判断矩阵的广义一致性变换及其排序的一种算法

针对不同标度构造的判断矩阵的一致性检验以及排序问题,给出了判断矩阵广义一致性变换的定义,并论证了判断矩阵经广义一致性变换后所具有的性质.通过对比分析指出本文的研究结论具有更广的应用范围,深化了对参数β的理解,给出了该参数取值范围的一个合理区间.最后,归纳出由不同标度构造的判断矩阵具体的广义一致性变换及其排序方法.     

薄油层SAGD开发蒸汽腔发育和生产指标预测

通过分析现场生产数据和数值模拟结果,将薄层稠油油藏蒸汽辅助重力驱油(SAGD)生产中蒸汽腔发育分为横向扩展和向下运移两个过程,并进行简化处理预测SAGD生产指标.联合质量守恒方程、能量守恒方程和周围地层散热模型得到一个描述蒸汽腔发育的综合表达式,该方程属于典型的第二类Volterra积分函数.通过拉普拉斯变换对Volterra积分函数进行半解析求解,最终得到不同时刻蒸汽腔发育状态.为验证模型的正确性,将模型的计算结果与CMG Stars的计算结果对比,整体误差小于5%.新模型可以方便简单地预测SAGD生产中蒸汽腔发育过程和生产动态指标,从而确定SAGD生产的极限油藏参数和合理的注采参数.     

A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space—time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained.     

New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics

Motivated by the widely used ansätz method and starting from the modified Riemann-Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.     

Classification of discrete equations linearizable by point transformation on a square lattice

We provide a complete set of linearizability conditions for nonlinear partial difference equations defined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to a Möbious transformation.     

Generating a New Higher-Dimensional Coupled Integrable Dispersionless System: Algebraic Structures,Bäcklund Transformation and Hidden Structural Symmetries

The prolongation structure methodologies of Wahlquist-Estabrook [H.D. Wahlquist and F.B. Estabrook, {J. Math. Phys.} 16 (1975) 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system. Based on the obtained prolongation structure, a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed. A Lie-Algebra representation of some hidden structural symmetries of the previous system, its Bäcklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived. In the wake of the previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new (2+1)-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation, which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention.     

Constructing infinite sequence exact solutions of nonlinear evolution equations

To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding Bäcklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.     

Lie symmetry group transformation for MHD natural convection flow of nanofluid over linearly porous stretching sheet in presence of thermal stratification

The magnetohydrodynamics(MHD) convection flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of thermal stratification are examined.The partial differential equations governing the problem under consideration are transformed by a special form of the Lie symmetry group transformations,i.e.,a one-parameter group of transformations into a system of ordinary differential equations which are numerically solved using the Runge-Kutta-Gillbased shooting method.It is concluded that the flow field,temperature,and nanoparticle volume fraction profiles are significantly influenced by the thermal stratification and the magnetic field.     

Preparation of Multilayered 1,2-Ethylene-silica Nanotubes Through a Dual-templating Approach

Multilayered 1,2-ethylene-silica nanotubes were prepared with cetyltrimethylammonium bromide(CTAB)as a template and(S)-β-citronellol(CN)as a co-structure-directing agent.For a better understanding of t...