New extragradient-type methods for solving variational inequalities

In this paper, we propose new methods for solving variational inequalities. The proposed methods can be viewed as a refinement and improvement of the method of He et al. [B.S. He, X.M. Yuan, J.J. Zhang, Comparison of two kinds of prediction–correction methods for monotone variational inequalities, Comp. Opt. Appl. 27 (2004) 247–267] by performing an additional projection step at each iteration and another optimal step length is employed to reach substantial progress in each iteration. Under certain conditions, the global convergence of the both methods is proved. Preliminary numerical experiments are included to illustrate the efficiency of the proposed methods.     

A practical implementation of high‐order RKDG models for the 1D open‐channel flow equations

This paper comprises an implementation of a fourth‐order Runge–Kutta discontinuous Galerkin (RKDG4) scheme for computing the open‐channel flow equations. The main features of the proposed methodology are simplicity and easiness in the implementation, which may be of possible interest to water resources numerical modellers. A version of the RKDG4 is blended with the Roe Riemann solver, an adaptive high‐order slope limiting procedure, and high‐order source terms approximations. A comparison of the performance of the proposed method with lower‐order RKDG models is performed showing a benefit of considering the RKDG4 model. The scheme is applied to computerize the Saint Venant system by considering benchmark tests that have exact solutions. Finally, numerical results are illustrated discussing the performance of the proposed high‐order model. Copyright © 2008 John Wiley & Sons, Ltd.     

High-Dimensional Adaptive Sparse Polynomial Interpolation and Applications to Parametric PDEs

We consider the problem of Lagrange polynomial interpolation in high or countably infinite dimension, motivated by the fast computation of solutions to partial differential equations (PDEs) depending on a possibly large number of parameters which result from the application of generalised polynomial chaos discretisations to random and stochastic PDEs. In such applications there is a substantial advantage in considering polynomial spaces that are sparse and anisotropic with respect to the different parametric variables. In an adaptive context, the polynomial space is enriched at different stages of the computation. In this paper, we study an interpolation technique in which the sample set is incremented as the polynomial dimension increases, leading therefore to a minimal amount of PDE solving. This construction is based on the standard principle of tensorisation of a one-dimensional interpolation scheme and sparsification. We derive bounds on the Lebesgue constants for this interpolation process in terms of their univariate counterpart. For a class of model elliptic parametric PDE’s, we have shown in Chkifa et al. (Modél. Math. Anal. Numér. 47(1):253–280, 2013) that certain polynomial approximations based on Taylor expansions converge in terms of the polynomial dimension with an algebraic rate that is robust with respect to the parametric dimension. We show that this rate is preserved when using our interpolation algorithm. We also propose a greedy algorithm for the adaptive selection of the polynomial spaces based on our interpolation scheme, and illustrate its performance both on scalar valued functions and on parametric elliptic PDE’s.     

Fabrication of microporous membranes from melt extruded polypropylene precursor films via stretching: Effect of annealing

In this work, the effects of annealing conditions on the microstructure of polypropylene(PP) precursor films and further on the porous structure and permeability of stretched membranes were investigated. Combinations of WAXD, FTIR, DSC and DMA results clearly showed the crystalline orientation and crystallinity of the precursor film increased with annealing temperature, while the molecular chain entanglements in the amorphous phase decreased. Changes in the deformation behavior suggested more lamellar separation occurred for the films annealed at higher temperatures. Surface morphologies of the membranes examined by SEM revealed more pore number and uniform porous structure as the annealing temperature increased. In accordance with the SEM results, the permeability of the membranes increased with annealing temperature. On the other hand, it was found that 10 min was almost enough for the annealing process to obtain the microporous membranes with an optimal permeability.     

Towards the limit of atropochiral stability: H-MIOP, an N-heterocyclic carbene precursor and cationic analogue of the H-MOP ligand

The configurational stability of biaryl motifs is addressed for the 1-naphthyl-N-benzimidazolyl motif substituted by a single diphenylphosphinyl group at the 2-position. The atropoenantiomers of the N-methylated cation H-MIOP, a less sterically locked analogue of the neutral H-MOP ligand, were resolved by enantiospecific cleavage of the N(2)C-P bond of the resolved enantiomers of BIMIONAP. The latter were obtained by enantiospecific N-methylation of the previously resolved enantiomers of neutral BIMINAP. PdCl(2) complexes of the P,C-chelating N-heterocyclic carbene (NHC)-phosphine ligands derived from (R)- and (S)-H-MIOP were prepared by two enantiospecific routes: by N(2)C-P bond cleavage from the (R)- and (S)-BIMIONAP-PdCl(2) complexes, or by simultaneous coordination of the P and C atoms of the in situ generated free NHC-phosphine. The enantiomerization pathways of H-MOP, H-MIOP, and corresponding NHC-phosphine have been investigated at the B3PW91/6-31G(d,p) level of theory. The calculated enantiomerization barriers of H-MOP and H-MIOP in acetonitrile are equal to 176.0 and 146.4 kJ mol(-1), respectively, and are mainly determined by the distortion of the naphthalene and/or benzimidazole motifs in the transition state. Beyond the stability of their optical rotation at room temperature, the respective calculated Oki's racemization temperatures of 334 and 225 °C allowed us to consider both ligands as configurationally stable.     

Effect of sterilization on non-woven polyethylene terephthalate fiber structures for vascular grafts

Non-woven polyethylene terephthalate (PET) fibers produced via melt blowing and compounded into a 6 mm diameter 3D tubular scaffold were developed with artery matching mechanical properties. This work compares the effects of ethylene oxide (EtO) and low temperature plasma (LTP) sterilization on PET surface chemistry and biocompatibility. As seen through X-ray photoelectron spectroscopy (XPS) analysis, LTP sterilization led to an increase in overall oxygen content and the creation of new hydroxyl groups. EtO sterilization induced alkylation of the PET polymer. The in vitro cytotoxicity showed similar fibroblastic viability on LTP- and EtO-treated PET fibers. However, TNF-α release levels, indicative of macrophage activation, were significantly higher when macrophages were incubated on EtO-treated PET fibers. Subcutaneous mice implantation revealed an inflammatory response with foreign body reaction to PET grafts independent of the sterilization procedure.     

Antioxidant activity,phytochemical screening,and total phenolic content of extracts from three genders of carob tree barks growing in Morocco

We evaluated the in vitro antioxidant property and phytochemical constituents of the crude ethyl acetate and methanol extract of the three genders of carob tree barks (spontaneous male, spontaneous female, and grafted female). The scavenging activity on DPPH (1,1-diphenyl-2-picrylhydrazyl) was determined, as well as the phenolic contents (Folin–Ciocalteu method) of both the extracts. The highest antioxidant activity and the higher amounts of total phenols were shown in methanol crude bark extract for the three genders. Variety significantly affected the phenol content and the antioxidant activity, with the spontaneous male variety globally showed a higher polyphenol concentration and antioxidant activity than the grafted female and spontaneous female.     

Inexact proximal point method for general variational inequalities

In this paper, we suggest and analyze a new inexact proximal point method for solving general variational inequalities, which can be considered as an implicit predictor-corrector method. An easily measurable error term is proposed with further relaxed error bound and an optimal step length is obtained by maximizing the profit-function and is dependent on the previous points. Our results include several known and new techniques for solving variational inequalities and related optimization problems. Results obtained in this paper can be viewed as an important improvement and refinement of the previously known results. Preliminary numerical experiments are included to illustrate the advantage and efficiency of the proposed method.