Cosmological Models with Fractional Derivatives and FractionalAction Functional

Cosmological models of a scalar field with dynamical equations containing fractional derivatives or derived from the Einstein-Hilbert action of fractional Order, are constructed. A number of exact solutions to those equations of fractional cosmological models in both cases is given.     

Some algorithms for numerical quadrature using the derivatives of the integrand in the integration interval

Some quadrature formulae using the derivatives of the integrand are discussed. As special cases are obtained generalizations of both the ordinary and the modified Romberg algorithms. In all cases the error terms are expressed in terms of Bernoulli polynomials and functions.     

半无限规划与方向导数

本文对半无限凸规划提出一个用方向导数表述的对偶问题，其对偶间隙为零．     

A nonlocal multi-point singular fractional integro-differential problem of Lane–Emden type

In this paper, using Riemann–Liouville integral and Caputo derivative, we study a nonlinear singular integro-differential equation of Lane–Emden type with nonlocal multi-point integral conditions. We prove the existence and uniqueness of solutions by application of Banach contraction principle. Also, we prove an existence result using Schaefer fixed point theorem. Then, we present some examples to show the applicability of the main results.     

About contingent epiderivatives

In this paper we analyze some questions concerning the contingent epiderivative. When the ordering cone is not necessarily pointed we introduce the notion of family of contingent epiderivatives. We also investigate the relationship between the contingent derivative and the generalized epiderivative. Furthermore, we give existence theorems with respect to Daniell cones. As a particular case, we study set-valued maps that take values in Rn.     

Constrained Controllability of Fractional Dynamical Systems

The article deals with the controllability results for fractional dynamical systems with prescribed controls represented by the fractional integrodifferential equation in finite dimensional spaces. Sufficient conditions for the controllability results of nonlinear fractional dynamical systems are obtained using the contraction mapping principle. Examples are included to illustrate the theory.     

Fractional diffusion-type equations with exponential and logarithmic differential operators

We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi et al. (2001)): the first equation considered here is obtained by adding an exponential differential (or shift) operator expressed in terms of the Riesz–Feller derivative. We prove that this produces a random component in the time-argument of the corresponding stable process, which is represented by the so-called Poisson process with drift. Analogously, if we add, to the space-fractional diffusion equation, a logarithmic differential operator involving the Riesz-derivative, we obtain, as a solution, the transition semigroup of a stable process subordinated by an independent gamma subordinator with drift. Finally, we show that an extension of the space-fractional diffusion equation, containing both the fractional shift operator and the Feller integral, is satisfied by the transition density of the process obtained by time-changing the stable process with an independent linear birth process with drift.     

咪唑衍生物的一锅法选择性合成

1-(2-氰乙基)咪唑与α,ω-二卤代烃、二溴苄及三溴苄选择性地发生季铵化反应,继而在碱作用下发生Hoffmann型消去反应,简便而高效地制备了3个系列咪唑衍生物:1-(ω-卤烷基)咪唑3a～3e、含中心功能基的双咪唑5a～5b和三咪唑6a～6b,并类似地制得相应的苯并咪唑衍生物7和8.     

Practical synthesis of 1,4-dioxane derivative of the closo-dodecaborate anion and its ring opening with acetylenic alkoxides

Practical method of synthesis of the 1,4-dioxane derivative of the closo-dodecaborate anion was developed. The cleavage of the dioxonium ring in [B₁₂H₁₁O(CH₂CH₂)₂O]⁻ with acetylenic alcohols gave rise to the preparation of closo-dodecaborate derivatives with terminal acetylene group. These compounds can be introduced into click reactions with phenylazide leading to the corresponding triazoles. The structures of (Bu₄N)[B₁₂H₁₁O(CH₂CH₂)₂O] and (Bu₄N)₂[B₁₂H₁₁(OCH₂CH₂)₂OCH₂CCH] · 0.5HOCH₂CCH were determined by single-crystal X-ray diffraction.