Let Mn(n≥2) be an immersed umbilic-free hypersurface in the(n+1)-dimensional unit sphere Sn+1. Then Mn is associated witha so-called M(o)bius metric g, and a M(o)bius second fundamental form Bwhich are invariants of ...Let Mn(n≥2) be an immersed umbilic-free hypersurface in the(n+1)-dimensional unit sphere Sn+1. Then Mn is associated witha so-called M(o)bius metric g, and a M(o)bius second fundamental form Bwhich are invariants of Mn under the M(o)bius transformation groupof Sn+1.In this paper, we classify all umbilic-free hypersurfaces withparallel M(o)bius second fundamental form.展开更多
This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on ce...This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on certain sets,relax the restriction about the rate of change of state variable in a system to be bounded in Marachkov's theorem and extend the related results in [4—7].展开更多
In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, wh...In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients： network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i） undirected graph for symmetric games; ii） directed graph for asymmetric games, and iii） d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games （FEGs） are discussed, which are i） two strategies and symmetric （S-2）; ii） two strategies and asymmetric （A-2）; and iii） three strategies and symmetric （S-3）. Three strategy updating rules （SUR） are introduced, which are i） Unconditional Imitation （UI）; ii） Fermi Rule（FR）; iii） Myopic Best Response Adjustment Rule （MBRA）. First, we review the fundamental evolutionary equation （FEE） and use it to construct network profile dynamics （NPD）of NEGs. To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation （FEE） of each player is discussed. Using FEEs, the network strategy profile dynamics （NSPD） is built by providing efficient algorithms. Finally, we consider three more complicated NEGs： i） NEG with different length historical information, ii） NEG with multi-species, and iii） NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.展开更多
In the present paper, some precise fundamental inequalities are introduced. Applying them,we obtain the precise estimate for the sum of deficiencies. Let f(z) be transcendental mero-morphic in the finite plane and k b...In the present paper, some precise fundamental inequalities are introduced. Applying them,we obtain the precise estimate for the sum of deficiencies. Let f(z) be transcendental mero-morphic in the finite plane and k be a positive integer. If ε is an arbitrary positive numberand a and b are two distinct finite complex numbers, then we have T(r,f)<(1+1/k)N (r,1/f)+(1+1/k)N (r,1/(f^(k)-1)) -N (r,1/(f(k+1))+εT(r,f)+S(r,f)and δ(a,f^(k))+δ(b,f^(k))≤1+1/(2k+1).展开更多
Purpose: To examine the associations among preschoolers fundamental motor skills, screen-time, physical activity(PA), and sedentary behavior(SB).Methods: Children ages 3à4 years were enrolled in a prospective obs...Purpose: To examine the associations among preschoolers fundamental motor skills, screen-time, physical activity(PA), and sedentary behavior(SB).Methods: Children ages 3à4 years were enrolled in a prospective observational trial of PA. Trained assessors conducted the Test of Gross Motor Development-3 rd edition(TGMD-3), and the Movement Assessment Battery for Children-2 nd edition, and parent-reported child screen-time and sociodemographic information. Children wore an accelerometer for 7 days to examine SB and total PA(TPA). TPA was further characterized as moderateto-vigorous PA(MVPA) or vigorous PA(VPA). Mixed linear models were calculated, controlling for age(for TGMD-3), sex, household income, and accelerometer wear time(for accelerometry models), with childcare center as a random effect. The primary analysis reported on the cross-sectional baseline data of 126 children with complete fundamental motor skill and screen-time data; a subanalysis included 88 children with complete accelerometry data.Results: Children were 3.4 § 0.5 years of age(54% girls; 46% white, 42% African American, 12% other). A total of 48% lived in households at or below the federal poverty level. Children engaged in 5.1 § 3.6 h/day of screen-time. Children's screen-time was inversely related to the Movement Assessment Battery for Children-2 nd edition, manual dexterity skills percentile(b(SE) = ?1.7(0.8), p = 0.049). In the accelerometry subsample,children engaged in 5.9 § 0.9 h/day of TPA of which 1.7 § 0.6 h/day was MVPA. Boys engaged in more MVPA and VPA and less SB compared with girls(all p < 0.05). A higher TGMD-3, total score(b(SE) = 0.4(0.2), p = 0.017) and locomotor score(b(SE) = 0.7(0.3), p = 0.018) were associated with more VPA but not with TPA or MVPA. Screen-time and television in the bedroom were not related to SB, TPA, MVPA, or VPA.Conclusion: Children's motor skills were positively related to VPA but inversely related to screen-time. Further inquiry into the implications of high exposure to screen-time in young child展开更多
A nonlinear amplifying loop mirror constructed from erbium-doped fiber is proposed for simultaneous amplification and compression of ultrashort fundamental solitons. Numerical simulations show that, the proposed devic...A nonlinear amplifying loop mirror constructed from erbium-doped fiber is proposed for simultaneous amplification and compression of ultrashort fundamental solitons. Numerical simulations show that, the proposed device performs efficient high-quality amplification and compression of solitons.展开更多
基金The First author is partially supported by grants of CSC,the National Natural Science Foundation of ChinaOutstanding Youth Foundation of Henan,Chinathe second author is partially Supported by the Alexander von Humboldt Stiftung,grant of Tsinghua University and Zhongdian grant of NSFC.
文摘Let Mn(n≥2) be an immersed umbilic-free hypersurface in the(n+1)-dimensional unit sphere Sn+1. Then Mn is associated witha so-called M(o)bius metric g, and a M(o)bius second fundamental form Bwhich are invariants of Mn under the M(o)bius transformation groupof Sn+1.In this paper, we classify all umbilic-free hypersurfaces withparallel M(o)bius second fundamental form.
文摘This paper gives several fundamental theorems for the stability, uniform stability, asymptotic stability and uniform asymptotic stability. Those theorems allow the derivative of Lyapunov functions to be positive on certain sets,relax the restriction about the rate of change of state variable in a system to be bounded in Marachkov's theorem and extend the related results in [4—7].
基金This work was partially supported by National Natural Science Foundation of China （Nos. 61273013, 61333001, 61104065, 61322307）.
文摘In this paper a comprehensive introduction for modeling and control of networked evolutionary games （NEGs） via semi-tensor product （STP） approach is presented. First, we review the mathematical model of an NEG, which consists of three ingredients： network graph, fundamental network game, and strategy updating rule. Three kinds of network graphs are considered, which are i） undirected graph for symmetric games; ii） directed graph for asymmetric games, and iii） d-directed graph for symmetric games with partial neighborhood information. Three kinds of fundamental evolutionary games （FEGs） are discussed, which are i） two strategies and symmetric （S-2）; ii） two strategies and asymmetric （A-2）; and iii） three strategies and symmetric （S-3）. Three strategy updating rules （SUR） are introduced, which are i） Unconditional Imitation （UI）; ii） Fermi Rule（FR）; iii） Myopic Best Response Adjustment Rule （MBRA）. First, we review the fundamental evolutionary equation （FEE） and use it to construct network profile dynamics （NPD）of NEGs. To show how the dynamics of an NEG can be modeled as a discrete time dynamics within an algebraic state space, the fundamental evolutionary equation （FEE） of each player is discussed. Using FEEs, the network strategy profile dynamics （NSPD） is built by providing efficient algorithms. Finally, we consider three more complicated NEGs： i） NEG with different length historical information, ii） NEG with multi-species, and iii） NEG with time-varying payoffs. In all the cases, formulas are provided to construct the corresponding NSPDs. Using these NSPDs, certain properties are explored. Examples are presented to demonstrate the model constructing method, analysis and control design technique, and to reveal certain dynamic behaviors of NEGs.
基金Project partially supported by the National Natural Science Foundation of China.
文摘In the present paper, some precise fundamental inequalities are introduced. Applying them,we obtain the precise estimate for the sum of deficiencies. Let f(z) be transcendental mero-morphic in the finite plane and k be a positive integer. If ε is an arbitrary positive numberand a and b are two distinct finite complex numbers, then we have T(r,f)<(1+1/k)N (r,1/f)+(1+1/k)N (r,1/(f^(k)-1)) -N (r,1/(f(k+1))+εT(r,f)+S(r,f)and δ(a,f^(k))+δ(b,f^(k))≤1+1/(2k+1).
基金supported by the Gulf States Collaborative Center for Health Policy Research (Gulf States-HPC) from the National Institute on Minority Health and Health Disparities of the National Institutes of Health (No. U54MD008602)the LSU Biomedical Collaborative Research Program+2 种基金funding support from the American Council on Exercisesupported in part by the National Institute of General Medical Sciences of the National Institutes of Health, which funds the Louisiana Clinical and Translational Science Center (No. U54 GM104940)supported in part by the NORC Center Grant entitled "Nutrition and Metabolic Health Through the Lifespan" sponsored by NIDDK (No. P30DK072476)
文摘Purpose: To examine the associations among preschoolers fundamental motor skills, screen-time, physical activity(PA), and sedentary behavior(SB).Methods: Children ages 3à4 years were enrolled in a prospective observational trial of PA. Trained assessors conducted the Test of Gross Motor Development-3 rd edition(TGMD-3), and the Movement Assessment Battery for Children-2 nd edition, and parent-reported child screen-time and sociodemographic information. Children wore an accelerometer for 7 days to examine SB and total PA(TPA). TPA was further characterized as moderateto-vigorous PA(MVPA) or vigorous PA(VPA). Mixed linear models were calculated, controlling for age(for TGMD-3), sex, household income, and accelerometer wear time(for accelerometry models), with childcare center as a random effect. The primary analysis reported on the cross-sectional baseline data of 126 children with complete fundamental motor skill and screen-time data; a subanalysis included 88 children with complete accelerometry data.Results: Children were 3.4 § 0.5 years of age(54% girls; 46% white, 42% African American, 12% other). A total of 48% lived in households at or below the federal poverty level. Children engaged in 5.1 § 3.6 h/day of screen-time. Children's screen-time was inversely related to the Movement Assessment Battery for Children-2 nd edition, manual dexterity skills percentile(b(SE) = ?1.7(0.8), p = 0.049). In the accelerometry subsample,children engaged in 5.9 § 0.9 h/day of TPA of which 1.7 § 0.6 h/day was MVPA. Boys engaged in more MVPA and VPA and less SB compared with girls(all p < 0.05). A higher TGMD-3, total score(b(SE) = 0.4(0.2), p = 0.017) and locomotor score(b(SE) = 0.7(0.3), p = 0.018) were associated with more VPA but not with TPA or MVPA. Screen-time and television in the bedroom were not related to SB, TPA, MVPA, or VPA.Conclusion: Children's motor skills were positively related to VPA but inversely related to screen-time. Further inquiry into the implications of high exposure to screen-time in young child
基金The authors acknowledge the support of the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU5096/98E).
文摘A nonlinear amplifying loop mirror constructed from erbium-doped fiber is proposed for simultaneous amplification and compression of ultrashort fundamental solitons. Numerical simulations show that, the proposed device performs efficient high-quality amplification and compression of solitons.
