We consider fractional isoperimetric problems of calculus of variations with double integrals via the recent modified Riemann–Liouville approach. A necessary optimality condition of Euler–Lagrange type, in the form of a multitime fractional PDE, is proved, as well as a sufficient condition and fractional natural boundary conditions. M.S.C. 2010: 49K21, 35R11.

This work considers the rigorous derivation of continuummodels of step motion starting from a mesoscopic Burton-Cabrera-Frank (BCF) type model following the work [Xiang, SIAM J. Appl. Math. 2002]. We prove that as the lattice parameter goes to zero, for a finite time interval, a modified discrete model converges to the strong solution of the limiting PDE with first order convergence rate.

ABSTRACT In order to improve patient care, OMEDIT (Observatory of drugs, medical devices and therapeutic innovation) Alsace, conducted a study to develop a Preferential list of Drugs adapted to the Elderly (PDE list) in nursing homes. The study conducted from December 2011 to June 2012 was organized in 4 phases: 1) creation of a preliminary list of drugs from those currently used in nursing hom...

The modification of core histone proteins in mouse 10T1/2 cells and human lung epitheloid (A549) cells by B(a)PDE in vivo and in vitro was found to be similar. Only histones H2A and H3 were extensively modified. Also other proteins, possibly A24 protein and the minor histone H1 species seem to be binding relatively high levels of this ultimate carcinogen. Butyrate treatment which causes hyperac...

Although promising for visualizing the structure of ordered tissues, MR diffusion tensor imaging (DTI) has been hampered by long acquisition time and low spatial resolution associated with its inherently low signal-to-noise ratio (SNR). Moreover, the uncertainty in the DTI measurements has a direct impact on the accuracy of structural renderings such as fiber streamline tracking. Noise removal ...

In this paper, by using scalar multiple integral cost functionals and the notion of convexity associated with a functional driven an uncertain multi-time controlled second-order Lagrangian, we develop new mathematical framework on multi-dimensional variational control problems mixed constraints implying partial differential equations (PDEs) inequations (PDIs). Concretely, introduce investigate ...

A method for trimming surfaces generated as solutions to Partial Differential Equations (PDEs) is presented. The work we present here utilises the 2D parameter space on which the trim curves are defined whose projection on the parametrically represented PDE surface is then trimmed out. To do this we define the trim curves to be a set of boundary conditions which enable us to solve a low order e...

This paper presents a method to extend PDE surfaces to high dimensional spaces. We review a common existing analytic solution, and show how it can be used straightforwardly to increase the dimension of the space the surface is embedded within. We then further develop a numerical scheme suitable for increasing the number of variables that parametrise the surface, and investigate some of the prop...