本文在文献[Agarwal et al.,J.Inequ.Appl,2008,Art.ID 908784,15 pages]和文献[Chen et al.,J.Inequ.Appl.,2009,Art.ID 258569,15 pages]的基础上,建立了一类新的非线性时滞积分不等式。第一个参考文献中不等式的未知函数u是一元函数...本文在文献[Agarwal et al.,J.Inequ.Appl,2008,Art.ID 908784,15 pages]和文献[Chen et al.,J.Inequ.Appl.,2009,Art.ID 258569,15 pages]的基础上,建立了一类新的非线性时滞积分不等式。第一个参考文献中不等式的未知函数u是一元函数,右端第一项是正常数c;第二个参考文献中不等式右端第一项也是正常数c,第二项的被积函数中只含未知函数线性因子;本文研究的不等式中未知函数是二元函数,右端第一项是不减的正函数,第二项被积函数中含有未知函数的非线性因子,积分号外还有一个非常数因子.最后,本文用研究不等式得到的结果讨论了时滞偏微分方程初边值问题的有界性.展开更多
By means of the frozen time approach and the Kronecker product, two criteria of asymptotic stability are derived for the linear, time variant dynamic systems with either short time delays or with weak feedback involvi...By means of the frozen time approach and the Kronecker product, two criteria of asymptotic stability are derived for the linear, time variant dynamic systems with either short time delays or with weak feedback involving arbitrary time delays, respectively. It is found that the asymptotic stability of these retarded dynamic systems is governed by the maximal and minimal singular values of the coefficient matrices and their time derivatives. (Author abstract) 10 Refs.展开更多
Consider the retarded difference equation x<sub>n</sub>-x<sub>n-1</sub>=F（-f（x<sub>n</sub>）+g（x<sub>n</sub>-k））, （*） where k is a positive integer, F,f,g:R→R a...Consider the retarded difference equation x<sub>n</sub>-x<sub>n-1</sub>=F（-f（x<sub>n</sub>）+g（x<sub>n</sub>-k））, （*） where k is a positive integer, F,f,g:R→R are continuous, F and f are increasing on R, and uF（u）】0 for all u≠0. We show that when f（y）≥g（y）（resp. f（y）≤g（y）） for y∈R, every solution of （*） tends to either a constant or -∞ （resp. ∞） as n→∞. Furthermore, if f（y）≡g（y） for y∈R, then every solution of （*） tends to a constant as n→∞.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
This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. ...This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.展开更多
A variation of parameters formula and Gronwall type integral inequality are proved for a differential equation involving general piecewise alternately advanced and retarded argument.
This paper is concerned with the periodic retarded functional differential equati-ons(RFDEs) with infinite delay. The sufficient conditions for the existence of noncon-stant positive periodic solutions are established...This paper is concerned with the periodic retarded functional differential equati-ons(RFDEs) with infinite delay. The sufficient conditions for the existence of noncon-stant positive periodic solutions are established by combining the theory of monotone semiflows generated by RFDEs with infinite delay and the fixed point theorems of solution operators. A nontrivial application of the results obtained here to a well-known nonautonomous Lotka-Volterra system with infinite delay is also presented.展开更多
In this paper, we consider the retarded Lienard-type equationwhere h is a nonnegative constant, f_1 , f_2, and g are continuous functions on R.Using Liapunov functional method, we obtain the sufficient conditions to ...In this paper, we consider the retarded Lienard-type equationwhere h is a nonnegative constant, f_1 , f_2, and g are continuous functions on R.Using Liapunov functional method, we obtain the sufficient conditions to ensurethe stability and boundedness of solutions for Eq.(1).展开更多
It has been proved that when the retarded effect (or multiple moment effect) of radiation fields is taken into account,the high order stimulated radiation and stimulated absorption probabilities of light are not the s...It has been proved that when the retarded effect (or multiple moment effect) of radiation fields is taken into account,the high order stimulated radiation and stimulated absorption probabilities of light are not the same so that time reversal symmetry would be violated,though the Hamiltonian of electromagnetic interaction is still unchanged under time reversal. The reason to cause time reversal symmetry violation is that certain filial or partial transition processes of bound atoms are forbidden or cannot be achieved due to the law of energy conservation and the special states of atoms themselves. These restrictions would cause the symmetry violation of time reversal of other filial or partial transition processes which can be actualized really. The symmetry violation is also relative to the asymmetry of initial states of bound atoms before and after time reversal. For the electromagnetic interaction between non-bound atoms and radiation field,there is no such kind of symmetry violation of time reversal. In this way,the current formula on the parameters of stimulated radiation and absorption of light with time reversal sym-metry should be revised. A more reliable foundation can be established for the theories of laser and nonlinear optics in which non-equilibrium processes are in-volved.展开更多
Supernumerary tooth in the upper central incisor region is called mesiodens. Mesiodens causes serious complications such as displacement, retarded eruption, and rotation in the adjacent permanent incisors, inducing in...Supernumerary tooth in the upper central incisor region is called mesiodens. Mesiodens causes serious complications such as displacement, retarded eruption, and rotation in the adjacent permanent incisors, inducing inhibition of oral development. This report was aimed to provide epidemiology of mesiodens in Japanese children. Using dental record, panoramic radiographs and images of cone-beam computed tomography in 128 non-syndromic child patients, patients’ age at their first visit, gender composition, shape of mesiodens, position of mesiodens, posture of mesiodens, and age distribution of the patients based on each complication were investigated. In addition to the survey, patient age was compared between the groups with and without each complication. Patients’ age ranged 3 - 10 years old. Male-to-female ratio was approximately 3:1. Conical shape (75%) and inverted position (49%) were the most frequent among the patients. Displacement was the commonest complication. Age comparison indicated that patients with displacement or retarded eruption consulted the dentist younger than those without the complications. The present study provided etiology of mesiodens in Japanese children that will contribute to daily clinical practice in the field of pediatric dentistry.展开更多
We establish explicit bounds on some more general retarded integral inequalities which can be used as convenient tools in some applications, and give some examples which show the feasibility of our results.
B. G Zhang introduced an oscillatory and asymptotic behaviour of the equation X′(t)+p(t)X(t-[t])=0, t≥0, (1) where [t] denotes the greatest integer function.Now, we consider in a broad sense the first order nonlinear
文摘本文在文献[Agarwal et al.,J.Inequ.Appl,2008,Art.ID 908784,15 pages]和文献[Chen et al.,J.Inequ.Appl.,2009,Art.ID 258569,15 pages]的基础上,建立了一类新的非线性时滞积分不等式。第一个参考文献中不等式的未知函数u是一元函数,右端第一项是正常数c;第二个参考文献中不等式右端第一项也是正常数c,第二项的被积函数中只含未知函数线性因子;本文研究的不等式中未知函数是二元函数,右端第一项是不减的正函数,第二项被积函数中含有未知函数的非线性因子,积分号外还有一个非常数因子.最后,本文用研究不等式得到的结果讨论了时滞偏微分方程初边值问题的有界性.
基金The project supported by the National Natural Science Foundation of China under the Grant of 59625511
文摘By means of the frozen time approach and the Kronecker product, two criteria of asymptotic stability are derived for the linear, time variant dynamic systems with either short time delays or with weak feedback involving arbitrary time delays, respectively. It is found that the asymptotic stability of these retarded dynamic systems is governed by the maximal and minimal singular values of the coefficient matrices and their time derivatives. (Author abstract) 10 Refs.
基金Project supported by NNSF (19601016) of China NSF (97-37-42) of Hunan
文摘Consider the retarded difference equation x<sub>n</sub>-x<sub>n-1</sub>=F（-f（x<sub>n</sub>）+g（x<sub>n</sub>-k））, （*） where k is a positive integer, F,f,g:R→R are continuous, F and f are increasing on R, and uF（u）】0 for all u≠0. We show that when f（y）≥g（y）（resp. f（y）≤g（y）） for y∈R, every solution of （*） tends to either a constant or -∞ （resp. ∞） as n→∞. Furthermore, if f（y）≡g（y） for y∈R, then every solution of （*） tends to a constant as n→∞.
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This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.
基金supported by FONDECYT 1080034APIS 29-11 DIUMCEDI 0052-10 UNAP
文摘A variation of parameters formula and Gronwall type integral inequality are proved for a differential equation involving general piecewise alternately advanced and retarded argument.
基金Project supported by NNSF of China (No:19971026).
文摘This paper is concerned with the periodic retarded functional differential equati-ons(RFDEs) with infinite delay. The sufficient conditions for the existence of noncon-stant positive periodic solutions are established by combining the theory of monotone semiflows generated by RFDEs with infinite delay and the fixed point theorems of solution operators. A nontrivial application of the results obtained here to a well-known nonautonomous Lotka-Volterra system with infinite delay is also presented.
文摘In this paper, we consider the retarded Lienard-type equationwhere h is a nonnegative constant, f_1 , f_2, and g are continuous functions on R.Using Liapunov functional method, we obtain the sufficient conditions to ensurethe stability and boundedness of solutions for Eq.(1).
文摘It has been proved that when the retarded effect (or multiple moment effect) of radiation fields is taken into account,the high order stimulated radiation and stimulated absorption probabilities of light are not the same so that time reversal symmetry would be violated,though the Hamiltonian of electromagnetic interaction is still unchanged under time reversal. The reason to cause time reversal symmetry violation is that certain filial or partial transition processes of bound atoms are forbidden or cannot be achieved due to the law of energy conservation and the special states of atoms themselves. These restrictions would cause the symmetry violation of time reversal of other filial or partial transition processes which can be actualized really. The symmetry violation is also relative to the asymmetry of initial states of bound atoms before and after time reversal. For the electromagnetic interaction between non-bound atoms and radiation field,there is no such kind of symmetry violation of time reversal. In this way,the current formula on the parameters of stimulated radiation and absorption of light with time reversal sym-metry should be revised. A more reliable foundation can be established for the theories of laser and nonlinear optics in which non-equilibrium processes are in-volved.
文摘Supernumerary tooth in the upper central incisor region is called mesiodens. Mesiodens causes serious complications such as displacement, retarded eruption, and rotation in the adjacent permanent incisors, inducing inhibition of oral development. This report was aimed to provide epidemiology of mesiodens in Japanese children. Using dental record, panoramic radiographs and images of cone-beam computed tomography in 128 non-syndromic child patients, patients’ age at their first visit, gender composition, shape of mesiodens, position of mesiodens, posture of mesiodens, and age distribution of the patients based on each complication were investigated. In addition to the survey, patient age was compared between the groups with and without each complication. Patients’ age ranged 3 - 10 years old. Male-to-female ratio was approximately 3:1. Conical shape (75%) and inverted position (49%) were the most frequent among the patients. Displacement was the commonest complication. Age comparison indicated that patients with displacement or retarded eruption consulted the dentist younger than those without the complications. The present study provided etiology of mesiodens in Japanese children that will contribute to daily clinical practice in the field of pediatric dentistry.
基金supported by the National Natural Sciences Foundation of China (10771118)Natural Sciences Foundation of Shandong Province (ZR2009AM011 and ZR2009AQ010)
文摘We establish explicit bounds on some more general retarded integral inequalities which can be used as convenient tools in some applications, and give some examples which show the feasibility of our results.
文摘B. G Zhang introduced an oscillatory and asymptotic behaviour of the equation X′(t)+p(t)X(t-[t])=0, t≥0, (1) where [t] denotes the greatest integer function.Now, we consider in a broad sense the first order nonlinear
