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.     

Transient absorption spectra of 2-hydroxybenzophenone photostabilizers

Transient absorption spectra (400–600 nm) of 2-hydroxybenzophenone and the methyl methacrylate copolymer of 2-hydroxy, 3-allyl, 4,4'-dimethoxybenzophenone following 355 nm excitation (7–480 ps delay) are reported. A short-lived, 435 nm transient (τ ≈ 10 ps in CH₂Cl₂) for both molecules is assigned to the lowest excited singlet before internal proton transfer. Weaker, broad T-T absorption is observed after 480 ps.     

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.     

Use of HPTLC,HPLC, and Densitometry for Qualitative Separation of Indole Alkaloids from Rauvolfia serpentina Roots

JPC – Journal of Planar Chromatography – Modern TLC - High-performance thin-layer chromatography (HPTLC) has been used for normal-phase separation of the components of hexane,...     

An integrated process for purification of lysozyme, ovalbumin, and ovomucoid from hen egg white

This article describes an integrated process for simultaneous purification of lysozyme, ovalbumin, and ovomucoid from hen egg white. The crude egg white extract was passed through a cation exchanger Streamline trade mark SP and the bound lysozyme was eluted with 5% ammonium carbonate, pH 9.0, containing 1 M NaCl after elution of avidin. This partially purified lysozyme was further purified 639-fold on dye-linked cellulose beads. Ovalbumin and ovomucoid did not bind to Streamline SP. Ovalbumin could be precipitated from this unbound fraction by 5% trichloroacetic acid, and ovomucoid was removed from the supernatant by precipitation with ethanol. The yields of lysozyme, ovomucoid, and ovalbumin were 77, 94, and 98%, respectively. All the purified proteins showed single bands on sodium dodecyl sulfate polyacrylamide gel electrophoresis. All the steps are easily scalable, and the process described here can be used for large-scale simultaneous purification of these proteins in the pure form.     

A cobalt(II)-selective PVC membrane based on a Schiff base complex of N,N′-bis(salicylidene)-3,4-diaminotoluene

A new PVC membrane electrode for Co²⁺ based on N,N′-bis(salicylidene)-3,4-diaminotoluene, an excellent neutral carrier, has been fabricated using sodium tetraphenylborate (NaTPB) as an anionic excluder and dioctylphthalte (DOP) as a solvent mediator. The electrode exhibits a linear potential response in the concentration range of 7.9 × 10⁻⁸ to 1.0 × 10⁻¹ M with a slope of 30 ± 0.2 mV per decade. The detection limit of the proposed sensor is 5.0 × 10⁻⁸ M and it can be used over a period of 5 months. The proposed sensor revealed good selectivity over a wide variety of other cations including alkali, alkaline earth, heavy and transition metals and could be used in the pH range of 2.0-9.0. This electrode was successfully applied for the determination of Co²⁺in real samples and as an indicator electrode in potentiometric titration of cobalt ions.     

Structural systematics for o-C(6)H(4)XY ligands with X,Y= O,NH, and S donor atoms. o-iminoquinone and o-iminothioquinone complexes of ruthenium and osmium

The structural features of quinone ligands are diagnostic of charge. The o-benzoquinone, radical semiquinonate, and catecholate electronic forms have C-O bond lengths and a pattern of ring C-C bond lengths that point to a specific mode of coordination. This correlation between ligand charge and structure has been extended to iminoquinone and iminothioquinone ligands, giving a charge-localized view of electronic structure for complexes of redox-active metal ions. The radical semiquinonate form of these ligands has been found to be a surprisingly common mode of coordination; however, the paramagnetic character of the radical ligand is often obscured in complexes containing paramagnetic metal ions. In this report, diamagnetic iminosemiquinonate (isq) and iminothiosemiquinonate (itsq) complexes of ls-d(5) Ru(III) with related complexes of osmium are reported. With osmium, the Os(IV)-amidophenolate (ap) redox isomer is formed. Electrochemical and spectral properties are described for Ru(PPh(3))(2)(isq)Cl(2), Ru(PPh(3))(2)(itsq)Cl(2), Os(PPh(3))(2)(ap)Br(2), Os(PPh(3))(2)(atp)Br(2), and Os(PPh(3))(2)(ap)H(2). Crystallographic characterization of Ru(PPh(3))(2)(isq)Cl(2), Ru(PPh(3))(2)(itsq)Cl(2), and Os(PPh(3))(2)(ap)H(2) was used to assign charge distributions.     

A simple and reliable semipreparative high-performance liquid chromatography technique for the isolation of marker-grade hyperforin from Hypericum perforatum L extract

The present work describes isolation of bioactive lipophilic constituent [namely, hyperforin from St. John's wort (Hypericum perforatum L.)], of approximately 98% purity by semipreparative high-performance liquid chromatography (LC). The extraction, isolation, and analysis of the collected compound is performed without the use of antioxidants and inert gas atmospheres at all the stages. Hyperforin, separated isocratically on a 12microm semiprep column, is obtained in high purity, lyophilized after the removal of the organic phase, and preserved at a low temperature. The purity of the collected marker compound is estimated by the use of LC-mass spectrometry and spectroscopic techniques.     

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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