On singularity and fine spectral structure of random continued fractions

We study properties of the distribution of a random variable of the continued fraction form where are independent and not necessarily identically distributed random variables. We prove the singularity of and study the fine spectral structure of such measures.     

Thermodynamic properties of 5(nitrophenyl) furan-2-carbaldehyde isomers

Background

The aim of the current work was to determine thermo dynamical properties of 5(2-nitro phenyl)-furan-2-carbaldehyde, 5(3-nitro phenyl)-furan-2-carbaldehyde and 5(4-nitro phenyl)-furan-2-carbaldehyde.

Results

The temperature dependence of saturated vapor pressure of 5(2-nitro phenyl)-furan-2-carbaldehyde, 5(3-nitro phenyl)-furan-2-carbaldehyde and 5(4-nitro phenyl)-furan-2-carbaldehyde was determined by Knudsen’s effusion method. The results are presented by the Clapeyron–Clausius equation in linear form, and via this form, the standard enthalpies, entropies and Gibbs energies of sublimation and evaporation of compounds were calculated at 298.15 K. The standard molar formation enthalpies of compounds in crystalline state at 298.15 K were determined indirectly by the corresponding standard molar combustion enthalpy, obtained using bomb calorimetry combustion.

Conclusions

Determination of the thermodynamic properties for these compounds may contribute to solving practical problems pertaining optimization processes of their synthesis, purification and application and it will also provide a more thorough insight regarding the theoretical knowledge of their nature.

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Graphical abstract: Generalized structural formula of investigated compounds and their formation enthalpy determination scheme in the gaseous state

     

Microstructural driven computational modeling of polymers

The key focus of this work is the polymer microstructure which is the origin of the overall material response. In elastomers random three-dimensional networks are formed by long macromolecules connected at the cross-links by vulcanization or permanent entanglements. The mechanical response of these materials is mainly entropic and is related to the number of conformations that flexible polymer chains can attain. The available kinetic theories link the entropy of a single chain to such microscopic quantities as the end-to-end distance between the cross-links or the constraining tube diameter among others. The central issue of micromechanically-based material modeling is the relation between these quantities and the macroscopic deformation. In this work this connection is established by a network homogenization approach. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The first example of an intramolecular Diels-Alder furan (IMDAF) reaction of iminium salts and its application in a short and simple synthesis of the isoindolo[1,2-a]isoquinoline core of the jamtine and hirsutine alkaloids

1-(2-Furyl)-3,4-dihydroisoquinolines, easily prepared from readily available phenethylamines, undergo tandem alkylation/[4+2]-cycloaddition with allyl halides. The reaction proceeds via 2-allyl-1-furyl-3,4-dihydroisoquinolinium salt formation and subsequent intramolecular exo-Diels-Alder reaction of furan with the allyl fragment (IMDAF reaction). The adducts formed include the basic structural element of the isoindolo[1,2-a]isoquinoline alkaloids jamtine and hirsutine.     

Modification of the lie‐algebraic scheme and approximation error estimations

A new modification of the the Lie‐algebraic scheme for solving partial differential equations with initial and boundary conditions based on constructing quasirepresentations of the Heisenberg‐Weyl algebra operators involving boundary conditions is proposed. Approximation errors for the modified scheme are evaluated. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Correctness of the first boundary-value problem and the Cauchy problem for some quasilinear parabolic systems without conditions at infinity

In the article, questions of the uniqueness of solutions of boundary-value problems and the Cauchy problem for parabolic systems without conditions on their behavior at infinity are studied. The continuous dependence of generalized solutions of the problems considered on the right-hand terms is proved. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 35–54, 2005.     

Self-assembly and multistage redox chemistry of strong electron acceptors on metal surfaces: polynitrofluorenes on gold and platinum

Nitrofluoren-9-one and nitrofluoren-9-dicyanomethylene electron acceptors 7, 8, and 11 functionalized with a terminal thioctic acid unit have been synthesized from 2,4,5,7-tetranitrofluorenone. The self-assembled monolayers (SAMs) of these compounds on gold, formed via gold-sulfur interaction, have been fully characterized by electrochemical, FTIR, ellipsometry, and contact angle measurements. Cyclic voltammetry of SAMs reveals two reversible single-electron reduction waves for fluorenone derivatives 7a,b and 11, and three single-electron reductions for the dicyanomethylene-fluorene 8b, providing the first observation of a radical trianion species in SAMs. The tendency of the thioctic anchor to form multilayers via disulfide links is noted.     

Theory and practice of long-period gratings: when a loss becomes a gain

Losses of cladding modes are part of the mechanism of operation of a long-period grating (LPG) when it is used as an optical filter. We present a LPG computer simulation that accounts for these losses. On the basis of this simulation, we show that losses result in qualitatively different LPG spectral behavior. There is an optimal loss value that provides sidelobe-free, 100% power transfer from the core to the cladding mode for a uniform LPG. We obtained a simple equation that relates this optimum lose value to the LPG length and the cross-coupling coefficient. Based on the results, we propose new approaches to LPG design in a fiber as well as in waveguide platforms for fiber-optic communication and sensor applications. A design of a LPG reconfigurable filter is suggested.     

A convenient method for the synthesis of 2-[(5-benzyl-1,3-thiazol-2-yl)imino]-1,3-thiazolidin-4-one derivatives

It was found that the reaction of 2-chloroacetamido/chloropropioamido-5-benzylthiazole with potassium thiocyanate gave, via rearrangement, 2-[(5-benzyl-1,3-thiazol-2-yl)imino]-1,3-thiazolidin-4-ones.