Bounds for the generalized Marcum function of the second kind

The Ramanujan Journal - This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use...     

Spectral Criteria for Design of an Optical Modulator Based on Frustrated Total Internal Reflection

The spectral study of an optical modulator based on the frustrated total internal reflection is presented under static and dynamic conditions. An optical modulator based on macroscopic moving parts makes spectrometers voluminous and has low compactness. The use of static or quasi-static optical modulators, such as the one proposed in this paper, avoids these problems. The study under static conditions reveals that the modulator equalises the spectral emittance of a black body. The modulation efficiency is defined by comparing the modulator with an ideal square chopper. Study under dynamic conditions reveals spectral criteria that must be met in the design of the mechanical system of the modulator to shift the maximum value of the modulation efficiency to the desired wavelength.     

Even and Odd Schrödinger Cat States in the Probability Representation of Quantum Mechanics

Journal of Russian Laser Research - We consider even and odd coherent states (Schrödinger cat states) in the probability representation of quantum mechanics. The probability representation of...     

Noise exposure of workers of the construction sector

Noise is one of the most highly found physical contaminants in the construction sector. The most negative effects caused by noise exposure are related to the hearing system and may produce professional deafness or even permanent deafness. As these effects have a very important influence on people’s health and well-being, it is necessary to assess the noise exposure and to develop mechanisms for studying and proposing preventive solutions.This work has studied the noise levels which the workers of the construction sector are exposed to. A number of representative measurements have been carried out using a sound level meter and a dosimeter to collect data from workers devoted to different tasks in the construction process. Analysis of the most important levels and indexes have been done with those data, and afterwards, they have been compared with the limits imposed by the different current regulations.     

Olefin epoxidations in the ionic liquid [C4mim][PF6] catalysed by oxodiperoxomolybdenum species in situ generated from molybdenum trioxide and urea–hydrogen peroxide: The synthesis and molecular structure of [Mo(O)(O2)2(4-MepyO)2]·H2O

Commercially available molybdenum(VI) compounds, including molybdenum trioxide, were successfully employed as catalyst precursors in the epoxidation of olefins with urea–hydrogen peroxide adduct (UHP) in the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate, [C₄mim][PF₆]. After oxidation, the corresponding epoxides were isolated by extraction with diethyl ether. Additionally the ionic liquid–catalyst mixture was recycled and reused in further catalytic cycles. The catalytic species is assumed to be an oxodiperoxomolybdenum species which forms in situ. A representative complex of this type was thus isolated and characterised. Reaction of excess 4-methylpyridine-1-oxide (4-MepyO) with MoO₃ dissolved in aqueous hydrogen peroxide afforded [Mo(O)(O₂)₂(4-MepyO)₂]·H₂O (1) as yellow crystals. Compound 1, an active epoxidation catalyst, was subsequently characterised and its structure determined by X-ray crystallography.     

New reactions in water: metal-free conversion of alcohols and ketones into alpha-iodoketones

Using water as the reaction medium, ketones can be transformed into alpha-iodoketones upon treatment with sodium iodide, hydrogen peroxide and an acid; interestingly, alpha-iodoketones can be also obtained from secondary alcohols through a metal-free tandem oxidation-iodination approach.     

Direct evidence for block-by-block growth in high-temperature superconductor ultrathin films

Charge neutrality and stoichiometry impose severe restrictions on the mechanisms of epitaxial growth of complex oxides. The fundamental question arises of what is the minimum growth unit when sample thickness is reduced beyond the size of the unit cell. We have investigated the growth mechanism of YBa2Cu3O7 cuprate superconductor, using a consistent approach based on the growth of noninteger numbers of YBa2Cu3O7 layers in YBa(2)Cu(3)O(7)/PrBa(2)Cu3O7 superlattices. Ex situ chemical and structural analysis evidence a 2D block-by-block mechanism in which the minimum growth units are complete unit cell blocks, growing coherently over large lateral distances.     

On the mechanism of the copper-mediated C-S bond formation in the intramolecular disproportionation of imine disulfides

The mechanism of the copper-mediated disproportionation of aromatic imine disulfides to benzothiazoles in the gas phase is investigated by experimental and theoretical methods. Application of infrared multiphoton dissociation and hydrogen/deuterium exchange experiments combined with density functional theory (DFT) calculations of the relevant molecular structures and the associated infrared spectra allows the identification of the observed ionic intermediates. The theoretical investigation of the possible reaction pathways supported by collision-induced dissociation experiments provides a consistent mechanistic picture of the reaction catalyzed by a single copper(I) ion. Activation of the substrate proceeds via homolytic sulfur-sulfur bond cleavage, yielding metal complexes in the formal +3 oxidation state; carbon-sulfur coupling and hydrogen-atom transfer complete the transformation to the products. Exploratory studies demonstrate that in the gas phase, the disproportionation of the imine disulfide can also be mediated by other metal ions via different either homo- or heterolytic mechanisms without involving high-valent intermediates.     

Isomorphous replacement of M(II) ions in M(II)-Gd(III) dimers (M(II) = Cu(II), Mn(II), Ni(II), Co(II), Zn(II)): magnetic studies of the products

Complexes [M(II)Gd(III){pyCO(OEt)pyC(OH)(OEt)py}?](ClO?)?·EtOH [M(II) = Cu(II) (1), Mn(II) (2), Ni(II) (3), Co(II) (4) and Zn(II) (5)] crystallize in the monoclinic Cc space group and contain one hexacoordinate M(II) ion and one enneacoordinate Gd(III) ion, bridged by three {pyCO(OEt)pyC(OH)(OEt)py}? ligands. Magnetic susceptibility measurements indicate a ferromagnetic interaction for 1 and antiferromagnetic interactions for 2-4. Using the ? = -J?(Gd(III))?(M(II)) spin Hamiltonian formalism, fits to the magnetic susceptibility data yielded J values of +0.32 cm?1 for 1, -1.7 cm?1 for 2, and -0.22 cm?1 for 3. In complex 4, the orbital contributions of Co(II) precluded the determination of the magnetic coupling. The complex follows the Curie-Weiss law with θ = -2.07 K (-1.44 cm?1).