柯西中值定理的逆问题及渐进性

讨论了柯西中值定理的逆问题,并将柯西中值定理"中间点"的渐进性在高阶柯西中值定理中作了推广,得到了一般性的结论.     

一种构造辅助函数法的应用

利用一个基本事实,即令F（x）＝ f （x）eg（x）,则F′（x）＝ eg（x）[ f′（x）＋ f （x）g′（x）],结合具体的实例,说明在一类涉及导数的数学问题中此种构造辅助函数法的应用。     

双曲空间形式中具有常平均曲率的超曲面(英文)

本文研究了双曲空间形式H~(n+1)(—1)中具有常平均曲率及两个离散主曲率(其中一个主曲率是1-重)的完备连通可定向的n-维超曲面M~n.利用活动标架,得到如果M~n的基本形式的模长满足刚性条件(1.3),那么M~n同构双曲柱面.     

The improved split‐step θ methods for stochastic differential equation

Two improved split‐step θ methods, which, respectively, named split‐step composite θ method and modified split‐step θ‐Milstein method, are proposed for numerically solving stochastic differential equation of Itô type. The stability and convergence of these methods are investigated in the mean‐square sense. Moreover, an approach to improve the numerical stability is illustrated by choices of parameters of these two methods. Some numerical examples show the accordance between the theoretical and numerical results. Further numerical tests exhibit not only the Hamiltonian‐preserving property of the improved split‐step θ methods for a stochastic differential system but also the positivity‐preserving property of the modified split‐step θ‐Milstein method for the Cox–Ingersoll–Ross model. Copyright © 2013 John Wiley & Sons, Ltd.     

Generalized Symplectic Mean Curvature Flows in Almost Einstein Surfaces

The authors mainly study the generalized symplectic mean curvature flow in an almost Einstein surface, and prove that this flow has no type-I singularity. In the graph case, the global existence and convergence of the flow at infinity to a minimal surface with metric of the ambient space conformal to the original one are also proved.     

Binding affinity of substituted ureido‐benzenesulfonamide ligands to the carbonic anhydrase receptor: A theoretical study of enzyme inhibition

The binding properties of a series of benzenesulfonamide inhibitors (4‐substituted‐ureido‐benzenesulfonamides, UBSAs) of human carbonic anhydrase II (hCA II) enzyme with active site residues have been studied using a hybrid quantum mechanical/molecular mechanical (QM/MM) model. To account for the important docking interactions between the UBSAs ligand and hCA II enzyme, a molecular docking program AutoDock Vina is used. The molecular docking results obtained by AutoDock Vina revealed that the docked conformer has root mean square deviation value less than 1.50 Å compared to X‐ray crystal structures. The inhibitory activity of UBSA ligands against hCA II is found to be in good agreement with the experimental results. The thermodynamic parameters for inhibitor binding show that hydrogen bonding, hydrophilic, and hydrophobic interactions play a major role in explaining the diverse inhibitory range of these derivatives. Additionally, natural bond orbital analysis is performed to characterize the ligand–metal charge transfer stability. The insights gained from this study have great potential to design new hCA‐II inhibitor, 4‐[3‐(1‐p‐Tolyl‐4‐trifluoromethyl‐1H‐pyrazol‐3‐yl)‐ureido]‐benzenesulfonamide, which belongs to the family of UBSA inhibitors and shows similar type of inhibitor potency with hCA II. This work also reveals that a QM/MM model and molecular docking method are computationally feasible and accurate for studying substrate–protein inhibition. © 2013 Wiley Periodicals, Inc.     

Symmetric esters derived from 1,3,4-oxadiazole: synthesis,mesomorphic properties and structural study by semi-empirical calculations

Three homologous series of symmetric esters derived from 2-alkylthio-5-(p -hydroxy)phenyl-1,3,4-oxadiazole (series 3, 4 and 5) were synthesized and their liquid crystalline properties investigated by optical microscopy and differential scanning calorimetry. Depending on the chain length, nematic and smectic C phases were observed in the series 3 ; smectic A and smectic C phases in series 4. None of the homologues of series 5 shows mesomorphic properties. These three series are compared with other previously reported oxadiazoles. A structural study of AM1 semi-empirical calculations is also described.     

考虑多元关联关系和语义变换的直觉不确定语言多属性决策方法

针对属性值为直觉不确定语言变量的多属性决策问题,提出一种不仅可以捕获属性间的多元关联关系并且能够满足决策者不同语义转换需求的多属性决策方法。首先,考虑已有运算法则缺少封闭性和灵活性,结合语言刻度函数,提出一种新的直觉不确定语言变量运算法则和排序方法。其次,根据新的运算法则,提出可以捕获属性间多元关联关系的直觉不确定语言Hamy平均及其加权形式,并对新算子的优良性质和特例进行了探讨和分析。进而,提出一种新的多属性决策方法。最后,通过算例和对比分析验证了该方法的有效性和优越性。