Phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions

One of the main problems of statistical physics is to describe all Gibbs measures corresponding to a given Hamiltonian. It is well known that such measures form a nonempty convex compact subset in the set of all probability measures. The purpose of this article is to investigate phase diagram and extreme Gibbs measures of the Ising model on a Cayley tree in the presence of competing binary and ternary interactions.     

Experimental and quantum chemical calculational studies on 2-[(4-propylphenylimino)methyl]-4-nitrophenol

The Schiff base compound 2-[(4-propylphenylimino)methyl]-4-nitrophenol has been synthesized and characterized by IR, UV–Vis, and X-ray single-crystal determination. The molecular geometry from X-ray determination of the title compound in the ground state has been compared using the Hartree–Fock (HF) and density functional theory (DFT) with the 6-31G(d) basis set. The calculated results show that the DFT and HF can well reproduce the structure of the title compound. The energetic behaviour of the title compound in solvent media was examined using the B3LYP method with the 6-31G(d) basis set by applying the Onsager and the polarizable continuum model (PCM). The results obtained with these methods reveal that the PCM method provides a more stable structure than Onsager's method. Using the TD-DFT method, electronic absorption spectra of the title compound have been predicted and good agreement with the TD-DFT method and the experimental determination was found. The predicted nonlinear optical properties of the title compound are much greater than those of urea. In addition, DFT calculations of the molecular electrostatic potential and NBO analysis of the title compound were carried out at the B3LYP/6-31G(d) level of theory.     

New imine compounds and their copper complexes: synthesis,characterization and comparative investigations of morphologic,mesomorphic, thermotropic,thermo-optical and thermodynamical properties

Investigations of the morphologic, mesomorphic, thermotropic, thermo-optical and thermodynamical properties of new imine compounds and their copper complexes, synthesized by our group, have been carried out. Temperature transformations of typical textures for mesophases, taking place in imine compounds and copper complexes, and the peculiarities of the biphasic regions at the direct and reverse mesophase–isotropic liquid and isotropic liquid–mesophase phase transitions have been investigated.     

W doped SnO2 growth via sol–gel routes and characterization: Nanocubes

The effects of W doping on the characteristical properties of SnO₂ thin films prepared by sol–gel spin coating method were investigated. The SnO₂ thin films were deposited at various W doping ratios and characterized by various measurements. XRD studies indicated that the undoped and W doped SnO₂ films had cubic and tetragonal phases. The SEM images of WTO thin films showed cubic shaped nanocubes corresponding to cubic phase and the smaller particles corresponding to tetragonal phase were formed on the film surfaces, and their distributions and sizes were dependent on the W doping ratio. EDX spectroscopy analyses showed that the calculated and participated atomic ratios of W/(W + Sn) (at.%) in the starting solution and in the WTO thin films were almost close. It was found that the sheet resistance depended on W doping ratio and 2.0 at.% W doped SnO₂ (WTO) exhibited lowest value of sheet resistance (7.11 × 10³ Ω/cm²).     

A Weighted Dispersive Estimate for Schrödinger Operators in Dimension Two

Let H = ?Δ + V, where V is a real valued potential on ${\mathbb {R}^2}$ satisfying ${\|V(x)|\lesssim \langle x \rangle^{-3-}}$ . We prove that if zero is a regular point of the spectrum of H = ?Δ + V, then $${\| w^{-1} e^{itH}P_{ac}f\|_{L^\infty(\mathbb{R}^2)} \lesssim \frac{1}{|t|\log^2(|t|)} \| w f\|_{L^1(\mathbb{R}^2)},\,\,\,\,\,\,\,\, |t| \geq 2}$$ , with w(x) = (log(2 + |x|))². This decay rate was obtained by Murata in the setting of weighted L ² spaces with polynomially growing weights.     

Flow Regimes in Packed Beds of Spheres from Pre-Darcy to Turbulent

Characteristics of flow regimes in porous media, along the processes of energy dissipation in each regime, are critical for applications of such media. The current work presents new experimental data for water flow in packed steel spheres of 1- and 3-mm diameters. The porosity of the porous media was about 35 % for both cases. The extensive dataset covered a broad range of flow Reynolds number such that several important flow regimes were encountered, including the elusive pre-Darcy regime, which is rarely or never seen in porous-media literature and turbulent regime. When compared to previous information, the results of this study are seen to add to the divergence of available data on pressure drop in packed beds of spheres. The divergence was also present in the coefficients of Ergun equation and in the Kozeny–Carman constant. The porous media of the current work were seen to exhibit different values of permeability and Forchheimer coefficient in each flow regime. The current data correlated well using the friction factor based on the permeability (measured in the Darcy regime) and the Reynolds number based on the same length scale. An attempt was made to apply recent theoretical results regarding the applicability of the quadratic and cubic Forchheimer corrections in the strong and weak inertia regime.     

Global existence and boundedness for a class of second-order nonlinear differential equations

In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form ${\left(r\left(t\right){\left|u^{\prime }\right|}^{p?2}{u}^{\prime }\right)}^{\prime }+g(t,u,u^{\prime })u^{\prime }+a\left(t\right)f\left(u\right)=e\left(t\right)\text{,}$ where $p>1$ is a real constant. The results are applicable to well-known Emden–Fowler and Lienard type equations. An illustrative example is also provided.     

Quadratic functions with prescribed spectra

We study a class of quadratic p-ary functions ${{\mathcal{F}}_{p,n}}$ from ${\mathbb{F}_{p^n}}$ to ${\mathbb{F}_p, p \geq 2}$ , which are well-known to have plateaued Walsh spectrum; i.e., for each ${b \in \mathbb{F}_{p^n}}$ the Walsh transform ${\hat{f}(b)}$ satisfies ${|\hat{f}(b)|^2 \in \{ 0, p^{(n+s)}\}}$ for some integer 0 ≤ s ≤ n ? 1. For various types of integers n, we determine possible values of s, construct ${{\mathcal{F}}_{p,n}}$ with prescribed spectrum, and present enumeration results. Our work generalizes some of the earlier results, in characteristic two, of Khoo et. al. (Des Codes Cryptogr, 38, 279–295, 2006) and Charpin et al. (IEEE Trans Inf Theory 51, 4286–4298, 2005) on semi-bent functions, and of Fitzgerald (Finite Fields Appl 15, 69–81, 2009) on quadratic forms.     

A construction of bent functions from plateaued functions

In this presentation, a technique for constructing bent functions from plateaued functions is introduced and analyzed. This generalizes earlier techniques for constructing bent from near-bent functions. Using this construction, we obtain a big variety of inequivalent bent functions, some weakly regular and some non-weakly regular. Classes of bent functions having some additional properties that enable the construction of strongly regular graphs are formed, and explicit expressions for bent functions with maximal degree are presented.