On the normalized Laplacian of Möbius phenylene chain and its applications

Let denote a molecular graph of linear [n] phenylene with n hexagons and n squares, and let the Möbius phenylene chain be the graph obtained from the by identifying the opposite lateral edges in reversed way. Utilizing the decomposition theorem of the normalized Laplacian characteristic polynomial, we study the normalized Laplacian spectrum of , which consists of the eigenvalues of two symmetric matrices ℒ _R and ℒ _Q of order 3n. By investigating the relationship between the roots and coefficients of the characteristic polynomials of the two matrices above, we obtain an explicit closed-form formula of the multiplicative degree-Kirchhoff index as well as the number of spanning trees of . Furthermore, we determine the limited value for the quotient of the multiplicative degree-Kirchhoff index and the Gutman index of .     

On the domain of fractional Laplacians and related generators of Feller processes

In this paper we study the domain of the generator of stable processes, stable-like processes and more general pseudo- and integro-differential operators which naturally arise both in analysis and as infinitesimal generators of Lévy- and Lévy-type (Feller) processes. In particular we obtain conditions on the symbol of the operator ensuring that certain (variable order) Hölder and Hölder–Zygmund spaces are in the domain. We use tools from probability theory to investigate the small-time asymptotics of the generalized moments of a Lévy or Lévy-type process ${(X_t)}_{t\ge 0}$,

$\underset{t\to 0}{\lim }?\frac{1}{t}({\mathbb{E}}^{x}f(X_t)?f(x)),x\in {\mathbb{R}}^d,$

for functions f which are not necessarily bounded or differentiable. The pointwise limit exists for fixed $x\in {\mathbb{R}}^d$ if f satisfies a Hölder condition at x. Moreover, we give sufficient conditions which ensure that the limit exists uniformly in the space of continuous functions vanishing at infinity. As an application we prove that the domain of the generator of ${(X_t)}_{t\ge 0}$ contains certain Hölder spaces of variable order. Our results apply, in particular, to stable-like processes, relativistic stable-like processes, solutions of Lévy-driven SDEs and Lévy processes.     

Synthesis and nanoimprinting of high refractive index and highly transparent polythioethers based on thiol-ene click chemistry

This work demonstrates the UV nanoimprinting lithography (UV-NIL) of high refractive index and highly transparent polythioethers based on thiol-ene click chemistry. Herein, 9,9-bis(3-mercaptopropylphenylether)fluorene (BMPF) is designed as a new thiol monomer with a high refractive index, high transparency, and good processability for UV-NIL. Colorless polythioethers are synthesized from BMPF and ene monomers under mild thiol-ene click reaction conditions. Excellent transmittance (96%) of 400 nm light is observed in all the polymer films and high refractive index values of 1.5972–1.6382 are attained. UV-NIL using thiol-ene photopolymerization affords polymer nanoimprinting patterns with various features on the order of 100–500 nm without any fractures. To the best of our knowledge, this is the first report on UV-NIL of high refractive index and highly transparent polymers. Through proper monomer and polymer design, novel polythioethers with suitable glass transition temperature (T _g) values are developed with high refractive index, high transparency, and good UV-NIL processability. Furthermore, UV-NIL based on thiol-ene click chemistry is accomplished at the nanoscale. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2175–2182     

Synthesis of polydithiourethanes and their thermal,optical, and mechanical properties originated from monomers structure

Polyaddition of various diisothiocyanates and dithiols was achieved with triethylamine in dimethylformamide at 25 °C for 12 h under nitrogen, and then the corresponding polydithiourethanes (PDTUs) were obtained with high yield and molecular weight without depending on the monomer structures, although the dithiol monomer of the low nucleophilicity was unsuitable for polyaddition in this system. The chemical and physical properties of the obtained PDTUs such as solvent solubility, glass transition temperature, thermal stability, transparency, refractive index, and tensile strength, were analyzed in detail by gel permeation chromatography, nuclear magnetic resonance, Fourier transform infrared–attenuated total reflection, ultraviolet–visible, differential scanning calorimetry, thermogravimetric analysis, and tensile testing measurements. These results proved that PDTUs and their cast films having the aliphatic diisothiocyanate and dithiol moieties exhibited excellent chemical and physical properties compared to that of the aromatic PDTUs. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2018 , 56, 2255–2262     

Temperature dependence of the properties of ternary systems ethanol + water + an aliphatic alkane (C6-C9)

The measures and calculation of different properties such as refractive index, density, speed of sound, excess molar volume, and isentropic compressibility of the ternary heterogeneous compounds by ethanol + water + (n-hexane, n-heptane, n-octane, n-nonane) have been performed in the range 288.15–323.15 K and atmospheric pressure. Attending to the accurate results of these models, the equation of state enclosing mixing rules is indicated as a simple estimation of the procedures of these properties for this kind of multicomponent systems.     

Influence of the e-beam irradiation and photo-oxidation aging on the structure and properties of LDPE-OMMT nanocomposite films

In this paper two systems, polyethylene (LDPE) and polyethylene/commercial organo-modified montmorillonite (LDPE/OMMT) nanocomposite, were subjected to e-beam irradiation at different doses and both the molecular modifications and mechanical properties have been investigated through solubility, FT-IR, calorimetric and tensile tests. Moreover, in some of the irradiated systems photo-oxidation aging was performed and its effects were studied. The results show an enhancement with irradiation of the positive effect of the nano-filler loading, related to the increase of the mechanical properties, due to the increase of the nano-filler polymer interaction.Nevertheless calorimetric and FT-IR data indicate that the well known reduction of LDPE/OMMT nanocomposite resistance to photo-oxidation ageing, with respect to LDPE, is amplified by ionizing radiation.     

Substituent electrophilicities in the NMR spectra of barbituric derivatives

Comparison of the ¹H and ¹³ C NMR spectra of a series of substituted 5‐benzylidene‐N,N′‐dimethylbarbituric acids (1) revealed chemical‐shift variations of different centers that correlated with the theoretical electrophilicities or with the substituent electrophilic constant σ_ω , in an example of the usefulness of these DFT‐based indices. Copyright © 2012 John Wiley & Sons, Ltd.     

Investigation of a UV-laser generated waveguide in a planar polymer chip using an improved interferometric method

Polymeric integrated-optical waveguides are prepared in a planar polymer chip by UV-laser lithographic methods. The waveguide samples are irradiated by an excimer laser at a wavelength Λ=248 nm with various irradiation parameters (different fluencies and irradiation doses). Mach-Zehnder interferometer is employed and the refractive index depth profiles of the waveguide samples are obtained. This profile covers two regions having exponential and Gaussian shapes. The model field distributions strongly depend on the refractive index of each region. The mode field distribution and the effective mode indices for each region have been calculated on the basis of a theoretical model and the experimentally measured data.     

Exact solution of functionally graded thick cylinder with finite length under longitudinally non-uniform pressure

Elastic analysis of a functionally graded thick-walled cylindrical pressure vessel is analytically studied in the present research. Gradation is considered for all mechanical properties along the thickness direction based on a power function. The constitutive relations are developed in the general cylindrical coordinate system for an axisymmetric pressurized cylinder. For simulation of these two deformation components, first order shear deformation theory is considered. The FG cylinder is subjected to longitudinally non-uniform pressure along the length of the cylinder. The present problem is applicable for simulation of non-uniform pressurized cylinder by fluids or gases.     

Nontrivial Solutions for p-Laplace Equations with Right-Hand Side Having p-Linear Growth at Infinity

ABSTRACT

The existence of a nontrivial solution for quasi-linear elliptic equations involving the p-Laplace operator and a nonlinearity with p-linear growth at infinity is proved. Techniques of Morse theory are employed.