B_n denotes the unit ball of C^n,(?)B_n its boundary, γ_n,and σ_n the normalized Lebesgue measures on B_n and (?)B_n respectively, H(B_n) the class of all functions holomorphic in B_n.
We define a generalization of Mackey first countability and prove that it is equivalent to being docile. A consequence of the main result is to give a partial affirmative answer to an old question of Mackey regarding ...We define a generalization of Mackey first countability and prove that it is equivalent to being docile. A consequence of the main result is to give a partial affirmative answer to an old question of Mackey regarding arbitrary quotients of Mackey first countable spaces. Some applications of the main result to spaces such as inductive limits are also given.展开更多
目的对慢性鼻窦炎患者的“鼻涕倒流”、“咳嗽”症状和术前鼻窦CT进行分析,评价它们之间的相互关系。方法对2005年3月至2005年6月间因慢性鼻窦炎拟行鼻内镜手术的63例患者术前及术后6个月症状做SNOT-20(Sino-Nasal Outcome Test 20)量...目的对慢性鼻窦炎患者的“鼻涕倒流”、“咳嗽”症状和术前鼻窦CT进行分析,评价它们之间的相互关系。方法对2005年3月至2005年6月间因慢性鼻窦炎拟行鼻内镜手术的63例患者术前及术后6个月症状做SNOT-20(Sino-Nasal Outcome Test 20)量表评估,并对其术前CT冠状位骨窗进行Lund-Mackey评分,比较不同的CT评分与SNOT-20量表中“鼻涕倒流”、“咳嗽”症状评分之间的异同,研究症状评分与CT评分之间的关系。结果术前“鼻涕倒流”症状的SNOT-20量表评分与后组鼻窦CT的Lund-Mackey评分之间的Pearson相关系数r为0．714(P<0．01),与前组鼻窦CT的Lund-Mackey评分之间的Pearson相关系数r为0．173 (P>0．05);“咳嗽”症状的SNOT-20量表评分与后组鼻窦和前组鼻窦CT的Lund-Mackey评分之间Pearson相关系数分别为0．213(P>0．05)和0．097(P>0．05)。结论“鼻涕倒流”症状与后组鼻窦病变有关。展开更多
A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adap...A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.展开更多
By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which a...By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which are convenient for application. Particularly we improve some results of Kalton.展开更多
This paper presents an adaptive step-size modified fractional least mean square （AMFLMS） algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptati...This paper presents an adaptive step-size modified fractional least mean square （AMFLMS） algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptation equation of the original MFLMS algorithm and also introduce a mechanism to adjust the order of the fractional derivative adaptively through a gradient-based approach. This approach permits an interesting achievement towards the performance of the filter in terms of handling nonlinear problems and it achieves less computational burden by avoiding the manual selection of adjustable parameters. We call this new algorithm the AMFLMS algorithm. The predictive performance for the nonlinear chaotic Mackey Glass and Lorenz time series was observed and evaluated using the classical LMS, Kernel LMS, MFLMS, and the AMFLMS filters. The simulation results for the Mackey glass time series, both without and with noise, confirm an improvement in terms of mean square error for the proposed algorithm. Its performance is also validated through the prediction of complex Lorenz series.展开更多
For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself ...For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.展开更多
In this paper, the author establishs general open mapping theorems for continuous, weakly continuous, closed and weakly singular linear maps respectively. From these general theorems, he deduces a lot of specific open...In this paper, the author establishs general open mapping theorems for continuous, weakly continuous, closed and weakly singular linear maps respectively. From these general theorems, he deduces a lot of specific open mapping theorems, which include some well-known theorems and some new interesting results. Particularly the author gives the extensions of Husain's open mapping theorem and Adasch's open mapping theorem.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘B_n denotes the unit ball of C^n,(?)B_n its boundary, γ_n,and σ_n the normalized Lebesgue measures on B_n and (?)B_n respectively, H(B_n) the class of all functions holomorphic in B_n.
文摘We define a generalization of Mackey first countability and prove that it is equivalent to being docile. A consequence of the main result is to give a partial affirmative answer to an old question of Mackey regarding arbitrary quotients of Mackey first countable spaces. Some applications of the main result to spaces such as inductive limits are also given.
文摘目的对慢性鼻窦炎患者的“鼻涕倒流”、“咳嗽”症状和术前鼻窦CT进行分析,评价它们之间的相互关系。方法对2005年3月至2005年6月间因慢性鼻窦炎拟行鼻内镜手术的63例患者术前及术后6个月症状做SNOT-20(Sino-Nasal Outcome Test 20)量表评估,并对其术前CT冠状位骨窗进行Lund-Mackey评分,比较不同的CT评分与SNOT-20量表中“鼻涕倒流”、“咳嗽”症状评分之间的异同,研究症状评分与CT评分之间的关系。结果术前“鼻涕倒流”症状的SNOT-20量表评分与后组鼻窦CT的Lund-Mackey评分之间的Pearson相关系数r为0．714(P<0．01),与前组鼻窦CT的Lund-Mackey评分之间的Pearson相关系数r为0．173 (P>0．05);“咳嗽”症状的SNOT-20量表评分与后组鼻窦和前组鼻窦CT的Lund-Mackey评分之间Pearson相关系数分别为0．213(P>0．05)和0．097(P>0．05)。结论“鼻涕倒流”症状与后组鼻窦病变有关。
基金Project supported by the Higher Education Commission of Pakistan
文摘A method of modifying the architecture of fractional least mean square （FLMS） algorithm is presented to work with nonlinear time series prediction. Here we incorporate an adjustable gain parameter in the weight adaptation equation of the original FLMS algorithm and absorb the gamma function in the fractional step size parameter. This approach provides an interesting achievement in the performance of the filter in terms of handling the nonlinear problems with less computational burden by avoiding the evaluation of complex gamma function. We call this new algorithm as the modified fractional least mean square （MFLMS） algorithm. The predictive performance for the nonlinear Mackey glass chaotic time series is observed and evaluated using the classical LMS, FLMS, kernel LMS, and proposed MFLMS adaptive filters. The simulation results for the time series with and without noise confirm the superiority and improvement in the prediction capability of the proposed MFLMS predictor over its counterparts.
文摘By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which are convenient for application. Particularly we improve some results of Kalton.
基金Project supported by the Higher Education Commission of Pakistan
文摘This paper presents an adaptive step-size modified fractional least mean square （AMFLMS） algorithm to deal with a nonlinear time series prediction. Here we incorporate adaptive gain parameters in the weight adaptation equation of the original MFLMS algorithm and also introduce a mechanism to adjust the order of the fractional derivative adaptively through a gradient-based approach. This approach permits an interesting achievement towards the performance of the filter in terms of handling nonlinear problems and it achieves less computational burden by avoiding the manual selection of adjustable parameters. We call this new algorithm the AMFLMS algorithm. The predictive performance for the nonlinear chaotic Mackey Glass and Lorenz time series was observed and evaluated using the classical LMS, Kernel LMS, MFLMS, and the AMFLMS filters. The simulation results for the Mackey glass time series, both without and with noise, confirm an improvement in terms of mean square error for the proposed algorithm. Its performance is also validated through the prediction of complex Lorenz series.
基金funded by Prince Sultan University,Riyadh,Saudi Arabia。
文摘For the unforced dynamical non-linear state–space model,a new Q1 and efficient square root extended kernel recursive least square estimation algorithm is developed in this article.The proposed algorithm lends itself towards the parallel implementation as in the FPGA systems.With the help of an ortho-normal triangularization method,which relies on numerically stable givens rotation,matrix inversion causes a computational burden,is reduced.Matrix computation possesses many excellent numerical properties such as singularity,symmetry,skew symmetry,and triangularity is achieved by using this algorithm.The proposed method is validated for the prediction of stationary and non-stationary Mackey–Glass Time Series,along with that a component in the x-direction of the Lorenz Times Series is also predicted to illustrate its usefulness.By the learning curves regarding mean square error(MSE)are witnessed for demonstration with prediction performance of the proposed algorithm from where it’s concluded that the proposed algorithm performs better than EKRLS.This new SREKRLS based design positively offers an innovative era towards non-linear systolic arrays,which is efficient in developing very-large-scale integration(VLSI)applications with non-linear input data.Multiple experiments are carried out to validate the reliability,effectiveness,and applicability of the proposed algorithm and with different noise levels compared to the Extended kernel recursive least-squares(EKRLS)algorithm.
文摘In this paper, the author establishs general open mapping theorems for continuous, weakly continuous, closed and weakly singular linear maps respectively. From these general theorems, he deduces a lot of specific open mapping theorems, which include some well-known theorems and some new interesting results. Particularly the author gives the extensions of Husain's open mapping theorem and Adasch's open mapping theorem.
