A generalization of Lomonosov's inequality and its applications to invariant subspaces

In this article we generalize Victor Lomonosov's famous inequality so as to be applicable to a wider class of functions. Then using it we prove that the adjoint of an algebra with a compactness property which is weaker than the PS property, employed by Victor Lomonosov, has nontrivial invariant subspaces.

     

Thermodynamic and lfer studies for the oxidation of anilines by the periodate ion

The various thermodynamic parameters for the periodate oxidation of six anilines, viz. aniline, p-chloroaniline, p-ethoxyaniline, o- and p-methoxyanilines and p-methylaniline have been reported and discussed. The validity of the isokinetic relationship and various linear free energy relationships (LFERs) have been tested and discussed. An attempt has been made to correlate these findings with the mechanism operative in these reactions.     

Toward artificial developmental regulators

A polyamide-peptide conjugate is designed which recruits sequence specifically the developmental regulator Exd to a cognate DNA site. In particular, an eight-ring hairpin polyamide (Im-Im-Py(C3H6NHR)-Py-gamma-Im-Py-Py-Py-beta-Dp) with a heptapeptide (R = Ac-Phe-Tyr-Pro-Trp-Met-Lys-Gly-) attached on a central ring was shown to induce cooperative binding of the Drosophila Hox protein cofactor Exd with a Kd of 4.4 nM in vitro, an order of magnitude more efficient than the natural Hox protein partner Ubx. The conjugate joins two sequence specific domains, one for DNA and one for the protein. This small molecule thus serves as a cooperative protein-DNA dimerizer, which mimics the natural Hox family of developmental regulators.     

Synthesis of N,N′-dimethyl-N,N′-dibutyl malonamide functionalized polymer and its sorption affinities towards U(VI) and Th(IV) ions

A novel chelating polymeric material was synthesized by chemical anchoring of N,N′-dimethyl-N,N′-dibutyl malonamide (DMDBMA) with chloromethylated polystyrene-divinyl benzene polymer. The polymeric material thus prepared was characterized by ¹³C NMR, FT-IR spectroscopy and CHN elemental analysis. The fabricated polymeric material exhibited superior binding for hexa-valent and tetra-valent metal ions such as U(VI) and Th(IV). Various physico-chemical properties of the functionalized polymer like phase adsorption kinetics, metal sorption mechanism and metal sorption capacity was studied in the static method. Adsorption kinetics studies show that <20 min was sufficient for >99.99% adsorption of Th(IV) and U(VI). The kinetics for adsorption of U(VI) and Th(IV) was found to follow the first order Lagergren rate kinetics. Adsorption of U(VI) on the malonamide functionalized polymer followed the Langmuir adsorption isotherm. The Langmuir monolayer adsorption phenomenon was also confirmed by the theoretical approach calculated based on the adsorption kinetics. The metal sorption capacities for uranium and thorium were found to be 18.78 ± 1.53 mg and 15.74 ± 1.59 mg/g of the chelating polymer at 3 M HNO₃, respectively.     

Diastereotopic effect in some N-substituted-3-methyl-4,1-benzoxazepine-2,5-diones

1H NMR assignment of seven differently N-substituted-3-methyl-4,1-benzoxazepine-2,5-diones (I) revealed that with the exception of allyl, N-methylene protons of the substituents exhibit diastereotopy due to presence of a chiral centre in the heterocyclic ring at C-3. The significant finding is that the methylenes at C-2' in the substituents n-propyl and n-butyl (Id, Ie) also show diastereotopy. However, the one closer to the chiral centre (at C-1') exhibits greater non-equivalence of its protons. The diastereotopic methylene groups reported in this study correspond to the simplest system AB on one hand and as complex as ABMM'X2 or ABMM'X3 on the other. Calculated spectra obtained from assigned set of data for most of the coupled protons were in good agreement with the observed ones.     

Kinetics and mechanism of reaction between mercuric bromide and silver iodide in solid state

Kinetics and mechanism of the reaction between mercuric bromide and silver iodide were studied in the solid state. It has been established that HgBr₂ reacts via the gaseous state and that the reaction proceeds through counter diffusion of Ag⁺ and Hg²⁺. Thermal and conductivity measurements indicate that the reaction is multistep. X-ray and chemical analyses show that HgBr₂ and AgI mixed in different molar ratios give rise to different products. The data for the lateral diffusion fitted the equation X_iⁿ = kt, where X_i is the thickness of the product layer at time t, and n and k are constants. Evidence for the formation of solid solutions between reactant and product phases is reported.