Direct pseudo‐spectral method for optimal control of obstacle problem – an optimal control problem governed by elliptic variational inequality

In this paper, a computational technique based on the pseudo‐spectral method is presented for the solution of the optimal control problem constrained with elliptic variational inequality. In fact, our aim in this paper is to present a direct approach for this class of optimal control problems. By using the pseudo‐spectral method, the infinite dimensional mathematical programming with equilibrium constraint, which can be an equivalent form of the considered problem, is converted to a finite dimensional mathematical programming with complementarity constraint. Then, the finite dimensional problem can be solved by the well‐developed methods. Finally, numerical examples are presented to show the validity and efficiency of the technique. Copyright © 2017 John Wiley & Sons, Ltd.     

Multi-objective optimization of a dimpled channel for heat transfer augmentation

Staggered arrays of dimples printed on opposite surfaces of a cooling channel is formulated numerically and optimized with hybrid multi-objective evolutionary algorithm and Pareto optimal front. As Pareto optimal front produces a set of optimal solutions, the trends of objective functions with design variables are predicted by hybrid multi-objective evolutionary algorithm. The problem is defined by three non-dimensional geometric design variables composed of dimpled channel height, dimple print diameter, dimple spacing, and dimple depth, to maximize heat transfer rate compromising with pressure drop. Twenty designs generated by Latin hypercube sampling were evaluated by Reynolds-averaged Navier–Stokes solver and the evaluated objectives were used to construct Pareto optimal front through hybrid multi-objective evolutionary algorithm. The optimum designs were grouped by k-means clustering technique and some of the clustered points were evaluated by flow analysis. With increase in dimple depth, heat transfer rate increases and at the same time pressure drop also increases, while opposite behavior is obtained for the dimple spacing. The heat transfer performance is related to the vertical motion of the flow and the reattachment length in the dimple.     

Porous triazine polymer: A novel catalyst for the three-component reaction

A new porous triazine-based covalent organic polymer (Triazine-COP) was prepared through the Schiff-base condensation of 2,4,6-tris(4-formyl phenoxy)-1,3,5-triazine and 4,4′-oxydianiline, under sonication. The synthesized Triazine-COP with a high surface area was stable in water and other organic solvents. In the next step, Au (III) ions were immobilized on the nitrogen-rich Triazine-COP that on the reduction with NaBH₄ produced the heterogeneous catalyst of gold clusters in nanosize (Au-NCs@Triazine-COPs). It was applied as an efficient catalyst for the A³ coupling reaction of alkynes, aldehydes with and amines. Both electron-withdrawing/releasing groups produced the corresponding propargylamines with high yields. The high activity of the Au-NCs@Triazine-COPs in this reaction was because of the nanoporous structure of the support that enables the high dispersion and an unhindered open environment for the NCs. The catalyst was reused up to 7 times without significant loss in activity.     

Asymmetric deformation density analysis in carbon nanotubes

Electrons and holes as charge carriers appear when a molecular system is exposed to external electric field. For nonsymmetric molecules, the distribution of charge carriers is also nonsymmetric. Although symmetric distribution of charge carriers is expected when the molecular system is symmetric, as the present work shows, they are not symmetric unexpectedly; that is, electrons and holes are not each other's mirror images. In this respect, asymmetric deformation density analysis is introduced to measure the extent of asymmetric distribution of electrons and holes as charge carriers when the symmetric system is exposed to symmetric external potential. Segments of (5,0) carbon nanotubes with different lengths are selected as symmetric systems, and a linear electric field is applied along the principal axis as symmetric potential. Results show that, at high electric fields, electrons tend to localize at the ends, while holes tend to occupy the middle area of carbon nanotube segments. While charge carriers play a vital role in molecular conductivity, asymmetric distribution of electrons and holes in symmetric systems has not yet been reported.     

Screening of allelopathic trees for their antifungal potential against Alternaria alternata strains isolated from dying-back Eucalyptus spp

Antifungal activity of methanolic extracts of leaves of three tree species, namely Azadirachta indica L., Syzygium cumini (L.) Skeels. and Melia azedarach L. was evaluated against two strains of Alternaria alternata, isolated from dying-back trees of two Eucalyptus spp., namely Eucalyptus citriodora and Eucalyptus globulus. All the concentrations (1,?2,?…?,?5% w/v) of the methanolic extracts of the three tree species significantly reduced the fungal biomass. There were reductions in the ranges 82-88%, 88-96% and 83-96% in the biomass of A. alternata strains due to different concentrations of the leaf extracts of S. cumini, A. indica and M. azedarach, respectively. Methanolic extract of M. azedarach was subjected to further fractionation using n-hexane, chloroform, ethyl acetate and n-butanol successively in the order of increasing polarity. Aqueous and n-butanol fractions gave promising results in the significant decrease in fungal biomass. This study concludes that aqueous and n-butanol fractions of methanolic leaf extract of M. azedarach can be used as biofungicides for the management of A. alternata.     

Volatile constituent distribution of Prangos coryombosa Boiss at two stages of growth

The volatile constituents obtained by hydrodistillation of the aerial parts of Prangos coryombosa at the vegetative and flowering stages were analysed by GC and GC-MS. Twenty-one and 28 compounds were identified from the oils obtained from the plant's aerial parts at the vegetative and flowering stages, respectively. The oil from the vegetative stage was dominated by β-elemene (22%) and spathulenol (12.5%), whereas the oil from the flowering period was characterised by β-elemene (40.7%) and kessane (10.7%). The main compounds of the oil at the flowering stage were isolated by TLC and their structures were elucidated by (1)H and (13)C NMR. The results have ecological and taxonomical significance.     

Application of desymmetrization protocol for the formal total synthesis of emericellamide B

A highly convergent formal total synthesis of emericellamide B, a 19-membered antibacterial depsipeptide is described. The key feature of the strategy is the generation of four stereogenic centers from a bicyclic precursor via desymmetrization technique and utilization for emericellamide B and related natural product synthesis.     

Simultaneous determination of 2‐arachidonoylglycerol, 1‐arachidonoylglycerol and arachidonic acid in mouse brain tissue using liquid chromatography/tandem mass spectrometry

Endocannabinoids (ECs), such as anandamide (AEA) and 2‐arachidonoylglycerol (2‐AG), modulate a number of physiological processes, including pain, appetite and emotional state. Levels of ECs are tightly controlled by enzymatic biosynthesis and degradation in vivo. However, there is limited knowledge about the enzymes that terminate signaling of the major brain EC, 2‐AG. Identification and quantification of 2‐AG, 1‐AG and arachidonic acid (AA) is important for studying the enzymatic hydrolysis of 2‐AG. We have developed a sensitive and specific quantification method for simultaneous determination of 2‐AG, 1‐AG and AA from mouse brain and adipose tissues by liquid chromatography/tandem mass spectrometry (LC/MS/MS) using a simple brain sample preparation method. The separations were carried out based on reversed phase chromatography. Optimization of electrospray ionization conditions established the limits of detection (S/N = 3) at 50, 25 and 65 fmol for 2‐AG, 1‐AG and AA, respectively. The methods were selective, precise (%R.S.D. < 10%) and sensitive over a range of 0.02–20, 0.01–10 and 0.05–50 ng/mg tissue for 2‐AG, 1‐AG and AA, respectively. The quantification method was validated with consideration of the matrix effects and the mass spectrometry (MS) responses of the analytes and the deuterium labeled internal standard (IS). The developed methods were applied to study the hydrolysis of 2‐AG from mouse brain extracts containing membrane bound monoacylglycerol lipase (MAGL), and to measure the basal levels of 2‐AG, 1‐AG and AA in mouse brain and adipose tissues. Copyright © 2009 John Wiley & Sons, Ltd.