This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtai...This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtained.展开更多
Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.
Some new sufficient conditions for the oscillation of the neutral equationddt[y（t）-R（t）y（t-r）]+P（t）y（t-τ）- Q（t）y（t-σ）=0, where P,Q,R∈C（[t0,∞）,R+) and r,τ,σ∈（0,∞）,are obtained for the case whe...Some new sufficient conditions for the oscillation of the neutral equationddt[y（t）-R（t）y（t-r）]+P（t）y（t-τ）- Q（t）y（t-σ）=0, where P,Q,R∈C（[t0,∞）,R+) and r,τ,σ∈（0,∞）,are obtained for the case where former results can not be applied in this paper.展开更多
The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonia...The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.展开更多
Loads generated after an air crash, ship collision, and other accidents may destroy very large floating structures （VLFSs） and create additional connector loads. In this study, the combined effects of ship collision...Loads generated after an air crash, ship collision, and other accidents may destroy very large floating structures （VLFSs） and create additional connector loads. In this study, the combined effects of ship collision and wave loads are considered to establish motion differential equations for a multi-body VLFS. A time domain calculation method is proposed to calculate the connector load of the VLFS in waves. The Longuet-Higgins model is employed to simulate the stochastic wave load. Fluid force and hydrodynamic coefficient are obtained with DNV Sesam software. The motion differential equation is calculated by applying the time domain method when the frequency domain hydrodynamic coefficient is converted into the memory function of the motion differential equation of the time domain. As a result of the combined action of wave and impact loads, high-frequency oscillation is observed in the time history curve of the connector load. At wave directions of 0° and 75°, the regularities of the time history curves of the connector loads in different directions are similar and the connector loads of C1 and C2 in the X direction are the largest. The oscillation load is observed in the connector in the Y direction at a wave direction of 75° and not at 0° This paper presents a time domain calculation method of connector load to provide a certain reference function for the future development of Chinese VLFS展开更多
The problem of mathematical simulation of motion of dynamic systems characteristics and their coincidence with real experimental data which correspond to these characteristics is investigated in this paper. Mathematic...The problem of mathematical simulation of motion of dynamic systems characteristics and their coincidence with real experimental data which correspond to these characteristics is investigated in this paper. Mathematical description of process will be named as adequate mathematical description if the results of mathematical simulation by the help of this description coincide with experiment with inaccuracy of initial data. The synthesis of such description is very important at mathematical modeling and forecast of motion of real physical phenomena. The specified problem is still poorly investigated and hardly adapted to formalization. The requirements to the adequate mathematical description of dynamic system are considered for the case when mathematical description of dynamic systems is represented by linear system of the ordinary differential equations. In this paper the mathematical model of process is given a priori with inexact parameters and then the models of external loads are being determined for which the results of simulation coincide with experiment. The methods of obtaining of the steady models of external loads are suggested. The example of the adequate description construction of the main mechanical line dynamics of rolling mill is given.展开更多
Effect of working temperature on the resistance characteristic including the permeability coefficient and the pressure drop evolution of a pleated stainless steel woven filter with a nominal pore size of 0.5 μm has b...Effect of working temperature on the resistance characteristic including the permeability coefficient and the pressure drop evolution of a pleated stainless steel woven filter with a nominal pore size of 0.5 μm has been studied. The permeability coefficient was obtained based on the pressure drop data and the Darcy＇s law. In three filtration experiments, pure carbon dioxide at 283 K, nitrogen at 85 K and liquid helium at 18 K are adopted, respectively. It is found that the permeability coefficient decreases at the working temperature due to the cold shrink of the filter element at cryogenic temperature. Then, two kinds of feed slurries, mixture of liquid nitrogen and solid carbon dioxide at 85 K, and mixture of liquid helium and solid nitrogen at 18 K, flow into the filter cell. The solid particles are deposited on the filter surface to form a filter cake and the purified liquid flows through the filter. It is found that the pressure drop evolution shows the same trend on these two temperatures, which can be divided into three stages with high filtration efficiency, indicating the feasibility of the filter for cryogenic application. However, variant cake resistances are obtained, which is resulted from the different interactions between solid particles in the feed slurry at lower working temperature.展开更多
Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. S...Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields. In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively.展开更多
In this paper, we establish the product formula for the fixed point index on product cone, andthen, as applications, consider the existence, nonexistence and multiplicity of positive solutions for a second-order ordin...In this paper, we establish the product formula for the fixed point index on product cone, andthen, as applications, consider the existence, nonexistence and multiplicity of positive solutions for a second-order ordinary differential system with parameters. The discussion is based on the product formula and thefundamental properties of the fixed point index.展开更多
In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic l...In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is n(n ≥ 1), it is obtained that n limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems, and that there are at most n + [(n+1)/2] limit cycles bifurcating from the periodic annulus between the center and the heteroclinic loop up to the first order in ε. Especially, for n = 1, 2, 3 and 4, a precise result on the maximal number of zeros of the first Melnikov function is derived.展开更多
The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,th...The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,the strongly nonlinear Duffing oscillator with third,fifth,and seventh powers of the amplitude,the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration.The obtained results via the approach are compared with ones achieved utilizing other techniques.The results indicate that the approach has a good agreement with other well-known methods.He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.展开更多
文摘This paper discusses a class of unstable second order neutral differential equations with positive and negative coeffcients. Sufficient conditions for all bounded solutions of the equations to be oscillatory are obtained.
文摘Some sufficient conditions are obtained for the oscillation of first order neutral differential_difference equations with positive and negative periodic coefficients.
文摘Some new sufficient conditions for the oscillation of the neutral equationddt[y（t）-R（t）y（t-r）]+P（t）y（t-τ）- Q（t）y（t-σ）=0, where P,Q,R∈C（[t0,∞）,R+) and r,τ,σ∈（0,∞）,are obtained for the case where former results can not be applied in this paper.
基金Supported by the National Natural Science Foundation of China under Grant No.10962004the Natural Science Foundation of Inner Mongolia under Grant No.2009BS0101+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No.20070126002the Cultivation of Innovative Talent of "211 Project"of Inner Mongolia University
文摘The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrix differential system. For the associated operator matrix, we find that the two diagonal block operators are Hamiltonian. Moreover, the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two block operators are demonstrated. Based on the completeness, the general solution of the free vibration of rectangular thin plates is given by double symplectie eigenfunction expansion method.
基金Foundation item： Supported by the National Natural Science Foundation of China （51309123）, National Key Basic Research and Development Plan （973 Plan, 2013CB036104）, Jiangsu Province Natural Science Research Projects in Colleges and Universities （13KJB570002）, Open Foundation of State Key Laboratory of Ocean Engineering （1407）, ＂Qing Lan Project＂ of Colleges and Universities in Jiangsu Province, Academic Program Development of Jiangsu Higher Education Institutions （PAPD）.
文摘Loads generated after an air crash, ship collision, and other accidents may destroy very large floating structures （VLFSs） and create additional connector loads. In this study, the combined effects of ship collision and wave loads are considered to establish motion differential equations for a multi-body VLFS. A time domain calculation method is proposed to calculate the connector load of the VLFS in waves. The Longuet-Higgins model is employed to simulate the stochastic wave load. Fluid force and hydrodynamic coefficient are obtained with DNV Sesam software. The motion differential equation is calculated by applying the time domain method when the frequency domain hydrodynamic coefficient is converted into the memory function of the motion differential equation of the time domain. As a result of the combined action of wave and impact loads, high-frequency oscillation is observed in the time history curve of the connector load. At wave directions of 0° and 75°, the regularities of the time history curves of the connector loads in different directions are similar and the connector loads of C1 and C2 in the X direction are the largest. The oscillation load is observed in the connector in the Y direction at a wave direction of 75° and not at 0° This paper presents a time domain calculation method of connector load to provide a certain reference function for the future development of Chinese VLFS
文摘The problem of mathematical simulation of motion of dynamic systems characteristics and their coincidence with real experimental data which correspond to these characteristics is investigated in this paper. Mathematical description of process will be named as adequate mathematical description if the results of mathematical simulation by the help of this description coincide with experiment with inaccuracy of initial data. The synthesis of such description is very important at mathematical modeling and forecast of motion of real physical phenomena. The specified problem is still poorly investigated and hardly adapted to formalization. The requirements to the adequate mathematical description of dynamic system are considered for the case when mathematical description of dynamic systems is represented by linear system of the ordinary differential equations. In this paper the mathematical model of process is given a priori with inexact parameters and then the models of external loads are being determined for which the results of simulation coincide with experiment. The methods of obtaining of the steady models of external loads are suggested. The example of the adequate description construction of the main mechanical line dynamics of rolling mill is given.
基金Supported by the Shanghai Committee of Science and Technology,China (03 DZ14014)
文摘Effect of working temperature on the resistance characteristic including the permeability coefficient and the pressure drop evolution of a pleated stainless steel woven filter with a nominal pore size of 0.5 μm has been studied. The permeability coefficient was obtained based on the pressure drop data and the Darcy＇s law. In three filtration experiments, pure carbon dioxide at 283 K, nitrogen at 85 K and liquid helium at 18 K are adopted, respectively. It is found that the permeability coefficient decreases at the working temperature due to the cold shrink of the filter element at cryogenic temperature. Then, two kinds of feed slurries, mixture of liquid nitrogen and solid carbon dioxide at 85 K, and mixture of liquid helium and solid nitrogen at 18 K, flow into the filter cell. The solid particles are deposited on the filter surface to form a filter cake and the purified liquid flows through the filter. It is found that the pressure drop evolution shows the same trend on these two temperatures, which can be divided into three stages with high filtration efficiency, indicating the feasibility of the filter for cryogenic application. However, variant cake resistances are obtained, which is resulted from the different interactions between solid particles in the feed slurry at lower working temperature.
基金Supported partly by National Natural Science Foundation of China under Grant No. 60221301 and 60334040 .Dedicated to Academician Han-Fu Chen on the occasion of his 70th birthday.
文摘Semi-tensor product of matrices is a generalization of conventional matrix product for the case when the two factor matrices do not meet the dimension matching condition. It was firstly proposed about ten years ago. Since then it has been developed and applied to several different fields. In this paper we will first give a brief introduction. Then give a survey on its applications to dynamic systems, to logic, to differential geometry, to abstract algebra, respectively.
基金supported by Natural Science Foundation in Jiangsu Province (Grant Nos.10KJB110004, 08KJD110010)National Natural Science Foundation of China (Grant Nos. 10971046, 10831005, 10671195)China Postdoctoral Science Foundation (Grant Nos. 20090450601)
文摘In this paper, we establish the product formula for the fixed point index on product cone, andthen, as applications, consider the existence, nonexistence and multiplicity of positive solutions for a second-order ordinary differential system with parameters. The discussion is based on the product formula and thefundamental properties of the fixed point index.
基金supported by the National Natural Science Foundation of China(No.11271261)the Natural Science Foundation of Anhui Province(No.1308085MA08)the Doctoral Program Foundation(2012)of Anhui Normal University
文摘In this paper, the authors consider limit cycle bifurcations for a kind of nonsmooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a heteroclinic loop around the origin. When the degree of perturbing polynomial terms is n(n ≥ 1), it is obtained that n limit cycles can appear near the origin and the heteroclinic loop respectively by using the first Melnikov function of piecewise near-Hamiltonian systems, and that there are at most n + [(n+1)/2] limit cycles bifurcating from the periodic annulus between the center and the heteroclinic loop up to the first order in ε. Especially, for n = 1, 2, 3 and 4, a precise result on the maximal number of zeros of the first Melnikov function is derived.
文摘The max-min approach is applied to mathematical models of some nonlinear oscillations.The models are regarding to three different forms that are governed by nonlinear ordinary differential equations.In this context,the strongly nonlinear Duffing oscillator with third,fifth,and seventh powers of the amplitude,the pendulum attached to a rotating rigid frame and the cubic Duffing oscillator with discontinuity are taken into consideration.The obtained results via the approach are compared with ones achieved utilizing other techniques.The results indicate that the approach has a good agreement with other well-known methods.He's max-min approach is a promising technique and can be successfully exerted to a lot of practical engineering and physical problems.
