Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^...Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^(m)ϕ^(2)with some measure condition.We prove the global L^(1)boundedness for T_(ϕ,a),when 1/<ρ≤1 and m<ρ-n+1/2.Our theorem improves some known results.展开更多
This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function term.To this end,the FOFR system ...This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function term.To this end,the FOFR system is first proposed,and the adomian decomposition method(ADM)is employed to resolve this fractional-order system.The stability of equilibrium points and the corresponding control schemes are assessed,and several classical tools such as Lyapunov exponents(LE),bifurcation diagrams,complexity analysis(CA),and 0–1 test are further extended to analyze the dynamical behaviors of FOFR.Then the global Mittag–Leffler attractive set(MLAS)and Mittag–Leffler positive invariant set(MLPIS)for the proposed financial risk(FR)system are discussed.Finally,a proficient reservoir-computing(RC)method is applied to forecast the temporal evolution of the complex dynamics for the proposed system,and some simulations are carried out to show the effectiveness and feasibility of the present scheme.展开更多
背景:程序性细胞死亡受体1(programmed death receptor-1,PD-1)在高糖环境下影响骨髓间充质干细胞成骨分化的作用机制尚不清楚。目的:探讨高糖环境中PD-1对大鼠骨髓间充质干细胞成骨分化的影响及其调控机制。方法:将大鼠骨髓间充质干细...背景:程序性细胞死亡受体1(programmed death receptor-1,PD-1)在高糖环境下影响骨髓间充质干细胞成骨分化的作用机制尚不清楚。目的:探讨高糖环境中PD-1对大鼠骨髓间充质干细胞成骨分化的影响及其调控机制。方法:将大鼠骨髓间充质干细胞随机分为正常糖组(5.6 mmol/L)、高糖组(30 mmol/L)、PD-1过表达组、PD-1过表达空载组、PD-1敲低组、PD-1敲低空载组、PI3K/AKT通路抑制剂组(PD-1敲低+5μmol/L LY294002)。通过在高糖培养基中培养大鼠骨髓间充质干细胞来模拟体外糖尿病环境,采用qRT-PCR检测大鼠骨髓间充质干细胞中PD-1及其配体PD-L1和成骨标志物Runx2、OSX的mRNA表达,采用碱性磷酸酶染色和茜素红S染色观察成骨分化能力,采用CCK-8检测细胞增殖情况,采用Western blot检测PD-1、PD-L1、p-PI3K、p-AKT的蛋白表达。结果与结论:①高糖组PD-1及PD-L1表达显著高于正常糖组,高糖组骨髓间充质干细胞的成骨分化能力较正常糖组显著下降;②敲低PD-1表达可以促进骨髓间充质干细胞的成骨分化、增加细胞增殖活性,同时激活PI3K/AKT通路;③加入PI3K/AKT通路抑制剂LY294002后,骨髓间充质干细胞成骨分化能力显著下降。结果表明:PD-1依赖于PI3K/AKT信号通路抑制高糖环境下大鼠骨髓间充质干细胞的成骨分化。展开更多
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
基金Supported by the National Natural Science Foundation of China(11801518)the Natural Science Foundation of Zhejiang Province(LQ18A010005)the Science Foundation of Zhejiang Education Department(Y201738640)。
文摘Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^(m)ϕ^(2)with some measure condition.We prove the global L^(1)boundedness for T_(ϕ,a),when 1/<ρ≤1 and m<ρ-n+1/2.Our theorem improves some known results.
基金Project jointly supported by the National Natural Science Foundation of China(Grant No.12372013)Program for Science and Technology Innovation Talents in Universities of Henan Province,China(Grant No.24HASTIT034)+3 种基金the Natural Science Foundation of Henan Province,China(Grant No.232300420122)the Humanities and Society Science Foundation from the Ministry of Education of China(Grant No.19YJCZH265)China Postdoctoral Science Foundation(Grant No.2019M651633)First Class Discipline of Zhejiang-A(Zhejiang University of Finance and Economics Statistics),the Collaborative Innovation Center for Data Science and Big Data Analysis(Zhejiang University of Finance and Economics-Statistics).
文摘This paper delves into the dynamical analysis,chaos control,Mittag–Leffler boundedness(MLB),and forecasting a fractional-order financial risk(FOFR)system through an absolute function term.To this end,the FOFR system is first proposed,and the adomian decomposition method(ADM)is employed to resolve this fractional-order system.The stability of equilibrium points and the corresponding control schemes are assessed,and several classical tools such as Lyapunov exponents(LE),bifurcation diagrams,complexity analysis(CA),and 0–1 test are further extended to analyze the dynamical behaviors of FOFR.Then the global Mittag–Leffler attractive set(MLAS)and Mittag–Leffler positive invariant set(MLPIS)for the proposed financial risk(FR)system are discussed.Finally,a proficient reservoir-computing(RC)method is applied to forecast the temporal evolution of the complex dynamics for the proposed system,and some simulations are carried out to show the effectiveness and feasibility of the present scheme.
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
