The paper is made of two parts.In first part,We give the growth and 1/4-theorems for spiral like maps on the unit ball in l^p.Particularly,corresponding results were given in B^p.In the second part,we give the growth ...The paper is made of two parts.In first part,We give the growth and 1/4-theorems for spiral like maps on the unit ball in l^p.Particularly,corresponding results were given in B^p.In the second part,we give the growth and 1/4-theorems for spirallike maps in an inner product space.We prove that the results is best.展开更多
The local well-posedness for the b-family equation in the critical space is studied.Applying the Littlewood-Paley decomposition method in the critical Besov spaces Bs2r with the index s=3/2 which is the generalization...The local well-posedness for the b-family equation in the critical space is studied.Applying the Littlewood-Paley decomposition method in the critical Besov spaces Bs2r with the index s=3/2 which is the generalization space of the Sobolev spaces Hs it is established that there is a maximal time T=Tu0＆gt;0 such that for the b-family equation there exists a unique solution utx∈C0TB3/221∩C10TB121 when the initial variable u0x ∈B3/221 is the critical regularity. Moreover the solution uxt depends continuously on the initial data u0x .Furthermore using the abstract Cauchy-Kowalevski theorem to prove the analytic regularity of the solutions for the b-family equation in a suitable scale of Banach spaces E it is shown that the solutions of the b-family are analytic in both variables globally in space and locally in time when the initial data is analytic.展开更多
Suppose {X,X n,n≥1} are the i.i.d. random variables with values in 2 type Banach space B,S n=∑nk=1X k,φ(x) is a increasing function on [0,+∞), φ(x)→+∞, and φ(x)x is no increasing; then we point out that the cl...Suppose {X,X n,n≥1} are the i.i.d. random variables with values in 2 type Banach space B,S n=∑nk=1X k,φ(x) is a increasing function on [0,+∞), φ(x)→+∞, and φ(x)x is no increasing; then we point out that the cluster set CS n2nφ(n) is ρK, where ρ= lim L 2nφ(n)<+∞, ∫ ∞e -ρ 2φ(x) 1xd x=+∞,X∈WM 2 0, and E‖X‖ 2φ(‖X‖)<+∞.展开更多
The Tanlu （Tancheng-Lujiang） fault is one of the major structures in eastern China, which cuts across different blocks and controls the tectonic activity. Using the seismic data from the China Earthquake Networks Ce...The Tanlu （Tancheng-Lujiang） fault is one of the major structures in eastern China, which cuts across different blocks and controls the tectonic activity. Using the seismic data from the China Earthquake Networks Center, we investigate the spatial variations of the b-value in the Dabie-Sulu （Jiangsu-Shandong） organic belt by calculating the b-value of each grid （1~ xl~） from 1970 to 2010. The study shows that： the b-value is smaller in the Tanlu fault and its adjacent area, which might suggest that the major earthquake recurrence period is relatively long due to the lower frequency of small earthquake activity. In both sides of Tanlu fault, the b-value is higher at the edge of Sulu block and the eastern part of Dabie orogenic belt. The b values are higher in North China central orogenic belt, and small earthquake activity which occurred along the central orogenic belt is frequent. Additionally, combined with geological and geophysical study, we find that the b-value has a certain correspondence relationship with the lithologic distribution, which informs us that seismic activity features are closely related to the inhomogeneous media in the crust.展开更多
In this paper,based on Gansu Digital Seismic Network data since 1990,we calculated b-value and ⊿ b-value of the neighborhood area before the 2013 Minxian-Zhangxian M_S6. 6,earthquake. The results show that the earthq...In this paper,based on Gansu Digital Seismic Network data since 1990,we calculated b-value and ⊿ b-value of the neighborhood area before the 2013 Minxian-Zhangxian M_S6. 6,earthquake. The results show that the earthquake occurred at the margin of the significantly lower b-value area in southeast of Gansu and before the earthquake the neighborhood area had an obviously abnormal ⊿ b-value. From the earthquake and the spatial distribution of low b-value, the region still has the possibility of generating dangerous strong earthquakes.展开更多
Classifying single-trial electroencephalogram(EEG)based motor imagery(MI)tasks is extensively used to control brain-computer interface(BCI)applications,as a communication bridge between humans and computers.However,th...Classifying single-trial electroencephalogram(EEG)based motor imagery(MI)tasks is extensively used to control brain-computer interface(BCI)applications,as a communication bridge between humans and computers.However,the low signal-to-noise ratio and individual differences of EEG can affect the classification results negatively.In this paper,we propose an improved common spatial pattern(B-CSP)method to extract features for alleviating these adverse effects.First,for different subjects,the method of Bhattacharyya distance is used to select the optimal frequency band of each electrode including strong event-related desynchronization(ERD)and event-related synchronization(ERS)patterns;then the signals of the optimal frequency band are decomposed into spatial patterns,and the features that can describe the maximum differences of two classes of MI are extracted from the EEG data.The proposed method is applied to the public data set and experimental data set to extract features which are input into a back propagation neural network(BPNN)classifier to classify single-trial MI EEG.Another two conventional feature extraction methods,original common spatial pattern(CSP)and autoregressive(AR),are used for comparison.An improved classification performance for both data sets(public data set:91.25%±1.77%for left hand vs.foot and84.50%±5.42%for left hand vs.right hand;experimental data set:90.43%±4.26%for left hand vs.foot)verifies the advantages of the B-CSP method over conventional methods.The results demonstrate that our proposed B-CSP method can classify EEG-based MI tasks effectively,and this study provides practical and theoretical approaches to BCI applications.展开更多
Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probabil...Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probability one,lim supn→∞‖Sn‖/cn = α0 < ∞ for a regular normalizing sequence {cn}1,where α 0 is a precise value.展开更多
文摘The paper is made of two parts.In first part,We give the growth and 1/4-theorems for spiral like maps on the unit ball in l^p.Particularly,corresponding results were given in B^p.In the second part,we give the growth and 1/4-theorems for spirallike maps in an inner product space.We prove that the results is best.
基金The Natural Science Foundation of Higher Education Institutions of Jiangsu Province(No.13KJB110012)
文摘The local well-posedness for the b-family equation in the critical space is studied.Applying the Littlewood-Paley decomposition method in the critical Besov spaces Bs2r with the index s=3/2 which is the generalization space of the Sobolev spaces Hs it is established that there is a maximal time T=Tu0＆gt;0 such that for the b-family equation there exists a unique solution utx∈C0TB3/221∩C10TB121 when the initial variable u0x ∈B3/221 is the critical regularity. Moreover the solution uxt depends continuously on the initial data u0x .Furthermore using the abstract Cauchy-Kowalevski theorem to prove the analytic regularity of the solutions for the b-family equation in a suitable scale of Banach spaces E it is shown that the solutions of the b-family are analytic in both variables globally in space and locally in time when the initial data is analytic.
文摘Suppose {X,X n,n≥1} are the i.i.d. random variables with values in 2 type Banach space B,S n=∑nk=1X k,φ(x) is a increasing function on [0,+∞), φ(x)→+∞, and φ(x)x is no increasing; then we point out that the cluster set CS n2nφ(n) is ρK, where ρ= lim L 2nφ(n)<+∞, ∫ ∞e -ρ 2φ(x) 1xd x=+∞,X∈WM 2 0, and E‖X‖ 2φ(‖X‖)<+∞.
基金jointly supported by the Fundamental Research Funds for the Central Universities of China(ZY20140202)the Spark Program of Earthquake Science and Technology(XH15040Y)
文摘The Tanlu （Tancheng-Lujiang） fault is one of the major structures in eastern China, which cuts across different blocks and controls the tectonic activity. Using the seismic data from the China Earthquake Networks Center, we investigate the spatial variations of the b-value in the Dabie-Sulu （Jiangsu-Shandong） organic belt by calculating the b-value of each grid （1~ xl~） from 1970 to 2010. The study shows that： the b-value is smaller in the Tanlu fault and its adjacent area, which might suggest that the major earthquake recurrence period is relatively long due to the lower frequency of small earthquake activity. In both sides of Tanlu fault, the b-value is higher at the edge of Sulu block and the eastern part of Dabie orogenic belt. The b values are higher in North China central orogenic belt, and small earthquake activity which occurred along the central orogenic belt is frequent. Additionally, combined with geological and geophysical study, we find that the b-value has a certain correspondence relationship with the lithologic distribution, which informs us that seismic activity features are closely related to the inhomogeneous media in the crust.
基金jointly sponsored by the Technology Research and Development Program of Institute of Earthquake Science,CEA(XH14049,XH15042)the Science Research Fund Programs of Gansu Province(Grant No.145RJZA186)+1 种基金the National Natural Science Foundation(41304048)Special Fund for the Seismic Industry of China(20160107)
文摘In this paper,based on Gansu Digital Seismic Network data since 1990,we calculated b-value and ⊿ b-value of the neighborhood area before the 2013 Minxian-Zhangxian M_S6. 6,earthquake. The results show that the earthquake occurred at the margin of the significantly lower b-value area in southeast of Gansu and before the earthquake the neighborhood area had an obviously abnormal ⊿ b-value. From the earthquake and the spatial distribution of low b-value, the region still has the possibility of generating dangerous strong earthquakes.
基金Project supported by the National Natural Science Foundation of China(Nos.61702454 and 61772468)the MOE Project of Humanities and Social Sciences,China(No.17YJC870018)+1 种基金the Fundamental Research Funds for the Provincial Universities of Zhejiang Province,China(No.GB201901006)the Philosophy and Social Science Planning Fund Project of Zhejiang Province,China(No.20NDQN260YB)
文摘Classifying single-trial electroencephalogram(EEG)based motor imagery(MI)tasks is extensively used to control brain-computer interface(BCI)applications,as a communication bridge between humans and computers.However,the low signal-to-noise ratio and individual differences of EEG can affect the classification results negatively.In this paper,we propose an improved common spatial pattern(B-CSP)method to extract features for alleviating these adverse effects.First,for different subjects,the method of Bhattacharyya distance is used to select the optimal frequency band of each electrode including strong event-related desynchronization(ERD)and event-related synchronization(ERS)patterns;then the signals of the optimal frequency band are decomposed into spatial patterns,and the features that can describe the maximum differences of two classes of MI are extracted from the EEG data.The proposed method is applied to the public data set and experimental data set to extract features which are input into a back propagation neural network(BPNN)classifier to classify single-trial MI EEG.Another two conventional feature extraction methods,original common spatial pattern(CSP)and autoregressive(AR),are used for comparison.An improved classification performance for both data sets(public data set:91.25%±1.77%for left hand vs.foot and84.50%±5.42%for left hand vs.right hand;experimental data set:90.43%±4.26%for left hand vs.foot)verifies the advantages of the B-CSP method over conventional methods.The results demonstrate that our proposed B-CSP method can classify EEG-based MI tasks effectively,and this study provides practical and theoretical approaches to BCI applications.
基金supported by National Natural Science Foundation of China (Grant Nos. 10901138,11071213,11026087)supported by National Natural Science Foundation of China (Grant No.11071214)+1 种基金Natural Science Foundation of Zhejiang Province (Grant No.R6100119)Program for New Century Excellent Talents in University
文摘Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probability one,lim supn→∞‖Sn‖/cn = α0 < ∞ for a regular normalizing sequence {cn}1,where α 0 is a precise value.
