In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we ...In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we study the representation problems of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces,obtain the algebraic representation continued equalities(l^(0)({X_(i)}))^(*)=^(A)(c00^(0)({X_(i)}))^(*)=Ac00({X_(i)^(*)}),(l^(0)(X))^(*)=^(A)(c0^(0)(X))^(*)=^(A)(c00^(0)(X))^(*)=^(A)C00(X^(0)),and the topological representation((c00^(0)({X_(i)}))^(*),sw^(*))=c00^(0)({X_(i)^(*)}),where sw^(*)is the sequen-tial weak star topology.For the sequences of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.展开更多
Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-norm...Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces are studied in this paper.The algebraic representation continued equalities l^(0)({X_(i)})*A=c^(0)_(00)({X_(i)})*A=c_(00)({X^(*)_(i)}),(l^(0)(X))^(*)A=(c^(0)(X))^(*)A=(c^(0)_0(X))^(*)A=(c^(0)_(00)(X))^(*)A=c_(00)(X^(*))are obtained in the first part.Under weak-star topology,the topological representation c^(0)_(00)({X_(i)})^(*),w^(*)=c^(0)_(00)({X^(*)_(i)})is obtained in the second part.For the sequence of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.展开更多
In this paper,we study the geometric ergodicity of continuous time Markov pro-cesses in general state space.For the geometric ergodic continuous time Markov processes,the condition π(f^(p))<∞,p>1 is added.Usin...In this paper,we study the geometric ergodicity of continuous time Markov pro-cesses in general state space.For the geometric ergodic continuous time Markov processes,the condition π(f^(p))<∞,p>1 is added.Using the coupling method,we obtain the existence of a full absorbing set on which continuous time Markov processes are f-geometric ergodic.展开更多
Motion recognition refers to the intelligent recognition of human motion using data collected from wearable sensors,which exceedingly has gained significant interest from both academic and industrial fields.However,te...Motion recognition refers to the intelligent recognition of human motion using data collected from wearable sensors,which exceedingly has gained significant interest from both academic and industrial fields.However,temporary-sudden activities caused by accidental behavior pose a major challenge to motion recognition and have been largely overlooked in existing works.To address this problem,the multi-dimensional time series of motion data is modeled as a Time-Frequency(TF)tensor,and the original challenge is transformed into a problem of outlier-corrupted tensor pattern recognition,where transient sudden activity data are considered as outliers.Since the TF tensor can capture the latent spatio-temporal correlations of the motion data,the tensor MPCA is used to derive the principal spatio-temporal pattern of the motion data.However,traditional MPCA uses the squared F-norm as the projection distance measure,which makes it sensitive to the presence of outlier motion data.Therefore,in the proposed outlier-robust MPCA scheme,the F-norm with the desirable geometric properties is used as the distance measure to simultaneously mitigate the interference of outlier motion data while preserving rotational invariance.Moreover,to reduce the complexity of outlier-robust motion recognition,we impose the proposed outlier-robust MPCA scheme on the traditional MPCANet which is a low-complexity deep learning network.The experimental results show that our proposed outlier-robust MPCANet can simultaneously improve motion recognition performance and reduce the complexity,especially in practical scenarios where the real-time data is corrupted by temporary-sudden activities.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11471236)
文摘In a paper published in Acta Mathematica Sinica(2016,59(4))we obtained some representation theorems for the conjugate spaces of some l^(0) type F-normed spaces.In this pa-per,for a sequence of normed spaces(X_(i)),we study the representation problems of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces,obtain the algebraic representation continued equalities(l^(0)({X_(i)}))^(*)=^(A)(c00^(0)({X_(i)}))^(*)=Ac00({X_(i)^(*)}),(l^(0)(X))^(*)=^(A)(c0^(0)(X))^(*)=^(A)(c00^(0)(X))^(*)=^(A)C00(X^(0)),and the topological representation((c00^(0)({X_(i)}))^(*),sw^(*))=c00^(0)({X_(i)^(*)}),where sw^(*)is the sequen-tial weak star topology.For the sequences of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.
基金Supported by the National Natural Science Foundation of China(11471236)
文摘Extending the results of an article published in(Acta Mathematica Sinica(2016,59(4))by the author,for a sequence of normed spaces{X_(i)},the representation problem of conjugate spaces of some l^(0)({X_(i)})type F-normed spaces are studied in this paper.The algebraic representation continued equalities l^(0)({X_(i)})*A=c^(0)_(00)({X_(i)})*A=c_(00)({X^(*)_(i)}),(l^(0)(X))^(*)A=(c^(0)(X))^(*)A=(c^(0)_0(X))^(*)A=(c^(0)_(00)(X))^(*)A=c_(00)(X^(*))are obtained in the first part.Under weak-star topology,the topological representation c^(0)_(00)({X_(i)})^(*),w^(*)=c^(0)_(00)({X^(*)_(i)})is obtained in the second part.For the sequence of inner product spaces and number fields with the usual topology,the concrete forms of the basic representation theorems are obtained at last.
基金Supported by the Natural Science Foundation of Hubei Province(2021CFB275)National Natural Science Foundation of China(12301667).
文摘In this paper,we study the geometric ergodicity of continuous time Markov pro-cesses in general state space.For the geometric ergodic continuous time Markov processes,the condition π(f^(p))<∞,p>1 is added.Using the coupling method,we obtain the existence of a full absorbing set on which continuous time Markov processes are f-geometric ergodic.
基金supported by the National Science Foundation of China under Grant No.62101467。
文摘Motion recognition refers to the intelligent recognition of human motion using data collected from wearable sensors,which exceedingly has gained significant interest from both academic and industrial fields.However,temporary-sudden activities caused by accidental behavior pose a major challenge to motion recognition and have been largely overlooked in existing works.To address this problem,the multi-dimensional time series of motion data is modeled as a Time-Frequency(TF)tensor,and the original challenge is transformed into a problem of outlier-corrupted tensor pattern recognition,where transient sudden activity data are considered as outliers.Since the TF tensor can capture the latent spatio-temporal correlations of the motion data,the tensor MPCA is used to derive the principal spatio-temporal pattern of the motion data.However,traditional MPCA uses the squared F-norm as the projection distance measure,which makes it sensitive to the presence of outlier motion data.Therefore,in the proposed outlier-robust MPCA scheme,the F-norm with the desirable geometric properties is used as the distance measure to simultaneously mitigate the interference of outlier motion data while preserving rotational invariance.Moreover,to reduce the complexity of outlier-robust motion recognition,we impose the proposed outlier-robust MPCA scheme on the traditional MPCANet which is a low-complexity deep learning network.The experimental results show that our proposed outlier-robust MPCANet can simultaneously improve motion recognition performance and reduce the complexity,especially in practical scenarios where the real-time data is corrupted by temporary-sudden activities.
