THE PARALLEL MULTISPLITTING METHOD FOR CONSISTENT SYMMETRIC POSITIVE(SEMI-)DEFINITE SYSTEMS

Main resultsTheorem 1 Let A be an n×n symmetric positive semidefinite matrix and let

Wind-induced responses of super-large cooling towers

Traditional gust load factor(GLF)method,inertial wind load(IWL)method and tri-component method(LRC+IWL)cannot accurately analyze the wind-induced responses of super-large cooling towers,so the real combination formulas of fluctuating wind-induced responses and equivalent static wind loads(ESWLSs)were derived based on structural dynamics and random vibration theory.The consistent coupled method(CCM)was presented to compensate the coupled term between background and resonant response.Taking the super-large cooling tower(H=215 m)of nuclear power plant in Jiangxi Province,China,which is the highest and largest in China,as the example,based on modified equivalent beam-net design method,the aero-elastic model for simultaneous pressure and vibration measurement of super-large cooling tower is firstly carried out.Then,combining wind tunnel test and CCM,the effects of self-excited force on the surface pressures and wind-induced responses are discussed,and the wind-induced response characteristics of background component,resonant component,coupled term between background and resonant response,fluctuating responses,and wind vibration coefficients are discussed.It can be concluded that wind-induced response mechanism must be understood to direct the wind resistant design for super-large cooling towers.

Solution of the Energy Level of Hydrogen-Like Atom for the Debye Shielding Potential

The first-order revision and the approximation analytical formula of the energy levels for hydrogen-like atoms under the condition of Debye shielding potential are achieved by means of the Rayleigh–Schr?dinger perturbation theory; meanwhile, the corresponding recurrence relations are obtained from the use of the solution of power series. Based on the above solutions and with the use of energy consistent method the equivalent value of second-order reversion under the condition of Debye shielding potential is produced as well and the result is compared with the data obtained by the numerical method. Besides, the critical bond-state and corresponding cut-off conditions are discussed.

Consistent Burgers equation expansion method and its applications to high-dimensional Burgers-type equations

In this paper,a novel method,named the consistent Burgers equation expansion(CBEE)method,is proposed to solve nonlinear evolution equations(NLEEs)by the celebrated Burgers equation.NLEEs are said to be CBEE solvable if they are satisfied by the CBEE method.In order to verify the effectiveness of the CBEE method,we take(2+1)-dimensional Burgers equation as an example.From the(1+1)-dimensional Burgers equation,many new explicit solutions of the(2+1)-dimensional Burgers equation are derived.The obtained results illustrate that this method can be effectively extended to other NLEEs.

OPTIMUM MODIFIED EXTRAPOLATED JACOBI METHOD FOR CONSISTENTLY ORDERED MATRICES

This paper is concerlled with the investigation of a twrvparametric linear stationary iterative method, called Modified Extrapolated Jacobi (MEJ) method, for solving linear systems Ax = b, where A is a nonsingular consistently ordered 2-cyclic matrix. We give sufficient and necessary conditions for strong convergence of the MEJ method and we determine the optimum extrapolation parameters and the optimum spectral radius of it, in the case where all the efornvalues of the block Jacobi iteration matrir associated with A are real. In the last section, we compare the MEJ with other known methods.

consistent Riccati expansion fractional partial differential equation Riccati equation modified Riemann–Liouville fractional derivative exact solution

In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie＇s modified Riemann–Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada–Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed.

Interaction Solutions for (1+1)-Dimensional Higher-Order Broer–Kaup System

The(1+1)-dimensional higher-order Broer–Kaup(HBK) system is studied by consistent tanh expansion(CTE) method in this paper. It is proved that the HBK system is CTE solvable, and some exact interaction solutions among different nonlinear excitations such as solitons, rational waves, periodic waves, corresponding images are explicitly given.

Various Kinds Waves and Solitons Interaction Solutions of Boussinesq Equation Describing Ultrashort Pulse in Quadratic Nonlinear Medium

The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.

Interaction Behaviours Between Solitons and Cnoidal Periodic Waves for (2＋1)-Dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada Equation

The consistent tanh expansion(CTE) method is employed to the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada(CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explicitly obtained. Concretely, we discuss a special kind of interaction solution in the form of tanh functions and Jacobian elliptic functions in both analytical and graphical ways. The results show that the profiles of the soliton-cnoidal periodic wave interaction solutions can be designed by choosing different values of wave parameters.

Nonlocal Symmetries and Interaction Solutions for Potential Kadomtsev-Petviashvili Equation

The nonlocal symmetry for the potential Kadomtsev-Petviashvili(pKP)equation is derived by the truncated Painleve analysis.The nonlocal symmetry is localized to the Lie point symmetry by introducing the auxiliary dependent variable.Thanks to localization process,the finite symmetry transformations related with the nonlocal symmetry are obtained by solving the prolonged systems.The inelastic interactions among the multiple-front waves of the pKP equation are generated from the finite symmetry transformations.Based on the consistent tanh expansion method,a nonauto-B(a|¨)cklund transformation(BT)theorem of the pKP equation is constructed.We can get many new types of interaction solutions because of the existence of an arbitrary function in the nonauto-BT theorem.Some special interaction solutions are investigated both in analytical and graphical ways.

New interaction solutions and nonlocal symmetry of an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form

The nonlocal symmetry is derived for an equation combining the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form from the truncated Painlevéexpansion method.The nonlocal symmetries are localized to the Lie point symmetry by introducing new auxiliary dependent variables.The finite symmetry transformation and the Lie point symmetry for the prolonged system are solved directly.Many new interaction solutions among soliton and other types of interaction solutions for the modified Calogero–Bogoyavlenskii–Schiff equation with its negative-order form can be obtained from the consistent condition of the consistent tanh expansion method by selecting the proper arbitrary constants.