Synthesis of Bi<Subscript>2</Subscript>O<Subscript>4</Subscript>@TiO<Subscript>2</Subscript> Heterojunction with Enhanced Visible Light Photocatalytic Activity

A novel Bi₂O₄@TiO₂ heterojunction was constructed by a simple two-step method. The charges migration between Bi₂O₄ and TiO₂ via the heterojunction improves the electron/hole separation efficiency. Furthermore, Bi₂O₄@TiO₂ heterostructures exhibit better adsorption capability for methyl orange molecular due to their higher specific surface area than pure Bi₂O₄. As a result, Bi₂O₄@TiO₂ hybrids show an improved visible light photocatalytic activity and photostability for the degradation of methyl orange.     

Electrochemical recognition of tryptophan enantiomers using self-assembled diphenylalanine structures induced by graphene quantum dots,chitosan and CTAB

Molecular self-assembly offers a promising route to the preparation of advanced materials for the construction of novel chiral sensing devices, and the inspiration for the development of such systems is often derived from simple biological models. Diphenylalanine (FF), an extensively studied short peptide, can self-assemble into highly ordered nano-/micro-structures. Here we report the electrochemical recognition of tryptophan enantiomers using three FF self-assembled structures produced in the presence of graphene quantum dots (GQDs), chitosan (CS) and cetyltrimethylammonium bromide (CTAB). Although the difference in the peak potentials of the enantiomers is very small, enantiomeric differences can be detected by the magnitude of the DPV current signals. The recognition efficiencies of the three self-assembled materials are different, due to the different structures formed during the self-assembly process.     

Enhancing effect of boron trifluoride diethyl etherate electrolytes on capacitance performance of electropolymerized poly[poly(<Emphasis Type="Italic">N</Emphasis>-vinyl-carbazole)] films

In this paper, poly[poly(N-vinyl-carbazole)] (PPVK) films electrodeposited in tetrahydrofuran (THF) containing 12 % boron trifluoride diethyl etherate (BFEE) were studied as electrode active material for supercapacitors. The morphology and thermal property were characterized by SEM, atomic force microscopy (AFM), and thermogravimetry (TG), respectively. The electrochemical capacitive behaviors of the PPVK films were also investigated by cyclic voltammetry, galvanostatic charge/discharge, and electrochemical impedance spectroscopy. The electrochemical results showed that the specific capacitance of PPVK films in CH₃CN solution was about 126 mF cm^?2 at 1.5 mA cm^?2 and the capacitance retention was only 14.4 % after 1000 cycles. It was exciting to improve the specific capacitance up to 169.3 mF cm^?2 at 1.5 mA cm^?2 and to make the cyclic stability increase to 81.8 % capacitance retention after 5000 cycles when the equivalent BFEE was added into the CH₃CN solution containing 0.05 M Bu₄NBF₄ electrolyte. These results clearly demonstrated that BFEE was an efficient promoter for the enhancement of the capacitance performance of PPVK films. Therefore, with the help of BFEE electrolyte, the PPVK films have potential application as capacitive materials in high-performance energy storage devices.     

Haezendonck–Goovaerts risk measure with a heavy tailed loss

Recently Haezendonck–Goovaerts (H–G) risk measure has received much attention in (re)insurance and portfolio management. Some nonparametric inferences have been proposed in the literature. When the loss variable does not have enough moments, which depends on the involved Young function, the nonparametric estimator in Ahn and Shyamalkumar (2014) has a nonnormal limit, which challenges interval estimation. Motivated by the fact that many loss variables in insurance and finance could have a heavier tail such as an infinite variance, this paper proposes a new estimator which estimates the tail by extreme value theory and the middle part nonparametrically. It turns out that the proposed new estimator always has a normal limit regardless of the tail heaviness of the loss variable. Hence an interval with asymptotically correct confidence level can be obtained easily either by the normal approximation method via estimating the asymptotic variance or by a bootstrap method. A simulation study and real data analysis confirm the effectiveness of the proposed new inference procedure for estimating the H–G risk measure.     

Liouville Type Theorems for PDE and IE Systems Involving Fractional Laplacian on a Half Space

In this paper, let α be any real number between 0 and 2, we study the Dirichlet problem for semi-linear elliptic system involving the fractional Laplacian:

$$\left \{\begin {array}{l} (-{\Delta })^{\alpha /2}u(x)=v^{q}(x),\ \ \ x\in \mathbb {R}^{n}_{+},\\ (-{\Delta })^{\alpha /2}v(x)=u^{p}(x),\ \ \ x\in \mathbb {R}^{n}_{+},\\ u(x)=v(x)=0,\ \ \ \ \ \ \ \ \ \ x\notin \mathbb {R}^{n}_{+}. \end {array}\right .\label {elliptic} $$

(1)

We will first establish the equivalence between PDE problem (1) and the corresponding integral equation (IE) system (Lemma 2). Then we use the moving planes method in integral forms to establish our main theorem, a Liouville type theorem for the integral system (Theorem 3). Then we conclude the Liouville type theorem for the above differential system involving the fractional Laplacian (Corollary 4).

     

Existence and uniqueness of perturbed reflected jump diffusion processes

In this article, we establish the existence of the solution to the càdlàg perturbed Skorohod problem. As an application, we obtain the existence and uniqueness of the solution to the perturbed reflected jump diffusion processes.     

悬链曲面上的点粒子动力学及扩展空间约束系统量子化

扩张型正则量子化方案的核心内容是位置、动量以及哈密顿量同时量子化. 通过分析悬链面上粒子的扩张型正则量子化方案, 并且与薛定谔理论进行比较, 发现内禀几何中二维悬链面给不出与薛定谔理论相一致的结果, 而考虑将二维悬链面嵌入在三维欧氏空间之后, 还需要将正则量子化方案进行扩张, 可以得到体系的几何势能和几何动量, 并与薛定谔理论相一致.     

Y2Ti2O7:Tm3+的制备及其发光性能研究

采用溶胶-凝胶法(Sol-gel)制备了不同烧结温度和Tm³⁺掺杂浓度的Y₂Ti₂O₇:xTm (x=0.005,0.01,0.03,0.05)荧光粉,分别采用X射线衍射分析仪(XRD)、透射电子显微镜(TEM)和荧光光谱仪对样品的晶型结构、形貌以及发光性能进行了表征。XRD结果表明,所得到的样品为单一立方相烧绿石结构。样品在361 nm紫外光激发下发射出 蓝光,其峰值波长为456 nm,对应于Tm³⁺的¹D₂→³F₄跃迁。1 000 ℃烧结的Y₂Ti₂O₇: 0.01Tm³⁺样品具有较好的发光性能。样品在456 nm处的相对发光强度随Tm³⁺掺杂浓度的增大先升高后降低,在Tm³⁺摩尔分数为1%时达到最大,即出现了浓度猝灭现象。