Solvent extraction studies of indium-mixed chelates withβ-diketones in benzene media

Mixed chelate formation of indium with severalβ-diketones has been studied from benzene media. The extraction of indium by BFA and FFA has been carried out as a function of pH and concentration of the ligand to ascertain the nature of the complexes. The extraction of indium by a mixture ofβ-diketones,viz., BFA-BA, BFA-DBM, FFA-BA, FFA-DBM, FFA-BFA and DBM-BA has also been studied as a function of the solution parameters. The nature of the mixed complexes formed as well as their equilibrium constants, statistical and stabilisation constants have been evaluated.     

Study of indium complexes by solvent extraction and ion exchange

Complexes of indium with hydroxy carboxylic acids like glycollic, mandelic and thioglycollic acids have been investigated by the method of competitive reactions using HTTA as the auxiliary ligand. An ion exchange study has been made in some cases to confirm the results. An ion exchange study of indium fluoride complexes has also been made. The data have been analysed for the stability constants of the indium complexes.     

Polarography of indium in glycollate medium

Reversible reduction of indium in glycollic acid has been followed by de polarography and the stability constants of the indium glycollate complexes calculated by the method of DeFord and Hume.     

Carrier-free separation of Sn113 from indium

A procedure for the separation of carrier-free Sn¹¹³ from deuteron bombarded indium is described. The method employed depends on the extraction of stannic cupferrate from mineral acid solution using carbon tetrachloride, followed by ignition of the complex.     

Polarography of indium in thioglycollic and ascorbic acid media

The polarographic reduction of indium in thioglycollic acid is reversible whereas in ascorbic acid it is quasireversible. The formal potentials have been determined by amalgam polarography and the stability constants calculated.     

A polarographic study of methionine complexes of cadmium and indium

The stability constants of methionine complexes of cadmium were determined polarographically by ths method of DeFord and Hume as β₁ =6·5 × 10³, β₂ = 1·7 × 10⁶ and β₃ = 2·1 · 10⁸. The indium complexes were studied by the modified method of Momoki and Ogawa and two complexes, with β₁ = 1·7 × 10⁸ and β₂ = 8·4 × 10¹³, were identified in the concentration range studied. The haf-wave potential of uncomplexed indium ion which cannot be measured directly owing to the irreversible nature of the reduction was calculated as — 0·503 Vvs. SCE.     

Extraction of indium,cadmium and thallium by dinonylnaphthalene sulfonic acid

The extraction of indium, cadmium and thallium by dinonylnaphthalene sulfonic acid (HD) from acid media has been studied. HD extracts the metal ion by an ion exchange mechanism. The nature of the species and the extent of aggregation has been evaluated. The effect of diluents on the extraction has also been studied and the results interpreted on the basis of aggregation of HD. A comparative study with solid ion exchangers has also been made.     

Solvent effects on proton chemical shifts in thiophenes

The effects of various polar and non-polar solvents on the proton chemical shifts in thiophene and its derivatives have been investigated. Results have been interpreted in terms of possible solute-solute, solute-solvent and solvent-solvent interactions in these systems.     

Solvent influences in the alkaline hydrolysis of esters in aqueous ethanol

The rate data for the alkaline hydrolysis of a number of monoesters, diesters and lactones have been obtained in varying compositions of aqueous ethanol. The application of the Amis and Laidler-Landskroener equations to the data yields reasonable values for the parameters representing the radius of the transition state for the hydrolysis confirming the ion-dipole nature of the reaction. An attempt to explain the rate data on the basis of the solvation requirements of the transition state has been made.     

Diffusion in Glassy Polymers: Sorption of a Finite Amount of Solvent

A family of 1-D moving boundary models describing the diffusion of a finite amount of a penetrant in a glassy polymer is studied. Local existence of a unique classical solution is obtained for a generic quasilinear model. Specific data are then chosen which can be found in the literature (cf. [6]) and global existence of the classical solution and its convergence to an equilibrium solution are proven. Finally a rigorous proof is provided for a formal perturbation argument proposed in [6] and used therein to estimate the rate of convergence of the solution towards the equilibrium.     

The root extraction problem

The Nth root extraction problem for germs of diffeomorphisms is the problem of finding a germ of diffeomorphism such that gN=f, where gN is the Nth iterate of g under composition. Depending on f and on the multiplier of g at the origin there can be formal and analytic obstructions to a solution of the problem. By considering an unfolding of f we explain these obstructions. Indeed each analytic obstruction corresponds to an accumulation of periodic points which, in turn, are an obstruction to taking an Nth root of the unfolding. We apply this to the problem of the section of a curvilinear angle in N equal parts in conformal geometry.     

Synergism in the extraction of cadmium

Synergism in the extraction of cadmium by mixtures of BFA and TOPO or TBP has been investigated. Extraction of cadmium was found negligible in the presence of BFA, TOPO or TBP alone while the addition of alkylphosphorus ester to the β-diketone resulted in considerable enhancement of the extraction. The nature of the adduct was found to be of the type [Gd (BFA)₂ (TOPO)₂] and the equilibrium constant for the reaction was also evaluated. Similar results were observed in the case of TBP, while DPSO did not enhance the extraction, indicating the donor strengths of the synergists to be in the order TOPO >TBP >DPSO. The coordination of alkylphosphate to the metal ion was confirmed by infrared spectra of the complexes in benzene.     

Polluting resource extraction and climate risk

Using a fossil fuel extraction model that treats the atmosphere as a depletable resource, we study the optimal price of carbon in the presence of endogenous uncertainty around a climatic regime shift. We find that the optimal carbon tax should account an uncertainty-adjusted cost term associated with the environment's scarcity. This term is shown to be sensitive to the natural sequestration rate of the atmosphere and to the probability surrounding a climate tail event. Our analysis also shows that in the presence of uncertainty, the shadow price of the environment should grow at a faster rate. Lastly, compared to the endogenous uncertainty case, we find that if the probability surrounding a regime shift is exogenously given, this shadow price should even grow at a higher rate.     

Cube root extraction in medieval mathematics

The algorithms used in Arabic and medieval European mathematics for extracting cube roots are studied with respect to algebraic structure and use of external memory (dust board, table, paper). They can be separated into two distinct groups. One contains methods used in the eastern regions from the 11th century, closely connected to Chinese techniques, and very uniform in structure. The other group, showing much wider variation, contains early Indian methods and techniques developed in central and western parts of the Arabic areas and in Europe. This study supports hypotheses previously formulated by Luckey and Chemla on an early scientific connection between China and Persia.     

Program extraction for 2-random reals

Let ${2-\textsf{RAN}}$ be the statement that for each real X a real 2-random relative to X exists. We apply program extraction techniques we developed in Kreuzer and Kohlenbach (J. Symb. Log. 77(3):853–895, 2012. doi:10.2178/jsl/1344862165), Kreuzer (Notre Dame J. Formal Log. 53(2):245–265, 2012. doi:10.1215/00294527-1715716) to this principle. Let ${{\textsf{WKL}_0^\omega}}$ be the finite type extension of ${\textsf{WKL}_0}$ . We obtain that one can extract primitive recursive realizers from proofs in ${{\textsf{WKL}_0^\omega} + \Pi^0_1-{\textsf{CP}} + 2-\textsf{RAN}}$ , i.e., if ${{\textsf{WKL}_0^\omega} + \Pi^0_1-{\textsf{CP}} + 2-\textsf{RAN} \, {\vdash} \, \forall{f}\, {\exists}{x} A_{qf}(f,x)}$ then one can extract from the proof a primitive recursive term t(f) such that ${A_{qf}(f,t(f))}$ . As a consequence, we obtain that ${{\textsf{WKL}_0}+ \Pi^0_1 - {\textsf{CP}} + 2-\textsf{RAN}}$ is ${\Pi^0_3}$ -conservative over ${\textsf{RCA}_0}$ .     

Algorithms for fast multidimensional signal extraction

In recent studies operator factorization techniques have been developed for problems associated with multidimensional control and image processing. In particular the “special factorization” of Gohberg and Krein and the Schur-Coleski factorization have both been extended to the multivariate setting. The present study focuses on computational aspects of the earlier results. Also of interest are implications for designing computer architectures which facilitate high-speed, online computation of the operator factors.     

Oxidation studies

Results on the oxidation of primary alcohols (methanol, ethanol,n-propanol,n-butanol and isobutanol) by peroxydisulfate in aqueous solution in the temperature range 50°–80°, under uncatalysed, Ag⁺ catalysed and deaerated conditions are presented. Oxygen was found to have a retarding effect on the rate of peroxydisulfate disappearance,\( - R_{S_2 O_3 ^ - } \), and the inhibition period was a maximum in the case of ethanol and isobutanol. Both under uncatalysed and Ag⁺ catalysed conditions\( - R_{S_2 O_3 ^ - } \) varied with [S₂O_8/=]^3/2 for all the alcohols;\( - R_{S_2 O_3 ^ - } \) was independent of alcohol concentration for all the alcohols except for methanol and ethanol where a one-half order with respect to [alcohol] was observed. In the Ag⁺ catalysed oxidation\( - R_{S_2 O_3 ^ - } \) varied as [Ag⁺]^1/2 with all the alcohols. The effect of [H⁺], ionic strength, temperature, initially added product of the reaction on the rate are discussed and the stoichiometries of the reactions determined. In the light of the observed results, reaction mechanisms are postulated with SO ₄ ^·? as the reactive species formed by thermal decomposition of S₂O ₈ ⁼ under uncatalysed conditions and by the interaction of Ag⁺ and S₂O_8/? under Ag⁺ catalysed conditions. The existence of Ag⁺⁺ in catalysed reactions is postulated. The values of rate constants, frequency factors, energies of activation entropies of activation, etc., were evaluated.     

Oxidation studies

The results on the kinetics of oxidation of HCHO and some alcohols,viz.,n-propanol, allyl alcohol, cyclohexanol and benzyl alcohol by ceric nitrate in nitric acid medium in the temperature range of 10–35° C. are presented. The active form of Ce⁴⁺ during the oxidation of the above organic substrates was assumed to be the neutral Ce(NO₃)₄. The mechanism of oxidation and thermodynamic parameters for the above compounds are also given.