In this paper, we prove some intersection theorems concerning noncompact sets with H-convex sections which generalize the corresponding results of Ma, Fan, Tarafdar, Lassonde and Shin-Tan to H-spaces without the linea...In this paper, we prove some intersection theorems concerning noncompact sets with H-convex sections which generalize the corresponding results of Ma, Fan, Tarafdar, Lassonde and Shin-Tan to H-spaces without the linear structure and to noncompact setting. An application to von Neumann type minimax theorems is given.展开更多
A class of implicit fuzzy differential inclusions （IFDIs） are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed s...A class of implicit fuzzy differential inclusions （IFDIs） are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation, respectively. A viable solution for a closed IFDI is proved to exist under the tangential condition. As an application, an implicit fuzzy differential equation, which comes from the drilling dynamics in petroleum engineering, is analyzed numerically. The obtained results can improve and extend some known results for fuzzy differential inclusions （FDIs） and fuzzy differential equations （FDEs）, which might be helpful in the analysis of fuzzy dynamic systems.展开更多
Motivated by recent understandings in the stochastic natures of gene expression, biochemical signaling, and spontaneous reversible epigenetic switchings, we study a simple deterministic cell population dynamics in whi...Motivated by recent understandings in the stochastic natures of gene expression, biochemical signaling, and spontaneous reversible epigenetic switchings, we study a simple deterministic cell population dynamics in which subpopulations grow with different rates and individual cells can bi-directionally switch between a small number of different epigenetic phenotypes. Two theories in the past, the population dynamics and thermodynamics of master equations, separately defined two important concepts in mathematical terms： thefitness in the former and the （non- adiabatic） entropy production in the latter. Both of them play important roles in the evolution of the cell population dynamics. The switching sustains the variations among the subpopulation growth, thus sustains continuous natural selection. As a form of Price＇s equation, the fitness increases with （i） natural selection through variations and （ii） a positive covariance between the per capita growth and switching, which represents a Lamarchian-like behavior. A negative covariance balances the natural selection in a fitness steady state —— ＂the red queen＂ scenario. At the same time the growth keeps the proportions of subpopulations away from the ＂intrinsic＂ switching equilibrium of individual cells, thus leads to a continuous entropy production. A covariance, between the per capita growth rate and the ＂chemical potential＂ of subpopulation, counteracts the entropy production. Analytical results are obtained for the limiting cases of growth dominating switching and vice versa.展开更多
文摘In this paper, we prove some intersection theorems concerning noncompact sets with H-convex sections which generalize the corresponding results of Ma, Fan, Tarafdar, Lassonde and Shin-Tan to H-spaces without the linear structure and to noncompact setting. An application to von Neumann type minimax theorems is given.
基金Project supported by the National Science Fund for Distinguished Young Scholars of China(No.51125019)the National Natural Science Foundation of China(No.11171237)the Scientific Research Fund of Sichuan Provincial Education Department(No.11ZA024)
文摘A class of implicit fuzzy differential inclusions （IFDIs） are introduced and studied. Some existence theorems under different conditions are proved with the selection theorems for the open situation and the closed situation, respectively. A viable solution for a closed IFDI is proved to exist under the tangential condition. As an application, an implicit fuzzy differential equation, which comes from the drilling dynamics in petroleum engineering, is analyzed numerically. The obtained results can improve and extend some known results for fuzzy differential inclusions （FDIs） and fuzzy differential equations （FDEs）, which might be helpful in the analysis of fuzzy dynamic systems.
文摘Motivated by recent understandings in the stochastic natures of gene expression, biochemical signaling, and spontaneous reversible epigenetic switchings, we study a simple deterministic cell population dynamics in which subpopulations grow with different rates and individual cells can bi-directionally switch between a small number of different epigenetic phenotypes. Two theories in the past, the population dynamics and thermodynamics of master equations, separately defined two important concepts in mathematical terms： thefitness in the former and the （non- adiabatic） entropy production in the latter. Both of them play important roles in the evolution of the cell population dynamics. The switching sustains the variations among the subpopulation growth, thus sustains continuous natural selection. As a form of Price＇s equation, the fitness increases with （i） natural selection through variations and （ii） a positive covariance between the per capita growth and switching, which represents a Lamarchian-like behavior. A negative covariance balances the natural selection in a fitness steady state —— ＂the red queen＂ scenario. At the same time the growth keeps the proportions of subpopulations away from the ＂intrinsic＂ switching equilibrium of individual cells, thus leads to a continuous entropy production. A covariance, between the per capita growth rate and the ＂chemical potential＂ of subpopulation, counteracts the entropy production. Analytical results are obtained for the limiting cases of growth dominating switching and vice versa.
