Compactness and Vitali’s compactness criterion in vector-valued F-seminormed function spaces

Results of compactness for vector-valued F-seminormed function spaces and a general Vitali’s compactness criterion under the W-property are exhibited.

     

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.     

Understanding the mechanism of direct visible-light-activated [2 + 2] cycloadditions mediated by Rh and Ir photocatalysts: combined computational and spectroscopic studies

The mechanism of [2 + 2] cycloadditions activated by visible light and catalyzed by bis-cyclometalated Rh(iii) and Ir(iii) photocatalysts was investigated, combining density functional theory calculations and spectroscopic techniques. Experimental observations show that the Rh-based photocatalyst produces excellent yield and enantioselectivity whereas the Ir-photocatalyst yields racemates. Two different mechanistic features were found to compete with each other, namely the direct photoactivation of the catalyst–substrate complex and outer-sphere triplet energy transfer. Our integrated analysis suggests that the direct photocatalysis is the inner working of the Rh-catalyzed reaction, whereas the Ir catalyst serves as a triplet sensitizer that activates cycloaddition via an outer-sphere triplet excited state energy transfer mechanism.

The mechanism of [2 + 2] cycloadditions activated by visible light and catalyzed by bis-cyclometalated Rh(iii) and Ir(iii) photocatalysts was investigated, combining density functional theory calculations and spectroscopic techniques.     

Approaches to primary tert-alkyl amines as building blocks

Primary tert-alkyl amines include analogues of amantadine, a fragment commonly linked to pharmacophoric groups to enhance biological activity. The preparation of primary tert-alkyl amines is considered to be a difficult problem. Four synthetic procedures, some of which have been previously reported for the synthesis of amines with primary (RCH₂NH₂) or secondary (RR'CHNH₂) alkyl and/or aryl groups, were tested for the synthesis of primary tert-alkyl amines (RR′R″CNH₂) in aliphatic series including adamantane adducts. These procedures included the formation and reduction of tert-alkyl azides, the Ritter reaction in standard and modified conditions, the addition of organometallic reagents to N-tert-butyl sulfinyl ketimines and one-pot reactions between nitriles and organometallic reagents in the presence of a Lewis acid, Τi(iPrO)₄ or CeCl_3. These synthetic routes are unexplored for primary tert-alkyl amines. Studies on the synthetic routes for primary tert-alkyl amines are currently lacking. The reaction conditions and substrate limitations were studied for each procedure, with the first procedure being the most general and applicable also for compounds bearing bulky adducts.     

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.     

Water droplets as template for next-generation self-assembled poly-(etheretherketone) with cardo membranes

Next generation PEEK-WC membranes have been fabricated by using an innovative self-assembly technique. Patterned architectures have been achieved via a solvent-reduced and water-assisted process, resulting in honeycomb packed geometry. The membranes exhibit monodisperse pores with size and shape comparable to those left by templating water droplets. Influencing factors for the formation of self-assembled poly-(etheretherketone) with Cardo [PEEK-WC] membranes have been evaluated, identifying the critical parameters for nucleation, growth, and propagation of the droplet-mobile arrays through the overall films. Structure-transport relationships have been discussed according to the results achieved from the implementation of membrane distillation processes, yielding indication about the suitability of self-assembled PEEK-WC films to work as interfaces in contactor operations.     

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...     

Correlating Structure and KA2 Catalytic Activity of ZnII Hydrazone Complexes

Two new Zn(II) complexes bearing tridentate hydrazone-based ligands with NNO or NNS donor atoms were synthesised and characterised by elemental analysis, infrared (IR) and nuclear magnetic resonance (NMR) spectroscopies, and single crystal X-ray diffraction methods. These complexes, together with four previously synthesised analogues, having hydrazone ligands with a NNO donor set of atoms, were successfully employed as catalysts in the ketone-amine-alkyne (KA²) coupling reaction, furnishing tetrasubstituted propargylamines, compounds with unique applications in organic chemistry. DFT calculations at the CAM-B3LYP/TZP level of theory were performed to elucidate the electronic structure of the investigated Zn(II) complexes, excellently correlating the structure of the complexes to their catalytic reactivity.     

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.