Let{Xn:n≥1}be a sequence of independent random variables with common general error distribution GED(v)with shape parameter v>0,and let Mn,r denote the r-th largest order statistics of X1,X2,...,Xn.With different n...Let{Xn:n≥1}be a sequence of independent random variables with common general error distribution GED(v)with shape parameter v>0,and let Mn,r denote the r-th largest order statistics of X1,X2,...,Xn.With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics|Mn,r|p are established.An alternative method is presented to estimate the probability of the r-th extremes.Numerical analyses are provided to support the main results.展开更多
For a general multidimensional denumerable state Markov process with any initial state probability vector, the probability density function and its LS transform of the first passage time to a certain given state set a...For a general multidimensional denumerable state Markov process with any initial state probability vector, the probability density function and its LS transform of the first passage time to a certain given state set are obtained and the algorithms for them are derived. It is proved that the resulting errors of the algorithms are both uniform in their respective arguments.Some numerical results are presented.展开更多
General expressions of first passage times for denumerable Markov processes are discussed and computation problems for busy periods and waiting times for queues corresponding to Markov processes are studied. In partic...General expressions of first passage times for denumerable Markov processes are discussed and computation problems for busy periods and waiting times for queues corresponding to Markov processes are studied. In particular, the simplified algorithms for busy periods and waiting times for queues corresponding to G//M/1 type and M/G/1 type Markov processes are derived and some numerical examples are presented.展开更多
The principle of real-time look-ahead was introduced and analysed. An adaptive parametric curve interpolator with a real-time look-ahead function was developed for non-uniform rational B-spline (NURBS) curves interpol...The principle of real-time look-ahead was introduced and analysed. An adaptive parametric curve interpolator with a real-time look-ahead function was developed for non-uniform rational B-spline (NURBS) curves interpolation, which considering the maximum acceleration/deceleration of the machine tool. In order to deal with the acceleration/deceleration around the feedrate sensitive corners, the look-ahead function was designed and illustrated. It can detect and adjust the feedrate adaptively. With the help of real-time look-ahead, the acceleration/deceleration can be limited to the range of the machine tool capacity. Thus, feedrate fluctuation is reduced. A NURBS curve interpolation experiment was provided to verify the feasibility and advantages of the proposed interpolator with a real-time look-ahead function.展开更多
In this paper,we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin(HDG)and weak Galerkin(WG)methods.By using the standard Brezzi theory on mixed methods,we carefu...In this paper,we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin(HDG)and weak Galerkin(WG)methods.By using the standard Brezzi theory on mixed methods,we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters.As a result,by taking appropriate limit of the stabilization parameters,we show that the HDG method converges to a primal conforming method and the WG method converges to a mixed conforming method.展开更多
This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vect...This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm with arbitrarily prescribed error can be efficiently applied to compute busy periods, busy cycles, waiting times, sojourn times, and relevant indices of various generic queueing systems and queueing networks. This paper also conducts a numerical experiment to implement the proposed algorithm.展开更多
Support vector machines are originally designed for binary classification. How to effectively extend it for multi-class classification is still an on-going research issue. In this paper, we consider kernel machines wh...Support vector machines are originally designed for binary classification. How to effectively extend it for multi-class classification is still an on-going research issue. In this paper, we consider kernel machines which are natural extensions of multi-category support vector machines originally proposed by Crammer and Singer. Based on the algorithm stability, we obtain the generalization error bounds for the kernel machines proposed in the paper.展开更多
This work deals with the numerical solution of singular perturbation system of ordinary differential equations with boundary layer. For the numerical solution of this problem fitted finite difference scheme on a unifo...This work deals with the numerical solution of singular perturbation system of ordinary differential equations with boundary layer. For the numerical solution of this problem fitted finite difference scheme on a uniform mesh is constructed and analyzed. The uniform error estimates for the approximate solution are obtained.展开更多
A survey of the main results of algorithmic studies of Markov processes and related stochastic models is shown. It consists of stationary solutions, transient solutions, first passage times, and multidimensional denum...A survey of the main results of algorithmic studies of Markov processes and related stochastic models is shown. It consists of stationary solutions, transient solutions, first passage times, and multidimensional denumerable state Markov processes. In conclusion, some remarks on further works are presented.展开更多
Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple ...Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple power series. We consider 1-periodic branched continued fraction of the special form which is an analog fraction with not equivalent variables if the values of that variables are fixed. We establish an analog of the parabola theorem for that fraction and estimate truncation error bounds for that fractions at some restrictions. We also propose to use weight coefficients for obtaining different parabolic regions for the same fraction without any additional restriction for first element.展开更多
文摘Let{Xn:n≥1}be a sequence of independent random variables with common general error distribution GED(v)with shape parameter v>0,and let Mn,r denote the r-th largest order statistics of X1,X2,...,Xn.With different normalizing constants the distributional expansions and the uniform convergence rates of normalized powered order statistics|Mn,r|p are established.An alternative method is presented to estimate the probability of the r-th extremes.Numerical analyses are provided to support the main results.
文摘For a general multidimensional denumerable state Markov process with any initial state probability vector, the probability density function and its LS transform of the first passage time to a certain given state set are obtained and the algorithms for them are derived. It is proved that the resulting errors of the algorithms are both uniform in their respective arguments.Some numerical results are presented.
基金the National Natural Science Foundation of China
文摘General expressions of first passage times for denumerable Markov processes are discussed and computation problems for busy periods and waiting times for queues corresponding to Markov processes are studied. In particular, the simplified algorithms for busy periods and waiting times for queues corresponding to G//M/1 type and M/G/1 type Markov processes are derived and some numerical examples are presented.
文摘The principle of real-time look-ahead was introduced and analysed. An adaptive parametric curve interpolator with a real-time look-ahead function was developed for non-uniform rational B-spline (NURBS) curves interpolation, which considering the maximum acceleration/deceleration of the machine tool. In order to deal with the acceleration/deceleration around the feedrate sensitive corners, the look-ahead function was designed and illustrated. It can detect and adjust the feedrate adaptively. With the help of real-time look-ahead, the acceleration/deceleration can be limited to the range of the machine tool capacity. Thus, feedrate fluctuation is reduced. A NURBS curve interpolation experiment was provided to verify the feasibility and advantages of the proposed interpolator with a real-time look-ahead function.
基金The work of both authors was partially supported by the Center for Computational Mathematics and ApplicationsThe Pennsylvania State University,and was partially supported by NSF grant DMS-1522615.
文摘In this paper,we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin(HDG)and weak Galerkin(WG)methods.By using the standard Brezzi theory on mixed methods,we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters.As a result,by taking appropriate limit of the stabilization parameters,we show that the HDG method converges to a primal conforming method and the WG method converges to a mixed conforming method.
文摘This paper proposes a uniformly convergent algorithm for the joint transform of the first passage time and the first passage number of steps for general Markov renewal processes with any initial state probability vector. The uniformly convergent algorithm with arbitrarily prescribed error can be efficiently applied to compute busy periods, busy cycles, waiting times, sojourn times, and relevant indices of various generic queueing systems and queueing networks. This paper also conducts a numerical experiment to implement the proposed algorithm.
基金Supported in part by the Specialized Research Fund for the Doctoral Program of Higher Education under grant 20060512001.
文摘Support vector machines are originally designed for binary classification. How to effectively extend it for multi-class classification is still an on-going research issue. In this paper, we consider kernel machines which are natural extensions of multi-category support vector machines originally proposed by Crammer and Singer. Based on the algorithm stability, we obtain the generalization error bounds for the kernel machines proposed in the paper.
文摘This work deals with the numerical solution of singular perturbation system of ordinary differential equations with boundary layer. For the numerical solution of this problem fitted finite difference scheme on a uniform mesh is constructed and analyzed. The uniform error estimates for the approximate solution are obtained.
文摘A survey of the main results of algorithmic studies of Markov processes and related stochastic models is shown. It consists of stationary solutions, transient solutions, first passage times, and multidimensional denumerable state Markov processes. In conclusion, some remarks on further works are presented.
文摘Branched continued fractions are one of the multidimensional generalization of the continued fractions. Branched continued fractions with not equivalent variables are an analog of the regular C-fractions for multiple power series. We consider 1-periodic branched continued fraction of the special form which is an analog fraction with not equivalent variables if the values of that variables are fixed. We establish an analog of the parabola theorem for that fraction and estimate truncation error bounds for that fractions at some restrictions. We also propose to use weight coefficients for obtaining different parabolic regions for the same fraction without any additional restriction for first element.