The Interplay of Photophysical Properties in Carbazole Fluorescent Oligomers

The photophysical properties and the organic synthesis using effective palladium‐catalyzed Suzuki coupling reactions from a series of carbazole derivatives are described and the relationships of the donor and acceptor groups are also investigated. The purification of the materials and its applications along with the corresponding photo‐physical characterizations were presented. With the advantages gained from 2D‐COSY spectra, which provide more correlated information between immediate atoms than ¹H‐NMR spectra and a series of further investigations were undertaken including powder X‐ray diffraction analysis, Infrared and Raman spectroscopy, constructing the composition conformation and chemical structure of the materials is more easily to achieve. Additionally, the optimized structure of the minimized energy geometries and spatial distributions of carbazole derivatives was calculated using density functional theory (DFT), new materials can be developed and designed selectively based on the method proposed in this work.     

Algorithms and Convergence Theorems for Mixed Equilibrium Problems in Hilbert Spaces

In this article, we study mixed equilibrium problems, and present algorithms and convergence theorems for the proposed algorithms, like proximal gradient method, Tikhonov regularization method, Mann’s type method, conjugate gradient method. As application, we study minimization problems.     

Steady-state solutions of a reaction–diffusion system arising from intraguild predation and internal storage

Intraguild predation is added to a mathematical model of competition between two species for a single nutrient with internal storage in the unstirred chemostat. At first, we established the sharp a priori estimates for nonnegative solutions of the system, which assure that all of nonnegative solutions belong to a special cone. The selection of this special cone enables us to apply the topological fixed point theorems in cones to establish the existence of positive solutions. Secondly, existence for positive steady state solutions of intraguild prey and intraguild predator is established in terms of the principal eigenvalues of associated nonlinear eigenvalue problems by means of the degree theory in the special cone. It turns out that positive steady state solutions exist when the associated principal eigenvalues are both negative or both positive.     

星型关联代数与星式M?bius反演

本文借助于非标准组合论中的星型有限结构,定义了星型关联代数,从而建立了局部星型有限集上的M?bius反演.由此在一个超结构扩大中,在非标准意义下,将M?bius反演推广到局部标准无限半序集上.文中几例显示,在非标准领域里,本文结果为探索离散数学与连续数学的某些反演的统一性提供了一种可能途径.     

Mesogenic properties of cycloalkylmethyl 4-(4'-octoxybiphenyl-4-carbonyloxy)benzoate

Four analogous compounds, cyclohexylmethyl 4-(4'-octoxybiphenyl-4-carbonyloxy)benzoate (2), cyclopentylmethyl 4-(4'-octoxybiphenyl-4-carbonyloxy)benzoate (3), cyclobutylmethyl 4-(4'-octoxylbiphenyl-4-carbonyloxy)benzoate (4) and cyclopropylmethyl 4-(4'-octoxylbiphenyl-4-carbonyloxy)benzoate (5) were prepared. They all exhibit SmA, SmC and SmX phases.     

The predissociation dynamics of the Ã1A″ state of HCN and DCN

Level-resolved lifetimes of the first excited state (ùA″) of hydrogen cyanide (HCN and DCN). obtained using the technique of vacuum ultraviole     

Evidence for replacing zinc with cobalt and iron atoms in epitaxial ZnO:CoFe-diluted magnetic semiconductors

The structure and local environment of ZnO:CoFe were investigated. An epitaxial structure of ZnO thin film doped with CoFe on Al₂O₃ substrate was confirmed by XRD. By fitting the Zn EXAFS spectra, the bond distances and coordination numbers of Zn atoms in the ZnO:CoFe show that Co and Fe ions replace some positions of zinc atoms. The XANES study of Zn and O also show that CoFe cluster formation in this system can be excluded.     

On the use of the reach-back characteristics method for calculation of dispersion

The Holly-Preissmann two-point finite difference scheme (HP method) has been popularly used for solving the advection equation. The key idea of this scheme is to solve the dependent variable (i.e. the concentration for the pollutant transport problem) by the method of characteristics with the use of cubic interpolation on the spatial axis. The interpolating polynomials of higher order are constructed by use of the dependent variable and its derivatives at two adjacent grid points. In this paper a new interpolating technique is introduced for incorporation with the Holly-Preissmann two-point method. The new method is denoted herein as the Holly-Preissmann reach-back method (HPRB) and allows the characteristics to project back several time steps beyond the present time level. Through stability analyses it has been observed that the increase of the reach-back time step numbers for the characteristics indeed reduces the numerical damping and dispersive phenomena. A schematic model has been constructed to demonstrate the merits of this new technique for the calculation of the pure advection and dispersion equations. Numerical experiments and comparisons with analytical solutions which support and demonstrate this new technique are presented.     

Generalized fibonacci cubes are mostly hamiltonian

The Hamiltonian problem is to determine whether a graph contains a spanning (Hamiltonian) path or cycle. Here we study the Hamiltonian problem for the generalized Fibonacci cubes, which are a new family of graphs that have applications in interconnection topologies [J. Liuand W.-J. Hsu, ?Distributed Algorithms for Shortest-Path, Deadlock-Free Routing and Broadcasting in a Class of Interconnection Topologies,”? International Parallel Processing Symposium (1992)]. We show that each member of this family contains a Hamiltonian path. Furthermore, we also characterize the members of this family that contain a Hamiltonian cycle.