基于张正友标定算法的内参数线性与非线性解算

基于张正友摄像机标定算法,从棋盘空间平面与像方平面的单应性关系出发,首先利用最小二乘方法解算单应性矩阵,然后通过单应性矩阵基本约束条件推导出两个约束方程,从而进行线性与非线性方式解算摄像机内参数。最后采用实际图像数据进行实验,验证了线性与非线性两种解算方法的可行性。

Using Symbolic Computation to Exactly Solve the Integrable Broer-Kaup Equations in （2＋1）-Dimensional Spaces

The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.

Computer Algebra and Solutions to the Karamoto-Sivashinsky Equation

The method of Riccati equation is extended for constructing travelling wave solutions of nonlinear partial differential equations. It is applied to solve the Karamoto-Sivashinsky equation and then its more new explicit solutions have been obtained. From the results given in this paper, one can see the computer algebra plays an important role in this procedure.

New Exact Travelling Wave Solutions for Generalized Zakharov-Kuzentsov EquationsUsing General Projective Riccati Equation Method

Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer algebraicsystem, we consider the generalized Zakharov-Kuzentsov equation with nonlinear terms of any order. As a result, wecan not only successfully recover the previously known travelling wave solutions found by existing various tanh methodsand other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shapedsolitons, bell-shaped solitons, singular solitons, and periodic solutions.

On New Invariant Solutions of Generalized Fokker-Planck Equation

The generalized one-dimensional Fokker-Planck equation is analyzed via potential symmetry method and the invariant solutions under potential symmetries are obtained. Among those solutions, some are new and first reported.

Direct Approach to Construct the Periodic Wave Solutions for Two Nonlinear Evolution Equations

With symbolic computation, the Hirota method and Riemann theta function are employed to directly construct the periodic wave solutions for the Hirota-Satsuma equation for shallow water waves and Boiti-Leon-Manna- Pempinelli equation. Then, the corresponding figures of the periodic wave solutions are given. Fhrthermore, it is shown that the known soliton solutions can be reduced from the periodic wave solutions.

Some Special Solutions of Three Nonlinear Lattices

Some soliton solutions and periodic solutions of hybrid lattice, discretized mKdV lattice, and modified Volterra lattice have been obtained by introducing a new method. This approach allows us to directly construct some explicit exact solutions for polynomial nonlinear differential-difference equations.

Influence of Pipe-Diameter on Water Hammer Phenomenon

The influence of parameters pertaining to the confinant structure on water hammer had been less studied than those relative to the fluid. One of them is the inner pipe-diameter, a basic structural-parameter that makes its influence in essential hydraulic topics such as head loss, in pipelines. In this paper, the objective is to analyze the inner-diameter influence on water hammer phenomenon. An analytical algorithm for solving the unsteady-one-dimensional water hammer model had been applied. It had allowed estimating the instantaneous head at any point of a single pipeline. The model was solved by mean of the Laplace＇s Transformed application and the anti-transforming procedure into the complex field. To determinate the influence of internal-diameter conduit on the pressure oscillation, four distinct inside-diameter values were introduced into the solution, successively. The first overpressure-peak at each case was tabulated along with the corresponding inner^liameter and a mathematical relation had been founded. The obtained results show a close dependence between both, over-pressure peaks and internal-pipe diameter. It was founded that this dependence is given in terms of a non-linear relation between them. It was further founded that the wave frequency is sensitive to the variation of the pipe-diameter.

Global Optimization Algorithm for Nonlinear Sum of Ratios Problems

In this paper, a global optimization algorithm is proposed for nonlinear sum of ratios problem （P）. The algorithm works by globally solving problem （P1） that is equivalent to problem （P）, by utilizing linearization technique a linear relaxation programming of the （P1） is then obtained. The proposed algorithm is convergent to the global minimum of （P1） through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming. Numerical results indicate that the proposed algorithm is feasible and can be used to globally solve nonlinear sum of ratios problems （P）.

Pyrolysis Characteristics and Kinetics of Municipal Solid Waste

Based on a systemic survey, the pyrolysis characteristics and apparent kinetics of the municipal solid waste （ MSW） under different conditions were researched using a special pyrolysis reactor, which could overcome the disadvantage of thermo-gravimetric analyzer. The thermal decomposition behaviour of MSW was investigated using thermo-gravimetric （ TG ） analysis at rates of 4.8,6.6,8.4, 12.0 and 13. 2 K/min. The pyrolysis characteristics of MSW were also studied in different function districts. The pyrolysis of MSW is a complex reaction process and three main stages are found according to the results. The first stage represents the degradation of cellulose and hemicellulose, with the maximum degradation rate occuring at 150℃ -200 ℃： the second stage represents dehydrochlorination and depolymerization of intermediate products and the differential thermogravimetric （ DTG ） curves have shoulder peaks at about 300℃： the third stage is the decomposition of the residual big molecular organic substance and lignin at 400 ℃- 600 ℃. Within the range of given experimental conditions, the results of non-linear fitting algorithm and experiment are in agreement with each other and the correlation coefficients are over0. 99. The kinetic characteristics are concerned with the material component and heating rate. The activation energy of reaction decreases with the increase of heating rate.

Iterative Construction of Solutions to Nonlinear Equations of Strongly Accretive Operators in Banach Spaces *

In this paper, we investigate the Ishikawa iteration process in a p -uniformly smooth Banach space X . Motivated by Deng and Tan and Xu , we prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator from X to X , or to the unique fixed point of T when T is a Lipschitzian and strictly pseudo contractive mapping from a bounded closed convex subset C of X into itself. Our results improve and extend Theorem 4.1 and 4.2 of Tan and Xu by removing the restrion lim n→∞β n=0 or lim n→∞α n= lim n→∞β n=0 in their theorems. These also extend Theorems 1 and 2 of Deng to the p -uniformly smooth Banach space setting.

Solution and Coupled Minimal-Maximal Quasi-Solutions of Nonlinear Non-monotone Operator Equations in Banach Spaces

Abstrac In this paper, we discuss the existence of the solution and coupled minimal and maximal quasi-solutions for nonlinear non-monotone operator equation x = A(x, x), improved and generalized many relevant results.

EXISTENCE,MULTIPLICITY AND STABILITY RESULTS FOR POSITIVE SOLUTIONS OF NONLINEAR p-LAPLACIAN EQUATIONS

This paper studies the existence of positive solutions of the Dirichlet problem for the nonlinear equation involving p-Laplacian operator: -△pu = λf(u) on a bounded smooth domain Ω in Rn. The authors extend part of the Crandall-Rabinowitz bifurcation theory to this problem. Typical examples are checked in detail and multiplicity of the solutions are illustrated. Then the stability for the associated parabolic equation is considered and a Fujita-type result is presented.

BLOW UP OF SOLUTIONS TO THE CAUCHY PROBLEM FOR NONLINEAR WAVE EQUATIONS

The author proves blow up of solutions to the Cauchy problem of certain nonlinear equations and, also, estimates the time when the blow up occurs.

A Dwindling Filter Line Search Algorithm for Nonlinear Equality Constrained Optimization

This paper proposes a dwindling filter line search algorithm for nonlinear equality constrained optimization. A dwindling filter, which is a modification of the traditional filter, is employed in the algorithm. The envelope of the dwindling filter becomes thinner and thinner as the step size approaches zero. This new algorithm has more flexibility for the acceptance of the trial step and requires less computational costs compared with traditional filter algorithm. The global and local convergence of the proposed algorithm are given under some reasonable conditions. The numerical experiments are reported to show the effectiveness of the dwindling filter algorithm.

ON THE NUMBER OF FIXED POINTS OF NONLINEAR OPERATORS AND APPLICATIONS

In this paper, the famous Amann three-solution theorem is generalized. Multiplicity question of fixed points for nonlinear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least six distinct fixed points of nonlinear operators is proved. The theoretical results are then applied to nonlinear system of Hammerstein integral equations.

A New Expanded Method for Solving Nonlinear Differential-difference Equation

A new expanded approach is presented to find exact solutions of nonlinear differential-difference equations. As its application, the soliton solutions and periodic solutions of a lattice equation are obtained.

The Existence of Three Positive Solutions for a Class of Nonlinear Three-Point Boundary Value Problem with p-Laplacian

This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, sufficient condition for the existence of at least three positive solutions to the nonlinear singular three-point boundary value problem is established

A priori estimates for classical solutions of fully nonlinear elliptic equations

For the fully nonlinear uniformly elliptic equation F(D2u) = 0, it is well known that the viscosity solutions are C2,α if the nonlinear operator F is convex (or concave). In this paper, we study the classical solutions for the fully nonlinear elliptic equation where the nonlinear operator F is locally C1,β a.e. for any 0 < β < 1. We will prove that the classical solutions u are C2,α. Moreover, the C2,α norm of u depends on n,F and the continuous modulus of D2u.

Multi-objective optimization for deepwater dynamic umbilical installation analysis

We suggest a method of multi-objective optimization based on approximation model for dynamic umbilical installation. The optimization aims to find out the most cost effective size, quantity and location of buoyancy modules for umbilical installation while maintaining structural safety. The approximation model is constructed by the design of experiment (DOE) sampling and is utilized to solve the problem of time-consuming analyses. The non-linear dynamic analyses considering environmental loadings are executed on these sample points from DOE. Non-dominated Sorting Genetic Algorithm (NSGA-II) is employed to obtain the Pareto solution set through an evolutionary optimization process. Intuitionist fuzzy set theory is applied for selecting the best compromise solution from Pareto set. The optimization results indicate this optimization strategy with approximation model and multiple attribute decision-making method is valid, and provide the optimal deployment method for deepwater dynamic umbilical buoyancy modules.