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1.
2.
The Riemann problem for the well-known Baer–Nunziato model of two-phase flows is solved. The system consists of seven partial differential equations with nonconservative terms. The most challenging problem is that this model possesses a double eigenvalue. Although characteristic speeds coincide, the curves of composite waves associated with different characteristic fields can be still constructed. They will also be incorporated into composite wave curves to form solutions of the Riemann problem. Solutions of the Riemann problem will be constructed when initial data are in supersonic regions, subsonic regions, or in both kinds of regions. A unique solution and solutions with resonance are also obtained.  相似文献   
3.
In this paper, we investigate the existence of triple positive solutions of boundary value problems for high-order fractional differential equation at resonance with singularities by using the fixed point index theory and the Leggett-Williams theorem. The spectral theory and some new height functions are also employed to establish the existence of triple positive solutions. The nonlinearity involved is arbitrary fractional derivative, and permits singularity.  相似文献   
4.
Porphyrin derivatives are known singlet oxygen sensitizers in photodynamic therapy (PDT). Energy transfer from a class of diolefinic laser dyes (DOLDs) as energy donors to the sodium salt of meso-tetrakis (4-sulfonatophenyl) porphyrin (TPPS) as the accepter of energy would extend the range of photon harvesting down to the UV-region. Energy transfer was substantially enhanced in the presence of metallic silver nanoparticles (AgNPs), as revealed by steady-state emission spectroscopy, lifetimes, and quantum mechanics. DOLDs under investigation are 2,5-distyrylpyrazine (DSP), 1,4-bis (β-pyridyl-2 vinyl) benzene (P2VB), and 1,4 bis (2-methylstyryl) benzene (MSB) as efficient donors of intense absorption in the UV-region. AgNPs enhance the rate of energy transfer from DOLDs to TPPS via bringing donor and acceptor into close- proximity with a concomitant increase in dipole–dipole interaction between excited state donor and ground-state acceptor. The DOLDs molecular structures were optimized using the DFT/CAM-B3LYP/6-311G++ (d, p) level of theory. The calculated electronic absorption spectra for the studied DOLDs in the gaseous phase and methanol solvent were studied using the time-dependent density functional theory (TD-DFT) at M06-2X/6-311G++ (2d,2p) level. The calculated absorption/emission spectra for DSP laser dye in methanol are obtained at the TD/ M06-2X/6-311G++(2d, 2p) method. Notably, all theoretical results of the molecular structures under study highly agreed with the practical optical results. Energy transfer rate constants (kET) amid energy donor/acceptor pairs were determined by Stern-Volmer constants (KSV) and donors' lifetime measurements. The KSV values indicate an enhanced Fluorescence Resonance Energy Transfer (FRET) efficiencies in the presence of negatively charged AgNPs. The critical transfer distances Ro were determined from the spectral overlap between the emission spectrum of donor and absorption spectrum of TTPS. These outcomes propose the application of designed metal-enhanced FRET for energy-transfer-based assays and photodynamic therapy (PDT) applications.  相似文献   
5.
N2O+ ions in the X2П(0,0,0) ground state were prepared by (3+1) resonance-enhanced multiphoton ionization (REMPI) of jet-cooled N2O molecules at 360.55 nm, and then photoexcited to various vibrational levels in the B2П state over a wavelength range of 243-278 nm, followed by dissociation. The photofragment excitation (PHOFEX) spectrum was recorded by measuring the intensity of NO+ ion fragments vs excitation wavelength. The rotational constants and spin-orbit coupling were obtained by fitting the rotational structures of the vibrational bands. Thus, the contributions of highly excited vibronic levels of A2Σ+ states were distinguished from the other bands, and the original band of B2П state was verified. The series of vibrational bands in the PHOFEX spectrum were assigned to the transition of B2П(v1,v2,v3) ←X2П. The average released kinetic energy of dissociation from the various B2П(v1,v2,v3) ionic states was obtained by fitting the spreading contour of the NO+ ion peak in time-of-flight mass spectra. Dissociation mechanisms of N2O+(B2П) were proposed with the aid of the theoretical potential energy surfaces of N2O+ ions.  相似文献   
6.
李丹  薛佳丹  郑旭明 《物理化学学报》2015,30(12):2216-2223
通过共振拉曼光谱实验和量子化学计算的方法研究了4-硝基咪唑(4NI)A-带激发态衰变动力学. 对4NI的振动光谱、紫外电子吸收光谱、荧光光谱和共振拉曼光谱进行了指认. 在全活化空间自洽场法(CASSCF)/6-31G(d)计算水平下获得了单重激发态S1(nOπ*)和S2(ππ*)和势能面交叉点S1(nOπ*)/S2(ππ*)的优化几何结构和能量, 分析了A-带共振拉曼光谱的强度模式特征, 获得了短时结构动力学, 并结合全活化空间自洽场法(CASSCF)理论计算结果确定了4NI 在S2(ππ*)态衰变通道主要是S2, FC→S2, min(ππ*)→S0辐射弛豫.  相似文献   
7.
氨基甲磺酸席夫碱-邻菲啰啉镍(Ⅱ)配合物与脱氧核糖核酸相互作用的共振散射光谱在311 nm处体系有共振光散射,据此提出了一种测定脱氧核糖核酸的新方法。优化的试验条件如下:1缓冲溶液的p H为7.5;2反应温度为37.5℃;3反应时间为25 min;4配合物的用量为1.1 m L。脱氧核糖核酸的线性范围为0.53~7.87 mg·L-1,方法的检出限为0.16 mg·L-1。方法用于人工试样的分析,回收率在99.7%~102%之间,测定值的相对标准偏差(n=9)为1.7%。  相似文献   
8.
We study the response of nonlinear wave systems in bounded domains at or near resonance. There are typically two qualitatively distinct types of response which may be observed relating to whether or not higher harmonics are themselves resonant. We introduce a variety of nonlinear model problems at or near resonance and study the subsequent response. We explain how the features of this problem such as the form of nonlinearity, boundary conditions, and the nature of spectrum play a fundamental role in the qualitative nature of the response. Numerical simulations are carried out to provide further explanation and comparison with analytic approximations. The results of this study provide a better understanding of the impact and interplay between nonlinear and boundary effects and thus in turn will contribute to providing new insights into various physically motivated problems in acoustics and other settings.  相似文献   
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10.
In this paper, we study the nonexistence and existence of positive solutions for the Kirchhoff type equation with nonlinearity having prescribed asymptotic behavior. Because of the structure of our equation, our nonexistence results have some special properties, and our conditions for positive solutions are also different from the existing results.  相似文献   
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