MULTILINEAR CALDER(O)N-ZYGMUND OPERATOR ON MORREY TYPE SPACES——In Memory of Professor Yongsheng Sun

In this paper, the authors study the boundedness of a class of multi-sublinear operators on the product of Morrey, Herz-Morrey and generalized Morrey spaces, respectively. As their special cases, the corresponding results of multilinear Calderón-Zygmund operator can be obtained.     

带变量核的广义高阶Marcinkiewicz积分交换子在Herz型Hardy空间的有界性

设A是R~n上的一个m阶可导函数,且D~λA∈Λ_β(0β1,|λ|=m),Ω(x,z)∈L~∞(R~n)×L~s(S~(n-1))(sn/(n-β))是零阶齐次函数且关于变量z满足消失条件.该文证明了广义高阶Marcinkiewicz积分交换子μ_Ω~A及其变形μ_Ω~A在Herz型Hardy空间的有界性.     

Novel numerical techniques for the finite moment log stable computational model for European call option

Option pricing models are often used to describe the dynamic characteristics of prices in financial markets. Unlike the classical Black–Scholes (BS) model, the finite moment log stable (FMLS) model can explain large movements of prices during small time steps. In the FMLS, the second-order spatial derivative of the BS model is replaced by a fractional operator of order α which generates an α-stable Lévy process. In this paper, we consider the finite difference method to approximate the FMLS model. We present two numerical schemes for this approximation: the implicit numerical scheme and the Crank–Nicolson scheme. We carry out convergence and stability analyses for the proposed schemes. Since the fractional operator routinely generates dense matrices which often require high computational cost and storage memory, we explore three methods for solving the approximation schemes: the Gaussian elimination method, the bi-conjugate gradient stabilized method (Bi-CGSTAB) and the fast Bi-CGSTAB (FBi-CGSTAB) in order to compare the cost of calculations. Finally, two numerical examples with exact solutions are presented where we also use extrapolation techniques to achieve higher-order convergence. The results suggest that the proposed schemes are unconditionally stable and convergent, and the FMLS model is useful for pricing options.     

TOEPLITZ-TYPE OPERATORS ON LEBESGUE SPACES

Let L be the infinitesimal generator of an analytic semigroup on L 2 (Rn)with Gaussian kernel bounds,and L-α/ 2 be the fractional integrals generated by L for 0< α     

固相萃取/液相色谱-串联质谱法测定食品中二甲基黄

建立了液相色谱-串联质谱(LC-MS/MS)测定食品中二甲基黄(DMY)的分析方法。样品经乙酸乙酯提取,二甲基黄专用固相萃取小柱(ProElut DMY SPE)净化,XDB-C18色谱柱(50 mm×4.6 mm,1.8μm)分离,并以5mmol/L乙酸铵水溶液(含0.1%(v/v)甲酸)-乙腈(含0.1%(v/v)甲酸)为流动相,梯度洗脱,电喷雾正离子模式(ESI~+)电离,多反应监测模式(MRM)检测,内标法定量。结果表明,DMY在0~50μg/L范围内线性关系良好,相关系数(r~2)均大于0.999。方法的检出限(LOD,S/N3)和定量限(LOQ,S/N10)分别为2μg/kg和10μg/kg。不同食品基质中,DMY在10、20和100μg/kg的添加水平下的平均加标回收率为93.3%~98.9%,相对标准偏差为1.6%~3.9%(n=6)。该方法有效补偿了液相色谱-串联质谱检测过程中的离子化抑制效应,灵敏度和准确度高,适用于腐乳、辣椒酱、禽蛋、豆干、糖果和火腿中DMY的测定。     

Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus

In this paper, analytical solutions to time-fractional partial differential equations in a multi-layer annulus are presented. The final solutions are obtained in terms of Mittag-Leffler function by using the finite integral transform technique and Laplace transform technique. In addition, the classical diffusion equation (α=1$\alpha =1$), the Helmholtz equation (α→0$\alpha \to 0$) and the wave equation (α=2$\alpha =2$) are discussed as special cases. Finally, an illustrative example problem for the three-layer semi-circular annular region is solved and numerical results are presented graphically for various kind of order of fractional derivative.     

关于Herz型空间中加权Hardy-Littlewood平均的一个注记

本文给出了加权Hardy-Littlewood平均在Herz型空间中关于权有界的充分必要条件.     

Multilinear oscillatory integrals with Calderón-Zygmund kernel

A criterion on some boundedness is obtained for a class of multilinear oscillatory singular integrals with Calderon-Zygmund standard kernel. Project supported by the National Natural Science Foundation of China (Grnat No. 19131080).     

Inhomogeneous discrete calderón reproducing formulas for spaces of homogeneous type

In this article a Littlewood-Paley theorem for a new kind of Littlewood-Paley g-functions over spaces of homogeneous type is presented. Based on it the authors establish inhomogeneous discrete Calderón reproducing formulas for spaces of homogeneous type, making use of Calderón-Zygmund operators.     

行和列和为常量的(0,1)-矩阵的计数

Let fs,t(m,n) be the number of (0,1) - matrices of size m x n such that each row has exactly s ones and each column has exactly t ones (sm = nt). How to determine fs,t(m,n)? As R. P. Stanley has observed (Enumerative CombinatoricsⅠ(1997), Example 1.1.3), the determination of fs,t(m, n) is an unsolved problem, except for very small s, t. In this paper the closed formulas for f2,2(n,n), f3,2(m,n), f4,2(m,n) are given. And recursion formulas and generating functions are discussed.