Functional ergodic limits for occupation time processes of site-dependent branching Brownian motions in R

We consider a kind of site-dependent branching Brownian motions whose branching laws depend on the site-branching factorσ(·).We focus on the functional ergodic limits for the occupation time processes of the models in R.It is proved that the limiting process has the form ofλξ(·),where A is the Lebesgue measure on IE andξ(·)is a real-valued process which is non-degenerate if and only ifσis integrable.Whenξ(·)is non-degenerate,it is strictly positive for t0.Moreover,ξconverges to O in finite-dimensional distributions if the integral ofσtends to infinity.     

Asyptotics for linear difference equations I:basic theory

We present here a unified treatment of asymptotic theory of linear difference equations. This is based on anadapted theory of discrete dichotomy. The obtained results narrow the gap between Poincarés Theorem and (the discrete analoue of) Levinson's Theorem.     

Differentially expressed genes selection via Laplacian regularized low-rank representation method

With the rapid development of DNA microarray technology and next-generation technology, a large number of genomic data were generated. So how to extract more differentially expressed genes from genomic data has become a matter of urgency. Because Low-Rank Representation (LRR) has the high performance in studying low-dimensional subspace structures, it has attracted a chunk of attention in recent years. However, it does not take into consideration the intrinsic geometric structures in data.In this paper, a new method named Laplacian regularized Low-Rank Representation (LLRR) has been proposed and applied on genomic data, which introduces graph regularization into LRR. By taking full advantages of the graph regularization, LLRR method can capture the intrinsic non-linear geometric information among the data. The LLRR method can decomposes the observation matrix of genomic data into a low rank matrix and a sparse matrix through solving an optimization problem. Because the significant genes can be considered as sparse signals, the differentially expressed genes are viewed as the sparse perturbation signals. Therefore, the differentially expressed genes can be selected according to the sparse matrix. Finally, we use the GO tool to analyze the selected genes and compare the P-values with other methods.The results on the simulation data and two real genomic data illustrate that this method outperforms some other methods: in differentially expressed gene selection.     

具有非局部时滞的扩散Nicholson苍蝇方程的波前解

研究了具有非局部时滞的扩散Nicholson苍蝇方程,其中时滞由一个定义在所有过去时间和整个一维空间区域上的积分卷积表示.当时滞核是强生成核时,根据线性链式技巧和几何奇异扰动理论,获得了小时滞时波前解的存在性.     

Reduced eigensystem representation of the linear density-density response function

The linear density-density response function represents a formulation of the generalized density response of a molecular (or extended) system to arbitrary perturbing potentials. We have recently established an approach for reducing the dimension of the (in principle infinite) eigenspace representation (the moment expansion) and generalized it to arbitrary self-adjoint, positive-definite, and compact linear operators. Here, we present a modified representation—the reduced eigensystem representation—which allows to define a trivial criterion for the convergence of the approximation to the density response. By means of this novel eigensystem-like structure, the remarkable reduction of the dimensionality becomes apparent for the calculation of the density-density response function.     

原子转移自由基聚合法用于以单分散树脂为基质的强阳离子交换色谱固定相的制备及其色谱性能研究

以7μm单分散交联聚甲基丙烯酸环氧丙酯树脂表面键合溴异丁酰溴为引发剂,以CuCl/CuCl2/2,2-联二吡啶(Bpy)为催化体系,采用封闭体系,在氮气保护下,以乙烯基苯磺酸钠(NaSS)为单体、N,N-二甲基甲酰胺(DMF)水溶液为溶剂,制备了强阳离子交换色谱(SCX)固定相,并用元素分析与红外光谱法对其进行了表征....     

基于苯乙烯和苯并噻二唑共聚场效应发光高分子材料的设计合成及性能研究

共轭高分子材料由于其优异的光电性能和可溶液加工等特性在有机光电器件中具有重要应用.本工作采用Stille偶联和Suzuki聚合反应,合成了两个由经典发光基元苯乙烯片段和共轭吸电子结构基元苯并噻二唑共聚的高分子材料聚（1,2-双（2,5-双（异辛氧基）亚苯基亚乙烯基-2,1,3-苯并噻二唑））（PVBT）和聚（1,2-双（2,5-双（正辛氧基）亚苯基亚乙烯基-2,1,3-苯并噻二唑））（nPVBT）.通过凝胶渗透色谱（GPC）、元素分析及差式扫描量热法（DSC）对PVBT和nPVBT两种高分子材料的结构及热稳定性进行表征,结果表明它们均具有良好的热稳定性,分解温度约380℃.由于烷氧基链的存在,两个材料具有良好的溶解性及成膜加工性.PVBT和nPVBT均表现出优异的发光特性,最大发射波长在590~605 nm范围,溶液下荧光量子产率为23%~35%,固态薄膜下量子产率为12%~20%.以这两个高分子材料薄膜作为活性层,所制备的顶栅-底接触型有机场效应晶体管器件显示出典型的p型电荷传输性能,空穴迁移率可达1.1×10^-4 cm²·V^-1·s^-1,开关比为10³~10⁴.本研究为发展高性能光电集成高分子材料提供了新思路,有望推动有机光电集成器件的研究.     

Pyridinylidenaminophosphines: Facile Access to Highly Electron-Rich Phosphines

Electron-rich tertiary phosphines are valuable species in chemical synthesis. However, their broad application as ligands in catalysis and reagents in stoichiometric reactions is often limited by their costly synthesis. Herein, we report the synthesis and properties of a series of phosphines with 1-alkylpyridin-4-ylidenamino and 1-alkylpyridin-2-ylidenamino substituents that are accessible in a very short and scalable route starting from commercially available aminopyridines and chlorophosphines. The determination of the Tolman electronic parameter (TEP) value reveals that the electron donor ability can be tuned by the substituent pattern at the aminopyridine backbone and it can exceed that of common alkylphosphines and N-heterocyclic carbenes. The potential of the new phosphines as strong nucleophiles in phosphine-mediated transformations is demonstrated by the formation of Lewis base adducts with CO₂ and CS₂. In addition, the coordination chemistry of the new phosphines towards Cu^I, Au^I, and Pd^II metal centers has been explored, and a convenient procedure to introduce the most basic phosphine into metal complexes starting from air-stable phosphonium salt is described.     

Strong Coupling and Laser Action of Ladder‐Type Oligo(p‐phenylene)s in a Microcavity

We investigate the coupling of ladder‐type quarterphenyl to the photon modes of a dielectric ZrO_x/SiO_x microcavity at ultraviolet wavelengths. For a relatively long cavity (≈10 μm) with high‐reflectivity mirrors (0.998), optically pumped laser action is demonstrated in the weak‐coupling regime. We observe single‐mode operation with a threshold of 0.4 mJ cm^?2. Strong coupling is achieved by using a short λ/2 cavity. We find pronounced anti‐crossing features of the molecular (0,0) and (0,1) vibronic transitions and the cavity mode in angle‐dependent reflectivity measurements providing Rabi splittings of (90±10) meV. All these features occur spectrally resonant to the exciton transition of ZnO demonstrating the potential of ladder‐type oligo(p‐phenylene)s for the construction of inorganic/organic hybrid microcavities.