This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's t...This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.展开更多
Due to the limitation and hesitation in one＇s knowledge, the membership degree of an element to a given set usually has a few different values, in which the conventional fuzzy sets are invalid. Hesitant fuzzy sets ar...Due to the limitation and hesitation in one＇s knowledge, the membership degree of an element to a given set usually has a few different values, in which the conventional fuzzy sets are invalid. Hesitant fuzzy sets are a powerful tool to treat this case. The present paper focuses on investigating the clustering technique for hesitant fuzzy sets based on the K-means clustering algorithm which takes the results of hierarchical clustering as the initial clusters. Finally, two examples demonstrate the validity of our algorithm.展开更多
The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion.I...The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion.It is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion.For this type of partial information control,one sufficient(a verification theorem) and one necessary conditions of optimality are proved.The control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.展开更多
A new organic dye, trans-4-[p-(N-hydroxyethyl-N-ethylamino)styryl]-N-methyl- pyridinium p-toluene sulfonate (HEASPS) has been synthesized and its structure has been determined. Pumped with a 1064 nm, 50 ps laser pulse...A new organic dye, trans-4-[p-(N-hydroxyethyl-N-ethylamino)styryl]-N-methyl- pyridinium p-toluene sulfonate (HEASPS) has been synthesized and its structure has been determined. Pumped with a 1064 nm, 50 ps laser pulses, 0.05 mol/L HEASPS/DMF solution showed the two-photon pumped (TPP) output/input efficiency of 9.1% which is higher than that of known TPP laser dyes trans-4-[p-(N-hydroxyethyl-N-methylamino) styryl]-N-methylpyridinium iodide (ASPI) and trans-4-[p-(N-hydroxyethyl-N-methylamino) styryl]-N-methylpyridinium p-toluene sulfonate (HMASPS) at the same experimental conditions.展开更多
We use a new method to study arrangement in CPl,define a class of nice point arrangements and show that if two nice point arrangements have the same combinatorics,then their complements are diffeomorphic to each other...We use a new method to study arrangement in CPl,define a class of nice point arrangements and show that if two nice point arrangements have the same combinatorics,then their complements are diffeomorphic to each other.In particular,the moduli space of nice point arrangements with same combinatorics in CPl is connected.It generalizes the result on point arrangements in CP3 to point arrangements in CPl for any l.展开更多
基金supported by National Basic Research Program of China (Grant No.2007CB814900)(Financial Risk)
文摘This is a survey on normal distributions and the related central limit theorem under sublinear expectation.We also present Brownian motion under sublinear expectations and the related stochastic calculus of It's type.The results provide new and robust tools for the problem of probability model uncertainty arising in financial risk,statistics and other industrial problems.
基金Supported by the National Natural Science Foundation of China(61273209)
文摘Due to the limitation and hesitation in one＇s knowledge, the membership degree of an element to a given set usually has a few different values, in which the conventional fuzzy sets are invalid. Hesitant fuzzy sets are a powerful tool to treat this case. The present paper focuses on investigating the clustering technique for hesitant fuzzy sets based on the K-means clustering algorithm which takes the results of hierarchical clustering as the initial clusters. Finally, two examples demonstrate the validity of our algorithm.
基金supported by Basic Research Program of China (Grant No.2007CB814904)National Natural Science Foundation of China (Grant No.10325101)Natural Science Foundation of Zhejiang Province (Grant No.Y605478,Y606667)
文摘The paper is concerned with a stochastic optimal control problem in which the controlled system is described by a fully coupled nonlinear forward-backward stochastic differential equation driven by a Brownian motion.It is required that all admissible control processes are adapted to a given subfiltration of the filtration generated by the underlying Brownian motion.For this type of partial information control,one sufficient(a verification theorem) and one necessary conditions of optimality are proved.The control domain need to be convex and the forward diffusion coefficient of the system can contain the control variable.
文摘A new organic dye, trans-4-[p-(N-hydroxyethyl-N-ethylamino)styryl]-N-methyl- pyridinium p-toluene sulfonate (HEASPS) has been synthesized and its structure has been determined. Pumped with a 1064 nm, 50 ps laser pulses, 0.05 mol/L HEASPS/DMF solution showed the two-photon pumped (TPP) output/input efficiency of 9.1% which is higher than that of known TPP laser dyes trans-4-[p-(N-hydroxyethyl-N-methylamino) styryl]-N-methylpyridinium iodide (ASPI) and trans-4-[p-(N-hydroxyethyl-N-methylamino) styryl]-N-methylpyridinium p-toluene sulfonate (HMASPS) at the same experimental conditions.
基金supported by National Natural Science Foundation of China(Grant No.10731030)Program of Shanghai Subject Chief Scientist (PSSCS) of Shanghai
文摘We use a new method to study arrangement in CPl,define a class of nice point arrangements and show that if two nice point arrangements have the same combinatorics,then their complements are diffeomorphic to each other.In particular,the moduli space of nice point arrangements with same combinatorics in CPl is connected.It generalizes the result on point arrangements in CP3 to point arrangements in CPl for any l.
