On linear and nonlinear Rossby waves in an ocean

This paper deals with recent developments of linear and nonlinear Rossby waves in an ocean. Included are also linear Poincaré, Rossby, and Kelvin waves in an ocean. The dispersion diagrams for Poincaré, Kelvin and Rossby waves are presented. Special attention is given to the nonlinear Rossby waves on a β-plane ocean. Based on the perturbation analysis, it is shown that the nonlinear evolution equation for the wave amplitude satisfies a modified nonlinear Schrödinger equation. The solution of this equation represents solitary waves in a dispersive medium. In other words, the envelope of the amplitude of the waves has a soliton structure and these envelope solitons propagate with the group velocity of the Rossby waves. Finally, a nonlinear analytical model is presented for long Rossby waves in a meridional channel with weak shear. A new nonlinear wave equation for the amplitude of large Rossby waves is derived in a region where fluid flows over the recirculation core. It is shown that the governing amplitude equations for the inner and outer zones are both KdV type, where weak nonlinearity is balanced by weak dispersion. In the inner zone, the nonlinear amplitude equation has a new term proportional to the 3/2 power of the difference between the wave amplitude and the critical amplitude, and this term occurs to account for a nonlinearity due to the flow over the vortex core. The solution of the amplitude equations with the linear shear flow represents the solitary waves. The present study deals with the lowest mode (n=1) analysis. An extension of the higher modes (n?2) of this work will be made in a subsequent paper.     

Asymptotic behavior of solutions of forced nonlinear neutral delay differential equations with impulses

Sufficient conditions for asymptotic behavior of the solutions of nonlinear forced neutral delay differential equations with impulses are found. The results given in [2,4,6,7] are generalized and improved.     

Flow injection analysis for calcium in serum,water and waste waters by spectrophotometry and by ion-selective electrode

The Flow Injection technique is shown to provide fast, reliable and sensitive methods for the determination of calcium in various aqueous as well as serum samples; spectrophotometric or potentiometric detection can be used. At sampling rates of 100–110 samples per hour, with 30-μl sample injections, high reproducibility of measurement and low reagent consumption are achieved in both methods. In the spectrophotometric method, the analytical readout is available within 12 s after sample injection at a total reagent consumption of 0.75 ml per analysis. The potentiometric measurement of the calcium activity in serum is placed on a reliable basis by alternating measurements of serum samples and aqueous standards without incurring any non-reproducible changes in potential between aqueous and serum solutions. This permits the simultaneous determination of pH and pCa, the analytical readout being available within XXX s of sample injection. The good agreement between the results obtained with the Flow Injection method and those attained by atomic absorption and EDTA titrations as well as pCa stat-measurements show that the new methods are potentially suitable for routine analysis.     

A family of vanadate esters of monoionized and diionized aromatic 1,2-diols: synthesis,structure, and redox activity

The concerned diols (general abbreviation, H(2)L) are catechol (H(2)L(1)) and its 3,5-Bu(t)(2) derivative (H(2)L(2)). Esters of the type VO(xsal)(HL), 2, are obtained by reacting H(2)L with VO(xsal)(H(2)O) or VO(xsal)(OMe)(HOMe), where xsal(2-) is the diionized salicylaldimine of glycine (x = g), L-alanine (x = a), or L-valine (x = v). The reaction of VO(acac)(2) with H(2)L and the salicylaldimine (Hpsal) of 2-picolylamine has furnished VO(psal)(L), 3. In the structures of VO(gsal)(HL(1)), 2a, and VO(vsal)(HL(2)), 2f, the HL(-) ligand is O,O-chelated, the phenolic oxygen lying trans to the oxo oxygen atom. The xsal(2-) coligand has a folded structure and the conformation of 2f is exclusively endo. In both 2a and 2f the phenolic oxygen atom is strongly hydrogen bonded (O...O, 2.60 A) to a carboxylic oxygen atom of a neighboring molecule. In VO(psal)(L(2)).H(2)O, 3b, the diionized diol is O,O-chelated to the metal and the water molecule is hydrogen bonded to a phenoxidic oxygen atom (O.O, 2.84 A). The C-O and C-C distances in the V(diol) fragment reveal that 2 is a pure catecholate and 3 is a catecholate-semiquinonate hybrid. In solution each ester gives rise to a single (51)V NMR signal (no diastereoisomers), which generally shifts downfield with a decrease in the ester LMCT band energy. The V(V)/V(IV) and catecholate-semiquinonate reduction potentials lie near -0.75 and 0.35, and 1.10 and 0.70 V vs SCE for 2 and 3, respectively. Molecular oxygen reacts smoothly with 2 quantitatively furnishing the corresponding o-quinone, and in the presence of H(2)L the reaction becomes catalytic. In contrast, type 3 esters are inert to oxygen. The initial binding of O(2) to 2 is proposed to occur via hydrogen bonding with chelated HL(-).     

Synthesis of azahelicenes through Mallory reaction of imine precursors: corannulene substrates provide an exception to the rule in oxidative photocyclizations of diarylethenes

Typically, the synthesis of phenanthrene-based polycyclic aromatic hydrocarbons relies on the Mallory reaction. In this approach, stilbene (PhCH CHPh)-based precursors undergo an oxidative photocyclization reaction to join the two adjacent aromatic rings into an extended aromatic structure. However, if one C C carbon atom is replaced by a nitrogen atom (C N), the synthesis becomes practically infeasible. Here, we show the very first examples of a successful Mallory reaction on stilbene-like imine precursors involving the molecularly curved corannulene nucleus. The isolated yields exceed 90% and the resulting single and double aza[4]helicenes exhibit adjustable high affinity for electrons.

First azahelicene synthesis from corannulene-based imine precursors is presented.     

Thiol-mediated radical cyclization: regioselective formation of indole-annulated sulfur heterocycles by tandem cyclization

Indole-2-yl-prop-2-ynyl sulfides, under thiophenol-mediated alkenyl radical cyclization conditions, afforded exclusively 4-thiophenyl-2,3,4,9-tetrahydrothiopyrano[2,3-b]indoles or 3-thiophenylmethyl-2,3,8-trihydrothieno[2,3-b]indoles depending on the substituent at the indole nitrogen.     

Cation exchange column chromatography in aqueous ammonium acetate: Separation of U(VI), Al(III), Sr(II), Ba(II) and Hg(II) from other metal ions

Summary A rigorous analysis of the effect of various concentrations (0.02–1.60M) of ammonium acetate on the distribution coefficients (K) of a number of metal ions using cation exchanger Dowex 50W-X8 (100–200 mesh NH₄ ⁺-form) has been made. On account of the low affinity of U(VI) for resin in 0.20M NH₄OAc it can be separated from all other metal ions. HighK values of Sr(II), Ba(II) and Hg(II) at higher 0.50M NH₄OAc are responsible for their separation from others. The abnormal column Chromatographic behaviour of Al(III) permits its separation from other metal ions including U(VI), Sr(II), Ba(II), Hg(II). A number of binary and ternary separations have been achieved.     

Investigation of nu(N-H) and nu(C-N) stretching modes of propylamine (C3H7NH2) in a binary system C3H7NH2 + CH3OH via concentration dependent Raman study and ab initio calculations

Raman spectra of propylamine (C3H7NH2) and its binary mixtures, C3H7NH2 + CH3OH with varying mole fractions of the reference system, C3H7NH2, C were recorded in two widely apart wavenumber regions, 3100-3600 cm(-1) and 1225-1325 cm(-1). In the former region, the two Raman bands at approximately 3305 and approximately 3326 cm(-1), obtained after the line shape analysis, which were assigned to symmetric nu(N-H) and anti-symmetric nu(N-H) stretching modes, respectively, show a downshift upon dilution. However, whereas the nu(N-H) anti-symmetric mode shows a shift of 18.6 cm(-1), the nu(N-H) symmetric mode shows a much smaller shift (5.7 cm(-1)) between neat liquid and high dilution, C = 0.1. This aspect has been explained using the optimized geometries calculated employing ab initio theory (MP2 level) for the neat C3H7NH2 and its different hydrogen-bonded complexes. The linewidth versus concentration plot for the nu(N-H) anti-symmetric stretching mode, however exhibits a distinct maxima at C = 0.4, which has been explained as a slight departure from the concentration fluctuation model. In the latter region, a symmetric peak is observed, which corresponds to nu(C-N) stretching mode, which shows an upshift upon dilution and an almost linear concentration dependence. This has also been explained in terms of the parameters obtained from the optimized geometries of the different hydrogen-bonded complexes.     

Synthesis of chiral α-amino acids

A novel method for the synthesis of chiral α-amino acids has been developed where the acid functionality was constructed by oxidizing a hydroxymethyl group introduced by Evans’ method in the α-position of an appropriate acid substrate and the amino part came from the amide of the original carboxyl group following a modified Hofmann rearrangement reaction.