Some new invariant pairs (t,3) for projective hjelmslev planes

Associated with every finite projective Hjelmslev plane is an invariant pair (t,r): t is the number of neighbours of a given point on a given line passing through it and r is the order of the underlying projective plane. The Drake-Lenz method [2],[3] of using auxiliary matrices for the constructions of projective Hjelmslev planes has become standard by now. This paper is intended to give some new constructions of projective Hjelmslev planes with invariant pairs (t,3) by making use of the generalization and improvement of the Drake-Lenz theorem [3] obtained by the author in [6] and [7]. The results of this paper add 8 new values to the list ([5], example 3.7(ii)) of invariant pairs (t,3) with t 1,000 for projective Hjelmslev planes.     

A multicomponent reaction efficiently producing arylmethylene 2-thiohydantoins

We describe here a multicomponent reaction that converts aryl/heteroaryl aldehydes efficiently into arylmethylene 2-thiohydantoins. 3-Formylindole behaves exceptionally giving a gem-diacetylthio derivative. A mechanistic study of the behaviour of 3-formylindole, which provides a new class of indole derivative, is described.     

Surface chemical modification of TEOS based silica aerogels synthesized by two step (acid-base) sol-gel process

The present paper describes the comparative studies on the hydrophobic and physical properties of the tetraethoxysilane (TEOS) based silica aerogels prepared by two step sol-gel process followed by supercritical drying. Silica alcogels were prepared by keeping the molar ratio of TEOS:methanol (MeOH):H₂O (acidic):H₂O (basic) constant at 1:33:3.5:3.5 with oxalic acid and ammonium hydroxide concentrations fixed at 0.001 and 1 M, respectively. In all, nine different co-precursors (CP) of the type R_nSiX_4 − n, have been used. The aerogels have been characterized by density, porosity, percentage of volume shrinkage, optical transmission, contact angle and thermal conductivity measurements. The surface chemical modification of silica aerogels was confirmed by the presence of CH and SiC peaks at 2900, 1450 and 840 cm⁻¹, respectively, from the Fourier transform-infrared spectroscopy (FT-IR). The microstructure of the aerogels was studied using transmission electron microscopy (TEM) and scanning electron microscopy (SEM) techniques. In addition to these studies, the stability of the hydrophobic aerogels against an organic impurity (methanol, in the present studies) in water has also been studied.     

Ovalbumin at oil–water interfaces: Adsorption and emulsification

In this article, we study the adsorption of protein ovalbumin (OVA) at corn oil (CO), soybean oil (SBO), olive oil (OO), and water interfaces along with the emulsification of these oils in water. The dynamic interfacial tension (IFT) measurements show a reduction in IFT in the order SBO–water?～?CO–water?>?OO–water, with OVA adsorption being dominated by the free diffusion of OVA at the interfaces. CO–water, OO–water, and SBO–water emulsions cream with time. The cream phase consists of jammed closed-packed oil droplets due to depletion-induced inter-droplet attractions with higher G′ and G″ (～700?Pa) for emulsions with 1?wt% OVA.     

Transport of liquids using superhydrophobic aerogels

The experimental results of the studies on the transportation of water droplets on a superhydrophobic silica aerogel-powder-coated surface are reported. The superhydrophobic silica aerogels were prepared using sol-gel processing of methyltrimethoxysilane (MTMS) precursor, methanol (MeOH) solvent, and base (NH4OH)-catalyzed water followed by supercritical drying using methanol solvent. The molar ratio of NH4OH/MTMS, H2O/MTMS, and MeOH/MTMS were varied from 1.7x10(-1) to 3.5x10(-1), 2 to 8, and 1.7 to 14, respectively, to find out the best-quality aerogels in terms of higher hydrophobicity and high droplet velocity. A specially built device was used for the measurement of velocity of water droplet of size 2.8 mm (+/-0.2 mm) on an inclined surface coated with superhydrophobic aerogel powder. Liquid marbles were prepared by rolling water droplets on aerogel powder and the marble(s) velocities on a noncoated inclined surface were compared with that of the water droplets. It was observed that the microstructure of the aerogel affects the droplet as well as marble velocities considerably. For an aerogel with uniform and smaller particles, the water droplet and marble velocities were observed to be maximum, i.e., 144 and 123 cm/s, respectively, whereas for the aerogels with bigger and nonuniform particles, the water droplet and marble velocities were observed to be minimum, i.e., 92 and 82 cm/s, respectively. The results have been discussed by taking into account the contact angles and microstructural observations.     

Pulse shapes reconfigured on a pulse-to-pulse time scale by using an array of injection-locked VCSELs

We demonstrate line-by-line pulse shaping of optical comb lines separated by 6.25 GHz. An array of injection-locked VCSELs independently modulate four optical comb lines at frequencies up to 3.125 GHz, updating the pulse shape on the time scale of the pulse period.     

Self-Assembled Surfactant-Polyoxovanadate Soft Materials as Tuneable Vanadium Oxide Cathode Precursors for Lithium-Ion Batteries

The mixing of [V₁₀O₂₈]⁶⁻ decavanadate anions with a dicationic gemini surfactant ( gem ) leads to the spontaneous self-assembly of surfactant-templated nanostructured arrays of decavanadate clusters. Calcination of the material under air yields highly crystalline, sponge-like V₂O₅ ( gem -V₂O₅ ). In contrast, calcination of the amorphous tetrabutylammonium decavanadate allows isolation of a more agglomerated V₂O₅ consisting of very small crystallites ( TBA -V₂O₅ ). Electrochemical analysis of the materials’ performance as lithium-ion intercalation electrodes highlights the role of morphology in cathode performance. The large crystallites and long-range microstructure of the gem -V₂O₅ cathode deliver higher initial capacity and superior capacity retention than TBA -V₂O₅ . The smaller crystallite size and higher surface area of TBA -V₂O₅ allow faster lithium insertion and superior rate performance to gem -V₂O₅ .