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.     

磷灰石结构荧光粉Ba10(PO4)6F2:Ce3+,Tb3+的合成、发光和能量传递

采用高温固相法合成了系列Ce~(3+)和Ce~(3+)/Tb~(3+)激活的具有磷灰石结构荧光粉Ba_(10)(PO_4)_6F_2。用X射线衍射(XRD)、扫描电镜(SEM)、激发和发射(PLE和PL)光谱对样品进行了表征分析。研究结果表明:所合成的荧光粉Ba_(10)(PO_4)_6F_2∶Ce~(3+),Tb~(3+)具有氟磷灰石结构,样品微观呈现不规则形貌。荧光粉Ba10-x(PO4)6F2∶x Ce~(3+)的相对发射强度随着x增加而增强,当x=0.09时,荧光强度达到最大。荧光粉Ba_(10)(PO_4)_6F_2∶Ce~(3+),Tb~(3+)的激发光谱为240～330 nm的宽带,发射光谱呈现出Ce~(3+)的5d→4f跃迁紫外光(335和358 nm)发射和Tb~(3+)的4f→4f跃迁绿光(542 nm)发射。光谱特性表明,发光过程中存在Ce~(3+)→Tb~(3+)能量传递,能量传递效率可以达到60%。计算Ce~(3+)和Tb~(3+)的临界距离为0.79 nm,能量传递机理是偶极-偶极交互作用。此外,详细论述了Ce~(3+)和Tb~(3+)之间的能量传递和发光的过程。通过调节Tb~(3+)的掺杂浓度,对荧光粉发光色坐标与Tb~(3+)的掺杂浓度之间的关系也进行了研究,随着Tb~(3+)的掺杂量从0增加0.52,荧光粉Ba_(10)(PO_4)_6F_2∶Ce~(3+),Tb~(3+)的发射光谱色坐标可以从(0.149 4,0.045 1)蓝色区变化到(0.280 1,0.585 3)绿色区。     

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。