A reliable approach to the solution of Navier–Stokes equations

In this paper we will demonstrate an affective approach of solving Navier–Stokes equations by using a very reliable transformation method known as the Cole–Hopf transformation, which reduces the problem from nonlinear into a linear differential equation which, in turn, can be solved effectively.     

Weighted intriguing sets of finite generalised quadrangles

We construct and analyse interesting integer valued functions on the points of a generalised quadrangle which lie in the orthogonal complement of a principal eigenspace of the collinearity relation. These functions generalise the intriguing sets introduced by Bamberg et al. (Combinatorica 29(1):1?C17, 2009), and they provide the extra machinery to give new proofs of old results and to establish new insight into the existence of certain configurations of generalised quadrangles. In particular, we give a geometric characterisation of Payne??s tight sets, we give a new proof of Thas?? result that an m-ovoid of a generalised quadrangle of order (s,s ²) is a hemisystem, and we give a bound on the values of m for which it is possible for an m-ovoid of the four dimensional Hermitian variety to exist.     

Development and Validation of HPTLC Method for Simultaneous Determination of Quercetin and Kaempferol in Leaves of Two Chemotypes of Centella asiatica

JPC – Journal of Planar Chromatography – Modern TLC - A simple, accurate and precise high-performance thin-layer chromatography (HPTLC) method was developed and validated for the...     

On the mechanism of the palladium-catalyzed β-arylation of ester enolates

The palladium‐catalyzed β‐arylation of ester enolates with aryl bromides was studied both experimentally and computationally. First, the effect of the ligand on the selectivity of the α/β‐arylation reactions of ortho‐ and meta‐fluorobromobenzene was described. Selective β‐arylation was observed for the reaction of o‐fluorobromobenzene with a range of biarylphosphine ligands, whereas α‐arylation was predominantly observed with m‐fluorobromobenzene for all ligands except DavePhos, which gave an approximate 1:1 mixture of α‐/β‐arylated products. Next, the effect of the substitution pattern of the aryl bromide reactant was studied with DavePhos as the ligand. We showed that electronic factors played a major role in the α/β‐arylation selectivity, with electron‐withdrawing substituents favoring β‐arylation. Kinetic and deuterium‐labeling experiments suggested that the rate‐limiting step of β‐arylation with DavePhos as the ligand was the palladium–enolate‐to‐homoenolate isomerization, which occurs by a β? H‐elimination, olefin‐rotation, and olefin‐insertion sequence. A dimeric oxidative‐addition complex, which was shown to be catalytically competent, was isolated and structurally characterized. A common mechanism for α‐ and β‐arylation was described by DFT calculations. With DavePhos as the ligand, the pathway leading to β‐arylation was kinetically favored over the pathway leading to α‐arylation, with the palladium–enolate‐to‐homoenolate isomerization being the rate‐limiting step of the β‐arylation pathway and the transition state for olefin insertion its highest point. The nature of the rate‐limiting step changed with PCy₃ and PtBu₃ ligands, and with the latter, α‐arylation became kinetically favored. The trend in selectivity observed experimentally with differently substituted aryl bromides agreed well with that observed from the calculations. The presence of electron‐withdrawing groups on these bromides mainly affected the α‐arylation pathway by disfavoring C? C reductive elimination. The higher activity of the ligands of the biaryldialkylphosphine ligands compared to their corresponding trialkylphosphines could be attributed to stabilizing interactions between the biaryl backbone of the ligands and the metal center, thereby preventing deactivation of the β‐arylation pathway.     

Quantitative selenium speciation in human urine by using liquid chromatography–electrospray tandem mass spectrometry

A liquid chromatography–electrospray-tandem mass spectrometry (ES-MS/MS) method was developed for the speciation analysis of four organic selenium species of relevance to human urinary metabolism, namely trimethylselenomium ion (TMSe⁺), selenomethionine (SeMet) and the two selenosugars, methyl 2-acetamido-2-deoxy-1-seleno-β-d-galactos/-glucos-amine (SeGalNAc and SeGluNAc, respectively). Their chromatographic separation was achieved by using a cation exchange pre-column coupled in-series with a reversed-phase high-performance liquid chromatography column, along with an isocratic mobile phase. Online detection was performed using ES-MS/MS in selective reaction monitoring mode. SeGalNAc was detected as the major human urinary metabolite of selenium in the samples analysed, whereas TMSe⁺ was detected in the urine of one volunteer before and after receiving a selenium supplement. SeMet was not detected as a urine excretory metabolite in this study. Spiking experiments performed with the urine samples revealed significant signal suppression caused by coeluting matrix constituents. To overcome such interferences, isotopically labelled ¹³CD₃⁸²SeGalNAc was used as an internal standard, whereas in the absence of an isotopically labelled internal standard for TMSe⁺, the standard addition method was applied. Quality control for the accurate quantitation of TMSe⁺ and SeGalNAc was carried out by analysing spiked human urine samples with appropriate selenium standards over a concentration range of 10–50 μg Se L⁻¹. The method has achieved a limit of detection in the presence of urine matrix comparable to that of HPLC-inductively coupled plasma-mass spectrometry for the four selenium species: 1.0 μg Se L⁻¹ for TMSe⁺, 5.6 μg Se L⁻¹ for SeMet, and 0.1 μg Se L⁻¹ for both SeGalNAc and SeGluNAc.     

2-O-alkylated para-benzamide α-helix mimetics: the role of scaffold curvature

The design and synthesis of a new 2-O-alklyated benzamide α-helix mimetic is described. Comparison with regioisomeric 3-O-alkylated benzamides permits a preliminary evaluation of the role that mimetic curvature has in determining molecular recognition properties.     

Synthesis of benzyl substituted naphthalenes from benzylidene tetralones

A convenient and efficient synthesis of novel highly substituted dimethoxybenzylnaphthalenes, which are precursors to several dihydroxynaphthoic acids, is described. The approach involves the use of aldol chemistry to provide a number of benzylidene tetralones, which are converted to the target naphthalenes in three steps, with good to excellent yields. Grignard reaction of intermediate benzyl tetralones provided 1-substituted benzyl naphthalenes. The reported synthesis is flexible and scalable and provides access to naphthalenes having a variety of substitution patterns. These benzyl substituted naphthalenes are being converted to naphthoic acids and the bioactivities of these compounds are currently being investigated.