The invariant sets and the solutions of the 1+2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the se...The invariant sets and the solutions of the 1+2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the set $$E_0 = \{ u:u_x = v_x F(u),u_y = v_y F(u)\} ,$$ where v is a smooth function of variables x, y and F is a smooth function of u. This extends the results of Galaktionov (2001) and for the 1+1-dimensional nonlinear evolution equations.展开更多
In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2....In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.展开更多
In this paper, we apply Aubry-Mather theory developed in recent years about monotone twist mappings to the study of the superlinear Duffing equation+g(x)=p(t), (0)where p(t)∈C^0(R) is periodic with period 1 and g(x) ...In this paper, we apply Aubry-Mather theory developed in recent years about monotone twist mappings to the study of the superlinear Duffing equation+g(x)=p(t), (0)where p(t)∈C^0(R) is periodic with period 1 and g(x) satisfies the superlinearity condition Consequently, this gives descriptions of the global dynamical behavior, particularly periodic solutions and quasi-periodic solutions of a wide class of Eq. (0), not requiring high order smoothness assumption.展开更多
This paper improves Tychonov ford point theorem and discusses the existence of solutions of nonlinear Fredholm integral equations on [0,+∞] in Banach spaces with Frechet space theory.
An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to swit...An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to switch from bad to good status. A matrix based on error logic is used to express current status u, expectant status u1 and transformation matrix T. It is u, u1, and T that are used to build error matrix equation T (u)= u1. This allows us to find a method whereby bad status “u” changes to good status “u1” by solving the equation. The conversion method that transform from current to expectant status can be obtained from the transformation matrix T. On this basis, this paper proposes a new kind of error matrix equation named “containing-type error matrix equation”. This equation is more suitable for analyzing the realistic question. The method of solving, existence and form of solution for this type of equation have been presented in this paper. This research provides a potential useful new technique for decision analysis.展开更多
The long-term behavior of the atmospheric evolution, which cannot be answered and solvedby the numerical experiments, must be undrstood before we design the numerical forecastmodels of the long-range weather and clima...The long-term behavior of the atmospheric evolution, which cannot be answered and solvedby the numerical experiments, must be undrstood before we design the numerical forecastmodels of the long-range weather and climate. It is necessary to carry out some studiesof basic theory. Based on the stationary external forcings, Chou studied the adjustment of the nonlinear atmospheric system tending to forcings in R^n. Then these resultswere extended to the infinite dimensional Hilbert space. For the real atmospheric system,展开更多
The nonlinear Kortewege-de Varies(KdV)equation is a functional description for modelling ion-acoustic waves in plasma,long internal waves in a density-stratified ocean,shallow-water waves and acoustic waves on a cryst...The nonlinear Kortewege-de Varies(KdV)equation is a functional description for modelling ion-acoustic waves in plasma,long internal waves in a density-stratified ocean,shallow-water waves and acoustic waves on a crystal lattice.This paper focuses on developing and analysing a resilient double parametric analytical approach for the nonlinear fuzzy fractional KdV equation(FFKdVE)under gH-differentiability of Caputo fractional order,namely the q-Homotopy analysis method with the Shehu transform(q-HASTM).A triangular fuzzy number describes the Caputo fractional derivative of orderα,0<α≤1,for modelling problem.The fuzzy velocity profiles with crisp and fuzzy conditions at different spatial positions are in-vestigated using a robust double parametric form-based q-HASTM with its convergence analysis.The ob-tained results are compared with existing works in the literature to confirm the efficacy and effectiveness of the method.展开更多
For a parametric algebraic system in finite fields, this paper presents a method for computing the cover and the refined cover based on the characteristic set method. From the cover, the author knows for what parametr...For a parametric algebraic system in finite fields, this paper presents a method for computing the cover and the refined cover based on the characteristic set method. From the cover, the author knows for what parametric values the system has solutions and at the same time presents the solutions in the form of proper chains. By the refined cover, the author gives a complete classification of the number of solutions for this system, that is, the author divides the parameter space into several disjoint components, and on every component the system has a fix number of solutions. Moreover, the author develops a method of quantifier elimination for first order formulas in finite fields.展开更多
This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space...This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space H0^2（0, 1） × L^2（0, 1）. The main step in this research is to show that there exists an absorbing set for the solution semiflow in the Hilbert space H0^3（0, 1） × H0^1（0, 1）.展开更多
A continuous map from a closed interval into itself is called a p-order Feigenbaum＇s map if it is a solution of the Feigenbaum＇s equation fP（λx）=λf（x）. In this paper, we estimate Hausdorff dimensions of likely...A continuous map from a closed interval into itself is called a p-order Feigenbaum＇s map if it is a solution of the Feigenbaum＇s equation fP（λx）=λf（x）. In this paper, we estimate Hausdorff dimensions of likely limit sets of some p-order Feigenbaum＇s maps. As an application, it is proved that for any 0 〈 t 〈 1, there always exists a p-order Feigenbaum＇s map which has a likely limit set with Hausdorff dimension t. This generalizes some known results in the special case of p =2.展开更多
Ranked-set sampling(RSS) often provides more efficient inference than simple random sampling(SRS).In this article,we propose a systematic nonparametric technique,RSS-EL,for hypoth-esis testing and interval estimation ...Ranked-set sampling(RSS) often provides more efficient inference than simple random sampling(SRS).In this article,we propose a systematic nonparametric technique,RSS-EL,for hypoth-esis testing and interval estimation with balanced RSS data using empirical likelihood(EL).We detail the approach for interval estimation and hypothesis testing in one-sample and two-sample problems and general estimating equations.In all three cases,RSS is shown to provide more efficient inference than SRS of the same size.Moreover,the RSS-EL method does not require any easily violated assumptions needed by existing rank-based nonparametric methods for RSS data,such as perfect ranking,identical ranking scheme in two groups,and location shift between two population distributions.The merit of the RSS-EL method is also demonstrated through simulation studies.展开更多
In this paper, we consider an inference method for recurrent event data in which the primary exposure covariate is assessed only in a validation set, while as an auxiliary covariate for the main exposure is available ...In this paper, we consider an inference method for recurrent event data in which the primary exposure covariate is assessed only in a validation set, while as an auxiliary covariate for the main exposure is available for the full cohort. Additive rate model is considered. The existing estimating equations in the absence of primary exposure are corrected by taking use of the validation data and auxiliary information, which yield consistent and asymptotically normal estimators of the regression parameters. The estimated baseline mean process is shown to converge weakly to a zero-mean Gaussian process. Extensive simulations are conducted to evaluate finite sample performance.展开更多
The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) descr...The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 10671156)the Program for New Century Excellent Talents in Universities (Grant No. NCET-04-0968)
文摘The invariant sets and the solutions of the 1+2-dimensional generalized thin film equation are discussed. It is shown that there exists a class of solutions to the equations, which are invariant with respect to the set $$E_0 = \{ u:u_x = v_x F(u),u_y = v_y F(u)\} ,$$ where v is a smooth function of variables x, y and F is a smooth function of u. This extends the results of Galaktionov (2001) and for the 1+1-dimensional nonlinear evolution equations.
文摘In this paper we discuss a relatively general kind of iterative functional equation G(x,f(x), ...,f n (x)) = 0 (for allx ∈J), whereJ is a connected closed subset of the real number axis ?,G∈C m (J n+1, ?) andn ≥ 2. Using the method of approximating fixed points by small shift of maps, choosing suitable metrics on functional spaces and finding a relation between uniqueness and stability of fixed points of maps of general spaces, we prove the existence, uniqueness and stability ofCm solutions of the above equation for any integer m ≥ 0 under relatively weak conditions, and generalize related results in reference in different aspects.
文摘In this paper, we apply Aubry-Mather theory developed in recent years about monotone twist mappings to the study of the superlinear Duffing equation+g(x)=p(t), (0)where p(t)∈C^0(R) is periodic with period 1 and g(x) satisfies the superlinearity condition Consequently, this gives descriptions of the global dynamical behavior, particularly periodic solutions and quasi-periodic solutions of a wide class of Eq. (0), not requiring high order smoothness assumption.
文摘This paper improves Tychonov ford point theorem and discusses the existence of solutions of nonlinear Fredholm integral equations on [0,+∞] in Banach spaces with Frechet space theory.
文摘An error matrix equation based on error matrix theory was presented in previous research of the error-eliminating theory. The purpose of solving the error matrix equation is to create a decision support on how to switch from bad to good status. A matrix based on error logic is used to express current status u, expectant status u1 and transformation matrix T. It is u, u1, and T that are used to build error matrix equation T (u)= u1. This allows us to find a method whereby bad status “u” changes to good status “u1” by solving the equation. The conversion method that transform from current to expectant status can be obtained from the transformation matrix T. On this basis, this paper proposes a new kind of error matrix equation named “containing-type error matrix equation”. This equation is more suitable for analyzing the realistic question. The method of solving, existence and form of solution for this type of equation have been presented in this paper. This research provides a potential useful new technique for decision analysis.
基金State Key Research Project on Dynamics and Predictive Theory of the Climate and the Doctor's Foundation of State Education Committee.
文摘The long-term behavior of the atmospheric evolution, which cannot be answered and solvedby the numerical experiments, must be undrstood before we design the numerical forecastmodels of the long-range weather and climate. It is necessary to carry out some studiesof basic theory. Based on the stationary external forcings, Chou studied the adjustment of the nonlinear atmospheric system tending to forcings in R^n. Then these resultswere extended to the infinite dimensional Hilbert space. For the real atmospheric system,
文摘The nonlinear Kortewege-de Varies(KdV)equation is a functional description for modelling ion-acoustic waves in plasma,long internal waves in a density-stratified ocean,shallow-water waves and acoustic waves on a crystal lattice.This paper focuses on developing and analysing a resilient double parametric analytical approach for the nonlinear fuzzy fractional KdV equation(FFKdVE)under gH-differentiability of Caputo fractional order,namely the q-Homotopy analysis method with the Shehu transform(q-HASTM).A triangular fuzzy number describes the Caputo fractional derivative of orderα,0<α≤1,for modelling problem.The fuzzy velocity profiles with crisp and fuzzy conditions at different spatial positions are in-vestigated using a robust double parametric form-based q-HASTM with its convergence analysis.The ob-tained results are compared with existing works in the literature to confirm the efficacy and effectiveness of the method.
基金supported by the National 973 Program of China under Grant No.2011CB302400the National Natural Science Foundation of China under Grant No.60970152
文摘For a parametric algebraic system in finite fields, this paper presents a method for computing the cover and the refined cover based on the characteristic set method. From the cover, the author knows for what parametric values the system has solutions and at the same time presents the solutions in the form of proper chains. By the refined cover, the author gives a complete classification of the number of solutions for this system, that is, the author divides the parameter space into several disjoint components, and on every component the system has a fix number of solutions. Moreover, the author develops a method of quantifier elimination for first order formulas in finite fields.
文摘This paper is devoted to prove the existence of an exponential attractor for the semiflow generated by a nonlinear Boussinesq equation. We formulate the Boussinesq equation as an abstract equation in the Hilbert space H0^2（0, 1） × L^2（0, 1）. The main step in this research is to show that there exists an absorbing set for the solution semiflow in the Hilbert space H0^3（0, 1） × H0^1（0, 1）.
文摘A continuous map from a closed interval into itself is called a p-order Feigenbaum＇s map if it is a solution of the Feigenbaum＇s equation fP（λx）=λf（x）. In this paper, we estimate Hausdorff dimensions of likely limit sets of some p-order Feigenbaum＇s maps. As an application, it is proved that for any 0 〈 t 〈 1, there always exists a p-order Feigenbaum＇s map which has a likely limit set with Hausdorff dimension t. This generalizes some known results in the special case of p =2.
基金supported by National Natural Science Foundation of China (Grant No. 10871037)
文摘Ranked-set sampling(RSS) often provides more efficient inference than simple random sampling(SRS).In this article,we propose a systematic nonparametric technique,RSS-EL,for hypoth-esis testing and interval estimation with balanced RSS data using empirical likelihood(EL).We detail the approach for interval estimation and hypothesis testing in one-sample and two-sample problems and general estimating equations.In all three cases,RSS is shown to provide more efficient inference than SRS of the same size.Moreover,the RSS-EL method does not require any easily violated assumptions needed by existing rank-based nonparametric methods for RSS data,such as perfect ranking,identical ranking scheme in two groups,and location shift between two population distributions.The merit of the RSS-EL method is also demonstrated through simulation studies.
基金Supported by the National Natural Science Foundation of China(No.11571263,11371299)
文摘In this paper, we consider an inference method for recurrent event data in which the primary exposure covariate is assessed only in a validation set, while as an auxiliary covariate for the main exposure is available for the full cohort. Additive rate model is considered. The existing estimating equations in the absence of primary exposure are corrected by taking use of the validation data and auxiliary information, which yield consistent and asymptotically normal estimators of the regression parameters. The estimated baseline mean process is shown to converge weakly to a zero-mean Gaussian process. Extensive simulations are conducted to evaluate finite sample performance.
基金supported by the National Natural Science Foundation of China (Grant No. 11002029)
文摘The generalized finite difference method (GFDM) used for irregular grids is first introduced into the numerical study of thelevel set equation, which is coupled with the theory of detonation shock dynamics (DSD) describing the propagation of thedetonation shock front. The numerical results of a rate-stick problem, a converging channel problem and an arc channel prob-lem for specified boundaries show that GFDM is effective on solving the level set equation in the irregular geometrical domain.The arrival time and the normal velocity distribution of the detonation shock front of these problems can then be obtainedconveniently with this method. The numerical results also confirm that when there is a curvature effect, the theory of DSDmust be considered for the propagation of detonation shock surface, while classic Huygens construction is not suitable anymore.
