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.     

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.     

An Efficient Straightforward Synthesis of (-)-Bulgecinine

(-)-Bulgecinine 1, a component of the antibiotic bulgecins, was efficiently synthesized from (S)-pyroglutaminol2.     

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.     

On extendable planes of order ten

It is well known that the only way of extending a projective plane of order n (conceivable orders are 2, 4 and 10) is adjoining a set of hyperovals to the given projective plane. A converse is proved in this note. It is shown as a corollary that the existence of an extendable plane of order 10 is equivalent to the existence of a quasi-symmetric 2-(111, 12, 10)-design.