On the summation of the Brillouin-Wigner type perturbation series

It is shown that if the ‘mean excitation energy’ assumption is introduced in the Brillouin-Wigner perturbation series, then the resulting series can be exactly summed. The implications of the result for calculating energy shift and for constructing trial functions are examined with special reference to the ground state of the helium atom.     

Auxiliary sets of matrices with new step parameter sequences

Constructions are given for auxiliary sets of matrices which have the previously unknown step parameter sequences (3,11,3), (2,2,8,11), (2,2,8,13), (2,2,9,11). As a consequence one obtains a projective Hjelmslev plane for each of the preceding four step parameter sequences.     

Desorption to delamination: dynamics of detachment in a colloidal thin film

Colloidal thin films of varying rigidity detaching from a substrate under an electric field induced stress are studied by video microscopy. For soft films, the process of detachment shows single-particle dynamics, analogous to desorption. For rigid films, a collective delamination spanning hundreds of particles occurs. A competition among the rigidity of the film, the interaction with the substrate, and the external stress leads to a correlation length over which the film delaminates at a critical stress. The phenomenon is described as a dynamical transition in a disordered elastic medium.     

Synthesis of optically active seven-membered 1,5-anhydrocarbasugars and 1,4,5-tribenzoyloxy-2-ethoxy cycloheptanes via [5+2] cycloaddition

[5+2] Cycloaddition followed by asymmetric dihydroxylation procedure have been utilized to prepare novel cyclitols. Accordingly, rac-2α-hydroxy-6α-ethoxy-1,5-anhydro cyclohept-3-ene, 10 derived from [5+2] cycloaddition of 3-oxidopyrylium ylide and vinyl ether has been recognized as a seven-membered carbasugar equivalent and elaborated to 1,4,5-tribenzoyloxy-2-ethoxy cycloheptanes through a flexible, regio- and stereoselective strategy involving Sharpless asymmetric dihydroxylation conditions to resolve the compounds obtained. The structures and relative configurations of newly synthesized (+)-2α-acetoxy-6α-ethoxy-3β,4β-dihydroxy-1,5-anhydro cycloheptane ((+)-12)); (−)-1β,4β,5β-tribenzoyloxy-6α-ethoxy cycloheptane ((−)-17) and (+)-1α,4α,5α-tribenzoyloxy-6β-ethoxy cycloheptane ((+)-17) are unambiguously established by single crystal X-ray analysis and duly supported by ¹H and ¹³C NMR spectroscopy data.     

Maximal arcs in designs

An (α,n)-arc in a 2-design is a set ofn points of the design such that any block intersects it in at most α points. For such an arc,n is bounded by 1+(r(α−1)/λ), with equality if and only if every block meets the arc in either 0 or α points. An (α,n) arc with equality in above is said to be maximal. A maximal block arc can be dually defined. This generalizes the notion of an oval (α=2) in a symmetric design due to Asmus and van Lint. The aim of this paper is to study the infinite family of possibly extendable symmetric designs other than the Hadamard design family and their related designs using maximal arcs. It is shown that the extendability corresponds to the existence of a proper family of maximal arcs. A natural duality between point and block arcs is established, which among other things implies a result of Cameron and van Lint that extendability of a given design in this family is equivalent to extendability of its dual. Similar results are proved for other related designs.     

TiCl4-promoted multicomponent reaction: a new entry to functionalized alpha-amino acids

TiCl(4)-promoted multicomponent reactions involving N-tosyl imino ester, cyclic enol ether, and silane reagents in a single one-pot operation provide functionalized alpha-amino acids with multiple stereogenic centers in good to excellent yields. Cis/trans selectivities with optically active substituted dihydrofurans have been investigated.     

Simultaneous Determination of Pioglitazone and Glimepiride by High-Performance Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC -     

New integer pairs for Hjelmslev planes

Associated with every finite projective Hjelmslev plane is an invariant pair(t, r); t is the order of the Hjelmslev plane andr is the order of the underlying projective plane. The aim of this paper is to give some new constructions of Hjelmslev planes with an invariant pair (t, 2). First we construct a PH-plane with the invariant pair (20, 2). Using this, 16 more invariant pairs (t, 2) witht 1000 are obtained. In all, we thus obtain 17 new PH-planes with invariant pairs (t, 2),t 1000.     

Quantitation of Oleanolic Acid in Oldenlandia corymbosa L. Whole-Plant Powder by High-Performance Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC - A sensitive, simple, and accurate high-performance thin-layer chro-matographic method has been established for determination of...