A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic exp...A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic expansion of solution for the problem is constructed and the uniform validity of the solution is obtained by using the method of upper and lower solution.展开更多
A class of epidemic virus transmission population dynamic system is considered. Firstly, using the functional homotopic analysis method, an initial approximate function is selected. Then, the arbitrary order approxima...A class of epidemic virus transmission population dynamic system is considered. Firstly, using the functional homotopic analysis method, an initial approximate function is selected. Then, the arbitrary order approximate analytic solutions are obtained successively. Finally, the accuracy of the obtained approximate analytic solutions is described. The influence of the various physical parameters for the epidemic virus transmission population dynamic system is discussed.展开更多
We report on the generation of a mid-infrared(mid-IR)frequency comb with a maximum average output power of250 mW and tunability in the 2.7-4.0μm region.The approach is based on a single-stage difference frequency gen...We report on the generation of a mid-infrared(mid-IR)frequency comb with a maximum average output power of250 mW and tunability in the 2.7-4.0μm region.The approach is based on a single-stage difference frequency generation(DFG)starting from a compact Yb-doped fiber laser system.The repetition rate of the near-infrared(NIR)comb is locked at 75 MHz.The phase noise of the repetition rate in the offset-free mid-IR comb system is measured and analyzed.Except for the intrinsic of NIR comb,environmental noise at low frequency and quantum noise at high frequency from the amplifier chain and nonlinear spectral broadening are the main noise sources of broadening the linewidth of comb teeth,which limits the precision of mid-IR dual-comb spectroscopy.展开更多
By taking a functional analytic point of view,we consider a family of distributions(continuous linear functionals on smooth functions),denoted by{μt,t>0},associated to the law of the iterated logarithm for Brownia...By taking a functional analytic point of view,we consider a family of distributions(continuous linear functionals on smooth functions),denoted by{μt,t>0},associated to the law of the iterated logarithm for Brownian motion on a compact manifold.We give a complete characterization of the collection of limiting distributions of{μt,t>0}.展开更多
基金Supported by the National Natural Science Foundation of China (10471039) the Natural Science Foundation of Zhejiang Province (102009)the Natural Science Foundation of Huzhou City (2004SZX0707).
文摘A class of semi-linear Robin problem is considered. Under appropriate assumptions, the existence and asymptotic behavior of its solution are studied more carefully. Using stretched variables, the formal asymptotic expansion of solution for the problem is constructed and the uniform validity of the solution is obtained by using the method of upper and lower solution.
基金Project supported by the National Natural Science Foundation of China(No.41275062)the Natural Science Foundation of Zhejiang Province of China(No.LY13A010005)
文摘A class of epidemic virus transmission population dynamic system is considered. Firstly, using the functional homotopic analysis method, an initial approximate function is selected. Then, the arbitrary order approximate analytic solutions are obtained successively. Finally, the accuracy of the obtained approximate analytic solutions is described. The influence of the various physical parameters for the epidemic virus transmission population dynamic system is discussed.
基金supported by the National Natural Science Foundation of China(Nos.11804096,11874153,and 11904105)the National Key R&D Program of China(Nos.2018YFA0306301 and 2017YFF0206000)the Shanghai Sailing Program(No.18YF1407300)。
文摘We report on the generation of a mid-infrared(mid-IR)frequency comb with a maximum average output power of250 mW and tunability in the 2.7-4.0μm region.The approach is based on a single-stage difference frequency generation(DFG)starting from a compact Yb-doped fiber laser system.The repetition rate of the near-infrared(NIR)comb is locked at 75 MHz.The phase noise of the repetition rate in the offset-free mid-IR comb system is measured and analyzed.Except for the intrinsic of NIR comb,environmental noise at low frequency and quantum noise at high frequency from the amplifier chain and nonlinear spectral broadening are the main noise sources of broadening the linewidth of comb teeth,which limits the precision of mid-IR dual-comb spectroscopy.
基金supported by Collaboration Grants for Mathematicians of the Simons Foundation (Grant No. 355480)
文摘By taking a functional analytic point of view,we consider a family of distributions(continuous linear functionals on smooth functions),denoted by{μt,t>0},associated to the law of the iterated logarithm for Brownian motion on a compact manifold.We give a complete characterization of the collection of limiting distributions of{μt,t>0}.
