Interaction phenomena among lump,periodic and kink wave solutions to a (3 + 1)-dimensional Sharma-Tasso-Olver-like equation

In this article, we consider a (3 + 1)-dimensional Sharma–Tasso–Olver-like (STOL) model describing dynamical propagation of nonlinear dispersive waves in inhomogeneous media. Applying Hirota's bilinear technique and a trial function, we explore nonlinear dynamical properties of basic solutions to the STOL model. We find that the fission fusion pattern occurs in the collision between the lump and kink waves, the collision between the lump and periodic waves, and the collision among the lump, kink and periodic waves, which is a novel fascinating collision pattern. We also observe that a large value of the coefficient in the periodic function produces a hybrid lump wave by fission in the collision solution. To better understand the dynamic properties of the obtained collision solutions, we plot a number of 3D and contour diagrams by choosing suitable parametric values with the aid of the computational software Maple 18.     

Bio-safety assessment of carbon quantum dots,N-doped and folic acid modified carbon quantum dots: A systemic comparison

The carbon quantum dots(CQDs) and their functionalized materials are promising in biomedical field because of their unique properties;meanwhile,a growing concern has been raised about the potential toxicity of these modified materials in biosystem.In this study,we synthesized original CQDs and two common functionalized CQDs including N-doped CQDs(NCQDs) and folic acid-modified CQDs(FACQDs),and compared the toxicity and biocompatibility with each other in vitro and in vivo.L929,C6 and normal cell MDCK were selected to detect the adverse reaction of these materials in vitro.No acute toxicity or obvious changes were noted from in vitro cytotoxicity studies with the dose of these CQD materials increasing to a high concentration at 1 mg/mL.Among these materials,the FA-CQDs show a much lower toxicity.Moreover,in vivo toxicity studies were performed on the nude mice for 15 days.The experimental animals in 10 or 15 mg/kg groups were similar with animals treated by phosphate buffer solution(PBS) after 15 days.The results of the multifa rious biochemical parameters also suggest that the functionalized products of CQDs do not influence the biological indicators at feasible concentration.Our findings in vitro and in vivo through toxicity tests demonstrate that CQDs and their modified materials are safe for future biological applications.     

A New Class of Multivariate Elliptically Contoured Distributions with Inconsistency Property

Methodology and Computing in Applied Probability - We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz...     

Stability analysis of fractional order fuzzy cellular neural networks with leakage delay and time varying delays

In this paper we investigated the stability of fractional order fuzzy cellular neural networks with leakage delay and time varying delays. Based on Lyapunov theory and applying bounded techniques of fractional calculation, sufficient criterion are established to guarantee the stability. Hybrid feedback control is applied to derive the proposed results. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.     

Templated synthesis and assembly with sustainable cellulose nanomaterial for functional nanostructure

Cellulose - Templated synthesis and assembly for nanostructured materials with tailored properties have received considerable attention. The powerful templates with predefined structures can guide...     

Surface‐Enhanced Raman Scattering Based on Controllable‐Layer Graphene Shells Directly Synthesized on Cu Nanoparticles for Molecular Detection

Graphene shells with a controllable number of layers were directly synthesized on Cu nanoparticles (CuNPs) by chemical vapor deposition (CVD) to fabricate a graphene‐encapsulated CuNPs (G/CuNPs) hybrid system for surface‐enhanced Raman scattering (SERS). The enhanced Raman spectra of adenosine and rhodamine 6G (R6G) showed that the G/CuNPs hybrid system can strongly suppress background fluorescence and increase signal‐to‐noise ratio. In four different types of SERS systems, the G/CuNPs hybrid system exhibits more efficient SERS than a transferred graphene/CuNPs hybrid system and pure CuNPs and graphene substrates. The minimum detectable concentrations of adenosine and R6G by the G/CuNPs hybrid system can be as low as 10^?8 and 10^?10 M , respectively. The excellent linear relationship between Raman intensity and analyte concentration can be used for molecular detection. The graphene shell can also effectively prevent surface oxidation of Cu nanoparticles after exposure to ambient air and thus endow the hybrid system with a long lifetime. This work provides a basis for the fabrication of novel SERS substrates.     

A mixed-finite volume element coupled with the method of characteristic fractional step difference for simulating transient behavior of semiconductor device of heat conductor and its numerical analysis

The mathematical system is formulated by four partial differential equations combined with initialboundary value conditions to describe transient behavior of three-dimensional semiconductor device with heat conduction. The first equation of an elliptic type is defined with respect to the electric potential, the successive two equations of convection dominated diffusion type are given to define the electron concentration and the hole concentration, and the fourth equation of heat conductor is for the temperature. The electric potential appears in the equations of electron concentration, hole concentration and the temperature in the formation of the intensity. A mass conservative numerical approximation of the electric potential is presented by using the mixed finite volume element, and the accuracy of computation of the electric intensity is improved one order. The method of characteristic fractional step difference is applied to discretize the other three equations, where the hyperbolic terms are approximated by a difference quotient in the characteristics and the diffusion terms are discretized by the method of fractional step difference. The computation of three-dimensional problem works efficiently by dividing it into three one-dimensional subproblems and every subproblem is solved by the method of speedup in parallel. Using a pair of different grids (coarse partition and refined partition), piecewise threefold quadratic interpolation, variation theory, multiplicative commutation rule of differential operators, mathematical induction and priori estimates theory and special technique of differential equations, we derive an optimal second order estimate in L²-norm. This numerical method is valuable in the simulation of semiconductor device theoretically and actually, and gives a powerful tool to solve the international problem presented by J. Douglas, Jr.     

Mild solution of semilinear impulsive integro‐differential evolution equation in Banach spaces

Through solving the problem step by step and by applying the method of a C₀ semigroup of operators combined with the Banach contraction theorem, we investigate the existence and uniqueness of a mild solution of semilinear impulsive integro‐differential evolution equation in Banach spaces. In addition, an explicit iterative approximation sequence of the mild solution is derived. The assumed conditions in the present theorems are weaker and more general, and the results obtained are the generalizations and improvements of some known results. Examples are also given to illustrate our main results. Copyright © 2017 John Wiley & Sons, Ltd.