S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate b...S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i（A, Ω, p） is equal to nonzero, where i（A, Ω, p） is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2].展开更多
The aim of this work is to identify the range of applicability of Arrhenius type temperature dependence for Ammonia Oxidizing Bacteria （AOB） subjected to tem- perature time gradients through continuous titrimetric t...The aim of this work is to identify the range of applicability of Arrhenius type temperature dependence for Ammonia Oxidizing Bacteria （AOB） subjected to tem- perature time gradients through continuous titrimetric tests. An innovative online differential titrimetric technique was used to continuously monitor the maximum biologic ammonia oxidation rate of the biomass selected in a pilot scale membrane bioreactor, as a function of temperature time gradients. The monitoring technique is based on the measurement of alkalinity and hydrogen peroxide con- sumption rates in two parallel reactors operated in non- limiting substrate conditions for AOB; both reactors were continuously fed with mixed liquor and in one of them AOB were inhibited with allylthiourea. The effects of temperature decrease rates in the range 1 to 4℃h^-1 were evaluated by controlling the titrimetric reactor in the temperature range 10℃-20℃. The dependence of growth kinetics on temperature time gradients and the range of applicability of Arrhenius model for temperature depen- dency of AOB growth kinetics were assessed. The Arrhenius model was found to be accurate only with temperature gradients lower than 2℃·h^-1. The estimated Arrhenius coefficients （θ） were shown to increase from 1.07 to 1.6 when the temperature decrease rate reached 4℃.h^-1.展开更多
A novel controller is proposed to regulate the DC-link voltage of a single phase active power filter （SPAPF）. The proposed switched fractional controller （SFC） consists of a conventional PI controller, a fractiona...A novel controller is proposed to regulate the DC-link voltage of a single phase active power filter （SPAPF）. The proposed switched fractional controller （SFC） consists of a conventional PI controller, a fractional order PI （FO-PI） controller and a decision maker that switches between them. Commonly, the conventional PI controller is used in regulation loops due to its advantages in steady-state but it is limited in transient state. On the other hand, the FO-PI controller overcomes these draw- backs but it causes dramatic degradation in control performances in steady-state because of the fractional calculus theory and the approximation method used to implement this kind of controller. Thus, the purpose of this paper is to switch to the PI controller in steady-state to obtain the best power quality and to switch to the FO-PI controller when external disturbances are detected to guarantee a fast transient state. To investigate the efficiency and accuracy of the SFC considering all robustness tests, an experimental setup has been established. The results of the SFC fulfill the requirements, confirm its high performances in steady and transient states and demon- strate its feasibility and effectiveness. The experiment results have satisfied the limit specified by the IEEE harmonic standard 519.展开更多
基金Supported in part by the Foundations of Education Ministry, Anhui Province, China (No: KJ2008A028)Education Ministry, Hubei Province, China (No: D20102502)
文摘S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i（A, Ω, p） is equal to nonzero, where i（A, Ω, p） is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point theorems of the completely continuous and weakly inward mapping, which generalize some famous theorems such as Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem etc. in the case of weakly inward mappings. In addition, our conclusions extend the famous fixed point theorem of cone expansion and compression to the case of weakly inward mappings. Moreover, the main results contain and generalize the corresponding results in the recent work[2].
文摘The aim of this work is to identify the range of applicability of Arrhenius type temperature dependence for Ammonia Oxidizing Bacteria （AOB） subjected to tem- perature time gradients through continuous titrimetric tests. An innovative online differential titrimetric technique was used to continuously monitor the maximum biologic ammonia oxidation rate of the biomass selected in a pilot scale membrane bioreactor, as a function of temperature time gradients. The monitoring technique is based on the measurement of alkalinity and hydrogen peroxide con- sumption rates in two parallel reactors operated in non- limiting substrate conditions for AOB; both reactors were continuously fed with mixed liquor and in one of them AOB were inhibited with allylthiourea. The effects of temperature decrease rates in the range 1 to 4℃h^-1 were evaluated by controlling the titrimetric reactor in the temperature range 10℃-20℃. The dependence of growth kinetics on temperature time gradients and the range of applicability of Arrhenius model for temperature depen- dency of AOB growth kinetics were assessed. The Arrhenius model was found to be accurate only with temperature gradients lower than 2℃·h^-1. The estimated Arrhenius coefficients （θ） were shown to increase from 1.07 to 1.6 when the temperature decrease rate reached 4℃.h^-1.
文摘A novel controller is proposed to regulate the DC-link voltage of a single phase active power filter （SPAPF）. The proposed switched fractional controller （SFC） consists of a conventional PI controller, a fractional order PI （FO-PI） controller and a decision maker that switches between them. Commonly, the conventional PI controller is used in regulation loops due to its advantages in steady-state but it is limited in transient state. On the other hand, the FO-PI controller overcomes these draw- backs but it causes dramatic degradation in control performances in steady-state because of the fractional calculus theory and the approximation method used to implement this kind of controller. Thus, the purpose of this paper is to switch to the PI controller in steady-state to obtain the best power quality and to switch to the FO-PI controller when external disturbances are detected to guarantee a fast transient state. To investigate the efficiency and accuracy of the SFC considering all robustness tests, an experimental setup has been established. The results of the SFC fulfill the requirements, confirm its high performances in steady and transient states and demon- strate its feasibility and effectiveness. The experiment results have satisfied the limit specified by the IEEE harmonic standard 519.
