Abstract Spatial soliton solutions of a class of generalized nonlinear Schrdinger equations in N space are discussed analytically and numerically. This achieved using a traveling wave method to formulate one soli...Abstract Spatial soliton solutions of a class of generalized nonlinear Schrdinger equations in N space are discussed analytically and numerically. This achieved using a traveling wave method to formulate one soliton solution and the P R method is employed to the numerical solutions and the interactions between the solitons for the generalized nonlinear systems in 2 space. The results presented show that the soliton phenomena are characteristics associated with the nonlinearities of the dynamical systems.展开更多
Soliton solutions of a class of generalized nonlinear evolution equations are discussed analytically and numerically. This is done by using a travelling wave method to formulate one soliton solution and the finite di...Soliton solutions of a class of generalized nonlinear evolution equations are discussed analytically and numerically. This is done by using a travelling wave method to formulate one soliton solution and the finite difference method to the numerical solutions and the interactions between the solitons for the generalized nonlinear Schrdinger equations. The characteristic behavior of the nonlinearity admitted in the system has been investigated and the soliton states of the system in the limit when α→0 and α→∞ have been studied. The results presented show that the soliton phenomenon is characteristics associated with the nonlinearities of the dynamical systems.展开更多
The chi-square test is a well-known goodness-of-fit test. It is available for arbitrary alternative hypothesis, particularly for a very general alternative. However, when the alternative is a “one-sided” hypothesis,...The chi-square test is a well-known goodness-of-fit test. It is available for arbitrary alternative hypothesis, particularly for a very general alternative. However, when the alternative is a “one-sided” hypothesis, which usually appears in genetic linkage analysis, the chi-square test does not use the information offered by the one-sided hypothesis.Therefore, it is possible that an appropriate one-sided test, which uses the information,will be better than the chi-square test. This paper gives such an efficient one-sided test.Monte Carlo simulation results show that it is more powerful than the chi-square test, and its power has been increased by 30 percent as compared with that of the chi-square test in most situations.展开更多
Let ξ be an irrational number with simple continued fraction expansion ξ = [a0;a1,··· ,ai,···] and pi be its ith convergent. Let Ci be de?ned by ξ ? pi = (?1)i/(Ciqiqi ). The qi qi +1 ...Let ξ be an irrational number with simple continued fraction expansion ξ = [a0;a1,··· ,ai,···] and pi be its ith convergent. Let Ci be de?ned by ξ ? pi = (?1)i/(Ciqiqi ). The qi qi +1 author proves the following theorem: Theorem. Let r > 1,R > 1 be two real numbers and q L = 1 + 1 + anan rR, K = 1 L + L2 ? 4 . r?1 R?1 +1 2 (r?1)(R?1) Then (i) Cn < r, Cn < R imply Cn > K; ?2 ?1 (ii) Cn > r, Cn > R imply Cn < K. ?2 ?1 This theorem generalizes the main result in [1].展开更多
A derivative-free frame-based conjugate gradients algorithm is presented. Convergence is shown for C^1 functions, and this is verified in numerical trials. The algorithm is tested on a variety of low dimensional probl...A derivative-free frame-based conjugate gradients algorithm is presented. Convergence is shown for C^1 functions, and this is verified in numerical trials. The algorithm is tested on a variety of low dimensional problems, some of which are ill-conditioned, and is also tested on problems of high dimension. Numerical results show that the algorithm is effective on both classes of problems. The results are compared with those from a discrete quasiNewton method, showing that the conjugate gradients algorithm is competitive. The algorithm exhibits the conjugate gradients speed-up on problems for which the Hessian at the solution has repeated or clustered eigenvalues. The algorithm is easily parallelizable.展开更多
Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric...Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ,we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that itimproves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given todetermine the number of iterations. We also show that when the number of replicates is less than orequal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of thosein [2] to the case of semiparametric regressions.展开更多
In this paper,we consider the simultaneous representation of pairs of integers as linear combinations in three prime variables and obtain a related numerical bound.
An iterative algorithm is proposed and analyzed based on a hybridized mixed finite element method for numerically solving two-phase generalized Stefan interface problems with strongly discontinuous solutions, conormal...An iterative algorithm is proposed and analyzed based on a hybridized mixed finite element method for numerically solving two-phase generalized Stefan interface problems with strongly discontinuous solutions, conormal derivatives, and coefficients. This algorithm iteratively solves small problems for each single phase with good accuracy and exchange information at the interface to advance the iteration until convergence, following the idea of Schwarz Alternating Methods. Error estimates are derived to show that this algorithm always converges provided that relaxation parameters are suitably chosen. Numeric experiments with matching and non-matching grids at the interface from different phases are performed to show the accuracy of the method for capturing discontinuities in the solutions and coefficients. In contrast to standard numerical methods, the accuracy of our method does not seem to deteriorate as the coefficient discontinuity increases.展开更多
文摘Abstract Spatial soliton solutions of a class of generalized nonlinear Schrdinger equations in N space are discussed analytically and numerically. This achieved using a traveling wave method to formulate one soliton solution and the P R method is employed to the numerical solutions and the interactions between the solitons for the generalized nonlinear systems in 2 space. The results presented show that the soliton phenomena are characteristics associated with the nonlinearities of the dynamical systems.
文摘Soliton solutions of a class of generalized nonlinear evolution equations are discussed analytically and numerically. This is done by using a travelling wave method to formulate one soliton solution and the finite difference method to the numerical solutions and the interactions between the solitons for the generalized nonlinear Schrdinger equations. The characteristic behavior of the nonlinearity admitted in the system has been investigated and the soliton states of the system in the limit when α→0 and α→∞ have been studied. The results presented show that the soliton phenomenon is characteristics associated with the nonlinearities of the dynamical systems.
文摘The chi-square test is a well-known goodness-of-fit test. It is available for arbitrary alternative hypothesis, particularly for a very general alternative. However, when the alternative is a “one-sided” hypothesis, which usually appears in genetic linkage analysis, the chi-square test does not use the information offered by the one-sided hypothesis.Therefore, it is possible that an appropriate one-sided test, which uses the information,will be better than the chi-square test. This paper gives such an efficient one-sided test.Monte Carlo simulation results show that it is more powerful than the chi-square test, and its power has been increased by 30 percent as compared with that of the chi-square test in most situations.
文摘Let ξ be an irrational number with simple continued fraction expansion ξ = [a0;a1,··· ,ai,···] and pi be its ith convergent. Let Ci be de?ned by ξ ? pi = (?1)i/(Ciqiqi ). The qi qi +1 author proves the following theorem: Theorem. Let r > 1,R > 1 be two real numbers and q L = 1 + 1 + anan rR, K = 1 L + L2 ? 4 . r?1 R?1 +1 2 (r?1)(R?1) Then (i) Cn < r, Cn < R imply Cn > K; ?2 ?1 (ii) Cn > r, Cn > R imply Cn < K. ?2 ?1 This theorem generalizes the main result in [1].
文摘A derivative-free frame-based conjugate gradients algorithm is presented. Convergence is shown for C^1 functions, and this is verified in numerical trials. The algorithm is tested on a variety of low dimensional problems, some of which are ill-conditioned, and is also tested on problems of high dimension. Numerical results show that the algorithm is effective on both classes of problems. The results are compared with those from a discrete quasiNewton method, showing that the conjugate gradients algorithm is competitive. The algorithm exhibits the conjugate gradients speed-up on problems for which the Hessian at the solution has repeated or clustered eigenvalues. The algorithm is easily parallelizable.
基金supported by a grant from the Natural Sciences and Engineering Research Council of Canada.
文摘Consider a repeated measurement partially linear regression model with anunknown vector parameter β_1, an unknown function g(·), and unknown heteroscedastic errorvariances. In order to improve the semiparametric generalized least squares estimator (SGLSE) of ,we propose an iterative weighted semiparametric least squares estimator (IWSLSE) and show that itimproves upon the SGLSE in terms of asymptotic covariance matrix. An adaptive procedure is given todetermine the number of iterations. We also show that when the number of replicates is less than orequal to two, the IWSLSE can not improve upon the SGLSE. These results are generalizations of thosein [2] to the case of semiparametric regressions.
基金Project supported by the National Natural Science Foundation of Chinathe Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry+2 种基金Shanghai's Shuguang Projectthe Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE,P. R. ChinaPartially supported by the Natural Sciences and Engineering Research Council of Canada
文摘In this paper,we consider the simultaneous representation of pairs of integers as linear combinations in three prime variables and obtain a related numerical bound.
文摘An iterative algorithm is proposed and analyzed based on a hybridized mixed finite element method for numerically solving two-phase generalized Stefan interface problems with strongly discontinuous solutions, conormal derivatives, and coefficients. This algorithm iteratively solves small problems for each single phase with good accuracy and exchange information at the interface to advance the iteration until convergence, following the idea of Schwarz Alternating Methods. Error estimates are derived to show that this algorithm always converges provided that relaxation parameters are suitably chosen. Numeric experiments with matching and non-matching grids at the interface from different phases are performed to show the accuracy of the method for capturing discontinuities in the solutions and coefficients. In contrast to standard numerical methods, the accuracy of our method does not seem to deteriorate as the coefficient discontinuity increases.
