A topological dynamical system is n-sensitive,if there is a positive constant such that in each non-empty open subset there are n distinct points whose iterates will be apart from the constant at least for a same mome...A topological dynamical system is n-sensitive,if there is a positive constant such that in each non-empty open subset there are n distinct points whose iterates will be apart from the constant at least for a same moment.The properties of n-sensitivity in minimal systems are investigated.It turns out that a minimal system is n-sensitive if and only if the n-th regionally proximal relation Q_n contains a point whose coordinates are pairwise distinct.Moreover,the structure of a minimal system which is n-sensitive but not(n+1)-sensitive(n≥2)is determined.展开更多
The regionally proximal relation of order d along arithmetic progressions,namely AP[d]for d 2 N,is introduced and investigated.It turns out that if(X;T)is a topological dynamical system with AP[d]=Δ,then each ergodic...The regionally proximal relation of order d along arithmetic progressions,namely AP[d]for d 2 N,is introduced and investigated.It turns out that if(X;T)is a topological dynamical system with AP[d]=Δ,then each ergodic measure of(X;T)is isomorphic to a d-step pro-nilsystem,and thus(X;T)has zero entropy.Moreover,it is shown that if(X;T)is a strictly ergodic distal system with the property that the maximal topological and measurable d-step pro-nilsystems are isomorphic,then AP[d]=RP[d]for each d 2 N.It follows that for a minimal 1-pro-nilsystem,AP[d]=RP[d]for each d 2 N.An example which is a strictly ergodic distal system with discrete spectrum whose maximal equicontinuous factor is not isomorphic to the Kronecker factor is constructed.展开更多
Limb-loaded walking using ankle weights has been widely applied to increase exercise intensity in older adults.Examining changes in the activation pattern between proximal(RFP)and distal(RFD)regions of the rectus femo...Limb-loaded walking using ankle weights has been widely applied to increase exercise intensity in older adults.Examining changes in the activation pattern between proximal(RFP)and distal(RFD)regions of the rectus femoris(RF)muscle is key to clarifying gait deficits in older adults.The aim of this study was to determine regional neuromuscular regulation within the RF muscle following three-month limb-loaded walking in older adults.The study participants were 22 healthy older adults(696.3 years)who walked at least 160 min per month.Surface electromyography(EMG)and motion capture were used to measure the neuromuscular activities of RFP and RFD and generate kinematic data on the left lower extremity on walking for 240 s at the preferred gait speed on a treadmill at pre-and post-intervention,respectively.Averaged rectified values(ARV)of RFP and RFD were normalized by maximum values of ARV during a gait cycle within ten consecutive gait cycles.Normalized ARV of RFP was greater than RFD at 30%–40%and 70%–90%of the gait cycle and hip joint flexion at 0%–100%,and the walking speed and swing timing at post-were greater than at pre-intervention(p<0.05).No significant differences were noted in the RFP to RFD activity ratio(RFP/RFD ratio)between pre-and post-intervention,and there was no correlation between the RFP activity level and hip flexion angle in the swing phase(p>0.05).The activity of RFP compared with RFD and hip joint flexion were increased following limb-loaded walking intervention in older adults.展开更多
We study several stronger versions of sensitivity for minimal group actions,including nsensitivity,thick n-sensitivity and blockily thick n-sensitivity,and characterize them by the regionally proximal relation.
基金the National Natural Science Foundation of China(Grant Nos.10501042,10531010)the Ministry of Education of China(Grant No.20050358053)
文摘A topological dynamical system is n-sensitive,if there is a positive constant such that in each non-empty open subset there are n distinct points whose iterates will be apart from the constant at least for a same moment.The properties of n-sensitivity in minimal systems are investigated.It turns out that a minimal system is n-sensitive if and only if the n-th regionally proximal relation Q_n contains a point whose coordinates are pairwise distinct.Moreover,the structure of a minimal system which is n-sensitive but not(n+1)-sensitive(n≥2)is determined.
基金This work was supported by National Natural Science Foundation of China(Grant Nos.11431012,11971455,11571335 and 11371339).
文摘The regionally proximal relation of order d along arithmetic progressions,namely AP[d]for d 2 N,is introduced and investigated.It turns out that if(X;T)is a topological dynamical system with AP[d]=Δ,then each ergodic measure of(X;T)is isomorphic to a d-step pro-nilsystem,and thus(X;T)has zero entropy.Moreover,it is shown that if(X;T)is a strictly ergodic distal system with the property that the maximal topological and measurable d-step pro-nilsystems are isomorphic,then AP[d]=RP[d]for each d 2 N.It follows that for a minimal 1-pro-nilsystem,AP[d]=RP[d]for each d 2 N.An example which is a strictly ergodic distal system with discrete spectrum whose maximal equicontinuous factor is not isomorphic to the Kronecker factor is constructed.
基金supported by AMED(Japan Agency for Medical Research and Development)[Grant number JP19le0110012].
文摘Limb-loaded walking using ankle weights has been widely applied to increase exercise intensity in older adults.Examining changes in the activation pattern between proximal(RFP)and distal(RFD)regions of the rectus femoris(RF)muscle is key to clarifying gait deficits in older adults.The aim of this study was to determine regional neuromuscular regulation within the RF muscle following three-month limb-loaded walking in older adults.The study participants were 22 healthy older adults(696.3 years)who walked at least 160 min per month.Surface electromyography(EMG)and motion capture were used to measure the neuromuscular activities of RFP and RFD and generate kinematic data on the left lower extremity on walking for 240 s at the preferred gait speed on a treadmill at pre-and post-intervention,respectively.Averaged rectified values(ARV)of RFP and RFD were normalized by maximum values of ARV during a gait cycle within ten consecutive gait cycles.Normalized ARV of RFP was greater than RFD at 30%–40%and 70%–90%of the gait cycle and hip joint flexion at 0%–100%,and the walking speed and swing timing at post-were greater than at pre-intervention(p<0.05).No significant differences were noted in the RFP to RFD activity ratio(RFP/RFD ratio)between pre-and post-intervention,and there was no correlation between the RFP activity level and hip flexion angle in the swing phase(p>0.05).The activity of RFP compared with RFD and hip joint flexion were increased following limb-loaded walking intervention in older adults.
基金Supported by NNSF of China(Grant Nos.11771264,11871188)NSF of Guangdong Province(Grant No.2018B030306024)。
文摘We study several stronger versions of sensitivity for minimal group actions,including nsensitivity,thick n-sensitivity and blockily thick n-sensitivity,and characterize them by the regionally proximal relation.
