On the validity of the Euler-Lagrange equation

The purpose of the present paper is to establish the validity of the Euler-Lagrange equation for the solution to the classical problem of the calculus of variations.     

Preparation and photoactivity of nanostructured anatase, rutile and brookite TiO2 thin films

Photoactive films consisting of pure anatase, brookite or rutile TiO2 were prepared by dip coating from water dispersions obtained by using TiCl4 as the precursor under similar mild experimental conditions.     

A polynomial path-following interior point algorithm for general linear complementarity problems

Linear Complementarity Problems (LCPs) belong to the class of \mathbbNP{\mathbb{NP}} -complete problems. Therefore we cannot expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Our aim is to construct interior point algorithms which, according to the duality theorem in EP (Existentially Polynomial-time) form, in polynomial time either give a solution of the original problem or detects the lack of property P_*([(k)\tilde]){\mathcal{P}_*(\tilde\kappa)} , with arbitrary large, but apriori fixed [(k)\tilde]{\tilde\kappa}). In the latter case, the algorithms give a polynomial size certificate depending on parameter [(k)\tilde]{\tilde{\kappa}} , the initial interior point and the input size of the LCP). We give the general idea of an EP-modification of interior point algorithms and adapt this modification to long-step path-following interior point algorithms.     

Adducts of 2-aminothiophenol with acetylenic nitriles or esters and their conversion into benzothiazoles and/or 1,4-benzothiazines

The reaction between 2-aminothiophenol 1 and acetylenic nitriles or esters 2a-d leads to the vinyl thio-ethers 3a-d. The conversion of 3 into benzothiazoles 8 and/or 1,4-benzothiazines 9 , in boiling dimethyl sulfoxide, has been achieved. A possible pathway involving benzothiazolines 5 as key intermediates is suggested.     

C–H⋅<Emphasis Type="Italic">s</Emphasis>O hydrogen bond networks in <Emphasis Type="Italic">E</Emphasis>- and Z-unsaturated esters of C-glycosides

Methyl E(Z)-4,7 anhydro-5-benzamido-6,8-di-O-benzoyl-2,3,5-trideoxy-d-allo-oct-2-enoate have been synthesized like intermediates and isolated as single crystals during the synthesis of pyrazole-related C nucleosides as synthetic product with cytotoxic activity.¹ Crystal structures of E(Z) isomers were determined by X-ray analysis. E isomer crystallizes in the triclinic crystal system, space group P1, a = 5.319(1) Å, b = 10.758(2) Å, c = 12.229(2) Å, α = 72.38(2)^∘, β = 89.97(2)^∘, γ = 87.07(2)^∘, D_x = 1.320 Mgm⁻³ and Z isomer in the orthorhombic crystal system, space group P2₁2₁2₁, a = 5.1297(13) Å, b = 19.667(5) Å, c = 25.871(6) Å, D_x = 1.348 Mgm⁻³. The molecular structure was solved by direct method on the basis of 2609 and 2727 unique reflections recorded at the temperature 293 K (E-isomer) and 173 K (Z-isomer) up to the final R-factor 0.0378 and 0.0435, respectively. C–H⋅sO contact networks were analyzed and the correlation established between the existence of the weak C–H⋅sO hydrogen bonds and the melting point of the single crystals.     

Fully On-Line Hyphenation of an Experimental OPLC Separation Unit with Diode-Array Detection and Mass-Spectrometry (OPLC-DAD-MS) for Analysis of Xanthine Compounds

JPC – Journal of Planar Chromatography – Modern TLC - The newly developed experimental OPLC separation unit 100 (OSU 100) has been used for fully on-line multiple hyphenation using the...     

Enantiomeric separation of new phytoalexin analogs with cyclofructan chiral stationary phases in normal‐phase mode

For the first time, three different derivatized cyclofructan chiral stationary phases were used for the direct high‐performance liquid chromatographic enantiomeric separation of 11 new racemic analogs of a natural indole phytoalexin. This class of compounds is known to have significant antiproliferative activity and other potentially useful pharmacological properties. The effect of various experimental factors was investigated to optimize the separations in the normal‐phase mode. It was found that the nature of polar modifier and additive in the mobile phase have significant impact on the enantioseparations. Better chiral recognition of analyzed compounds was achieved on (R)‐naphthylethyl carbamate cyclofructan 6 than on isopropyl carbamate cyclofructan 6 and dimethylphenyl carbamate cyclofructan 7. The thermodynamic parameters showed that the chiral separation was enthalpy controlled in all cases.     

Performance of idealized column structures under high pressure

We have examined the influence of the longitudinal temperature and pressure gradients in columns operated under very high pressures on the coefficients of the van Deemter equation under the idealized condition of complete radial uniformity. These gradients change the diffusion coefficients over the length of the column, and the equation takes a new form, where the classical linear C-term is replaced by more complex forms that capture the effects of these axial gradients. The details of the derivations are shown and the implications are discussed.