Basic series identities and combinatorics

Analogous to P.A. MacMahon’s combinatorial interpretations of the Rogers–Ramanujan identities, we interpret two basic series identities combinatorially in two different ways—using split \((n+t)\)-color partitions and the modified lattice paths. This leads to two new 3-way combinatorial identities. We conclude by posing three significant open problems.     

On the compositions and strengths of charge-transfer complexes

The compositions of charge-transfer complexes of urea and thiourea with some aromatic hydrocarbons (naphthalene, anthracene, phenanthrene and biphenyl) have been established through phase diagram studies. The enthalpies and entropies of fusion of these complexes have been estimated by differential scanning calorimetry. It is observed that the relative stabilities of the solid-state charge-transfer complexes in the donor-acceptor systems studied cannot be predicted from the areas under the curves of the congruent compounds in the phase diagrams.

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Zusammenfassung Die Zusammensetzung von Donator-Akzeptor-Komplexen von Harnstoff und Thioharnstoff mit einigen aromatischen Kohlenwasserstoffen, nämlich Naphthalin, Anthracen, Phenanthren und Biphenyl, wurde durch Phasendiagrammuntersuchungen ermittelt. Schmelzenthalpie und -entropie dieser Komplexe wurden mittels DSC bestimmt. Es wurde festgestellt, daß die relative Stabilität der festen Donator-Akzeptor-Komplexe nicht aus der Fläche unter der Kurve im Phasendiagramm der kongruenten Verbindungen vorausgesagt werden kann.

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One of the authors (R.S.) is grateful to I.C.A.R. (India) for financial assistance.     

Thermochemistry of some π-π charge transfer complexes formed between methylbenzene donors and π-electron acceptors

The heats of formation for- ^* charge transfer interactions have been computed from the charge transfer spectra of molecular complexes formed between methylbenzene donors and-electron acceptors.Miss Rajni Sachdeva and Anita Singla are grateful to I.C.A.R. (India) and C. S. I. R. (India), respectively, for financial assistance.     

Generation and detection of optical vortices using all fiber-optic system

We demonstrate simultaneous generation, propagation and detection of optical vortices using all fiber-optic system. A fiber-optic Y-coupler was used for generating spherical and doughnut beams, simultaneously. Gaussian (TEM₀₀) beam emitted from CW red He-Ne laser is coupled into the fiber coupler and is converted into vortex beam via second arm of fiber which propagates with azimuthal phase dependence having well defined orbital angular momentum. The phase structure of vortex beam was detected by interfering both the beams using simple fiber-optic interferometer. The present all fiber-optic system might find application for detecting, sensing physical parameters and is simple and cost effective for generating and detecting optical vortices.     

On the electrophilicity of hydroxyl radical: a laser flash photolysis and computational study

The rate coefficients for reactions of hydroxyl radical with aromatic hydrocarbons were measured in acetonitrile using a novel laser flash photolysis method. Comparison of kinetic data obtained in acetonitrile with those obtained in aqueous solution demonstrates an unexpected solvent effect on the reactivity of hydroxyl radical. In particular, reactions of hydroxyl radical with benzene were faster in water than in acetonitrile, and by a significant factor of 65. Computational studies, at the B3LYP and CBS-QB3 levels, have confirmed the rate enhancement of hydroxyl radical addition to benzene via calculation of the transition states in the presence of explicit solvent molecules as well as a continuum dielectric field. The origin of the rate enhancement lies entirely in the structures of the transition states and not in the pre-reactive complexes. The calculations reveal that the hydroxyl radical moiety becomes more anionic in the transition state and, therefore, looks more like hydroxide anion. In the transition states, solvation of the incipient hydroxide anion is more effective with water than with acetonitrile and provides the strong energetic advantage for a polar solvent capable of hydrogen bonding. At the same time, the aromatic unit looks more like the radical cation in the transition state. The commonly held view that hydroxyl radical is electrophilic in its reactions with DNA bases is, therefore, strongly dependent on the ability of the organic substrate to stabilize the resulting radical cation.     

Approximate solutions of certain integral equations for the diffraction by two strips

Integral equations associated with the diffraction of obliquely incident plane waves of various kinds by two coplanar and parallel infinite strips and slits are solved approximately for low frequencies. The solutions are presented as expansions in terms of a suitable perturbation parameter.

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Résumé Certaines équations intégrales en relation avec la diffraction d'ondes planes, de types divers, incidentes par rapport à deux bandes et deux fentes coplanaires infinies, sont résolues approximativement pour les basses fréquences. Les solutions sont présentées sous forme de développements dependant d'un paramètre de perturbation approprié.

     

Synergic effect of Type II ZnO/BiVO4 magnetic heterostructures for visible light-driven degradation of bisphenol A and methyl violet

Construction of an effective heterojunction for unimpeded flow of photogenerated charges and their prolonged separation is imperative for environmental photocatalysis. Herein, we have designed an efficient magnetic ZnO/BiVO₄ type-II heterostructure, which was employed for proficient degradation of persistent methyl violet dye with an efficiency of 97.6% in 90 min and a hazardous organic pollutant, namely, bisphenol A. UV-DRS and photoluminescence studies demonstrated that the fabricated nanocomposite exhibited effective light absorption and prolonged charge separation, thereby resulting in high photocatalytic efficacy under visible light irradiation. The efficacy of developed magnetic ZnO/BiVO₄ was also compared with pristine BiVO₄ and undoped magnetic ZnO, which indicated that the constructed heterostructure displayed approximately threefold and sixfold activity in contrast with bare BiVO₄ and undoped magnetic ZnO nanoparticles, respectively. Radical trapping studies, ESR analysis along with GC-MS analysis were conducted to elucidate the mechanistic pathway during the photodegradation process. This work provides a rational technical approach and research ideas for photocatalytic degradation of harmful organic pollutants in an environment-friendly manner by employing energy-efficient LEDs. Besides, good recyclability of catalyst makes it a promising candidate for large-scale applications.