Topological crystalline insulators （TCIs） have attracted worldwide interest since their theoretical predication and have created exciting opportunities for studying topological quantum physics and for exploring spin...Topological crystalline insulators （TCIs） have attracted worldwide interest since their theoretical predication and have created exciting opportunities for studying topological quantum physics and for exploring spintronic appli- cations. In this work, we successfully synthesize PbTe nanowires via the chemical vapor deposition method and demonstrate the existence of topological surface states by their 2D weak anti-localization effect and Shubnikov-de Haas oscillations. More importantly, the surface state contributes ~61% of the total conduction, suggesting dom- inant surface transport in PbTe nanowires at low temperatures. Our work provides an experimental groundwork for researching TCIs and is a step forward for the applications of PbTe nanowires in spintronic devices.展开更多
Oscillatory behavior of solutions of second order nonlinear difference equation is studied. Oscillation criteria for its solutions are given. Examples are given in the text to illustrate the results.
For reversible systems of infinite dimension we prove an infinitely dimensional KAM theorem with an application to the network of weakly coupled oscillators of friction. The KAM theorem shows that there are many invar...For reversible systems of infinite dimension we prove an infinitely dimensional KAM theorem with an application to the network of weakly coupled oscillators of friction. The KAM theorem shows that there are many invariant tori of infinite dimension, and thus many almost periodic solutions, for the reversible systems.展开更多
In this paper,we first introduce the weak Lipschitz spaces WLip_(q,α),1<q<∞,0<α<1 which are the analog of weak Lebesgue spaces L^(q,∞)in the setting of Lipschitz space.We obtain the equivalence between...In this paper,we first introduce the weak Lipschitz spaces WLip_(q,α),1<q<∞,0<α<1 which are the analog of weak Lebesgue spaces L^(q,∞)in the setting of Lipschitz space.We obtain the equivalence between the norm ||·||_(Lipα)and ||·||_(()WLip_(q,α)).As an application,we show that the commutator M_(β)~b is bounded from L~p to L^(q,∞) for some p ∈(1,∞) and 1/p-1/q=(α+β)/n if and only if b is in Lip_(α).We also introduce the weak central bounded mean oscillation space WCBMO_(q,α) and give a characterization of WCBMO_(q,α) via the boundedness of the commutators of Hardy type operators.展开更多
基金Supported by the National Key Research and Development Program of China under Grant No 2016YFA0300803the National Basic Research Program of China under Grant No 2014CB921101the National Natural Science Foundation of China under Grant Nos 61474061 and 61674079
文摘Topological crystalline insulators （TCIs） have attracted worldwide interest since their theoretical predication and have created exciting opportunities for studying topological quantum physics and for exploring spintronic appli- cations. In this work, we successfully synthesize PbTe nanowires via the chemical vapor deposition method and demonstrate the existence of topological surface states by their 2D weak anti-localization effect and Shubnikov-de Haas oscillations. More importantly, the surface state contributes ~61% of the total conduction, suggesting dom- inant surface transport in PbTe nanowires at low temperatures. Our work provides an experimental groundwork for researching TCIs and is a step forward for the applications of PbTe nanowires in spintronic devices.
基金This research was supposed by the NSF of China (10071043)Shandong Province (Q2001A03).
文摘Oscillatory behavior of solutions of second order nonlinear difference equation is studied. Oscillation criteria for its solutions are given. Examples are given in the text to illustrate the results.
基金Supported by NNSFC and NCET-04-0365in part by STCSM-06ZR14014
文摘For reversible systems of infinite dimension we prove an infinitely dimensional KAM theorem with an application to the network of weakly coupled oscillators of friction. The KAM theorem shows that there are many invariant tori of infinite dimension, and thus many almost periodic solutions, for the reversible systems.
基金Supported by the National Natural Science Foundation of China (Grant No.11871452)the Natural Science Foundation of Henan Province (Grant No.202300410338)the Nanhu Scholar Program for Young Scholars of Xinyang Normal University。
文摘In this paper,we first introduce the weak Lipschitz spaces WLip_(q,α),1<q<∞,0<α<1 which are the analog of weak Lebesgue spaces L^(q,∞)in the setting of Lipschitz space.We obtain the equivalence between the norm ||·||_(Lipα)and ||·||_(()WLip_(q,α)).As an application,we show that the commutator M_(β)~b is bounded from L~p to L^(q,∞) for some p ∈(1,∞) and 1/p-1/q=(α+β)/n if and only if b is in Lip_(α).We also introduce the weak central bounded mean oscillation space WCBMO_(q,α) and give a characterization of WCBMO_(q,α) via the boundedness of the commutators of Hardy type operators.
