The method of integrating factors is used to study the conservation laws of the Herglotz type Birkhoffian systems in this paper.Firstly,the definition of the integrating factors of the Herglotz type Birkhoffian system...The method of integrating factors is used to study the conservation laws of the Herglotz type Birkhoffian systems in this paper.Firstly,the definition of the integrating factors of the Herglotz type Birkhoffian systems is given.Secondly,the relationship between the integrating factors and conservation laws is studied,and the conservation theorems of Herglotz type Birkhoff's equations and their inverse theorems are established.Thirdly,two types of generalized Killing equations for calculating integrating factors are given.Finally,as an example,a linear damped oscillator is taken.This example can be transformed into a Herglotz type Birkhoffian system.The resulting conservation theorems are used to find the conserved quantities for this example.展开更多
Connection methods are essential for integrating environmental factors with machine learning models for landslide susceptibility assessments.However,current research does not consider the different characteristics of ...Connection methods are essential for integrating environmental factors with machine learning models for landslide susceptibility assessments.However,current research does not consider the different characteristics of continuity and discreteness within environmental factors and therefore does not analyze the suitability of various connection methods for different factor types.Moreover,the applicability of connection methods remains unclear when slope units are used as the basic assessment units.This study employed slope units as mapping units.The original data of 15 environmental factors,including 12 continuous and three discrete factors,and two connection methods,i.e.,frequency ratio(FR)and modified FR(MFR),were separately used to construct the input datasets for landslide susceptibility modeling.The performance of four widely used machine learning models,random forest(RF),support vector machine(SVM),logistic regression(LR),and multilayer perceptron(MLP),was analyzed to evaluate the suitability of the connection methods for landslide susceptibility mapping.The results show that,in contrast to the decision tree-based RF model,the use of different connection methods for different factor types significantly influences the results of nontree models,including SVM,MLP,and LR.SVM model is the most sensitive to factor types and connection methods.When the MFR is used as the connection method,it improves the mapping results,especially for the SVM model.This shows that it is essential to consider the different characteristics of the data and select an appropriate environmental factor connection strategy to increase the effectiveness of landslide susceptibility evaluation.Furthermore,this study explored the role of connective methods from a sample distribution perspective,providing a theoretical foundation for the more rational and effective integration of environmental factors.展开更多
In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical syst...In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.展开更多
The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integ...The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.展开更多
In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of ...In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of integrating factors is given for the system. The necessary conditions for the existence of the conserved quantity for the system are studied. The conservation theorem and its inverse for the system are established. Finally, an example is given to illustrate the application of the results.展开更多
The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are g...The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.展开更多
The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF me...The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.展开更多
In order to improve the precision of mining subsidence prediction, a mathematical model using Support Vector Machine （SVM） was established to calculate the displacement factor. The study is based on a comprehensive ...In order to improve the precision of mining subsidence prediction, a mathematical model using Support Vector Machine （SVM） was established to calculate the displacement factor. The study is based on a comprehensive analysis of factors affecting the displacement factor, such as mechanical properties of the cover rock, the ratio of mining depth to seam thickness, dip angle of the coal seam and the thickness of loose layer. Data of 63 typical observation stations were used as a training and testing sample set. A SVM regression model of the displacement factor and the factors affecting it was established with a kernel function, an insensitive loss factor and a properly selected penalty factor. Given an accurate calculation algorithm for testing and analysis, the results show that an SVM regression model can calcu- late displacement factor precisely and reliable precision can be obtained which meets engineering requirements. The experimental results show that the method to calculation of the displacement factor, based on the SVM method, is feasible. The many factors affecting the displacement factor can be consid- ered with this method. The research provides an efficient and accurate approach for the calculation of displacement in mining subsidence orediction.展开更多
This paper proposes a new Adomian decomposition method by using integrating factor.Nonlinear models are solved by this method to get more reliable and efficient numerical results.It can also solve ordinary differentia...This paper proposes a new Adomian decomposition method by using integrating factor.Nonlinear models are solved by this method to get more reliable and efficient numerical results.It can also solve ordinary differential equations where the traditional one fails.Besides,the complete error analysis for this method is presented.展开更多
We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrat...We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrating factors is given for the system. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse are established for the system, an example is given to illustrate the application of the result.展开更多
For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geomet...For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.展开更多
For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the paramet...For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results.展开更多
In this paper, we study the behavior of the solution at the crack edges for a nearly circular crack with developing cusps subject to shear loading. The problem of finding the resulting force can be written in the form...In this paper, we study the behavior of the solution at the crack edges for a nearly circular crack with developing cusps subject to shear loading. The problem of finding the resulting force can be written in the form of a hypersingular integral equation. The equation is then trans-formed into a similar equation over a circular region using conformal mapping. The equation is solved numerically for the unknown coefficients, which will later be used in finding the stress intensity factors. The sliding and tearing mode stress intensity factors are evaluated for cracks and displayed graphically. Our results seem to agree with the existing asymptotic solution.展开更多
Let (P, Q) be a C1 vector field defined in an open subset U IR2. We call inverse integrating factor a C1 solution V(x, y) of the equation . In previous works it has been shown that this function plays an important ro...Let (P, Q) be a C1 vector field defined in an open subset U IR2. We call inverse integrating factor a C1 solution V(x, y) of the equation . In previous works it has been shown that this function plays an important role in the problem of the center and in the determination of limit cycles. In this paper we obtain necessary conditions for a polynomial vector field (P, Q) to have a polynomial inverse integrating factor.展开更多
State functions play important roles in thermodynamics.Different from the process function,such as the exchanged heatδQ and the applied workδW,the change of the state function can be expressed as an exact differenti...State functions play important roles in thermodynamics.Different from the process function,such as the exchanged heatδQ and the applied workδW,the change of the state function can be expressed as an exact differential.We prove here that,for a generic thermodynamic system,only the inverse of the temperature,namely 1/T,can serve as the integration factor for the exchanged heatδQ.The uniqueness of the integration factor invalidates any attempt to define other state functions associated with the exchanged heat,and in turn,reveals the incorrectness of defining the entransy E_(vh)=CVT^(2)/2 as a state function by treating T as an integration factor.We further show the errors in the derivation of entransy by treating the heat capacity C_(V)as a temperature-independent constant.展开更多
Current Situation and Problems of the Treatment in Advanced Prostate Cancer In recent years,the incidence of prostate cancer shows a rising trend in China with an increase of 70%and has been the first place in the gro...Current Situation and Problems of the Treatment in Advanced Prostate Cancer In recent years,the incidence of prostate cancer shows a rising trend in China with an increase of 70%and has been the first place in the growth rate of malignant tumor in the male reproductive system. Prostate cancer has become a serious threat to male senior’s health.Because of the application of展开更多
A high-order accuracy time discretization method is developed in this paper to solve the one-dimensional nonlinear Dirac(NLD)equation.Based on the implicit integration factor(IIF)method,two schemes are proposed.Centra...A high-order accuracy time discretization method is developed in this paper to solve the one-dimensional nonlinear Dirac(NLD)equation.Based on the implicit integration factor(IIF)method,two schemes are proposed.Central differences are applied to the spatial discretization.The semi-discrete scheme keeps the conservation of the charge and energy.For the temporal discretization,second-order IIF method and fourth-order IIF method are applied respectively to the nonlinear system arising from the spatial discretization.Numerical experiments are given to validate the accuracy of these schemes and to discuss the interaction dynamics of the NLD solitary waves.展开更多
Weighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh.There are three weights including the arithmetic,the ...Weighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh.There are three weights including the arithmetic,the harmonic,and the geometric weight in the weighted discontinuous Galerkin scheme.For the time discretization,we treat the nonlinear diffusion coefficients explicitly,and apply the semiimplicit integration factormethod to the nonlinear ordinary differential equations arising from discontinuous Galerkin spatial discretization.The semi-implicit integration factor method can not only avoid severe timestep limits,but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method.Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.展开更多
Objective To investigate the integral dissolution model based on biological potency in order to evaluate the dissolution of Compound Chinese materia medica（CCMM） in vitro. Methods The contents of paeoniflorin, phill...Objective To investigate the integral dissolution model based on biological potency in order to evaluate the dissolution of Compound Chinese materia medica（CCMM） in vitro. Methods The contents of paeoniflorin, phillyrin, ginsenoside Rg1, and adenosine of ten batches of Compound Biejia Ruangan Tablet（CBRT） were determined at different times. The self-defined weighting coefficient based on the contents has been created to establish the integral dissolution model. In addition, the biological potency of CBRT was measured by MTT assay. Then, the f2 similar factor was used to evaluate the similarity of the batches. Results Compared with batch a, some batches’ f2 values of paeoniflorin and adenosine were less than 50, while f2 values of ginsenoside Rg1, phillyrin, and integral component were more than 50. Likewise, ginsenoside Rg1, phillyrin, and integral component were all in good correlation with biological dissolution. Conclusion The results of the integral dissolution based on biological test of CBRT demonstrate that the bioassay method may be a promising supplement for its quality evaluation.展开更多
基金Supported by the National Natural Science Foundation of China(12272248)。
文摘The method of integrating factors is used to study the conservation laws of the Herglotz type Birkhoffian systems in this paper.Firstly,the definition of the integrating factors of the Herglotz type Birkhoffian systems is given.Secondly,the relationship between the integrating factors and conservation laws is studied,and the conservation theorems of Herglotz type Birkhoff's equations and their inverse theorems are established.Thirdly,two types of generalized Killing equations for calculating integrating factors are given.Finally,as an example,a linear damped oscillator is taken.This example can be transformed into a Herglotz type Birkhoffian system.The resulting conservation theorems are used to find the conserved quantities for this example.
基金supported by the National Key Research and Development Program of China(No.2023YFC3007202)Joint Research Project on Meteorological Capacity Enhancement of the China Meteorological Administration(No.23NLTSZ009)Project of the Department of Science and Technology of Sichuan Province(No.2024YFHZ0098)。
文摘Connection methods are essential for integrating environmental factors with machine learning models for landslide susceptibility assessments.However,current research does not consider the different characteristics of continuity and discreteness within environmental factors and therefore does not analyze the suitability of various connection methods for different factor types.Moreover,the applicability of connection methods remains unclear when slope units are used as the basic assessment units.This study employed slope units as mapping units.The original data of 15 environmental factors,including 12 continuous and three discrete factors,and two connection methods,i.e.,frequency ratio(FR)and modified FR(MFR),were separately used to construct the input datasets for landslide susceptibility modeling.The performance of four widely used machine learning models,random forest(RF),support vector machine(SVM),logistic regression(LR),and multilayer perceptron(MLP),was analyzed to evaluate the suitability of the connection methods for landslide susceptibility mapping.The results show that,in contrast to the decision tree-based RF model,the use of different connection methods for different factor types significantly influences the results of nontree models,including SVM,MLP,and LR.SVM model is the most sensitive to factor types and connection methods.When the MFR is used as the connection method,it improves the mapping results,especially for the SVM model.This shows that it is essential to consider the different characteristics of the data and select an appropriate environmental factor connection strategy to increase the effectiveness of landslide susceptibility evaluation.Furthermore,this study explored the role of connective methods from a sample distribution perspective,providing a theoretical foundation for the more rational and effective integration of environmental factors.
基金Natural Science Foundation of High Education of Jiangsu Province of China，"Qing Lan" Project Foundation of Jiangsu Province
文摘In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.
基金The project supported by Natural Science Foundation of Heilongjiang Province of China under Grant No. 9507
文摘The integrating factors and conservation theorems of nonholonomic dynamical system of relative motion are studied. First, the dynamical equations of relative motion of system are written. Next, the definition of integrating factors is given, and the necessary conditions for the existence of the conserved quantities are studied in detail. Then, the conservation theorem and its inverse of system are established. Finally, an example is given to illustrate the application of the result.
基金Project supported by the Heilongjiang Natural Science Foundation of China （Grant No 9507）
文摘In this paper the conservation theorems of the constrained Birkhoffian systems are studied by using the method of integrating factors. The differential equations of motion of the system are written. The definition of integrating factors is given for the system. The necessary conditions for the existence of the conserved quantity for the system are studied. The conservation theorem and its inverse for the system are established. Finally, an example is given to illustrate the application of the results.
基金The project supported by the Natural Science Foundation of Heilongjiang Province of China under Grant No. 9507
文摘The conservation theorems of the generalized Lagrangian equations for nonconservative mechanical system are studied by using method of integrating factors. Firstly, the differential equations of motion of system are given, and the definition of integrating factors is given. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the result.
文摘The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.
基金the Research and Innovation Program for College and University Graduate Students in Jiangsu Province (No.CX10B_141Z)the National Natural Science Foundation of China (No.41071273) for support of this project
文摘In order to improve the precision of mining subsidence prediction, a mathematical model using Support Vector Machine （SVM） was established to calculate the displacement factor. The study is based on a comprehensive analysis of factors affecting the displacement factor, such as mechanical properties of the cover rock, the ratio of mining depth to seam thickness, dip angle of the coal seam and the thickness of loose layer. Data of 63 typical observation stations were used as a training and testing sample set. A SVM regression model of the displacement factor and the factors affecting it was established with a kernel function, an insensitive loss factor and a properly selected penalty factor. Given an accurate calculation algorithm for testing and analysis, the results show that an SVM regression model can calcu- late displacement factor precisely and reliable precision can be obtained which meets engineering requirements. The experimental results show that the method to calculation of the displacement factor, based on the SVM method, is feasible. The many factors affecting the displacement factor can be consid- ered with this method. The research provides an efficient and accurate approach for the calculation of displacement in mining subsidence orediction.
文摘This paper proposes a new Adomian decomposition method by using integrating factor.Nonlinear models are solved by this method to get more reliable and efficient numerical results.It can also solve ordinary differential equations where the traditional one fails.Besides,the complete error analysis for this method is presented.
基金The project supported by National Natural Science Foundation of China under Grant No. 10272034 and the Doctoral Program Foundation of China under Grnt No. 20030558025
文摘We present a general approach to the construction of conservation laws for the nonholonomic singular Lagrange system. Firstly, the differential equations of motion of the system are written, the definition of integrating factors is given for the system. Next, the necessary conditions for the existence of the conserved quantity are studied in detail. Finally, the conservation theorem and its inverse are established for the system, an example is given to illustrate the application of the result.
文摘For reaction-diffusion equations in irregular domains with moving boundaries,the numerical stability constraints from the reaction and diffusion terms often require very restricted time step sizes,while complex geometries may lead to difficulties in the accuracy when discretizing the high-order derivatives on grid points near the boundary.It is very challenging to design numerical methods that can efficiently and accurately handle both difficulties.Applying an implicit scheme may be able to remove the stability constraints on the time step,however,it usually requires solving a large global system of nonlinear equations for each time step,and the computational cost could be significant.Integration factor(IF)or exponential time differencing(ETD)methods are one of the popular methods for temporal partial differential equations(PDEs)among many other methods.In our paper,we couple ETD methods with an embedded boundary method to solve a system of reaction-diffusion equations with complex geometries.In particular,we rewrite all ETD schemes into a linear combination of specificФ-functions and apply one state-of-the-art algorithm to compute the matrix-vector multiplications,which offers significant computational advantages with adaptive Krylov subspaces.In addition,we extend this method by incorporating the level set method to solve the free boundary problem.The accuracy,stability,and efficiency of the developed method are demonstrated by numerical examples.
基金the Natural Science Foundation of Higher Education Institution of Jiangsu Province of China under Grant Nos.04KJA130135 and 08KJB13002
文摘For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results.
基金supported by the Ministry Of Higher Education Malaysia for the Fundamental Research Grant scheme,project No. 01-04-10-897FRthe NSF scholarship
文摘In this paper, we study the behavior of the solution at the crack edges for a nearly circular crack with developing cusps subject to shear loading. The problem of finding the resulting force can be written in the form of a hypersingular integral equation. The equation is then trans-formed into a similar equation over a circular region using conformal mapping. The equation is solved numerically for the unknown coefficients, which will later be used in finding the stress intensity factors. The sliding and tearing mode stress intensity factors are evaluated for cracks and displayed graphically. Our results seem to agree with the existing asymptotic solution.
基金the DGICYT grant, number PB96-1153 The third author is partially supported by the University of Lleida Project P98-207.
文摘Let (P, Q) be a C1 vector field defined in an open subset U IR2. We call inverse integrating factor a C1 solution V(x, y) of the equation . In previous works it has been shown that this function plays an important role in the problem of the center and in the determination of limit cycles. In this paper we obtain necessary conditions for a polynomial vector field (P, Q) to have a polynomial inverse integrating factor.
基金This work was supported by the National Natural Science Foundation of China(NSFC)(Grants No.11534002,No.12088101,No.U1530402,No.U1930403,No.11775001,No.11534002,and No.11825001)the National Basic Research Program of China(Grants No.2016YFA0301201).
文摘State functions play important roles in thermodynamics.Different from the process function,such as the exchanged heatδQ and the applied workδW,the change of the state function can be expressed as an exact differential.We prove here that,for a generic thermodynamic system,only the inverse of the temperature,namely 1/T,can serve as the integration factor for the exchanged heatδQ.The uniqueness of the integration factor invalidates any attempt to define other state functions associated with the exchanged heat,and in turn,reveals the incorrectness of defining the entransy E_(vh)=CVT^(2)/2 as a state function by treating T as an integration factor.We further show the errors in the derivation of entransy by treating the heat capacity C_(V)as a temperature-independent constant.
基金Supported by the National Natural Science Foundation of China(No.30873268)
文摘Current Situation and Problems of the Treatment in Advanced Prostate Cancer In recent years,the incidence of prostate cancer shows a rising trend in China with an increase of 70%and has been the first place in the growth rate of malignant tumor in the male reproductive system. Prostate cancer has become a serious threat to male senior’s health.Because of the application of
基金the National Natural Science Foundation of China(No.11671044)the Science Challenge Project(No.TZ2016001)the Beijing Municipal Education Commission(No.PXM2017014224000020).
文摘A high-order accuracy time discretization method is developed in this paper to solve the one-dimensional nonlinear Dirac(NLD)equation.Based on the implicit integration factor(IIF)method,two schemes are proposed.Central differences are applied to the spatial discretization.The semi-discrete scheme keeps the conservation of the charge and energy.For the temporal discretization,second-order IIF method and fourth-order IIF method are applied respectively to the nonlinear system arising from the spatial discretization.Numerical experiments are given to validate the accuracy of these schemes and to discuss the interaction dynamics of the NLD solitary waves.
基金the National Nature Science Foundation of China(11171038)R.Zhang’s work was also supported by Brazilian Young Talent Attraction Program via National Council for Scientific and Technological Development(CNPq).J.Zhu and A.Loula’s works were partially supported by CNPq.X.Cui’s work was partially supported by the National Natural Science Foundation of China(11271054)+1 种基金the Science Foundation of CAEP(2010A0202010,2012B0202026)the Defense Industrial Technology Development Program(B1520110011).
文摘Weighted interior penalty discontinuous Galerkin method is developed to solve the two-dimensional non-equilibrium radiation diffusion equation on unstructured mesh.There are three weights including the arithmetic,the harmonic,and the geometric weight in the weighted discontinuous Galerkin scheme.For the time discretization,we treat the nonlinear diffusion coefficients explicitly,and apply the semiimplicit integration factormethod to the nonlinear ordinary differential equations arising from discontinuous Galerkin spatial discretization.The semi-implicit integration factor method can not only avoid severe timestep limits,but also takes advantage of the local property of DG methods by which small sized nonlinear algebraic systems are solved element by element with the exact Newton iteration method.Numerical results are presented to demonstrate the validity of discontinuous Galerkin method for high nonlinear and tightly coupled radiation diffusion equation.
基金Major Scientific and Technological Specialized Project for Significant New.Formulation of New Drugs(No.2011ZX09201-201-14)National Natural Science Foundation of China(No.81073069)
文摘Objective To investigate the integral dissolution model based on biological potency in order to evaluate the dissolution of Compound Chinese materia medica（CCMM） in vitro. Methods The contents of paeoniflorin, phillyrin, ginsenoside Rg1, and adenosine of ten batches of Compound Biejia Ruangan Tablet（CBRT） were determined at different times. The self-defined weighting coefficient based on the contents has been created to establish the integral dissolution model. In addition, the biological potency of CBRT was measured by MTT assay. Then, the f2 similar factor was used to evaluate the similarity of the batches. Results Compared with batch a, some batches’ f2 values of paeoniflorin and adenosine were less than 50, while f2 values of ginsenoside Rg1, phillyrin, and integral component were more than 50. Likewise, ginsenoside Rg1, phillyrin, and integral component were all in good correlation with biological dissolution. Conclusion The results of the integral dissolution based on biological test of CBRT demonstrate that the bioassay method may be a promising supplement for its quality evaluation.
