Applications of F-expansion method to the coupled KdV system

An extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics is presented, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the homogeneous balance principle and the extended F-expansion, more periodic wave solutions expressed by Jacobi elliptic functions for the coupled KdV equations are derived. In the limit cases, the solitary wave solutions and the other type of travelling wave solutions for the system are also obtained.

Exact solutions for the coupled Klein-Gordon-Schrǒdinger equations using the extended F-expansion method

The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.

PSRDP:A Parallel Processing Method for Pulsar Baseband Data

To address the problem of real-time processing of ultra-wide bandwidth pulsar baseband data,we designed and implemented a pulsar baseband data processing algorithm(PSRDP)based on GPU parallel computing technology.PSRDP can perform operations such as baseband data unpacking,channel separation,coherent dedispersion,Stokes detection,phase and folding period prediction,and folding integration in GPU clusters.We tested the algorithm using the J0437-4715 pulsar baseband data generated by the CASPSR and Medusa backends of the Parkes,and the J0332+5434 pulsar baseband data generated by the self-developed backend of the Nan Shan Radio Telescope.We obtained the pulse profiles of each baseband data.Through experimental analysis,we have found that the pulse profiles generated by the PSRDP algorithm in this paper are essentially consistent with the processing results of Digital Signal Processing Software for Pulsar Astronomy(DSPSR),which verified the effectiveness of the PSRDP algorithm.Furthermore,using the same baseband data,we compared the processing speed of PSRDP with DSPSR,and the results showed that PSRDP was not slower than DSPSR in terms of speed.The theoretical and technical experience gained from the PSRDP algorithm research in this article lays a technical foundation for the real-time processing of QTT(Qi Tai radio Telescope)ultra-wide bandwidth pulsar baseband data.

A General Calculating Method of Rotor’s Torsional Stiffness Based on Stiffness Influence Coefficient

In order to develop a general calculating rotor’s torsional stiffness based on stiffness influence coefficient for different rotor assembling, the calculation method of the torsional stiffness influence coefficient of equal thickness disc is researched in this paper at first. Then the torsional stiffness influence coefficient λ of equal thickness disc is fit to a binary curved face and a calculation equation is obtained based on a large quantity of calculating data, which lays the foundation for research on a general calculating method of rotor torsional stiffness. Thirdly a simplified calculation method for equivalent stiffness diameter of stepped equal thickness disc and cone disc in the steam turbine generators is suggested. Finally a general calculating program for calculating rotor’s torsional vibration features is developed, and the torsional vibration features of a verity of steam turbine rotors are calculated for verification. The calculating results show that stiffness influence coefficient λ of equal-thickness disc depends on parameters of B and H, as well as the stiffness influence coefficient λ;and discs with complex structure can be simplified to equal-thickness discs with little error by using the method suggested in this paper;error can be controlled within 1% when equivalent diameter of stiffness is calculated by this method.

B-CONVERGENCE PROPERTIES OF GENERAL LINEAR METHODS

In this paper, for general linear methods applied to strictly dissipative initial value problem in Hilbert spaces, we prove that algebraic stability implies B-convergence, which extends and improves the existing results on Runge-Kutta methods. Specializing our results for the case of multi-step Runge-Kutta methods, a series of B-convergence results are obtained.

APPLICATIONS OF STAIR MATRICES AND THEIR GENERALIZATIONS TO ITERATIVE METHODS

Stair matrices and their generalizations are introduced. The definitions and some properties of the matrices were first given by Lu Hao. This class of matrices provide bases of matrix splittings for iterative methods. The remarkable feature of iterative methods based on the new class of matrices is that the methods are easily implemented for parallel computation. In particular, a generalization of the accelerated overrelaxation method （GAOR） is introduced. Some theories of the AOR method are extended to the generalized method to include a wide class of matrices. The convergence of the new method is derived for Hermitian positive definite matrices. Finally, some examples are given in order to show the superiority of the new method.

General displacement arch-cantilever element method for stress analysis of arch dam

Based on the general displacement method and the basic hypothesis of the trial load method, a new advanced trial load method, the general displacement arch-cantilever element method, was proposed to derive the transformation relation of displacements and loads between the surface nodes and middle plane nodes. This method considers the nodes on upstream and downstream surfaces of the arch dam to be exit nodes （master nodes）, and the middle plane nodes to be slave nodes. According to the derived displacement and load transformation matrices, the equilibrium equation treating the displacement of middle plane nodes as a basic unknown variable is transformed into one that treats the displacement of upstream and downstream nodes as a basic unknown variable. Because the surface nodes have only three degrees of freedom （DOF）, this method can be directly coupled with the finite element method （FEM）, which is used for foundation simulation to analyze the stress of the arch dam with consideration of dam-foundation interaction. Moreover, using the FEM, the nodal load of the arch dam can be easily obtained. Case studies of a typical cylindrical arch dam and the Wudongde arch dam demonstrate the robustness and feasibility of the proposed method.

FREE VIBRATION OF ANISOTROPIC RECTANGULAR PLATES BY GENERAL ANALYTICAL METHOD

According to the differential equation for transverse displacement function of anisotropic rectangular thin plates in free vibration, a general analytical solution is established. This general solution, composed of the composite solutions of trigonometric function and hyperbolic function, can satisfy the problem of arbitrary boundary conditions along four edges. The algebraic polynomial with double sine series solutions can also satisfy the problem of boundary conditions at four corners. Consequently, this general solution can be used to solve the vibration problem of anisotropic rectangular plates with arbitrary boundaries accurately. The integral constants can be determined by boundary conditions of four edges and four corners. Each natural frequency and vibration mode can be solved by the determinate of coefficient matrix from the homogeneous linear algebraic equations equal to zero. For example, a composite symmetric angle ply laminated plate with four edges clamped has been calculated and discussed.

Pulsar Candidate Classification Using a Computer Vision Method from a Combination of Convolution and Attention

Artificial intelligence methods are indispensable to identifying pulsars from large amounts of candidates.We develop a new pulsar identification system that utilizes the CoAtNet to score two-dimensional features of candidates,implements a multilayer perceptron to score one-dimensional features,and relies on logistic regression to judge the corresponding scores.In the data preprocessing stage,we perform two feature fusions separately,one for one-dimensional features and the other for two-dimensional features,which are used as inputs for the multilayer perceptron and the CoAtNet respectively.The newly developed system achieves 98.77%recall,1.07%false positive rate(FPR)and 98.85%accuracy in our GPPS test set.

Secondary Nonlinear Stability of General Linear Methods for Stiff Initial Value Problems

In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties. In this paper, we extend these results to general linear methods and to more generalproblem class Kστ. The concepts of (k, p, q)-secondary stability and (k, p. q)-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraicstability conditions while retaining the virtues of a nonlinear test problem.

Improvement and Exploration of Teaching Methods for General Entomology in Agriculture and Forestry Colleges and Universities

According to characteristics of General Entomology and existing problems in teaching process,it came up with methods and countermeasures for improving teaching General Entomology,including improving practical ability of students through enhancing all links of practice teaching,and stimulating learning interest of students through improving methods of course examination.

Parallel Implicit-Explicit General Linear Methods

High-order discretizations of partial differential equations(PDEs)necessitate high-order time integration schemes capable of handling both stiff and nonstiff operators in an efficient manner.Implicit-explicit(IMEX)integration based on general linear methods(GLMs)offers an attractive solution due to their high stage and method order,as well as excellent stability properties.The IMEX characteristic allows stiff terms to be treated implicitly and nonstiff terms to be efficiently integrated explicitly.This work develops two systematic approaches for the development of IMEX GLMs of arbitrary order with stages that can be solved in parallel.The first approach is based on diagonally implicit multi-stage integration methods(DIMSIMs)of types 3 and 4.The second is a parallel generalization of IMEX Euler and has the interesting feature that the linear stability is independent of the order of accuracy.Numerical experiments confirm the theoretical rates of convergence and reveal that the new schemes are more efficient than serial IMEX GLMs and IMEX Runge-Kutta methods.

Static Analysis of Doubly-Curved Shell Structures of Smart Materials and Arbitrary Shape Subjected to General Loads Employing Higher Order Theories and Generalized Differential Quadrature Method

The article proposes an Equivalent Single Layer(ESL)formulation for the linear static analysis of arbitrarily-shaped shell structures subjected to general surface loads and boundary conditions.A parametrization of the physical domain is provided by employing a set of curvilinear principal coordinates.The generalized blendingmethodology accounts for a distortion of the structure so that disparate geometries can be considered.Each layer of the stacking sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum.In addition,re-entrant auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model.The unknown variables are described employing a generalized displacement field and pre-determined through-the-thickness functions assessed in a unified formulation.Then,a weak assessment of the structural problem accounts for shape functions defined with an isogeometric approach starting fromthe computational grid.Ageneralizedmethodology has been proposed to define two-dimensional distributions of static surface loads.In the same way,boundary conditions with three-dimensional features are implemented along the shell edges employing linear springs.The fundamental relations are obtained from the stationary configuration of the total potential energy,and they are numerically tackled by employing the Generalized Differential Quadrature(GDQ)method,accounting for nonuniform computational grids.In the post-processing stage,an equilibrium-based recovery procedure allows the determination of the three-dimensional dispersion of the kinematic and static quantities.Some case studies have been presented,and a successful benchmark of different structural responses has been performed with respect to various refined theories.

General Expression of LRC Method in Estimation of Bridge’s Equivalent Static Wind Load

According to the relationship between load and response, the equivalent static wind load(ESWL) of a structure can be estimated by load-response correlation(LRC) method, which can be accurately used to estimate the background ESWL of a structure. The derivation of the classical expression of LRC formula is based on a specific command response at a critical position, and the ESWL distribution has only one form in this case. In this paper, a general expression of LRC formula is derived based on a specific command response at all positions. For the general expression, ESWLs can be expressed by load-response correlation coefficients, response-response correlation coefficients, RMS values of the fluctuating wind loads, and peak factor in the form of matrices. By comparing the expressions of LRC method, it was found that the classical expression was only one form of the general one. The general expression which introduces the response-response correlation coefficients provided more options for structural engineers to estimate ESWLs and offered further insights into the LRC method. Finally, a cable-stayed bridge, a rigid three span continuous girder bridge, and a suspension bridge were used to verify the correctness of the general expression of LRC method.

Application Research of Sonar Detection Method in Melting Exploration at the Bottom of Piles

Karst landforms are widely distributed in China,and are most common in Yunnan,Guizhou and Guangxi.If the development of karst caves at the bottom of the piles cannot be accurately ascertained before the construction of bridge pile foundations,accidents such as hole collapse,slurry leakage,and drill sticking will easily occur.In this paper,the principle and method of sonar detection for detecting karst caves at the bottom of bridge piles was introduced,and the sonar detection data and the cave situation at the bottom of the pile during the construction process in combination with the case of Yunnan Zhenguo Highway Project was analyzed,which verifies the practicability and reliability of sonar detection method reliability.

On the feasibility of variable separation method based on Hamiltonian system for plane magnetoelectroelastic solids

The eigenvalue problem of an infinite-dimensional Hamiltonian operator appearing in the isotropic plane magnetoelectroelastic solids is studied. First, all the eigenvalues and their eigenfunctions in a rectangular domain are solved directly. Then the completeness of the eigenfunction system is proved, which offers a theoretic guarantee of the feasibility of variable separation method based on a Hamiltonian system for isotropic plane magnetoelectroelastic solids. Finally, the general solution for the equation in the rectangular domain is obtained by using the symplectic Fourier expansion method.

EXACT SOLUTIONS FOR GENERAL VARIABLE-COEFFICIENT KdV EQUATION

By asing the nonclassical method of symmetry reductions, the exact solutions for general variable coefficient KdV equation with dissipative loss and nonuniformity terms are obtained. When the dissipative loss and nonuniformity terms don't exist, the multisoliton solutions are found and the corresponding Painleve II type equation for the variable coefficient KdV equation is given.

A general solution for Stokes flow and its application to the problem of a rigid plate translating in a fluid

A general solution for 3D Stokes flow is given which is different from, and more compact than the exist ing ones and more compact than them in that it involves only two scalar harmonic functions. The general solution deduced is combined with the potential theory method to study the Stokes flow induced by a rigid plate of arbitrary shape trans lating along the direction normal to it in an unbounded fluid. The boundary integral equation governing this problem is derived. When the plate is elliptic, exact analytical results are obtained not only for the drag force but also for the ve locity distributions. These results include and complete the ones available for a circular plate. Numerical examples are provided to illustrate the main results for circular and ellip tic plates. In particular, the elliptic eccentricity of a plate is shown to exhibit significant influences.

GENERAL DECAY FOR A QUASILINEAR SYSTEM OF VISCOELASTIC EQUATIONS WITH NONLINEAR DAMPING

In this paper, we consider a system of coupled quasilinear viscoelastic equa- tions with nonlinear damping. We use the perturbed energy method to show the general decay rate estimates of energy of solutions, which extends some existing results concerning a general decay for a single equation to the case of system, and a nonlinear system of viscoelastic wave equations to a quasilinear system.

Optimization of a precise integration method for seismic modeling based on graphic processing unit

General purpose graphic processing unit （GPU） calculation technology is gradually widely used in various fields. Its mode of single instruction, multiple threads is capable of seismic numerical simulation which has a huge quantity of data and calculation steps. In this study, we introduce a GPU-based parallel calculation method of a precise integration method （PIM） for seismic forward modeling. Compared with CPU single-core calculation, GPU parallel calculating perfectly keeps the features of PIM, which has small bandwidth, high accuracy and capability of modeling complex substructures, and GPU calculation brings high computational efficiency, which means that high-performing GPU parallel calculation can make seismic forward modeling closer to real seismic records.