Strange evaluations of Fox–Wright function

By means of inversion techniques and four known hypergeometric series identities, eight summation formulas for the Fox–Wright function are established. They can give numerous summation formulas for 2-balanced hypergeometric series when the parameters are specified.     

Synthesis of poly[(2‐oxo‐1,3‐dioxolane‐4‐yl) methyl methacrylate‐co‐ethyl acrylate] by incorporation of carbon dioxide into epoxide polymer and the miscibility behavior of its blends with poly(methyl methacrylate) or poly(vinyl chloride)

This study was related to the investigation of the chemical fixation of carbon dioxide to a copolymer bearing epoxide and the application of the cyclic carbonate group containing copolymer‐to‐polymer blends. In the synthesis of poly[(2‐oxo‐1,3‐dioxolane‐4‐yl) methyl methacrylate‐co‐ethyl acrylate] [poly(DOMA‐co‐EA)] from poly(glycidyl methacrylate‐co‐ethyl acrylate) [poly(GMA‐co‐EA)] and CO₂, quaternary ammonium salts showed good catalytic activity. The films of poly(DOMA‐co‐EA) with poly(methyl methacrylate) (PMMA) or poly(vinyl chloride) (PVC) blends were cast from N,N′‐dimethylformamide solution. The miscibility of the blends of poly(DOMA‐co‐EA) with PMMA or PVC have been investigated both by DSC and visual inspection of the blends. The optical clarity test and DSC analysis showed that poly(DOMA‐co‐EA) containing blends were miscible over the whole composition range. The miscibility behaviors were discussed in terms of Fourier transform infrared spectra and interaction parameters based on the binary interaction model. © 2001 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 39: 1472–1480, 2001     

Using Fox Derivatives in Treating Groups of the Form F/[R′, F]

For a factor group with respect to periodic part of a group of the form F/[R′, F], an embedding in the matrix group is defined. The criteria for a matrix to belong to an image of this group and for elements to be conjugate are specified. Some statements having a direct bearing on groups of the form in question are proved. Application of the results obtained allows us to refine the answer in [7] to a question by O. Chapuis concerning the universal classification of ∀-free soluble groups with two generators. Supported by RFBR grant No. 02-01-00293 and by FP “Universities of Russia” grant No. UR.04.01.227. __________ Translated from Algebra i Logika, Vol. 45, No. 1, pp. 114–125, January–February, 2006.     

Dynamic mechanical thermal analysis transitions of partially and fully substituted cellulose fatty esters

The main transitions of cellulose fatty esters with different degrees of substitution (DSs) were investigated with dynamic mechanical thermal analysis. Two distinct main relaxations were observed in partially substituted cellulose esters (PSCEs). They were attributed to the glass‐transition temperature and to the chain local motion of the aliphatic substituents. The temperatures of both transitions decreased when DS or the number of carbon atoms (n) of the acyl substituent increased. Conversely, all the transitions of fully substituted cellulose esters occurred within a narrow temperature range, and they did not vary significantly with n. This phenomenon was explained by the formation of a crystalline phase of the fatty substituents. The presence of few residual OH groups in PSCEs was responsible for a large increase in the storage bending modulus, and it eliminated the effect of n on damping. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 281–288, 2003     

时间分数阶扩散-反应方程

1、引言 当前,对含有非整数阶导数和积分的方程的研究正引起越来越多学者的关注,这类分数阶导数和积分将广泛应用于科学和工程的各个领域．     

有限区间上的分数阶扩散-波方程定解问题与Laplace变换

求解了如下的分数阶扩散-波方程定解问题0Dαtu=2ux2,00,0<α≤2,u(0,t;α)=0,u(1,t;α)=θ(t),u(x,0+;α)=0,当1<α≤2时,还有ut(x,0+;α)=0.其中θ(t)是Heaviside单位阶跃函数,0Dαt为关于时间t的α阶Caputo分数阶导数算子,u=u(x,t;α)为时间t的因果函数(即t<0时恒为零的函数).利用Laplace变换的复围道积分反演和离散化反演及FoxH函数理论,给出在计算上对大的t和小的t分别适用的解的表达式.     

Solutions for a generalized fractional anomalous diffusion equation

In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which subjects to the natural boundaries and the generic initial condition. We obtain explicit analytical expressions for the probability distribution and study the relation between our solutions and those obtained within the maximum entropy principle by using the Tsallis entropy.