Simultaneous approximation for the Bézier variant of Baskakov-Beta operators

In the present paper, we study the rate of convergence in simultaneous approximation for the Bézier variant of the Baskakov-Beta operators by using the decomposition technique of functions of bounded variation.     

Study of geometrical parameters in N-H...N type of hydrogen bonds

Geometrical parameters associated with N-H ... N types of hydrogen bonds have been analysed using crystal structure data on nucleic acids, amino acids and related compounds. Histograms depicting the frequency distribution of N-H ... N length (l) and H-N ... N angle (θ) have been drawn and conclusions on the favoured geometry of such bonds have been arrived at. The distribution ofl shows a pronounced maximum in the range between 2.9? and 3.0? with an overall average of 2.98 ?. The θ distribution shows a pronounced maximum for the hydrogen bond angle in the range 0°-10°, with a rapid fall-off in frequency for nonlinear hydrogen bonds. The frequency shows a cos⁶θ dependence as compared to cos²θ dependence term used earlier to predict the angular dependence of hydrogen bond potential energy in proteins and polypeptides.     

Nuclear Magnetic Resonance Studies in Gases

There are several reasons why nuclear magnetic resonance (NMR) studies in gases are important. At low pressures the interactions in the gas phase are essentially governed by two body collisions. It is therefore possible to study the intermolecular forces between two molecules approaching one another during collision from their influence on the chemical shifts of the nuclei of the molecules under considerations. The experimental measurements allow one to learn how the chemical shift is perturbed because of the presence of other molecules. This knowledge can then be transferred to interpret solvent effects in condensed phases and for detection of any solvent-solute interactions in such systems.     

Studies on drug–DNA complexes,adriamycin–d‐(TGATCA)2 and 4′‐epiadriamycin–d‐(CGATCG)2, by phosphorus‐31 nuclear magnetic resonance spectroscopy

The complexes of adriamycin–d‐(TGATCA)₂ and 4′‐epiadriamycin–d‐(CGATCG)₂ are studied by one‐ and two‐dimensional ³¹P nuclear magnetic resonance spectroscopy (NMR) at 500 MHz in the temperature range 275–328 K and as a function of drug to DNA ratio (0.0–2.0). The binding of drug to DNA is clearly evident in ³¹P? ³¹P exchange NOESY spectra that shows two sets of resonances in slow chemical exchange. The phosphate resonances at the intercalating steps, T1pG2/C1pG2 and C5pA6/C5pG6, shift downfield up to 1.7 ppm and that at the adjacent step shift downfield up to 0.7 ppm, whereas the central phosphate A3pT4 is relatively unaffected. The variations of chemical shift with drug to DNA ratio and temperature as well as linewidths are different in each of the two complexes. These observations reflect change in population of B_I/B_II conformation, stretching of backbone torsional angle ζ, and distortions in O? P? O bond angles that occur on binding of drug to DNA. To the best of our knowledge, there are no solution studies on 4′‐epiadriamycin, a better tolerated drug, and binding of daunomycin or its analogue to d‐(TGATCA)₂ hexamer sequence. The studies report the use of ³¹P NMR as a tool to differentiate various complexes. The specific differences may well be the reasons that are responsible for different antitumor action of these drugs due to different binding ability and distortions in DNA. Copyright © 2009 John Wiley & Sons, Ltd.     

Proton magnetic resonance studies of the association of amino methyl pyridines

Proton magnetic resonance studies of the solutions of (a) 2-amino, 3-methyl pyridine and (b) 2-amino, 6-methyl pyridine in carbontetrachloride show that in these molecules there is an equilibrium between monomers and hydrogen-bonded dimers. The equilibrium constants for the two cases have been obtained. Evidence has also been obtained to show that chloroform forms hydrogen bond with the ring nitrogen of these compounds. These NMR results have been compared with those obtained earlier from infra-red studies.     

Proton magnetic resonance in coumarins

The high resolution proton magnetic resonance spectra of AB, ABC and ABCD systems in fourteen coumarins have been studied. Chemical shifts and spin coupling constants for the protons in various positions in the benzo-α-pyrone ring have been obtained. The spectrum of coumarin confirms the ethylenic nature of double bond between carbon atoms in positions 3 and 4. The chemical shifts for the phenyl protons are in conformity with the reactivities of the coumarins at various positions in the ring. A linear relation has been observed between the chemical shift for proton in 8 position in various 6 substituted coumarins and the Hammett’s constants (σ) for substituents in themeta position. The NMR spectra offer a very convenient method for distinguishing between 3 and 4 substituted coumarins on account of the large chemical shift for the protons in positions 3 and 4. The results do not substantiate resonance of the naphthalene type in coumarin as suggested to explain its dipole moment.     

Proton spin-spin interactions inm-disubstituted benzenes

The NMR spectra ofm-disubstituted benzenes, in which one of the substituents is kept constant and the other varied have been analysed. It has been shown that the proton-proton interactions in these molecules are not influenced by the inductive and resonance effects of the substituent but depend on its steric effect. A measure of the relative steric effects of different substituents is thus suggested. The results have been compared with other methods of measuring steric effects.     

Loss of collectivity in 79Rb

High-spin states in ⁷⁹Rb were populated in the reaction at E(beam) = 60 MeV. The lifetimes of the excited states of the positive-parity yrast band and of the negative-parity band in ⁷⁹Rb were measured by the Doppler Shift Attenuation Method. The deduced transition quadrupole moments Q_t are found to have a decreasing trend with rotational frequency for both the bands, consistent with those found experimentally in neighbouring nuclei. An erratum to this article is available at .