Optical and static dielectric study of a terminally fluorinated liquid crystalline compound

Optical and static dielectric studies on a terminally fluorinated liquid crystalline compound have been carried out. Measurements of temperature variation of refractive indices of the compound are done by using thin prism method. A four-parameter model is validated by fitting the experimentally measured values of refractive indices, birefringence and average refractive indices of the compound with the theoretical ones. Refractive index and density data are utilized for determination of orientational order parameter. The temperature variation of dielectric permittivities of the compound are measured by a LCR meter.     

Applications of Markov spectra for the weighted partition network by the substitution rule

The weighted self-similar network is introduced in an iterative way. In order to understand the topological properties of the self-similar network, we have done a lot of research in this field.Firstly, according to the symmetry feature of the self-similar network, we deduce the recursive relationship of its eigenvalues at two successive generations of the transition-weighted matrix.Then, we obtain eigenvalues of the Laplacian matrix from these two successive generations.Finally, we calculate an accurate expression for the eigentime identity and Kirchhoff index from the spectrum of the Laplacian matrix.     

Synthesis and characterization of 9,9‐bis(4‐hydroxyphenyl and 4‐aminophenyl)dibenzofluorenes: Novel fluorene‐based monomers

Two novel 9,9‐difunctionalized fluorene‐type monomers, 9,9‐bis(4‐hydroxyphenyl‐ and 4‐aminophenyl)‐2,3:6,7‐dibenzofluorenes, are synthesized by the reaction of dibenzenzofluorenone with phenol and aniline. These monomers are used for the preparation of polyester and polyimide as the typical polymers to evaluate the property change such as thermal stability caused by the benzene rings fused to the fluorene skeleton with keeping good solubility, in comparison with the polymers derived from simple fluorenone. In fact, these two new polymers have the fairly enhanced thermal stability and refractive index value along with satisfactory solubility in organic solvents, enough to emphasize the fusion effect. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2602–2605     

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.     

Some properties of the Owen T-function

Some new relations for the Owen function are obtained including differentiation and integration formulas, integral representations and series. Applications of the Owen function in probability theory and in communication theory are shown.     

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