Objective: In the acid-fast staining experiment of pathological tissues, sulfuric acid and hydrochloric acid were used to evaluate the staining results, so as to get the best staining method. Methods: Using sulfuric a...Objective: In the acid-fast staining experiment of pathological tissues, sulfuric acid and hydrochloric acid were used to evaluate the staining results, so as to get the best staining method. Methods: Using sulfuric acid differentiation solution and hydrochloric acid differentiation solution, the paraffin blocks of pathological tissues known to contain Mycobacterium tuberculosis were compared to evaluate the staining effect. Results: When 0.5% hydrochloric acid differentiation solution is used and the differentiation time is 6 s, the dyeing effect is better than that of sulfuric acid differentiation solution.展开更多
In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s p...In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s periodic solution theorem. Anexample of application is given at the end.展开更多
In this paper, we propose to replace the Chebyshev series used in pseudospectral methods with the equivalent Chebyshev economized power series that can be evaluated more rapidly. We keep the rest of the implementation...In this paper, we propose to replace the Chebyshev series used in pseudospectral methods with the equivalent Chebyshev economized power series that can be evaluated more rapidly. We keep the rest of the implementation the same as the spectral method so that there is no new mathematical principle involved. We show by numerical examples that the new approach works well and there is indeed no significant loss of solution accuracy. The advantages of using power series also include simplicity in its formulation and implementation such that it could be used for complex systems. We investigate the important issue of collocation point selection. Our numerical results indicate that there is a clear accuracy advantage of using collocation points corresponding to roots of the Chebyshev polynomial.展开更多
In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′(t) + p(t)x′(t) + q(t)x(t) = f(t, x(t)).By using Krasnoselskii fixed point...In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′(t) + p(t)x′(t) + q(t)x(t) = f(t, x(t)).By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.展开更多
In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal...In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal asymptotic solution by Lyuternik- Vishik 's method. Finally, by means of the energy estimates we obtain the bound of the remainder of the asymptotic solution.展开更多
For the famous Feigenbaum's equations, in this paper, we established its constructive theorem of the peak-unimodal, then we found out other paths to explore the peak-unimodal solutions. For example, we proceed on ...For the famous Feigenbaum's equations, in this paper, we established its constructive theorem of the peak-unimodal, then we found out other paths to explore the peak-unimodal solutions. For example, we proceed on the direction to try the non-symmetrical continuous peak-unimodal solutions and C1 solutions.展开更多
In the studies of nonlinear partial differential equations, the influence, from the singularities of coefficients to the singularities of solution, is a field that has not been dealt with. In this paper, we discuss a ...In the studies of nonlinear partial differential equations, the influence, from the singularities of coefficients to the singularities of solution, is a field that has not been dealt with. In this paper, we discuss a simple case of semilinear equations under the frame of the space of conormal distributions. We prove the result that the solution has the same singularities on the hypersurface in which the coefficients have the conormal singularities.展开更多
After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. ...After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:展开更多
In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an alg...In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary e>0 .展开更多
In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation (PDE) was invesigated in a fixed domain for valuing two assets of American (call-max/put-min) options...In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation (PDE) was invesigated in a fixed domain for valuing two assets of American (call-max/put-min) options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.展开更多
A sufficient condition is obtained for every solution of the nonlinear retarded differential equationx'(t) +f(t,x(t-τ)) =0to tend to zero as t→∞ , which extends and improves the corresponding results obtained b...A sufficient condition is obtained for every solution of the nonlinear retarded differential equationx'(t) +f(t,x(t-τ)) =0to tend to zero as t→∞ , which extends and improves the corresponding results obtained by Ladas, Sficas and Gopalsamy.展开更多
This paper studies the smoothness of solutions of the higher dimensional polynomial-like iterative equation. The methods given by Zhang Weinian([7]) and by Kulczvcki M, Tabor j.([3]) are improved by constructing a new...This paper studies the smoothness of solutions of the higher dimensional polynomial-like iterative equation. The methods given by Zhang Weinian([7]) and by Kulczvcki M, Tabor j.([3]) are improved by constructing a new operator for the structure of the equation in order to apply fixed point theorems. Existence, uniqueness and stability of continuously differentiable solutions are given.展开更多
In this paper, we prove the existence and uniqueness of positive solutions for a system of multi-order fractional differential equations. The system is used to represent constitutive relation for viscoelastic model of...In this paper, we prove the existence and uniqueness of positive solutions for a system of multi-order fractional differential equations. The system is used to represent constitutive relation for viscoelastic model of fractional differential equations. Our results are based on the fixed point theorems of increasing operator and the cone theory, some illustrative examples are also presented.展开更多
In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic ...In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.展开更多
In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the...In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.展开更多
By discussing the zeros of periodic.solutions we give in this paper a criterion for the existence of exactly n+1 simple 4-periodic solutions of the differential delay equation x(T)= -f(x(t-1)).
In this paper,using Mawhin's continuation theorem in the theory of coincidence degree,we first prove the general existence theorem of periodic solutions for F.D.Es with infinite delay:dx(t)/dt=f(t,x_t),x(t)∈R^n,w...In this paper,using Mawhin's continuation theorem in the theory of coincidence degree,we first prove the general existence theorem of periodic solutions for F.D.Es with infinite delay:dx(t)/dt=f(t,x_t),x(t)∈R^n,which is an extension of Mawhin's existence theorem of periodic solutions of F.D.Es with finite delay.Second,as an application of it,we obtain the existence theorem of positive periodic solutions of the Lotka-Volterra equations:dx(t)/dt=x(t)(a-kx(t)-by(t)),dy(t)/dt=-cy(t)+d integral from n=0 to +∞ x(t-s)y(t-s)dμ(s)+p(t).展开更多
In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence o...In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence of periodic solutions of a type of neutral functional equation system are obtained,and at the same time, we present a method with formula shows how to find the periodicsolutions.展开更多
In this paper we discuss the types and criteria of nonoscillatory solutions for the fol-lowing second order neutral functional differential equation with nonpositive coefficients
文摘Objective: In the acid-fast staining experiment of pathological tissues, sulfuric acid and hydrochloric acid were used to evaluate the staining results, so as to get the best staining method. Methods: Using sulfuric acid differentiation solution and hydrochloric acid differentiation solution, the paraffin blocks of pathological tissues known to contain Mycobacterium tuberculosis were compared to evaluate the staining effect. Results: When 0.5% hydrochloric acid differentiation solution is used and the differentiation time is 6 s, the dyeing effect is better than that of sulfuric acid differentiation solution.
文摘In this paper. four sufficiency theorems of existence of periodic solutions for aclass of retarded functional differential equations are given. The result of thesetheorems is better than the well-known Yoshizawa’s periodic solution theorem. Anexample of application is given at the end.
文摘In this paper, we propose to replace the Chebyshev series used in pseudospectral methods with the equivalent Chebyshev economized power series that can be evaluated more rapidly. We keep the rest of the implementation the same as the spectral method so that there is no new mathematical principle involved. We show by numerical examples that the new approach works well and there is indeed no significant loss of solution accuracy. The advantages of using power series also include simplicity in its formulation and implementation such that it could be used for complex systems. We investigate the important issue of collocation point selection. Our numerical results indicate that there is a clear accuracy advantage of using collocation points corresponding to roots of the Chebyshev polynomial.
基金The Science Research Plan(Jijiaokehezi[2016]166)of Jilin Province Education Department During the 13th Five-Year Periodthe Science Research Starting Foundation(2015023)of Jilin Agricultural University
文摘In this paper, we study the existence of multiple positive periodic solutions for the second order differential equation x′′(t) + p(t)x′(t) + q(t)x(t) = f(t, x(t)).By using Krasnoselskii fixed point theorem, we establish some criteria for the existence and multiple positive periodic solutions for this differential equation.
文摘In this paper we consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the energy estimates of the solutionand its derivatives and construct the formal asymptotic solution by Lyuternik- Vishik 's method. Finally, by means of the energy estimates we obtain the bound of the remainder of the asymptotic solution.
基金Projects supported by National Natural Science Foundation of China
文摘For the famous Feigenbaum's equations, in this paper, we established its constructive theorem of the peak-unimodal, then we found out other paths to explore the peak-unimodal solutions. For example, we proceed on the direction to try the non-symmetrical continuous peak-unimodal solutions and C1 solutions.
文摘In the studies of nonlinear partial differential equations, the influence, from the singularities of coefficients to the singularities of solution, is a field that has not been dealt with. In this paper, we discuss a simple case of semilinear equations under the frame of the space of conormal distributions. We prove the result that the solution has the same singularities on the hypersurface in which the coefficients have the conormal singularities.
文摘After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:
文摘In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary e>0 .
基金Project supported by the National Natural Science Foundation of China (Grant No.10271072)
文摘In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation (PDE) was invesigated in a fixed domain for valuing two assets of American (call-max/put-min) options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.
文摘A sufficient condition is obtained for every solution of the nonlinear retarded differential equationx'(t) +f(t,x(t-τ)) =0to tend to zero as t→∞ , which extends and improves the corresponding results obtained by Ladas, Sficas and Gopalsamy.
文摘This paper studies the smoothness of solutions of the higher dimensional polynomial-like iterative equation. The methods given by Zhang Weinian([7]) and by Kulczvcki M, Tabor j.([3]) are improved by constructing a new operator for the structure of the equation in order to apply fixed point theorems. Existence, uniqueness and stability of continuously differentiable solutions are given.
基金Foundation item:The NSF(11071097,11101217)of Chinathe NSF(BK20141476)of Jiangsu Province of China
文摘In this paper, we prove the existence and uniqueness of positive solutions for a system of multi-order fractional differential equations. The system is used to represent constitutive relation for viscoelastic model of fractional differential equations. Our results are based on the fixed point theorems of increasing operator and the cone theory, some illustrative examples are also presented.
基金Supported by National Natural Science Foundation of China(Grant Nos.11271380,11031002 and 11371058)Research Fund for the Doctoral Program of Higher Education(Grant No.20110003110004)+1 种基金the Grant of BeijingEducation Committee Key Project(Grant No.KZ201310028031)Natural Science Foundation of GuangdongProvince of China(Grant No.S2013010013212)
文摘In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.
文摘In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.
基金Chinese National Foundation for Natural Sciences.
文摘By discussing the zeros of periodic.solutions we give in this paper a criterion for the existence of exactly n+1 simple 4-periodic solutions of the differential delay equation x(T)= -f(x(t-1)).
基金This project is supported by the National Natural Science Foundation of Chinathe Laboratory for Nonlinear Mechanics of Continuous Media of Academia Sinica
文摘In this paper,using Mawhin's continuation theorem in the theory of coincidence degree,we first prove the general existence theorem of periodic solutions for F.D.Es with infinite delay:dx(t)/dt=f(t,x_t),x(t)∈R^n,which is an extension of Mawhin's existence theorem of periodic solutions of F.D.Es with finite delay.Second,as an application of it,we obtain the existence theorem of positive periodic solutions of the Lotka-Volterra equations:dx(t)/dt=x(t)(a-kx(t)-by(t)),dy(t)/dt=-cy(t)+d integral from n=0 to +∞ x(t-s)y(t-s)dμ(s)+p(t).
文摘In this paper, using Fourier series, we study the problem of the existence of periodic solutionsof a type of periodic neutral differential difference system. Some necessary and sufficient conditionsfor the existence of periodic solutions of a type of neutral functional equation system are obtained,and at the same time, we present a method with formula shows how to find the periodicsolutions.
文摘In this paper we discuss the types and criteria of nonoscillatory solutions for the fol-lowing second order neutral functional differential equation with nonpositive coefficients