In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, ...In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, the （2＋1）-dimensional Lax pair is reduced to （1＋1）-dimensional Lax pair, whose compatibility yields the reduction of the ANNV equation. Based on the obtained reductions of the ANNV equation, a lot of new exact solutions for the ANNV equation are found. This shows that for an integrable system, both the symmetry and the reductions can be obtained through its corresponding Lax pair.展开更多
To master theoretical calculation for dust removal efficiency of high pressure atomization in an underground coal mine, the corresponding atomization characteristics and dust removal efficiency were both comprehensive...To master theoretical calculation for dust removal efficiency of high pressure atomization in an underground coal mine, the corresponding atomization characteristics and dust removal efficiency were both comprehensively studied in theory by virtue of related theories of hydromechanics and aerosol.According to actual measurements of flow coefficients and atomization angles of X-type swirl nozzle,computational formula was derived for atomized particle sizes of such a nozzle in conjunction with relevant empirical equation. Moreover, a mathematical model for applying high pressure atomization to dust removal in underground coal mine was also established to deduce theoretical computation formula of fractional efficiency. Then, Matlab was adopted to portray the relation curve between fractional efficiency and influence factors. In addition, a theoretical formula was also set up for removal efficiency of respirable dust and total coal dust based on dust size and frequency distribution equations. In the end,impacts of dust characteristic parameters on various dust removal efficiencies were analyzed.展开更多
Abstract In terms of the solutions of an auxiliary ordinary differential equation, a new algebraic method, which contains the terms of first-order derivative of functions f （ξ）, is constructed to explore the new so...Abstract In terms of the solutions of an auxiliary ordinary differential equation, a new algebraic method, which contains the terms of first-order derivative of functions f （ξ）, is constructed to explore the new solitary wave solutions for nonlinear evolution equations. The method is applied to a compound KdV-Burgers equation, and abundant new solitary wave solutions are obtained. The algorithm is also applicable to a large variety of nonlinear evolution equations.展开更多
By considering the fluctuation of grand potential f~ around equilibrium with respect to small one-particle density fluctuations δpα（r→）, the phase instability of restricted primitive model （RPM） of ionic system...By considering the fluctuation of grand potential f~ around equilibrium with respect to small one-particle density fluctuations δpα（r→）, the phase instability of restricted primitive model （RPM） of ionic systems is investigated. We use the integral equation theory to calculate the direct correlation functions in the reference hypernetted chain approximation and obtain the spinodai line of RPM. Our anaiysis explicitly indicates that the gas-fluid phase instability is induced by k = 0 fluctuation mode, while the fluid-solid phase instability is related to k ≠ 0 fluctuation modes. The spinodai line is qualitatively consistent with the result of computer simulations by others.展开更多
According to features of current undergraduate curriculum design in the teaching of art and science, and combing exploration and the problems that exist during the process of teaching of basic theory of art and scienc...According to features of current undergraduate curriculum design in the teaching of art and science, and combing exploration and the problems that exist during the process of teaching of basic theory of art and science, this paper taking design courses of interactive introduction for example, it tries to innovate classroom teaching methods of exhibition of art and technology, interactive art and technology are principle theoretical classes of their major. Making good use of initiative of self- learning is the core element to help students in subjects learning, we constantly improve and perfect teaching concepts and classroom teaching mode to create the space for students to learn and explore actively, make personalized study according to their own characteristics, we make students experience the interest of freedom, autonomy, inquiry learning, enjoy the delight of appearance of personality and vitality of the burst of life vigor. Combining personal teaching experience, we should explore the way to led art students to learn with initiative in principle theoretical classes of their major.展开更多
The char-set method of polynomial equations-solving is naturally extended to the differential case which gives rise to an algorithmic method of solving arbitrary systems of algebrico-differential equations.As an illus...The char-set method of polynomial equations-solving is naturally extended to the differential case which gives rise to an algorithmic method of solving arbitrary systems of algebrico-differential equations.As an illustration of the method,the Devil's Problem of Pommaret is solved in details.展开更多
The author proves that the on the singular set of a local solution to existence of an optimal control problem. right-hand term of a p-Laplace equation is zero the equation. Such a result is used to study the
A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is const...A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is constructed.And then,by using the theory of differential inequalities the uniformly validity of solution is proved.展开更多
The crossflow instability of a three-dimensional (3-D) boundary layer is an important factor which affects the transition over a swept-wing.In this report,the primary instability of the incompressible flow over a swep...The crossflow instability of a three-dimensional (3-D) boundary layer is an important factor which affects the transition over a swept-wing.In this report,the primary instability of the incompressible flow over a swept wing is investigated by solving nonlinear parabolized stability equations (NPSE).The Floquet theory is applied to study the dependence of the secondary and high-frequency instabilities on curvature,Reynolds number and angle of swept (AOS).The computational results show that the curvature in the present case has no significant effect on the secondary instabilities.It is generally believed that the secondary instability growth rate increases with the magnitude of the nonlinear mode of crossflow vortex.But,at a certain state,when the Reynolds number is 3.2 million,we find that the secondary instability growth rate becomes smaller even when the magnitude of the nonlinear mode of the crossflow vortex is larger.The effect of the angle of swept at 35,45 and 55 degrees,respectively,is also studied in the framework of the secondary linear stability theory.Larger angles of swept tend to decrease the spanwise spacing of the crossflow vortices,which correspondingly helps the stimulation of 'z' mode.展开更多
基金Natural Science Foundation of Shandong Province under Grant Nos.2004zx16 and Q2005A01
文摘In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, the （2＋1）-dimensional Lax pair is reduced to （1＋1）-dimensional Lax pair, whose compatibility yields the reduction of the ANNV equation. Based on the obtained reductions of the ANNV equation, a lot of new exact solutions for the ANNV equation are found. This shows that for an integrable system, both the symmetry and the reductions can be obtained through its corresponding Lax pair.
基金Financial provided by the National Natural Science Foundation of China (Nos. 51574123 and U1361118)the China Postdoctoral Science Foundation (No. 2015M 582118)
文摘To master theoretical calculation for dust removal efficiency of high pressure atomization in an underground coal mine, the corresponding atomization characteristics and dust removal efficiency were both comprehensively studied in theory by virtue of related theories of hydromechanics and aerosol.According to actual measurements of flow coefficients and atomization angles of X-type swirl nozzle,computational formula was derived for atomized particle sizes of such a nozzle in conjunction with relevant empirical equation. Moreover, a mathematical model for applying high pressure atomization to dust removal in underground coal mine was also established to deduce theoretical computation formula of fractional efficiency. Then, Matlab was adopted to portray the relation curve between fractional efficiency and influence factors. In addition, a theoretical formula was also set up for removal efficiency of respirable dust and total coal dust based on dust size and frequency distribution equations. In the end,impacts of dust characteristic parameters on various dust removal efficiencies were analyzed.
基金the Science and Technology Foundation of Guizhou Province under Grant No.20072009
文摘Abstract In terms of the solutions of an auxiliary ordinary differential equation, a new algebraic method, which contains the terms of first-order derivative of functions f （ξ）, is constructed to explore the new solitary wave solutions for nonlinear evolution equations. The method is applied to a compound KdV-Burgers equation, and abundant new solitary wave solutions are obtained. The algorithm is also applicable to a large variety of nonlinear evolution equations.
基金Supported by National Natural Science Foundation of China under Grant No.10325418
文摘By considering the fluctuation of grand potential f~ around equilibrium with respect to small one-particle density fluctuations δpα（r→）, the phase instability of restricted primitive model （RPM） of ionic systems is investigated. We use the integral equation theory to calculate the direct correlation functions in the reference hypernetted chain approximation and obtain the spinodai line of RPM. Our anaiysis explicitly indicates that the gas-fluid phase instability is induced by k = 0 fluctuation mode, while the fluid-solid phase instability is related to k ≠ 0 fluctuation modes. The spinodai line is qualitatively consistent with the result of computer simulations by others.
文摘According to features of current undergraduate curriculum design in the teaching of art and science, and combing exploration and the problems that exist during the process of teaching of basic theory of art and science, this paper taking design courses of interactive introduction for example, it tries to innovate classroom teaching methods of exhibition of art and technology, interactive art and technology are principle theoretical classes of their major. Making good use of initiative of self- learning is the core element to help students in subjects learning, we constantly improve and perfect teaching concepts and classroom teaching mode to create the space for students to learn and explore actively, make personalized study according to their own characteristics, we make students experience the interest of freedom, autonomy, inquiry learning, enjoy the delight of appearance of personality and vitality of the burst of life vigor. Combining personal teaching experience, we should explore the way to led art students to learn with initiative in principle theoretical classes of their major.
基金The present paper is in honor of late Professor R.Thom as a great mathematician, a great scientist,also a great thinker of modern times.
文摘The char-set method of polynomial equations-solving is naturally extended to the differential case which gives rise to an algorithmic method of solving arbitrary systems of algebrico-differential equations.As an illustration of the method,the Devil's Problem of Pommaret is solved in details.
基金the National Natural Science Foundation of China (No. 10671040) the Foundationfor the Author of National Excellent Doctoral Dissertation of China (No. 200522)the Program forNew Century Excellent Talents in University of China (No. 06-0359)
文摘The author proves that the on the singular set of a local solution to existence of an optimal control problem. right-hand term of a p-Laplace equation is zero the equation. Such a result is used to study the
基金the National Natural Science Foundation of China (Nos.40676016 and 40876010)the National Basic Research Program (973) of China (Nos.2003CB415101-03 and 2004CB418304)+2 种基金the Knowledge Innovation Project of Chinese Academy of Sciences (No.KZCX2-YW-Q03-08)LASG State Key Laboratory Special FundE-Institutes of Shanghai Municipal Education Commission (No.E03004)
文摘A class of differential-difference reaction diffusion equations with a small time delay is considered.Under suitable conditions and by using the method of the stretched variable,the formal asymptotic solution is constructed.And then,by using the theory of differential inequalities the uniformly validity of solution is proved.
基金supported by the National Natural Science Foundation of China(Grant Nos. 90505005 and 10932005)
文摘The crossflow instability of a three-dimensional (3-D) boundary layer is an important factor which affects the transition over a swept-wing.In this report,the primary instability of the incompressible flow over a swept wing is investigated by solving nonlinear parabolized stability equations (NPSE).The Floquet theory is applied to study the dependence of the secondary and high-frequency instabilities on curvature,Reynolds number and angle of swept (AOS).The computational results show that the curvature in the present case has no significant effect on the secondary instabilities.It is generally believed that the secondary instability growth rate increases with the magnitude of the nonlinear mode of crossflow vortex.But,at a certain state,when the Reynolds number is 3.2 million,we find that the secondary instability growth rate becomes smaller even when the magnitude of the nonlinear mode of the crossflow vortex is larger.The effect of the angle of swept at 35,45 and 55 degrees,respectively,is also studied in the framework of the secondary linear stability theory.Larger angles of swept tend to decrease the spanwise spacing of the crossflow vortices,which correspondingly helps the stimulation of 'z' mode.
