We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vec...We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.展开更多
Researches are being carried out world-wide to understand the nature of temperature change during recent past at different geographical scales so that comprehensive inferences can be drawn about recent temperature tre...Researches are being carried out world-wide to understand the nature of temperature change during recent past at different geographical scales so that comprehensive inferences can be drawn about recent temperature trend and future climate. Detection of turning points in time series of meteorological parameters puts challenges to the researches. In this work, the temperature time series from 1941 to 2010 for Asansol observatory, West Bengal, India, has been considered to understand the nature, trends and change points in the data set using sequential version of Mann-Kendall test statistic. Literatures suggest that use of this test statistic is the most appropriate for detecting climatic abrupt changes as compared to other statistical tests in use. This method has been employed upon monthly average temperatures recorded over the said 70 years for detection of abrupt changes in the average temperature of each of the months. The approximate potential trend turning points have been calculated separately for each month (January to December). Sequential version of Mann-Kendall test statistic values for the months of July and August is significant at 95% confidence level (p 0.05). The average temperature for most of the other months has shown an increasing trend but more significant rise in July and August temperature has been recognized since 1960s.展开更多
The paper considers the asymptotic solution of two-point boundary value problems εy” + A(x)y’ = 0, 0 ≤ x ≤ 1, when 0 1, A(x) is smooth with isolated zeros, y(0) = 0 and y(1) = 1. By using perturbation method, the...The paper considers the asymptotic solution of two-point boundary value problems εy” + A(x)y’ = 0, 0 ≤ x ≤ 1, when 0 1, A(x) is smooth with isolated zeros, y(0) = 0 and y(1) = 1. By using perturbation method, the limit asymptotic solutions of various cases are obtained. We provide a reliable and direct method for solving similar problems. The limiting solutions are constants in this paper, except in narrow boundary and interior layers of nonuniform convergence. These provide simple examples of boundary layer resonance.展开更多
Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) ...Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) gamma = 0 (- a < x < b, 0 epsilon 1), where f(x ; 0) has several multiple zero points in ( - n, b). the necessary conditions for exhibiting resonance is given, and the uniformly valid asymptotic solutions and the estimations of remainder terms are obtained.展开更多
Bu tler旅游地生命周期模型作为一个很有用的理论工具,虽然已被广泛应用于旅游地发展演化过程的研究之中,但在实际应用中也面临着一些不可忽视的困境。通过对Bu tler旅游地生命周期模型的分析发现,该模型在应用中存在以下难题:难以获得...Bu tler旅游地生命周期模型作为一个很有用的理论工具,虽然已被广泛应用于旅游地发展演化过程的研究之中,但在实际应用中也面临着一些不可忽视的困境。通过对Bu tler旅游地生命周期模型的分析发现,该模型在应用中存在以下难题:难以获得真实有效的历史数据,难以客观地对旅游地进行阶段划分,难以进行科学预测,难以适用于所有的旅游地。在上述分析基础上,认为科学统计旅游数据、全面参考旅游相关指标、注重研究空间的不同尺度、注意对未知因素的考虑等是化解上述困境的合理之道。展开更多
文摘We consider the bifurcation of singular points near a double fold point in Z2 -symmetric nonlinear equations with two parameters,where the linearization has a two dimensional null space spanned by a symmetric null vector and an ami-symmetric null vector. In particular, we show the existence of a turning point path and a pitchfork point path passing ihrough the double fold point and they are the only singular points nearby. Their nondegeneracy is confirmed. A supporting numerical example is also provided. The main tools for our analysis as well as the compulation are some extended systems.
文摘Researches are being carried out world-wide to understand the nature of temperature change during recent past at different geographical scales so that comprehensive inferences can be drawn about recent temperature trend and future climate. Detection of turning points in time series of meteorological parameters puts challenges to the researches. In this work, the temperature time series from 1941 to 2010 for Asansol observatory, West Bengal, India, has been considered to understand the nature, trends and change points in the data set using sequential version of Mann-Kendall test statistic. Literatures suggest that use of this test statistic is the most appropriate for detecting climatic abrupt changes as compared to other statistical tests in use. This method has been employed upon monthly average temperatures recorded over the said 70 years for detection of abrupt changes in the average temperature of each of the months. The approximate potential trend turning points have been calculated separately for each month (January to December). Sequential version of Mann-Kendall test statistic values for the months of July and August is significant at 95% confidence level (p 0.05). The average temperature for most of the other months has shown an increasing trend but more significant rise in July and August temperature has been recognized since 1960s.
文摘The paper considers the asymptotic solution of two-point boundary value problems εy” + A(x)y’ = 0, 0 ≤ x ≤ 1, when 0 1, A(x) is smooth with isolated zeros, y(0) = 0 and y(1) = 1. By using perturbation method, the limit asymptotic solutions of various cases are obtained. We provide a reliable and direct method for solving similar problems. The limiting solutions are constants in this paper, except in narrow boundary and interior layers of nonuniform convergence. These provide simple examples of boundary layer resonance.
文摘Boundary value problem; for third-order ordinary differential equations with turning points are studied as follows : epsilon gamma ' ' + f(x ; epsilon) gamma ' + g(x ; epsilon) gamma ' +h(x ; epsilon) gamma = 0 (- a < x < b, 0 epsilon 1), where f(x ; 0) has several multiple zero points in ( - n, b). the necessary conditions for exhibiting resonance is given, and the uniformly valid asymptotic solutions and the estimations of remainder terms are obtained.
