The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct m...The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.展开更多
[Objective] The study is aimed to timely grasp the growth and develop- ment process of summer maize and comprehensively evaluate the impact of envi- ronmental factors on the growth and development of maize in north Hu...[Objective] The study is aimed to timely grasp the growth and develop- ment process of summer maize and comprehensively evaluate the impact of envi- ronmental factors on the growth and development of maize in north Huanguaihai re- gion. [Method] The phenophase, leaf unfolding rate, grain filling rate and yield char- acteristics of Zhengdan 958 and Xianyu 335 were analyzed at N 37°53′, E115°42′. [Result] The summer corn Zhengdan 958 and Xianyu335 emerged in 6 days after sowing with the growing period of 111 d, grain-filling stage lasting 66 days, and the leaf unfolding rate and grain filling rate were accelerated with the increase of tem- perature. In the last 6 d before harvest （October 5-11）, Zhengdan 958 and Xi- anyu335 contributed to the yield by 6.61% and 4.20%, respectively. The two crops a year cropping system made it hard for the summer maize to achieve maturing harvest in north Huanghuaihai region. [Conclusion] The maize production could be significantly improved through selecting early maturing varieties, early sowing, timely late harvest, ensuring maize effective accumulated temperature and sufficient grout- ing time after pollination.展开更多
Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soli...Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.展开更多
In this paper, applying the dependent and independent variables transformations as well as the Jacobi elliptic function expansion method, the envelope periodic solutions to one-dimensional Gross-Pitaevskii equation in...In this paper, applying the dependent and independent variables transformations as well as the Jacobi elliptic function expansion method, the envelope periodic solutions to one-dimensional Gross-Pitaevskii equation in Bose-Einstein condensates are obtained.展开更多
This paper studies the transient departure process of M^x/G/1 queueing system with single server vacation. We present a simple probability decomposition method to derive the expected number of departures occurring in ...This paper studies the transient departure process of M^x/G/1 queueing system with single server vacation. We present a simple probability decomposition method to derive the expected number of departures occurring in finite time interval from any initial state and the asymptotic expansion of the expected number. Especially, we derive some more practical results for some special cases.展开更多
Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic pot...Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.展开更多
We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization ...We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil(2001).展开更多
Based on the invariant expansion method, some reasonable approximate solutions of coupled Korteweg-de Vries （KdV） equations with different linear dispersion relations have been obtained. These solutions contain not ...Based on the invariant expansion method, some reasonable approximate solutions of coupled Korteweg-de Vries （KdV） equations with different linear dispersion relations have been obtained. These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacob/elliptic functions. The results also show that if the arbitrary constants are selected suitably, the approximate solutions may become the exact ones.展开更多
In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expans...In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expansion for the transition density, we prove the existence and uniqueness of both quasi-stationary distribution (qsd) and mean ratio quasi-stationary distribution (mrqsd). The later is shown to be closely related to laws of large numbers (LLN) and to quasi-ergodicity. We further show that the mrqsd is the unique stationary distribution of a certain limiting ergodic diffusion process of the BM conditioned on not having been killed. We also show that a phase transition occurs from mrqsd to qsd. On the other hand, we study the large deviation behavior related to the above problems. A key observation is that the mrqsd is the unique minimum of certain large deviation rate function. We further prove that the limiting diffusion process also satisfies a large deviation principle with the rate function attaining its unique minimum at the mrqsd. These give interpretations of the mrqsd from different points of view, and establish some intrinsic connections among the above topics. Some general results concerning Yaglom limit, moment convergence and LLN are also obtained.展开更多
The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explici...The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.展开更多
文摘The Jacobian elliptic function expansion method for nonlinear differential-different equations and its algorithm are presented by using some relations among ten Jacobian elliptic functions and successfully construct more new exact doubly-periodic solutions of the integrable discrete nonlinear Schrodinger equation. When the modulous m → 1or 0, doubly-periodic solutions degenerate to solitonic solutions including bright soliton, dark soliton, new solitons as well as trigonometric function solutions.
基金Supported by the Foundation of China Agricultural Research System for Maize Industry(CARS-02-48)~~
文摘[Objective] The study is aimed to timely grasp the growth and develop- ment process of summer maize and comprehensively evaluate the impact of envi- ronmental factors on the growth and development of maize in north Huanguaihai re- gion. [Method] The phenophase, leaf unfolding rate, grain filling rate and yield char- acteristics of Zhengdan 958 and Xianyu 335 were analyzed at N 37°53′, E115°42′. [Result] The summer corn Zhengdan 958 and Xianyu335 emerged in 6 days after sowing with the growing period of 111 d, grain-filling stage lasting 66 days, and the leaf unfolding rate and grain filling rate were accelerated with the increase of tem- perature. In the last 6 d before harvest （October 5-11）, Zhengdan 958 and Xi- anyu335 contributed to the yield by 6.61% and 4.20%, respectively. The two crops a year cropping system made it hard for the summer maize to achieve maturing harvest in north Huanghuaihai region. [Conclusion] The maize production could be significantly improved through selecting early maturing varieties, early sowing, timely late harvest, ensuring maize effective accumulated temperature and sufficient grout- ing time after pollination.
文摘Using a further modified extended tanh-function method, rich new families of the exact solutions for the (2+ 1)-dimensional Broer-Kaup (BK) system, comprising the non-traveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions, are obtained.
基金Supported by National Natural Science Foundation of China under Grant No. 90511009
文摘In this paper, applying the dependent and independent variables transformations as well as the Jacobi elliptic function expansion method, the envelope periodic solutions to one-dimensional Gross-Pitaevskii equation in Bose-Einstein condensates are obtained.
基金This research is supported by Natural Science Foundation of the Education Department of Sichuan Province （[2006]A067） and the Talent Introduction Foundation of Sichuan Normal University. Acknowledgments The author thanks referees for their many helpful comments and suggestions for the improvement of this paper.
文摘This paper studies the transient departure process of M^x/G/1 queueing system with single server vacation. We present a simple probability decomposition method to derive the expected number of departures occurring in finite time interval from any initial state and the asymptotic expansion of the expected number. Especially, we derive some more practical results for some special cases.
基金Supported by National Natural Science Foundation of China under Grant Nos.11375030 and 61304133
文摘Using an improved homogeneous balance principle and an F-expansion technique, we construct the new exact periodic traveling wave solutions to the(3+1)-dimensional Gross–Pitaevskii equation with repulsive harmonic potential. In the limit cases, the solitary wave solutions are obtained as well. We also investigate the dynamical evolution of the solitons with a time-dependent complicated potential.
基金supported by National Natural Science Foundation of China(Grant No.11401595)
文摘We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil(2001).
基金Supported by National Natural Science Foundation of China under Grant No.11104248Zhejiang Provincial Natural Science Foundation of China under Grant No.LQ12A01008Project of Education of Zhejiang Province under Grant No.Y201327716
文摘Based on the invariant expansion method, some reasonable approximate solutions of coupled Korteweg-de Vries （KdV） equations with different linear dispersion relations have been obtained. These solutions contain not only bell type soliton solutions but also periodic wave solutions that expressed by Jacob/elliptic functions. The results also show that if the arbitrary constants are selected suitably, the approximate solutions may become the exact ones.
基金supported by National Natural Science Foundation of China(Grant No. 10971253)
文摘In this paper, we prove some limit theorems for killed Brownian motion during its life time. The emphases are on quasi-stationarity and quasi-ergodicity and related problems. On one hand, using an eigenfunction expansion for the transition density, we prove the existence and uniqueness of both quasi-stationary distribution (qsd) and mean ratio quasi-stationary distribution (mrqsd). The later is shown to be closely related to laws of large numbers (LLN) and to quasi-ergodicity. We further show that the mrqsd is the unique stationary distribution of a certain limiting ergodic diffusion process of the BM conditioned on not having been killed. We also show that a phase transition occurs from mrqsd to qsd. On the other hand, we study the large deviation behavior related to the above problems. A key observation is that the mrqsd is the unique minimum of certain large deviation rate function. We further prove that the limiting diffusion process also satisfies a large deviation principle with the rate function attaining its unique minimum at the mrqsd. These give interpretations of the mrqsd from different points of view, and establish some intrinsic connections among the above topics. Some general results concerning Yaglom limit, moment convergence and LLN are also obtained.
基金Supported by the National Natural Science Foundation of Zhejiang Province under Grant No.LZ15A050001the National Natural Science Foundation of China under Grant No.11675146
文摘The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.
