Let T be pure subnormal operator. In this paper necessary and sufficiert conditions that T=N+K are given,where N is normal, K is quasinormal and NK=KN.
There should be high resolution demand that is better than 1000 DPI(dot per inch) for high precision image scanning system. This paper introduced the two-level computer controlled system that consisted of LS-3500 film...There should be high resolution demand that is better than 1000 DPI(dot per inch) for high precision image scanning system. This paper introduced the two-level computer controlled system that consisted of LS-3500 film scanner, AST386/33 monitoring control level and Intel 8031 single chip computer that is used as DDC level. The formula for scanning image data processing and methods of statistic parameters calculating are described.展开更多
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 explici...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.展开更多
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...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.展开更多
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 alg...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.展开更多
Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a （2＋ l）-dimensional cubic nonlinear Schrodinger （NLS） equation and its corresponding cyl...Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a （2＋ l）-dimensional cubic nonlinear Schrodinger （NLS） equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution.展开更多
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 repor...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.展开更多
In this paper,based on the forms and structures of Wronskian solutions to soliton equations,a Wronskianform expansion method is presented to find a new class of interaction solutions to the Kadomtsev-Petviashvili equa...In this paper,based on the forms and structures of Wronskian solutions to soliton equations,a Wronskianform expansion method is presented to find a new class of interaction solutions to the Kadomtsev-Petviashvili equation.One characteristic of the method is that Wronskian entries do not satisfy linear partial differential equation.展开更多
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- Pemp...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.展开更多
In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ ...In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ = M∨N） when nest M or N is a countable nest, or S belongs to algφ^-1 when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T = US where S ∈ DN^-1 and U is unitary as N be a countable nest.展开更多
By attacking the linear programming problems from their dual side,a new general algorithm for linear programming is developed.At each iteration,the algorithm finds a feasible descent search direction by handling a lea...By attacking the linear programming problems from their dual side,a new general algorithm for linear programming is developed.At each iteration,the algorithm finds a feasible descent search direction by handling a least square problem associated with the dual system,using QR decomposition technique.The new method is a combination of pivot method and interior-point method.It in fact not only reduces the possibility of difficulty arising from degeneracy,but also has the same advantages as pivot method in warm-start to resolve linear programming problems.Numerical results of a group of randomly constructed problems are very encouraging.展开更多
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 so...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.展开更多
The cone theorem and the fixed point index are used to investigate the positive solution of singular superlinear boundary value problem for a fourth order nonlinear differential equation.
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...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.展开更多
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 linearizat...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）.展开更多
Genetic algorithms (GAs) employ the evolutionary process of Darwin’s nature selection theory to find the solutions of optimization problems. In this paper, an implementation of genetic algorithm is put forward to sol...Genetic algorithms (GAs) employ the evolutionary process of Darwin’s nature selection theory to find the solutions of optimization problems. In this paper, an implementation of genetic algorithm is put forward to solve a classical transportation problem, namely the Hitchcock’s Transportation Problem (HTP), and the GA is improved to search for all optimal solutions and identify them automatically. The algorithm is coded with C++ and validated by numerical examples. The computational results show that the algorithm is efficient for solving the Hitchcock’s transportation problem.展开更多
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 ...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.展开更多
As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many o...As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.展开更多
文摘Let T be pure subnormal operator. In this paper necessary and sufficiert conditions that T=N+K are given,where N is normal, K is quasinormal and NK=KN.
文摘There should be high resolution demand that is better than 1000 DPI(dot per inch) for high precision image scanning system. This paper introduced the two-level computer controlled system that consisted of LS-3500 film scanner, AST386/33 monitoring control level and Intel 8031 single chip computer that is used as DDC level. The formula for scanning image data processing and methods of statistic parameters calculating are described.
文摘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.
文摘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.
基金The project supported by National Natural Science Foundation of China under Grant No.10072013the National Key Basic Research Development Program under Grant No.G1998030600
文摘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.
基金The project supported by K.C. Wong Magna Fund in Ningbo University, National Natural Science Foundation of China under Grant Nos. 10747141 and 10735030；Zhejiang Provincial Natural Science Foundations of China under Grant No. 605408；Ningbo Natural Science Foundation under Grant Nos. 2007A610049 and 2006A610093；National Basic Research Program of China （973 Program 2007CB814800）；Program for Changjiang Scholars and Innovative Research Team in University （IRTO734）
文摘Making use of the direct method proposed by Lou et al. and symbolic computation, finite symmetry transformation groups for a （2＋ l）-dimensional cubic nonlinear Schrodinger （NLS） equation and its corresponding cylindrical NLS equations are presented. Nine related linear independent infinitesimal generators can be obtained from the finite symmetry transformation groups by restricting the arbitrary constants in infinitesimal forms. Some exact solutions are derived from a simple travelling wave solution.
文摘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.
基金Supported by the Young Teachers Science Foundation of Beijing University of Civil Engineering and Architecture under Grant No.100602707
文摘In this paper,based on the forms and structures of Wronskian solutions to soliton equations,a Wronskianform expansion method is presented to find a new class of interaction solutions to the Kadomtsev-Petviashvili equation.One characteristic of the method is that Wronskian entries do not satisfy linear partial differential equation.
基金Supported by the National Natural Science Foundation of China under Grant No.60772023the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.BUAA-SKLSDE-09KF-04+1 种基金Beijing University of Aeronautics and Astronautics,by the National Basic Research Program of China (973 Program) under Grant No.2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos.20060006024 and 200800130006,Chinese Ministry of Education
文摘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.
基金Supported by the National Science Foundation of China(90205019)
文摘In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ = M∨N） when nest M or N is a countable nest, or S belongs to algφ^-1 when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T = US where S ∈ DN^-1 and U is unitary as N be a countable nest.
文摘By attacking the linear programming problems from their dual side,a new general algorithm for linear programming is developed.At each iteration,the algorithm finds a feasible descent search direction by handling a least square problem associated with the dual system,using QR decomposition technique.The new method is a combination of pivot method and interior-point method.It in fact not only reduces the possibility of difficulty arising from degeneracy,but also has the same advantages as pivot method in warm-start to resolve linear programming problems.Numerical results of a group of randomly constructed problems are very encouraging.
基金中国博士后科学基金，国家重点基础研究发展计划(973计划)，Doctor Start-up Foundation of Liaoning Province，Science Research Plan of Liaoning Education Bureau
文摘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.
基金Sponsored by the National Natural Science Foundation of China (Grant No.10271034).
文摘The cone theorem and the fixed point index are used to investigate the positive solution of singular superlinear boundary value problem for a fourth order nonlinear differential equation.
文摘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.
基金Foundation item： Supported by the National Natural Science Foundation of China（10671057） Supported by the Natural Science Foundation of Henan Institute of Science and Technology（06054）
文摘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）.
文摘Genetic algorithms (GAs) employ the evolutionary process of Darwin’s nature selection theory to find the solutions of optimization problems. In this paper, an implementation of genetic algorithm is put forward to solve a classical transportation problem, namely the Hitchcock’s Transportation Problem (HTP), and the GA is improved to search for all optimal solutions and identify them automatically. The algorithm is coded with C++ and validated by numerical examples. The computational results show that the algorithm is efficient for solving the Hitchcock’s transportation problem.
基金Supported by National Natural Science Foundation of China( No. 50378061).
文摘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.
基金Supported by National Natural Science Foundation of China (No.10871144)the Seed Foundation of Tianjin University (No.60302023)
文摘As a basic mathematical structure,the system of inequalities over symmetric cones and its solution can provide an effective method for solving the startup problem of interior point method which is used to solve many optimization problems.In this paper,a non-interior continuation algorithm is proposed for solving the system of inequalities under the order induced by a symmetric cone.It is shown that the proposed algorithm is globally convergent and well-defined.Moreover,it can start from any point and only needs to solve one system of linear equations at most at each iteration.Under suitable assumptions,global linear and local quadratic convergence is established with Euclidean Jordan algebras.Numerical results indicate that the algorithm is efficient.The systems of random linear inequalities were tested over the second-order cones with sizes of 10,100,,1 000 respectively and the problems of each size were generated randomly for 10 times.The average iterative numbers show that the proposed algorithm can generate a solution at one step for solving the given linear class of problems with random initializations.It seems possible that the continuation algorithm can solve larger scale systems of linear inequalities over the secondorder cones quickly.Moreover,a system of nonlinear inequalities was also tested over Cartesian product of two simple second-order cones,and numerical results indicate that the proposed algorithm can deal with the nonlinear cases.
