Some results on linear nabla Riemann-Liouville fractional difference equations

In this paper, we establish some criteria for boundedness, stability properties, and separation of solutions of autonomous nonlinear nabla Riemann-Liouville scalar fractional difference equations. To derive these results, we prove the variation of constants formula for nabla Riemann-Liouville fractional difference equations.     

Ξ^-t quasibound state instead of ΛΛnn bound state

The coupledΛΛnn-Ξ-pnn system was studied to investigate whether the inclusion of channel coupling is able to bind theΛΛnn system.We use a separable potential three-body model of the coupledΛΛnn-Ξ-pnn system and a variational four-body calculation with realistic interactions.Our results exclude the possibility of aΛΛnn bound state by a large margin.Instead,we found aΞ-t quasibound state above theΛΛnn threshold.     

Mass distribution and skewness for passive scalar transport in pipes with polygonal and smooth cross sections

We extend our previous results characterizing the loading properties of a diffusing passive scalar advected by a laminar shear flow in ducts and channels to more general cross‐sectional shapes, including regular polygons and smoothed corner ducts originating from deformations of ellipses. For the case of the triangle and localized, cross‐wise uniform initial distributions, short‐time skewness is calculated exactly to be positive, while long‐time asymptotics shows it to be negative. Monte Carlo simulations confirm these predictions, and document the timescale for sign change. The equilateral triangle appears to be the only regular polygon with this property—all others possess positive skewness at all times. Alternatively, closed‐form flow solutions can be constructed for smooth deformations of ellipses, and illustrate how both nonzero short‐time skewness and the possibility of multiple sign switching in time is unrelated to domain corners. Exact conditions relating the median and the skewness to the mean are developed which guarantee when the sign for the skewness implies front (more mass to the right of the mean) or back (more mass to the left of the mean) “loading” properties of the evolving tracer distribution along the pipe. Short‐ and long‐time asymptotics confirm this condition, and Monte Carlo simulations verify this at all times. The simulations are also used to examine the role of corners and boundaries on the distribution for short‐time evolution of point source , as opposed to cross‐wise uniform, initial data.     

计算代数方程组孤立奇异解的符号数值方法

求解代数方程组是计算代数几何的最基本问题之一,孤立奇异解的计算则是其中最具挑战性的课题之一,在科学与工程计算中有着广泛的应用,如机器人、计算机视觉、机器学习、人工智能、运筹学、密码学和控制论等.本文结合作者的研究成果,综述了符号数值方法在计算代数系统孤立奇异解、特别是近似奇异解精化与验证方面的研究进展,并对未来的研究方向提出了展望.     

Possible Alterations of Local Gravitational Field Inside a Superconductor

We calculate the possible interaction between a superconductor and the static Earth’s gravitational fields, making use of the gravito-Maxwell formalism combined with the time-dependent Ginzburg–Landau theory. We try to estimate which are the most favorable conditions to enhance the effect, optimizing the superconductor parameters characterizing the chosen sample. We also give a qualitative comparison of the behavior of high–Tc and classical low–Tc superconductors with respect to the gravity/superfluid interplay.     

一类非线性发展方程的精确解

利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Molecularly engineered graphene surfaces for sensing applications: A review

Graphene is scientifically and commercially important because of its unique molecular structure which is monoatomic in thickness, rigorously two-dimensional and highly conjugated. Consequently, graphene exhibits exceptional electrical, optical, thermal and mechanical properties. Herein, we critically discuss the surface modification of graphene, the specific advantages that graphene-based materials can provide over other materials in sensor research and their related chemical and electrochemical properties. Furthermore, we describe the latest developments in the use of these materials for sensing technology, including chemical sensors and biosensors and their applications in security, environmental safety and diseases detection and diagnosis.     

计算富勒烯结构的新方法:曲率定理*

介绍了利用曲率定理计算富勒烯结构的方法,证明了富勒烯结构中五元环数恒为12,与传统的欧拉定理法进行了对比,凸显了曲率定理法在研究多面体结构时直观形象的特点,强调了数学方法对解决化学问题和认识化学模型的重要性。