Existence of positive solutions of mixed fractional integral boundary value problem with p(t)-Laplacian operator

Ricerche di Matematica - In this paper, we investigate a mixed fractional integral boundary value problem with p(t)-Laplacian operator. Firstly, we derive the Green function through the direct...     

聚合型硼氢化物(BH3)n(n=1-3)的几何结构与光谱的研究

采用不同方法B3P86,B3LYP,MP2和LSDA,结合Dunning的相关一致基组cc-PVTZ,对聚合型硼氢化物(BH₃)_n(n=1-3)分子的可能几何构型进行优化计算,得出最稳定构型的几何参数、电子结构、振动频率和光谱等性质参数,并给出了最稳定结构的总能量(E_T),结合能(E_BT),平均结合能(E_av),电离势(E_IP),能隙(E_g),费米能级(E_F)等.结果表明:采用密度泛函DFT中的方法B3P86计算的能量最低,结构参数更接近文献值;三种硼氢化物分子基态都为1重态,电子态分别为¹A',¹A和¹A; BH₃分子的最稳定几何构型为平面三角形结构;B₂H₆为对称性乙烯式D_2h立体结构,H-B之间生成氢桥式三中心双电子键;B₃H₉为C_3ν立体结构,也生成氢桥式三中心双电子键,但三个氢桥三中心双电子键彼此隔离.最后分析了三种氢化物的红外和拉曼光谱、平均结合能、电离势、能隙和费米能级等特性,说明(BH₃)_n(n=1-3)三分子中B₂H₆最稳定,H-B桥键键长比端键更长,最强峰红外光谱强度最大. 关键词： 聚合型硼氢化物 几何构型 光谱     

无配体参与钯催化烯烃与芳基三烷氧基硅烷的交叉偶联反应

考察了钯催化下一系列烯烃化合物与不同芳基三烷氧基硅烷的反应,发展了一种新型无配体参与的Heck类型反应方法.研究表明:以Pd(OAc)2为催化剂,在K2CO3,n-Bu4NF 3H2O和AgOAc存在下,该Heck类型反应能够得到中等及优良的偶联产率,并且表现出较高的区域选择性和立体选择性.根据实验结果以及相关文献,对该Heck类型偶联反应的可能机理进行了探讨.     

Existence and uniqueness of nontrivial solutions for eigenvalue boundary value problem of nonlinear fractional differential equation

In this paper, we study the existence and uniqueness of a nontrivial solution to eigenvalue problems for the following nonlinear fractional differential equation of the form $$\begin{aligned} \left\{ \begin{array}{l} -D^{\alpha }_{0^{+}}u(t)=\lambda [f(t, u(t), D^{\beta }_{0^{+}}u(t))+g(t)],~~ 0 where \(\lambda \) is a parameter, \(D^{\alpha }_{0^{+}},D^{\beta }_{0^{+}}\) are two standard Riemann–Liouville fractional derivatives, \(0<\beta <1<\alpha \le 2,\alpha -\beta >1,f: [0,1]\times {\mathbb{R }}\times {\mathbb{R }}\rightarrow {\mathbb{R }}\) is continuous, and \(g(t): (0, 1)\rightarrow [0, +\infty )\) is Lebesgue integrable. We obtain several sufficient conditions of the existence and uniqueness of nontrivial solution of the above eigenvalue problems when \(\lambda \) is in some interval. Our approach is based on the Leray–Schauder nonlinear alternative. In addition, some examples are included to demonstrate the main result.     

Luminescence of the compounds Y0.5 − x Li1.5PO4:Eu x

In this paper for the first time, the compounds Y_{0.5 ? x} Li_1.5PO₄:Eu _x (YLP:Eu) were synthesized by the simple method of solid state reaction. The technology takes much time dry low temperature and little time calcined to synthesize rare earth phosphates. Their structures were analyzed by X-ray powder diffraction experiment. The excitation and emission spectra were measured at room temperature. Y_{0.5 ? x} Li_1.5PO₄:Eu _x shows the characteristice emissions of Eu³⁺ (⁵ D ₀-⁷ F _{1, 2, 3, 4} transitions dominated by ⁵ D ₀-⁷ F ₄). Incorporation of Li⁺ ions in the phosphors promote the crystallinity, reduce the amount of Y₂O₃, and lower the cost of production, moreover, transition dominated by ⁵ D ₀-⁷ F ₄ is important for a number of practical applications.     

Synthesis and luminescent properties of BaGd2O4:Dy3+, an novel scintillating phosphor

The BaGd_2?x O₄:xDy³⁺ (0 ≤ x ≤ 0.08) phosphors were synthesized at 1,300 °C in air by the solid-state reaction route. The as-synthesized phosphors were characterized by X-ray powder diffraction, photoluminescence excitation spectra, photoluminescence (PL) spectra, X-ray excited luminescence (XEL) spectra, and thermoluminescence (TL) spectra. It is found that the quenching concentration of Dy³⁺ ions in BaGd₂O₄ host is dependent on the selected excitation wavelength. The optimal PL intensity for the investigated BaGd_2?x O₄:xDy³⁺ phosphors is found to be x = 0.01, 0.02, and 0.04, upon excitation by 234, 277, and 350 nm ultraviolet light, respectively. The energy transfer among Dy³⁺ ions upon excitation by 350 nm is confirmed to be an electric dipole–dipole interaction mechanism based on the fitting of Huang’s rule. In addition, the intensive XEL from BaGd₂O₄:Dy³⁺ phosphor is observed by the naked eyes at room temperature, and TL properties of the investigated phosphors are analyzed and discussed. All the results imply that the investigated phosphors could be a promising scintillating phosphor.     

嘌呤衍生物在葫芦［6］脲单轮烷键合固定相上的色谱行为

在反相和正相色谱模式下,研究了几种嘌呤衍生物在葫芦［6］脲单轮烷键合硅胶固定相上的高效液相色谱行为,并在反相模式下与ODS固定相进行了比较,考察了流动相中甲醇含量、流动相pH值和离子强度对嘌呤化合物保留的影响。研究结果表明:在反相模式下,嘌呤化合物与葫芦［6］脲单轮烷键合相之间存在多种相互作用,除疏水作用外,分离过程中还存在与ODS不同的色谱分离机制。在正相条件下,多作用力的色谱分离机制同样存在。葫芦［6］脲单轮烷键合相与溶质之间存在疏水、氢键、π-π和偶极-偶极等多种作用力,协同作用提高了固定相对嘌呤化合物的分离选择性。     

Emission analysis of Li6LuY(BO3)3:Tb3+,Dy3+ phosphors

In this paper, we present the synthesis and luminescence properties of Tb³⁺ and Dy³⁺-doped lithium lutetium yttrium borate (Li₆LuY(BO₃)₃) phosphors. We have adopted the well-known solid state reaction method for the synthesis of these phosphors. The emission intensities of the synthesized phosphors were found to reach their maximum, when doped by 1 mol% of Tb³⁺ and 3 mol% of Dy³⁺, beyond which emission intensities decrease due to concentration quenching. The homogeneous phase, crystalline structure and uniform morphology of the synthesized phosphors were confirmed by X-ray diffraction analysis (XRD) and Scanning electron microscopy (SEM). The X-ray and UV–VIS-induced luminescence, decay time and CIE chromaticity were investigated for the synthesized phosphors.The X-ray induced integrated light yield was measured to be 82% for Li₆LuY(BO₃)₃:Tb³⁺ (LLYBO) and 59% for Li₆LuY(BO₃)₃:Dy³⁺ of that of commercially available X-ray imaging material; Gd₂O₂S:Tb³⁺ (Gadox).LLYBO:Tb³⁺ phosphor displayed five major emission bands that correspond to ⁵D_j → ⁷F_j transitions. The 1931 Commission Internationale de l'Eclairage (CIE) chromaticity coordinates were also measured.     

Anomalous europium luminescence in LaF3

Optical spectra (absorption, emission, excitation, decay) and dielectric relaxation were measured for divalent europium and partially for ytterbium in lanthanum fluoride crystals. Optical absorption of LaF₃–Eu²⁺ contains not only asymmetric weakly structured band at 245 nm but also less intense bands at 330, 380 nm. Broadband Eu²⁺ emission at 600 nm appeared below 80 K with decay time 2.2 μs at 7.5 K. Emission at 600 nm is attributed to so-called anomalous luminescence. Bulk conductivity is directly proportional to absorption coefficient of Eu²⁺ bands. Dielectric relaxation peak of LaF₃–EuF₃ is attributed to rotation of dipoles Eu²⁺-anion vacancy. The long-wavelength absorption at 300–400 nm region are assigned to transitions from 4f⁷Eu²⁺ ground state to states of neighbouring fluorine vacancy.