范畴Ω-Cat的极限和余极限

Ω-范畴具有范畴论和序理论的双重意义,可为计算机程序语言的语义提供量化的模型,本文给出了范畴Ω-Cat中极限和余极限的定义,同时研究了范畴Ω-Cat与范畴Set之间极限和余极限的关系。     

随机环境中伴有移民两性分枝过程的极限性质

本文在独立同分布的随机环境下,建立带有移民的两性分枝过程{Zn}n≥0,且移民人口数依赖当前人口数,证得{Zn}n≥0和{(Fn,Mn)}n≥1是随机环境中的马氏链,并得到第n代每个配对单元平均增长率{rk}k≥0的极限性质,从而推广了经典两性分枝过程的相关理论.     

一个分数阶微分方程四点边值问题正解的存在性

本文研究下面的分数阶微分方程四点边值问题Dα0+u(t)+f(t,u(t))=0,0相似文献   

On the use of response surface strategy to elucidate the electrophoretic migration of carbohydrates and optimize their separation

This paper focuses on the optimization with a design of experiments of a new CE method for the simultaneous separation of four carbohydrates of interest (fructose, glucose, lactose, and sucrose) and five potentially interfering carbohydrates (ribose, xylose, maltose, mannose, and galactose) with a highly alkaline separation electrolyte for subsequent applications to food, beverage, forensic, or pharmaceutical samples. First, the factors that potentially affect the carbohydrate migration were identified: NaOH concentration in the separation electrolyte, separation temperature, and separation electrolyte conductivity. A central composite design was then carried out to determine and model the effects of these three factors on normalized migration times and separation efficiency. From the model, an optimization of the separation was carried out using a desirability analysis based on resolutions between adjacent peaks and analysis time. The optimum conditions obtained were a separation electrolyte composed of 98 mM NaOH and 120 mM NaCl to adjust the conductivity at 4.29 S/m and a separation temperature fixed at 26.5°C. Finally, these conditions were experimentally confirmed and the robustness of the obtained separation was checked.     

孙子定理教学新探

改进了孙子定理的教学方法.     

Palm oil hydrolysis catalyzed by lipases under ultrasound irradiation--the use of experimental design as a tool for variables evaluation

Diacylglycerol oil has been increasingly recognized by its good nutritional properties and therefore, different technologies have been developed for obtaining it. The present work focuses on the diacylglycerol production by hydrolysis reaction of the palm oil using the PS IM and TL IM commercial lipases as biocatalysts under ultrasound irradiation. An experimental design (central composite rotatable design - CCRD) adopting surface response was applied as a tool to evaluate the optimal reaction conditions beyond a restrict number of experiments. Reactions were performed in an ultrasound equipment and different variables were investigated, such as temperature (30-55 °C), enzyme content (1-2 wt.% of oil mass), mechanical stirring (300-700 rpm) and reaction time. Both, PS IM and TL IM enzymes showed the best results after 1 h and 30 min of reaction under 30 °C and, applying 300 rpm as stirring. On these conditions, the diacylglycerol yield was around 34% and 39%, respectively; considering that 1% PS IM was applied for the first one and, 2% TL IM for the second one. Therefore, it was obtained good yield of a diacylglycerol-rich oil in shorter reaction times under sonication and soft conditions. The mathematic model proposed suggested a satisfactorily representation of the process and good correlation among the experimental results and the theoretical values predicted by the model equation were achieved.     

Limit theorems for BSDE with local time applications to non-linear PDE

Given a d -dimensional Wiener process W , with its natural filtration F t , a F T -measurable random variable ξ in R , a bounded measure x on R , and an adapted process ( s , y , z ) M h ( s , y , z ), we consider the following BSDE: Y t = ξ + Z t T h ( s , Y s , Z s ) d s + Z R ( L T a ( Y ) m L t a ( Y )) x (d a ) m Z t T Z s d W s for 0 h t h T . Here L t a ( Y ) stands for the local time of Y at level a . For h =0, we establish the existence and the uniqueness of the processes ( Y , Z ), and if h is continuous with linear growth we establish the existence of a solution. We prove limit theorems for solutions of backward stochastic differential equations of the above form. Those limit theorems permit us to deduce that any solution of that equation is the limit, in a strong sense, of a sequence of semi-martingales, which are solutions of ordinary BSDEs of the form Y t = ξ + Z t T f ( Y s ) Z s 2 d s m Z t T Z s d W s . A comparison theorem for BSDEs involving measures is discussed. As an application we obtain, with the help of the connection between BSDE and PDE, some corresponding limit theorems for a class of singular non-linear PDEs and a new probabilistic proof of the comparison theorem for PDEs.     

Martingale approach to limit theorems for jump processes

We consider the weak convergence of laws of càdiàg processes determined by a sequence of operators with singularly perturbed terms. We study the problem in the martingale approach, which was formulated to establish weak limit theorems for continuous processes by Papanicolaou, Stroock and Varadhan. However, in this paper, limit processes are not necessarily continuous but càdiàg. In particular, we consider a homogenization problem of càdiàg processes in the framework of martingale problem.     

泰勒公式的一种新证法

利用罗尔定理结合高等代数的行列式计算技巧,可证n阶可导函数f （x）的辅助多项式P（x）具有特定的 n阶导数,并运用该结果给出泰勒公式的一种新证法。     

On Graph-realizable Sets of Periods

We characterize sets of periods of cycles which arbitrary continuous graph maps may have. In this investigation, we need the spectral decomposition for graph maps [Blokh, A.M. "On dynamical systems on one-dimensional branched manifolds", Theory Funct. Funct. Anal. Appl. Kharkov 46 (1986) pp. 8-18 (Russian); 47 (1986) pp. 67-77; 48 (1987) pp. 32-46] briefly described in "The Spectral Decomposition" Section.