics 1, pp. 147–48] to continuous-time Markov processes with normal generators. As examples, we discuss random walks on compact commutative hypergroups as well as certain random walks on non-commutative, compact groups.     

Certain strict topologies on the space of regular Borel measures on locally compact groups

Let G   denote a locally compact Hausdorff group and M(G)$M(G)$ be the space of all bounded complex-valued regular Borel measures on G  . In this paper, we define two strict topologies on M(G)$M(G)$ and study various properties of these topologies such as metrizability, barrelledness and completeness. We also determine the dual space of M(G)$M(G)$ and consider various continuity properties for the convolution product on M(G)$M(G)$ under these topologies.     

AN EIGENSPACE CHARACTERIZATION OF LORENTZ-IMPROVING MEASURES ON COMPACT GROUPS

Abstract

A measure μ on a compact group is called Lorentz-improving if for some 1 > p > ∞ and 1 → q ₁ > q ₂ ∞ μ *L (p, q ₂) ? L(p, q ₁). Let T _μ denote the operator on L ² defined by T _μ(f) = μ * f. Lorentz-improving measures are characterized in terms of the eigenspaces of T _μ, if T _μ is a normal operator, and in terms of the eigenspaces of |T _μ| otherwise. This result generalizes our recent characterization of Lorentz-improving measures on compact abelian groups and is modelled after Hare's characterization of L ^p -improving measures on compact groups.     

颜色可调Sr3Y（BO3）3∶Tm3+，Dy3+荧光粉的发光性能及能量传递

采用高温固相法制备了Sr_3Y(BO_3)_3:xTm~(3+),yDy~(3+)荧光粉,并通过XRD、SEM和荧光光谱仪对样品的物相、微观形貌、发光性能、能量传递机制和CIE色坐标进行了分析。结果表明:Sr_3Y(BO_3)_3:xTm~(3+)荧光粉在监测波长为359 nm时发射蓝光,Tm~(3+)的浓度淬灭点为x=0.08;在Sr_3Y(BO_3)_3:0.08Tm~(3+),yDy~(3+)荧光粉中,随着Dy~(3+)掺杂浓度的增加,Tm~(3+)的发光强度降低而Dy~(3+)发光强度却先增加后降低,Dy~(3+)的浓度淬灭点为y=0.1;通过改变Dy~(3+)掺杂浓度或改变激发光的波长,均可实现发射光的颜色可调;在Tm~(3+)-Dy~(3+)离子之间存在能量传递。当Dy~(3+)掺杂浓度(物质的量分数)为0.15时能量传递效率达75.14%,能量传递机制为电偶极-电偶极相互作用。     

基于水分散纳米无定形水杨酸甲酯铽配合物的三价铬离子高灵敏荧光传感器

为扩大稀土荧光配合物的应用范围,满足水溶液中微量铬的高灵敏高选择性探测要求,制备了一种基于水分散纳米无定形水杨酸甲酯铽配合物(A-MS-Tb)的高灵敏三价铬离子荧光传感器。结果表明:在水溶液中直接反应合成的配合物A-MS-Tb为无定形的纳米沉淀,其粒子尺度在50～100 nm之间,具有与报道的配合物晶体类似的组成。该配合物在494、549、591和625 nm处呈现出强的荧光发射,归属于铽离子的5D4→7FJ(J=6,5,4,3)能级跃迁。A-MS-Tb与晶体配合物的显著差别在于其在水中的悬浮稳定性和荧光稳定性更好,这对于其作为荧光材料和离子传感器非常重要。尤其突出的是,当将三价铬离子加入到它的水悬浮溶液中后,会减弱配体与铽离子之间的配位作用,导致其绿色荧光被淬灭。据此,构建了一种高灵敏测定溶液中铬离子浓度的荧光探针,并对其分析的选择性、灵敏度和抗干扰能力进行了评价。