Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theore...Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan.In a sense,our results reach the optimal form.展开更多
A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemio- logical threshold, known as the reproduction nu...A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemio- logical threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co- exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuber- culosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.展开更多
Rational composite design is highly important for the development of high-performance composite polymer electrolytes(CPEs)for solid-state lithium(Li)metal batteries.In this work,Li closo-borohydride,Li_(2)B_(12)H_(12)...Rational composite design is highly important for the development of high-performance composite polymer electrolytes(CPEs)for solid-state lithium(Li)metal batteries.In this work,Li closo-borohydride,Li_(2)B_(12)H_(12),is introduced to poly(vinylidene fluoride)-Li-bis-(trifluoromethanesulfonyl)imide(PVDF-LiTFSI)with a bound N-methyl pyrrolidone plasticizer to form a novel CPE.This CPE shows superb Li^(+)conduction properties,as evidenced by its conductivity of 1.43×10^(-4) S cm^(-1) and Li^(+)transference number of 0.34 at 25℃.Density functional theory calculations reveal that Li_(2)B_(12)H_(12),which features electron-deficient multicenter bonds,can facilitate the dissociation of LiTFSI and enhance the immobilization of TFSI to improve the Li^(+)conduction properties of the CPE.Moreover,the fabricated CPE exhibits excellent electrochemical,thermal,and mechanical stability.The addition of Li_(2)B_(12)H_(12) can help form a protective layer at the anode/electrolyte interface,thereby preventing unwanted reactions.The above benefits of the fabricated CPE contribute to the high compatibility of the electrode.Symmetric Li cells can be stably cycled at 0.2mA cm^(-2) for over 1200 h,and Li||LiFePO_(4) cells can deliver a reversible specific capacity of 140mAh g^(-1) after 200 cycles at 1C at 25℃ with a capacity retention of 98%.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11061012)the NaturalScience Foundation of Guangxi Province(No.2012GXNSFAA053010)
文摘Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan.In a sense,our results reach the optimal form.
文摘A deterministic model for evaluating the impact of voluntary testing and treatment on the transmission dynamics of tuberculosis is formulated and analyzed. The epidemio- logical threshold, known as the reproduction number is derived and qualitatively used to investigate the existence and stability of the associated equilibrium of the model system. The disease-free equilibrium is shown to be locally-asymptotically stable when the reproductive number is less than unity, and unstable if this threshold parameter exceeds unity. It is shown, using the Centre Manifold theory, that the model undergoes the phenomenon of backward bifurcation where the stable disease-free equilibrium co- exists with a stable endemic equilibrium when the associated reproduction number is less than unity. The analysis of the reproduction number suggests that voluntary tuber- culosis testing and treatment may lead to effective control of tuberculosis. Furthermore, numerical simulations support the fact that an increase voluntary tuberculosis testing and treatment have a positive impact in controlling the spread of tuberculosis in the community.
基金supported by the National Natural Science Foundation of China(51971146 and 51971147)the Major Program for the Scientific Research Innovation Plan of Shanghai Education Commission(2019-01-07-00-07-E00015)+3 种基金Shanghai Outstanding Academic Leaders PlanGuangxi Key Laboratory of Information Materials(Guilin University of Electronic Technology,201017-K)Shanghai Rising-Star Program(20QA1407100)the General Program of Natural Science Foundation of Shanghai(20ZR1438400).
文摘Rational composite design is highly important for the development of high-performance composite polymer electrolytes(CPEs)for solid-state lithium(Li)metal batteries.In this work,Li closo-borohydride,Li_(2)B_(12)H_(12),is introduced to poly(vinylidene fluoride)-Li-bis-(trifluoromethanesulfonyl)imide(PVDF-LiTFSI)with a bound N-methyl pyrrolidone plasticizer to form a novel CPE.This CPE shows superb Li^(+)conduction properties,as evidenced by its conductivity of 1.43×10^(-4) S cm^(-1) and Li^(+)transference number of 0.34 at 25℃.Density functional theory calculations reveal that Li_(2)B_(12)H_(12),which features electron-deficient multicenter bonds,can facilitate the dissociation of LiTFSI and enhance the immobilization of TFSI to improve the Li^(+)conduction properties of the CPE.Moreover,the fabricated CPE exhibits excellent electrochemical,thermal,and mechanical stability.The addition of Li_(2)B_(12)H_(12) can help form a protective layer at the anode/electrolyte interface,thereby preventing unwanted reactions.The above benefits of the fabricated CPE contribute to the high compatibility of the electrode.Symmetric Li cells can be stably cycled at 0.2mA cm^(-2) for over 1200 h,and Li||LiFePO_(4) cells can deliver a reversible specific capacity of 140mAh g^(-1) after 200 cycles at 1C at 25℃ with a capacity retention of 98%.
