On a class of nonlinear integral equations of Urysohn's type

In this paper we study an interesting class of nonlinear integral equations of Urysohn's type, namely,

$\text{u(x) +}\text{∑}\text{j=l}\text{n}\text{∫}{}_{\mathrm{\Omega }}\text{k}{}_{\mathrm{j}}\text{(x,y)f}{}_{\mathrm{j}}\text{(y, u(y)) dy= v(x)}\text{(x ∈ Ω)}$

. It is shown that such an equation can be considered as a nonlinear operator equation of Hammerstein type in an appropriate Banach space. One can in this way extend the theory of nonlinear operator equations of Hammerstein type (except for the part which uses variational methods) to this class of equations.     

Generalized prolate spheroidal wave functions

The following equation $$(1 - x^2 )d^2 y/dx^2 + [(\beta - \alpha - (\alpha + \beta + 2)x]dy/dx + (\chi (c) - c^2 x^2 )y = 0$$ has been solved wherex(c) a separation constant is the characteristic value and is a function ofc. This solution is a generalization of spheroidal wave function into the series form ofP _n ^α;β (x),α andβ both separately are greater than ?1. The finite transform and its properties have been defined and a boundary value problem has been solved applying these tools.     

Electrophoresis simulations using Chebyshev pseudo-spectral method on a moving mesh

We present the implementation and demonstration of the Chebyshev pseudo-spectral method coupled with an adaptive mesh method for performing fast and highly accurate electrophoresis simulations. The Chebyshev pseudo-spectral method offers higher numerical accuracy than all other finite difference methods and is applicable for simulating all electrophoresis techniques in channels with open or closed boundaries. To improve the computational efficiency, we use a novel moving mesh scheme that clusters the grid points in the regions with poor numerical resolution. We demonstrate the application of the Chebyshev pseudo-spectral method on a moving mesh for simulating nonlinear electrophoretic processes through examples of isotachophoresis (ITP), isoelectric focusing (IEF), and electromigration-dispersion in capillary zone electrophoresis (CZE) at current densities as high as 1000 A/m. We also show the efficacy of our moving mesh method over existing methods that cluster the grid points in the regions with large concentration gradients. We have integrated the adaptive Chebyshev pseudo-spectral method in the open-source SPYCE simulator and verified its implementation with other electrophoresis simulators.     

Kinetik der Entladung von Zn2+ und Ni2+ an der Quecksilbertropfelektrode in einem Thiomalatmedium

Zusammenfassung Wir untersuchten auf polarographischem Wege die Kinetik der Entladung von Zn²⁺ und Ni²⁺ an der Quecksilbertropfelektrode in einem Thiomalatmedium konstanter Ionenstärke (=0,5). Wir stellten fest, daß die Reduktion von Zn²⁺ und Ni²⁺ irreversibel verläuft und berechneten daher die kinetischen Parameter (Übertragungskoeffizient , Geschwindigkeitskonstante der HinreaktionK _f,h ^o ) nach dem theoretischen Verfahren vonKoutecky in der vonMeites undIsrael erweiterten Form.

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Kinetics of discharge of Zn²⁺ and Ni²⁺ at the D.M.E. in thiomalate media

Kinetics of discharge of Zn²⁺ and Ni²⁺ have been studied polarographically in thiomalate media of constant ionic strength (=0.5) at the dropping mercury electrode. The reduction of both Zn²⁺ and Ni²⁺ was found to be irreversible. Hence, the kinetic parameters (transfer coefficient , and forward rate constantK _j,h ^o ) have been calculated byKoutecky's theoretical treatment as extended byMeites andIsrael.

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Mit 2 Abbildungen     

o-Iodosobenzoate as an oxidimetric titrant

o-Iodosobenzoate has been used as a titrant at pH 7 with potassium iodide and starch as indicator, under Andrews' titration conditions with iodine monochloride as preoxidant, and in acid medium with potassium bromide and Methyl Red as indicator. Methods are described for the determination of tetrathionate (through disulphide cleavage by cysteine), hydrogen sulphite, thiosulphate, xanthates, cysteine and glutathione in certain combinations (involving masking of sulphite and thiols with acrylonitrile). Hexacyanoferrate(II) is determined in the presence of arsenic(III), antimony(III) and thallium(I). Sulphathiazole, sulphadiazine and sulphamerazine consume six equivalents of bromine per mole, but phthalation or diazotization of the aromatic amino group prevents disubstitution of bromine in the benzene ring. Chloramphenicol is determined by reduction of its aromatic nitro group to an amino group, followed by bromination. Rutin and vitamin C react with eight and two equivalents of bromine per mole respectively.     

Synthesis, X-ray structure and properties of a new nitrite-bound copper(II) complex with 2-(3,5- dimethylpyrazol-1-ylmethyl)pyridine in a CuN4(O) coordination

Synthesis and characterization of a nitrite-bound copper(II) compound [CuL⁴)₂(ONO)]ClO₄ have been achieved (L⁴ = 2-(3,5-dimethylpyrazol-1-ylmethyl)pyridine]. The bidentate ligand L⁴ provides a pyridine and a pyrazole donor site; however, they are separated by a methylene spacer. The complex has been structurally characterized and it belongs to only a handful of complexes having nitrito-bound mononuclear copper(II) centre. The metal atom has a distorted square pyramidal geometry with the copper atom displaced from the equatorial plane by 0.25 Å. In MeCN solution the green complex exhibits a broad ligand-field transition at 655 nm with a shoulder at 675 nm and in dichloromethane-toluene glass (80 K) it exhibits an EPR spectral feature characteristic of the unpaired electron in the d_x²−y² orbital. Variable-temperature (80–300 K) magnetic susceptibility measurements in the solid state as well as room temperature measurement in MeCN solution reveal mononuclear magnetically dilute copper(II) centre. When examined by cyclic voltammetry (MeCN solution) it displays electrochemically irreversible Cu^II---Cu^I response [cathodic peak potential, E_pc (V vs saturated calomel electrode (SCE)): −0.32]. An oxidative response is observed at 1.14 V, probably due to bound-nitrite oxidation and is partially removed to generate a solvated complex at the electrode surface. The latter species gives rise to reversible Cu^II---Cu^I redox response [ ].     

Stability of AQUO-organic silver iodide sol

Summary The coagulation concentration for silver iodide sol, both in presence of pyridine and dioxane, increases for mono- and bivalent coagulating electrolyte. In presence of a mixture of pyridine and dioxane in equal volume, the coagulation concentration assumes an intermediate value, which is nearer to dioxane. However, in presence of dioxane more bivalent electrolyte is needed than in presence of pyridine. If a bivalent coagulating electrolyte is added to a sol containing a mixture of pyridine and dioxane, the amount of electrolyte required to coagulate is less than pyridine and greater than dioxane. Thus silver iodide sol is more stable toward mono- and bivalent coagulating electrolytes. The degree of stabilization increases with the decrease of the dielectric constant of the dispersing medium. The intermediate values for dioxane pyridine mixture is accountable by the fact that dioxane acts as a solvent for pyridine. The PH value of the sol increases up to the coagulation point. Beyond this, there is an abrupt decrease. When the particles settle down completely a rise in PH is again noted on the further addition of electrolytes. The increase in the electrical conductance is more significant after coagulation. These changes have been explained by adsorption of the ions and due to the release of ions from the electrical double layer.

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Zusammenfassung Die Koagulationskonzentration für Silberjodidsol in Gegenwart von Pyridin und Dioxan steigt für ein- und zweiwertige Elektrolyte an. In Gegenwart einer Mischung zu gleichen Volumen erh?lt man mittlere Werte, n?her denen zu Dioxan. Für Koagulation in Gegenwart von Dioxan ist jedoch mehr zweiwertiger Elektrolyt notwendig als in Gegenwart von Pyridin. Bei Koagulation mit zweiwertigem Elektrolyt verbraucht ein Sol mit der Mischung von Pyridin und Dioxan weniger als für Pyridin und mehr als für Dioxan. Daher ist das Silbersol gegenüber ein- und zweiwertigen Elektrolyten stabiler. Der Grad der Stabilisierung w?chst mit abnehmender Dielektrizit?tskonstante des Dispersionsmediums. Die Zwischenwerte der Dioxan-Pyridin-Mischungen lassen sich verstehen durch die Tatsache, da? Dioxan als L?sungsmittel für Pyridin wirkt. Der PH-Wert des Sols w?chst bis zum Koagulationspunkt, darüberhinaus erfolgt ein steiler Abfall. Wenn die Teilchen vollst?ndig absetzen, ist bei weiterer Zugabe von Elektrolyt ein erneuter Anstieg im PH feststellbar. Der Anstieg der elektrolytischen Leitf?higkeit wird nach der Koagulation ausgepr?gter. Diese ?nderungen lassen sich durch Ionenadsorption und Freiwerden von Ionen aus der elektrischen Doppelschicht erkl?ren.

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Our thanks are due to Prof. R. C. Mehrotra for providing all the facilities for this work and to Prof. S. Ghosh of Allahabad University for helpful discussions. Thanks are also due to the University Grants Commission, Government of India, for the award of a research scholarship to one of us (V. K. S.).     

Spectrophotometric determination of traces of selenium(IV) in various environmental samples using the flow-injection technique (FIT)

A simple, sensitive, and rapid flow-injection spectrophotometric method was developed for the determination of trace amounts of selenium(IV). The method is based on the oxidation reaction of 3-methyl-2-benzothiazolinone hydrazone hydrochloride (MBTH) by selenium(IV) followed by the coupling reaction with chromotropic acid (4.5-dihydroxy naphthalene-2.7-disulphonic acid) in a basic medium (phosphate buffer, pH 10.5) to give a pink derivative with λ_max 530 nm that is stable for more than 7 days at 35°C. The reaction and flow conditions of the full experimental design were optimized. A detection limit (2s) of 0.25 μg/L Se(IV) was obtained at a sampling rate of 10 samples per hour. Beer’s law is obeyed for a Se(IV) concentration range of 0.05–0.5 μg/mL at the wavelength of maximum absorption. The detailed study of various interference ions indicates that the method is highly selective. The method was successfully applied to the determination of traces of selenium(IV) in various water samples. The results obtained were in good agreement with those obtained by the reported methods at the 95% confidence level. The text was submitted by the authors in English.     

Kinetics of substitution of aquo ligands fromcis-diaquo-bis-(biguanide) cobalt(III) and chromium(III) ions by aspartic acid in ethanol—water mixtures

The kinetics of substitution of aqua ligands fromcis-diaqua-bis(biguanide)cobalt(III) and chromium(III) ions by aspartic acid in EtOH–H₂O media have been studied spectrophotometrically in the 30 to 45°C range. We propose the following rate law for the anation

Effect of methylene blue on the capacity of the dropping mercury electrode

Summary The effect of methylene blue under different conditions of p_H, concentration and frequency of the a. c. ripple used has been investigated on the capacity of the dropping mercury electrode. All the peaks caused by methylene blue at different p_H values have been interpreted as due to the reduction of the methylene blue, as indicated by the comprehensive study of the peaks. The halt at about 0.58 Volt at p_H 5.8 is due to desorption which develops into a satellite peak if potassium nitrate is used as indifferent electrolyte. It is found that the peak at 1.35 Volt at p_H 12.3, first increases with increase in concentration and then diminishes at still higher concentrations. The causes of this have been discussed. The effect of frequency reveals that the reduction reactions involved are rather slow.

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Zusammenfassung Der Effekt von Methylenblau unter verschiedenen Verh?ltnissen von Wasserstoff-Ionen-Konzentration, Konzentration und Frequenz des überlagerten Wechselstroms auf die Kapazit?t der Quecksilbertropfelektrode war Gegenstand der Untersuchung. Alle dem Methylenblau zuzuschreibenden Maxima bei verschiedenen p_H- Werten lassen sich interpretieren durch eine Reduktion des Methylenblau, wie die eingehende Untersuchung der Maxima zeigt. Der Konstanzbereich bei etwa 0,58 Volt und p_H 5,8 ist einer Desorption zuzuschreiben, die ein Begleitmaximum entwickelt, wenn Kaliumnitrat als indifferenter Elektrolyt verwendet wird. Das Maximum bei 1,35 Volt und p_H 12,3 w?chst zun?chst bei Steigerung der Konzentration und nimmt dann bei noch h?heren Konzentrationen wieder ab. Die Gründe hierfür werden diskutiert. Der Frequenzeffekt zeigt an, da? die Reduktionsreaktionen ziemlich niedrig sind.