Counterexamples to Mercat’s conjecture

In this paper, we provide counterexamples to Mercat’s conjecture on vector bundles on algebraic curves. For any \({n \geq 4}\), we provide examples of curves lying on K3 surfaces and vector bundles on those curves which invalidate Mercat’s conjecture in rank n.     

Microwave assisted synthesis,spectroscopic and antibacterial studies of bis(cyclopentadienyl)hafnium(IV) derivatives with benzil bis(aroyl hydrazones)

The reactions of (η⁵-C₅H₅)₂HfCl₂ with benzil bis(hydrazones) (LH₂), derived from benzil and aromatic acid hydrazides (benzoic, 2-chlorobenzoic, 4-chlorobenzoic, 2-methylbenzoic or 4-methoxybenzoic) have been studied in anhydrous tetrahydrofuran in the presence of n-butylamine by both conventional methods and by microwave heating. Binuclear complexes of type [{(η⁵-C₅H₅)₂HfCl}₂(L)] were obtained in both cases. Tentative structural conclusions are drawn for the reaction products based upon analyses, electrical conductance, magnetic moment and spectral (UV–vis, IR, ¹H NMR and ¹³C NMR) data. A FAB-mass spectrum of one compound was also recorded to confirm the binuclear structures. Studies were conducted to assess the growth inhibiting potential of the complexes and free ligands against various bacterial strains.     

The RNA2-PNA2 hybrid i-motif-a novel RNA-based building block

We report the formation of a hybrid RNA2-PNA2 i-motif comprised of two RNA and two PNA strands based on the sequence specific self assembly of RNA, with potential as a building block for structural RNA nanotechnology.     

Concentration control for protein crystallization via a continuously-fed crystallization chamber

A continuously-fed crystallization chamber that allows for kinetic path control through the crystallization phase diagram (from labile/nucleation to metastable/growth) was fabricated and used to crystallize lysozyme. A lumped kinetic model was developed, and parameters for heterogeneous nucleation kinetics were determined. Heterogeneous nucleation was found to have faster nucleation kinetics and slower growth kinetics than homogeneous nucleation, as expected. The major contributions of the new device are (1) to allow better control of the chemical environment for studies of crystal nucleation and growth, and (2) to allow lumped-model analysis of those studies to extract kinetic parameters.     

Nonvanishing of Siegel Poincaré series

We prove that, under suitable conditions, certain Siegel Poincaré series of exponential type of even integer weight and degree 2 do not vanish identically. We also find estimates for twisted Kloosterman sums and Salié sums in all generality.     

Nonlinear dynamic range compression deconvolution

We introduce a dynamic range image compression technique for nonlinear deconvolution; the impulse response of the distortion function and the noisy distorted image are jointly transformed to pump a clean reference beam in a two-beam coupling arrangement. The Fourier transform of the pumped reference beam contains the deconvolved image and its conjugate. In contrast to standard deconvolution approaches, for which noise can be a limiting factor in the performance, this approach allows the retrieval of distorted signals embedded in a very high-noise environment.     

A micro-scale multi-frequency reactance measurement technique to detect bacterial growth at low bio-particle concentrations

The technique described enables the user to detect the presence and proliferation of bacteria through an increase in the bulk capacitance (C) of the suspension, which is proportional to the bacteria count, at practical frequencies less than 1 MHz. The geometry of the micro-capillary design employed increases the bulk resistance (R) of the medium, thus increasing its RC time. This makes the measured reactance sensitive to changes in the bulk capacitance, which is usually masked by the much larger surface capacitance. The sensitivity is further enhanced by the existence of a minimum in the value of the reactance at a frequency proportional to the inverse medium RC time. The value of this reactance minimum and the frequency at which the minimum is recorded are dependent on the bacteria count and permit the detection of an initial concentration of approximately 100 CFU ml(-1) of E. coli within 3 hours of incubation, in comparison with the previous reported values of about 8 hours, with an initial load of 1000 CFU ml(-1).     

Synthesis, spectroscopic, thermal and antifungal studies on lanthanum(III) and praseodymium(III) derivatives of 1,1-diacetylferrocenyl hydrazones

A series of new coordination complexes of La(III) and Pr(III) with hydrazones, derived from 1,1-diacetylferrocene and different aromatic acid hydrazides have been synthesized and characterized by elemental analyses, electrical conductance, magnetic moment, IR, (1)H NMR, UV-vis spectra and molar conductance. The thermal behaviour of the complexes under non-isothermal condition was investigated by TG and DTG techniques. The antifungal activity of hydrazones and their corresponding complexes were also investigated.     

Triplex formation with alpha-L-LNA (alpha-L-ribo-configured locked nucleic acid)

Using UV melting and CD spectroscopy, we show that alpha-l-LNA-modified oligonucleotides possess the ability to form triplexes at pH 6.8 with significantly increased thermostability relative to DNA triplexes.