主要运用内部项的拟Fredholm性质研究了2 × 2上三角型算子矩阵的拟Fredholm谱,并拓展到无界2 × 2上三角型算子矩阵的拟Fredholm谱。给出了具体例子加以说明结论的有效性。The Quasi-Fredholm Spectrum of 2 × 2 upper tr...主要运用内部项的拟Fredholm性质研究了2 × 2上三角型算子矩阵的拟Fredholm谱,并拓展到无界2 × 2上三角型算子矩阵的拟Fredholm谱。给出了具体例子加以说明结论的有效性。The Quasi-Fredholm Spectrum of 2 × 2 upper triangular operator matrices is studied by using the Quasi-Fredholm property of its internal entries, and extended to the Quasi-Fredholm spectrum of the triangular operator matrices on the unbounded 2 × 2. The example is given to illustrate the validity of the result.展开更多
In this paper,we give some properties for the so-calledε-pseudo weakly demicompact linear operators acting on Banach spaces with respect to a closed linear operator.Some sufficient conditions on the entries of an unb...In this paper,we give some properties for the so-calledε-pseudo weakly demicompact linear operators acting on Banach spaces with respect to a closed linear operator.Some sufficient conditions on the entries of an unbounded 2×2 block operator matrix L_(0)ensuring itsε-pseudo weak demicompactness are provided.In addition,we apply the obtained results to discuss the incidence of some perturbation results on the behavior of essential pseudospectra of L_(0).The results are formulated in terms of some denseness conditions on the topological dual space.展开更多
In this paper,we used higher order Haar wavelet method(HOHWM),introduced by Majak et al.[1],for approximate solution of second order integro-diferential equations(IDEs)of second-kind.It is improvement of long-establis...In this paper,we used higher order Haar wavelet method(HOHWM),introduced by Majak et al.[1],for approximate solution of second order integro-diferential equations(IDEs)of second-kind.It is improvement of long-established Haar wavelet collocation method(HWCM)which has been much popular among researchers and has many applications in literature.Present study aims to improve the numerical results of second order IDEs from first order rate of convergence in case of HWCM to the second and fourth order rate of convergence using HOHWM,depending on parameterλfor values 1 and 2,respectively.Several problems available in the literature of both,Volterra and Fredholm type of IDEs,are tested and compared with HWCM to illustrate the performance of our proposed method.展开更多
An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into ...An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into an equivalent system,and the k-order backward differentiation formula(BDF k)and central difference formula are used to discretize the temporal and spatial derivatives,respectively.Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms,the proposed scheme is based on the SAV idea and can be treated semi-implicitly,taking into account both accuracy and effectiveness.Numerical results are presented to demonstrate the high-order convergence(up to fourth-order)of the developed schemes and it is computationally efficient in long-time computations.展开更多
This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is ...This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is an autoregressive model of order p,representing a time series with dependencies on its p previous values.Additionally,the study evaluates the accuracy of both explicit and numerical integral equation(NIE)solutions for AR(p)using the TEWMA control chart,focusing on the absolute percentage relative error.The results indicate that the explicit and approximate solutions are in close agreement.Furthermore,the study investigates the performance of exponentially weighted moving average(EWMA)and TEWMA control charts in detecting changes in the process,using the relative mean index(RMI)as a measure.The findings demonstrate that the TEWMA control chart outperforms the EWMA control chart in detecting process changes,especially when the value ofλis sufficiently large.In addition,an analysis using historical data from the SET index between January 2024 and May 2024 and historical data of global annual plastic production,the results of both data sets also emphasize the superior performance of the TEWMA control chart.展开更多
文摘主要运用内部项的拟Fredholm性质研究了2 × 2上三角型算子矩阵的拟Fredholm谱,并拓展到无界2 × 2上三角型算子矩阵的拟Fredholm谱。给出了具体例子加以说明结论的有效性。The Quasi-Fredholm Spectrum of 2 × 2 upper triangular operator matrices is studied by using the Quasi-Fredholm property of its internal entries, and extended to the Quasi-Fredholm spectrum of the triangular operator matrices on the unbounded 2 × 2. The example is given to illustrate the validity of the result.
文摘In this paper,we give some properties for the so-calledε-pseudo weakly demicompact linear operators acting on Banach spaces with respect to a closed linear operator.Some sufficient conditions on the entries of an unbounded 2×2 block operator matrix L_(0)ensuring itsε-pseudo weak demicompactness are provided.In addition,we apply the obtained results to discuss the incidence of some perturbation results on the behavior of essential pseudospectra of L_(0).The results are formulated in terms of some denseness conditions on the topological dual space.
文摘In this paper,we used higher order Haar wavelet method(HOHWM),introduced by Majak et al.[1],for approximate solution of second order integro-diferential equations(IDEs)of second-kind.It is improvement of long-established Haar wavelet collocation method(HWCM)which has been much popular among researchers and has many applications in literature.Present study aims to improve the numerical results of second order IDEs from first order rate of convergence in case of HWCM to the second and fourth order rate of convergence using HOHWM,depending on parameterλfor values 1 and 2,respectively.Several problems available in the literature of both,Volterra and Fredholm type of IDEs,are tested and compared with HWCM to illustrate the performance of our proposed method.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12001210 and 12261103)the Natural Science Foundation of Henan(Grant No.252300420308)the Yunnan Fundamental Research Projects(Grant No.202301AT070117).
文摘An efficient and accurate scalar auxiliary variable(SAV)scheme for numerically solving nonlinear parabolic integro-differential equation(PIDE)is developed in this paper.The original equation is first transformed into an equivalent system,and the k-order backward differentiation formula(BDF k)and central difference formula are used to discretize the temporal and spatial derivatives,respectively.Different from the traditional discrete method that adopts full implicit or full explicit for the nonlinear integral terms,the proposed scheme is based on the SAV idea and can be treated semi-implicitly,taking into account both accuracy and effectiveness.Numerical results are presented to demonstrate the high-order convergence(up to fourth-order)of the developed schemes and it is computationally efficient in long-time computations.
基金the National Science,Research and Innovation Fund(NSRF)King Mongkuts University of Technology North Bangkok under contract no.KMUTNB-FF-68-B-08.
文摘This study aims to examine the explicit solution for calculating the Average Run Length(ARL)on the triple exponentially weighted moving average(TEWMA)control chart applied to autoregressive model(AR(p)),where AR(p)is an autoregressive model of order p,representing a time series with dependencies on its p previous values.Additionally,the study evaluates the accuracy of both explicit and numerical integral equation(NIE)solutions for AR(p)using the TEWMA control chart,focusing on the absolute percentage relative error.The results indicate that the explicit and approximate solutions are in close agreement.Furthermore,the study investigates the performance of exponentially weighted moving average(EWMA)and TEWMA control charts in detecting changes in the process,using the relative mean index(RMI)as a measure.The findings demonstrate that the TEWMA control chart outperforms the EWMA control chart in detecting process changes,especially when the value ofλis sufficiently large.In addition,an analysis using historical data from the SET index between January 2024 and May 2024 and historical data of global annual plastic production,the results of both data sets also emphasize the superior performance of the TEWMA control chart.
