分数扩散模型的参数估计及其应用

研究分数扩散模型的参数估计及其应用问题.分数扩散模型是一类由分数Brownian运动驱动的随机微分方程.主要结果有:(1)利用二次变差方法给出模型中扩散系数的估计量,通过最小二乘法给出模型中漂移系数的估计量;(2)证明这些估计量的一致收敛性和渐近正态性;(3)利用MCMC方法对此估计量进行验证,并通过R软件将上述模型以及参数估计量应用到SHIBOR利率中进行实证研究.     

非自治Plate方程时间依赖强拉回吸引子的存在性

结合Plinio等人([Plinio D,Duane G S,Temarn R,Time-dependent attractor for the oscillon equation,Discrete Contin Dyn Syst,2011,29(1):141-167.])提出的时间依赖全局吸引子概念,运用压缩函数的方法,证明了带有时间依赖系数的非自治Plate方程时间依赖拉回吸引子在空间H~4(Ω)∩H~2_0(Ω)×H~2_0(Ω)中的存在性.     

Silica‐supported polymeric monolithic column with a mixed mode of hydrophilic and strong cation‐exchange interactions for microcolumn liquid chromatography

A novel sulfonic acid group containing hydrophilic strong cation‐exchange monolith was prepared by in situ coating 5 μm bare silica particles with the copolymers of glycidyl methacrylate and pentaerythritol triacrylate and further sulfonating the prepared polymer matrix with Na₂SO₃ inside a 150 μm id capillary. The preparation conditions were investigated, and the method was described in detail. The prepared column was characterized by comparing with its counterparts reported previously in terms of matrix morphology, preparation reproducibility, permeability, swelling–shrinking behavior, mechanical stability, hydrophilicity, binding capacity, and column efficiency. The swelling–shrinking behavior of the present column in solvents of different polarities was negligible, the hydrophobicity could be suppressed at the acetonitrile concentrations higher than 40% v/v, and the binding capacities were 256 μequiv/mL and 20.1 mg/mL for Cu²⁺ and lysozyme, respectively. The minimum theoretical plate heights were 8, 10, and 13 μm, and the values of the C term in van Deemter equation were 9, 12, and 35 ms for the test analytes of Na⁺, thiourea, and cytidine 5ʹ‐monophosphate, respectively. This column exhibited an excellent performance in the separations of monovalent inorganic cations, uncharged polar, and charged polar compounds.     

Hölder Continuity of the Saddle Point Set for Real-Valued Functions

This paper is concerned with Hölder continuity of the solution to a saddle point problem. Some new su?cient conditions for the uniqueness and Hölder continuity of the solution for a perturbed saddle point problem are established. Applications of the result on Hölder continuity of the solution for perturbed constrained optimization problems are presented under mild conditions. Examples are given to illustrate the obtained results.     

Relationships between the canonical ascending and descending central series of ideals of an associative algebra

We consider the canonical descending and ascending central series of ideals of an associative algebra. In particular, we prove that some ideal in the descending central series is finite-dimensional if and only if some ideal in the ascending central series is finite-codimensional. This result is the associative algebra analogue of results due to Reinhold Baer and Philip Hall in group theory and Ian Stewart in Lie algebra. We also prove various related results.     

On the theta completions for maximal subalgebras

Let L be a finite dimensional Lie algebra. Then for a maximal subalgebra M of L, a 𝜃-completion for M is a subalgebra C of L such that CM and M_L?C and C∕M_L contains no non-zero ideal of L∕M_L, properly. And a 𝜃-completion C of M is said to be a strong 𝜃-completion, if C = L or there exists a subalgebra B of L such that C be maximal in B and B is not a 𝜃-completion for M. These are analogous to the concepts of 𝜃-completion and strong 𝜃-completion of a maximal subgroup of a finite group. Now, we consider the influence of these concepts on the structure of a finite dimensional Lie algebra.     

Reservoir Engineering Strong Magnomechanical Entanglement via Dual-Mode Cooling

A hybrid cavity magnomechanical system to transfer the bipartite entanglements and achieve the strong microwave photon–phonon entanglement based on the reservoir engineering approach is constructed. The magnon mode is coupled to the microwave cavity mode via magnetic dipole interaction and to the phonon mode via magnetostrictive force (optomechanical-like). It is shown that the initial magnon-phonon entanglement can be transferred to the photon-phonon subspace in the case of these two interactions cooperating. In the reservoir-engineering parameter regime, the initial entanglement is directionally transferred to the photon-phonon subsystem, so a strong bipartite entanglement in which the magnon mode acts as the cold reservoir to effectively cool the Bogoliubov mode delocalized over the cavity and the mechanical deformation mode is obtained. Moreover, dual-mode cooling is realized by engineering the dissipation of photon and phonon modes within the target mode, which allows entanglement to be further enhanced. The results indicate that the steady-state entanglement is robust against temperature. The dual-mode cooling reservoir engineering scheme can potentially be extended to other three-mode quantum systems.     

Boosting Hydrogen Evolution at Visible Light Wavelengths by Using a Photocathode with Modal Strong Coupling between Plasmons and a Fabry-Pérot Nanocavity

Hot-hole injection from plasmonic metal nanoparticles to the valence band of p-type semiconductors and reduction by hot electrons should be improved for efficient and tuneable reduction to obtain beneficial chemical compounds. We employed the concept of modal strong coupling between plasmons and a Fabry-Pérot (FP) nanocavity to enhance the hot-hole injection efficiency. We fabricated a photocathode composed of gold nanoparticles (Au−NPs), p-type nickel oxide (NiO), and a platinum film (Pt film) (ANP). The ANP structure absorbs visible light over a broad wavelength range from 500 nm to 850 nm via hybrid modes based on the modal strong coupling between the plasmons of Au−NPs and the FP nanocavity of NiO on a Pt film. All wavelength regions of the hybrid modes of the modal strong coupling system promoted hot-hole injection from the Au−NPs to NiO and proton/water reduction by hot electrons. The incident photon-to-current efficiency based on H₂ evolution through water/proton reduction by hot electrons reached 0.2 % at 650 nm and 0.04 % at 800 nm.     

一类强非线性机械基础系统的亚谐振动解析解

建立了机械基础动力系统的强非线性动力学模型，利用能量法对该系统的周期解进行了解析研究，确定了系统动态参数满足周期解的条件、系统的周期解以及解的稳定性判别式。发现了亚谐振动，并给出了系统在满足周期解条件下的一组参数对应的主振动、1／3亚谐振动和1／5亚谐振动。最后利用数值积分方法计算了系统在给定条件下的主振动及亚谐振动解，考察了解析解的正确性。     

Sustained photon pulse revivals from inhomogeneously broadened spin ensembles

A very promising recent trend in applied quantum physics is to combine the advantageous features of different quantum systems into what is called “hybrid quantum technology”. One of the key elements in this new field will have to be a quantum memory enabling to store quanta over extended periods of time. Systems that may fulfill the demands of such applications are comb‐shaped spin ensembles coupled to a cavity. Due to the decoherence induced by the inhomogeneous ensemble broadening, the storage time of these quantum memories is, however, still rather limited. Here we demonstrate how to overcome this problem by burning well‐placed holes into the spectral spin density leading to spectacular performance in the multimode regime. Specifically, we show how an initial excitation of the ensemble leads to the emission of more than a hundred well‐separated photon pulses with a decay rate significantly below the fundamental limit of the recently proposed “cavity protection effect”.