The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple ba...The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.展开更多
Based on a method of finite element model and combined with matrix theory, a method for solving differential equation with variable coefficients is proposed. With the method, it is easy to deal with the differential e...Based on a method of finite element model and combined with matrix theory, a method for solving differential equation with variable coefficients is proposed. With the method, it is easy to deal with the differential equations with variable coefficients. On most occasions and due to the nonuniformity nature, nonlinearity property can cause the equations of the kinds. Using the model, the satisfactory valuable results with only a few units can be obtained.展开更多
In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part,...In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.展开更多
Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations unde...Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition. By this method, the general computation formal is obtained. Its convergence in proved. We can get analytic expressions which converge to exact solution and its higher order derivatives uniformy Four numerical examples are given, which indicate that satisfactory results can he obtanedby this method.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
The irreversible mechanism of heat engines is studied in terms of <em>thermodynamic consistency</em> and thermomechanical dynamics (TMD) which is proposed for a method to study nonequilibrium irreversible ...The irreversible mechanism of heat engines is studied in terms of <em>thermodynamic consistency</em> and thermomechanical dynamics (TMD) which is proposed for a method to study nonequilibrium irreversible thermodynamic systems. As an example, a water drinking bird (DB) known as one of the heat engines is specifically examined. The DB system suffices a rigorous experimental device for the theory of nonequilibrium irreversible thermodynamics. The DB nonlinear equation of motion proves explicitly that nonlinear differential equations with time-dependent coefficients must be classified as independent equations different from those of constant coefficients. The solutions of nonlinear differential equations with time-dependent coefficients can express emergent phenomena: nonequilibrium irreversible states. The <em>couplings</em> among mechanics, thermodynamics and time-evolution to nonequilibrium irreversible state are defined when the internal energy, thermodynamic work, temperature and entropy are integrated as a spontaneous thermodynamic process in the DB system. The physical meanings of the time-dependent entropy, <em>T</em>(<em>t</em>)d<em>S</em>(<em>t</em>), , internal energy, d<span style="white-space:nowrap;"><em>Ɛ</em></span>(<em>t</em>), and thermodynamic work, dW(<em>t</em>), are defined by the progress of time-dependent Gibbs relation to thermodynamic equilibrium. The thermomechanical dynamics (TMD) approach constitutes a method for the nonequilibrium irreversible thermodynamics and transport processes.展开更多
Friction force(f)usually increases with the normal load(N)macroscopically,according to the classic law of Da Vinci–Amontons(f=μN),with a positive and finite friction coefficient(μ).Herein near-zero and negative dif...Friction force(f)usually increases with the normal load(N)macroscopically,according to the classic law of Da Vinci–Amontons(f=μN),with a positive and finite friction coefficient(μ).Herein near-zero and negative differential friction(ZNDF)coefficients are discovered in two-dimensional(2D)van der Waals(vdW)magnetic CrI_(3)commensurate contacts.It is identified that the ferromagnetic–antiferromagnetic phase transition of the interlayer couplings of the bilayer CrI_(3)can significantly reduce the interfacial sliding energy barriers and thus contribute to ZNDF.Moreover,phase transition between the in-plane(p_(x)and p_(y))and out-of-plane(p_(z))wave-functions dominates the sliding barrier evolutions,which is attributed to the delicate interplays among the interlayer vdW,electrostatic interactions,and the intralayer deformation of the CrI_(3)layers under external load.The present findings may motivate a new concept of slide-spintronics and are expected to play an instrumental role in design of novel magnetic solid lubricants applied in various spintronic nano-devices.展开更多
To provide accurate base data about the genetic sourees of Yellow River carps, the genetic diversity in a^ficially bred population and wild population of Yellow River carps from Henan Province was analyzed with mieros...To provide accurate base data about the genetic sourees of Yellow River carps, the genetic diversity in a^ficially bred population and wild population of Yellow River carps from Henan Province was analyzed with mierosatellite markers. The results showed that 16 alleles were detected at six microsateUite loci in each population. The average effective number of alleles (Ne) was 2. 350 in artificially bred population and 2. 085 in wild population. The observed heterozygosity (Ho) of artificially bred population, wild population and mixed population was 0. 614, 0. 576 and 0. 601 ; and the unbiased expected heterozygesity ( He ) was 0. 569, 0.535 and 0.559 ; and the polymorphism infonnatian content (PlC) was 0.474, 0.428 and 0.468, respectively. The PIC of the six loci ranged from 0.304 to 0. 864. The analysis of the genetic differentiation for the six microsatellitc loci in the two populations showed that the genetic differentiation coefficient ( F,, ) at only one microsatellite locus HLJ483 was greater than 0.05, and that at five rnicrosatellite loci were less than 0.05, which was consistent with the standard of non- genetic differentiation between populations (F,, = 0 -0.05). The average F,, at the six loci was 0.02, and the gene flow value (Nm) at all loci was greater than 1 and the average of Nm was 12.202. The results indicate that there is relatively abundant genetic diversity in Yellow River carps.展开更多
A thorough investigation of the systemd^2y(x):dx^2+p(x)y(x)=0with periodic impulse coefficientsp(x)={1,0≤x<x_0(2π>0> -η, x_0≤x<2π(η>p(x)=p(x+2π),-∞<x<∞is given, and the method can be appl...A thorough investigation of the systemd^2y(x):dx^2+p(x)y(x)=0with periodic impulse coefficientsp(x)={1,0≤x<x_0(2π>0> -η, x_0≤x<2π(η>p(x)=p(x+2π),-∞<x<∞is given, and the method can be applied to one with other periodic impulse coefficients.展开更多
In this paper, we apply Malliavin calculus to discuss when the solutions of stochastic differen-tial equations (SDE's) with time-dependent coefficients have smooth density. Under Hormander'scondition,we conclu...In this paper, we apply Malliavin calculus to discuss when the solutions of stochastic differen-tial equations (SDE's) with time-dependent coefficients have smooth density. Under Hormander'scondition,we conclude that the solutions of the SDE's have smooth density. As a consequence,we get the hypoellipticity for inhomogeneous differential operators.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
This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric meaning and the kinetic physical meani...This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric meaning and the kinetic physical meaning of fractional differential are clearly explained in view of information theory and kinetics, respectively. Secondly, it puts forward and discusses the definitions and theories of fractional stationary point, fractional equilibrium coefficient, fractional stable coefficient, and fractional grayscale co-occurrence matrix. At the same time, it particularly discusses frac- tional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly, it discusses in detail the structures and parameters of nxn any order fractional differential mask on negative x-coordinate, positive x-coordi- nate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal, respectively. Furthermore, it discusses the numerical implementation algorithms of fractional differential mask for digital image. Lastly, based on the above-mentioned discus- sion, it puts forward and discusses the theory and implementation of fractional differential filter for digital image. Experiments show that the fractional differential-based image operator has excellent feedback for enhancing the textural details of rich-grained digital images.展开更多
文摘The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.
文摘Based on a method of finite element model and combined with matrix theory, a method for solving differential equation with variable coefficients is proposed. With the method, it is easy to deal with the differential equations with variable coefficients. On most occasions and due to the nonuniformity nature, nonlinearity property can cause the equations of the kinds. Using the model, the satisfactory valuable results with only a few units can be obtained.
基金Provincial Science and Technology Foundation of Guizhou
文摘In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.
文摘Many engineering problems can be reduced to the solution of a variable coefficient differential equation. In this paper, the exact analytic method is suggested to solve variable coefficient differential equations under arbitrary boundary condition. By this method, the general computation formal is obtained. Its convergence in proved. We can get analytic expressions which converge to exact solution and its higher order derivatives uniformy Four numerical examples are given, which indicate that satisfactory results can he obtanedby this method.
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The irreversible mechanism of heat engines is studied in terms of <em>thermodynamic consistency</em> and thermomechanical dynamics (TMD) which is proposed for a method to study nonequilibrium irreversible thermodynamic systems. As an example, a water drinking bird (DB) known as one of the heat engines is specifically examined. The DB system suffices a rigorous experimental device for the theory of nonequilibrium irreversible thermodynamics. The DB nonlinear equation of motion proves explicitly that nonlinear differential equations with time-dependent coefficients must be classified as independent equations different from those of constant coefficients. The solutions of nonlinear differential equations with time-dependent coefficients can express emergent phenomena: nonequilibrium irreversible states. The <em>couplings</em> among mechanics, thermodynamics and time-evolution to nonequilibrium irreversible state are defined when the internal energy, thermodynamic work, temperature and entropy are integrated as a spontaneous thermodynamic process in the DB system. The physical meanings of the time-dependent entropy, <em>T</em>(<em>t</em>)d<em>S</em>(<em>t</em>), , internal energy, d<span style="white-space:nowrap;"><em>Ɛ</em></span>(<em>t</em>), and thermodynamic work, dW(<em>t</em>), are defined by the progress of time-dependent Gibbs relation to thermodynamic equilibrium. The thermomechanical dynamics (TMD) approach constitutes a method for the nonequilibrium irreversible thermodynamics and transport processes.
基金supported by the National Natural Science Foundation of China(Nos.12074345,12174349,11674289,11804306,11634011 and U2030120)Henan Provincial Key Science and Technology Research Projects(No.212102210130).
文摘Friction force(f)usually increases with the normal load(N)macroscopically,according to the classic law of Da Vinci–Amontons(f=μN),with a positive and finite friction coefficient(μ).Herein near-zero and negative differential friction(ZNDF)coefficients are discovered in two-dimensional(2D)van der Waals(vdW)magnetic CrI_(3)commensurate contacts.It is identified that the ferromagnetic–antiferromagnetic phase transition of the interlayer couplings of the bilayer CrI_(3)can significantly reduce the interfacial sliding energy barriers and thus contribute to ZNDF.Moreover,phase transition between the in-plane(p_(x)and p_(y))and out-of-plane(p_(z))wave-functions dominates the sliding barrier evolutions,which is attributed to the delicate interplays among the interlayer vdW,electrostatic interactions,and the intralayer deformation of the CrI_(3)layers under external load.The present findings may motivate a new concept of slide-spintronics and are expected to play an instrumental role in design of novel magnetic solid lubricants applied in various spintronic nano-devices.
基金Supported by the Joint Funds for Fostering Talents of National Natural Science Foundation of China and Henan Province(U1304324)
文摘To provide accurate base data about the genetic sourees of Yellow River carps, the genetic diversity in a^ficially bred population and wild population of Yellow River carps from Henan Province was analyzed with mierosatellite markers. The results showed that 16 alleles were detected at six microsateUite loci in each population. The average effective number of alleles (Ne) was 2. 350 in artificially bred population and 2. 085 in wild population. The observed heterozygosity (Ho) of artificially bred population, wild population and mixed population was 0. 614, 0. 576 and 0. 601 ; and the unbiased expected heterozygesity ( He ) was 0. 569, 0.535 and 0.559 ; and the polymorphism infonnatian content (PlC) was 0.474, 0.428 and 0.468, respectively. The PIC of the six loci ranged from 0.304 to 0. 864. The analysis of the genetic differentiation for the six microsatellitc loci in the two populations showed that the genetic differentiation coefficient ( F,, ) at only one microsatellite locus HLJ483 was greater than 0.05, and that at five rnicrosatellite loci were less than 0.05, which was consistent with the standard of non- genetic differentiation between populations (F,, = 0 -0.05). The average F,, at the six loci was 0.02, and the gene flow value (Nm) at all loci was greater than 1 and the average of Nm was 12.202. The results indicate that there is relatively abundant genetic diversity in Yellow River carps.
基金This work is supported by the National Science Fund of Peop1e's Republic of China
文摘A thorough investigation of the systemd^2y(x):dx^2+p(x)y(x)=0with periodic impulse coefficientsp(x)={1,0≤x<x_0(2π>0> -η, x_0≤x<2π(η>p(x)=p(x+2π),-∞<x<∞is given, and the method can be applied to one with other periodic impulse coefficients.
基金The project supported by National Natural Science Foundation of China Crant 18971061
文摘In this paper, we apply Malliavin calculus to discuss when the solutions of stochastic differen-tial equations (SDE's) with time-dependent coefficients have smooth density. Under Hormander'scondition,we conclude that the solutions of the SDE's have smooth density. As a consequence,we get the hypoellipticity for inhomogeneous differential operators.
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
基金Supported by China Postdoctoral Science Foundation (Grant No. 20060401016), Fondation Franco-Chinoise Pour La Science Et Ses Applications (FFCSA)the National Natural Science Foundation of China (Grant No. 60572033)the Doctor Foundation of China National Education Department (Grant No. 20060610021)
文摘This paper mainly discusses fractional differential approach to detecting textural features of digital image and its fractional differential filter. Firstly, both the geo- metric meaning and the kinetic physical meaning of fractional differential are clearly explained in view of information theory and kinetics, respectively. Secondly, it puts forward and discusses the definitions and theories of fractional stationary point, fractional equilibrium coefficient, fractional stable coefficient, and fractional grayscale co-occurrence matrix. At the same time, it particularly discusses frac- tional grayscale co-occurrence matrix approach to detecting textural features of digital image. Thirdly, it discusses in detail the structures and parameters of nxn any order fractional differential mask on negative x-coordinate, positive x-coordi- nate, negative y-coordinate, positive y-coordinate, left downward diagonal, left upward diagonal, right downward diagonal, and right upward diagonal, respectively. Furthermore, it discusses the numerical implementation algorithms of fractional differential mask for digital image. Lastly, based on the above-mentioned discus- sion, it puts forward and discusses the theory and implementation of fractional differential filter for digital image. Experiments show that the fractional differential-based image operator has excellent feedback for enhancing the textural details of rich-grained digital images.