Crystal chemistry of three new monodimensional fluorometalates templated with ethylenediamine

Three new monodimensional hybrid metal (Ti, In, Al) fluorides are synthesized with ethylenediamine (en) as a templating agent in solvothermal conditions assisted by microwave heating. All structures involve inorganic chains built up from TiO₂F₄ octahedra connected by two opposite O²⁻ vertices in [H₂en]·(TiOF₄) (I), from InF₆(H₂O) pentagonal bipyramids linked by F–F edges in [H₂en]·(InF₄(H₂O))₂·H₂O (II) and from (Al₇F₃₀)⁹⁻ polyanions sharing two opposite AlF₆ octahedra in [H₂en]₃·(Al₆F₂₄) (III). I is tetragonal, P4/ncc, a = 12.761(3) Å, c = 8.041(3) Å; II is orthorhombic, F2dd, a = 6.904(5) Å, b = 16.559(5) Å, c = 19.777(4) Å and III is monoclinic, P2₁/n, a = 9.387(2) Å, b = 6.710(2) Å, c = 21.513(6) Å, β = 97.18(3)°.     

Photooxidation of acyclovir with thermally generated triplet excited ketones. A comparison with type I and II photosensitizers

The antiviral drug acyclovir (Ac, 1) was treated with triplet excited ketones, which have been generated in thermal decomposition of 3-(hydroxymethyl)-3,4,4-trimethyl-1,2-dioxetane (HTMD), in the dark. Three major oxidation products were detected by means of spectroscopic measurements. The products were (2-hydroxyethoxy) methyl spiroiminodihydantoin (2), (2-hydroxyethoxy) methyl (amino)-2-imino-1,2-dihydroimidazole-5-one (3), and 2,2-diamino-4-[(2-hydroxyethoxy) methyl) amino)-5-[2H]-oxazolone (4). Equal amounts of type I and type II photooxidation products were found, as could be established by comparison with predominant type I (riboflavin) and type II (rose bengal) photosensitizers. The concentration and time profiles for the HTMD-induced oxidation of Ac were also determined. The participation of singlet oxygen in HTMD-induced oxidation was confirmed by the substantial D(2)O effect in the formation of spiroiminodihydantoin (2).     

On the solution of a class of the reduced wave equation and the Riccati differential equation

In this paper we present an “iteration” technique for a class of differential equation having the form z^″=λz, where λ is a function in C^∞. We show that we can construct not only the general solution of the reduced wave equation but also the general solution of the Riccati differential equation by using this iteration technique if the given function λ is satisfies the condition

     

Around Jensen’s inequality for strongly convex functions

In this paper we use basic properties of strongly convex functions to obtain new inequalities including Jensen type and Jensen–Mercer type inequalities. Applications for special means are pointed out as well. We also give a Jensen’s operator inequality for strongly convex functions. As a corollary, we improve the Hölder-McCarthy inequality under suitable conditions. More precisely we show that if \(Sp\left( A \right) \subset \left( 1,\infty \right) \), then

$$\begin{aligned} {{\left\langle Ax,x \right\rangle }^{r}}\le \left\langle {{A}^{r}}x,x \right\rangle -\frac{{{r}^{2}}-r}{2}\left( \left\langle {{A}^{2}}x,x \right\rangle -{{\left\langle Ax,x \right\rangle }^{2}} \right) ,\quad r\ge 2 \end{aligned}$$

and if \(Sp\left( A \right) \subset \left( 0,1 \right) \), then

$$\begin{aligned} \left\langle {{A}^{r}}x,x \right\rangle \le {{\left\langle Ax,x \right\rangle }^{r}}+\frac{r-{{r}^{2}}}{2}\left( {{\left\langle Ax,x \right\rangle }^{2}}-\left\langle {{A}^{2}}x,x \right\rangle \right) ,\quad 0<r<1 \end{aligned}$$

for each positive operator A and \(x\in \mathcal {H}\) with \(\left\| x \right\| =1\).

     

A new one-dimensional hybrid material lattice: AC conductivity and structural characterization of [C<Subscript>7</Subscript>H<Subscript>12</Subscript>N<Subscript>2</Subscript>][CdCl<Subscript>4</Subscript>]

The present paper reports the synthesis, crystal structure, ¹³C and ¹¹¹Cd cross-polarization magic-angle spinning nuclear magnetic resonance(CP-MAS-NMR) analysis and ac conductivity for a new organic–inorganic hybrid salt, [C₇H₁₂N₂][CdCl₄]. The compound crystallizes in the triclinic system, space group P\( \overline 1 \), with unit cell dimensions: a?=?7.1050(3) Å, b?=?8.9579(3) Å, c?=?9.4482(3) Å, α?=?81.415(1)°, β?=?89.710(2)°, γ?=?85.765(1)°, V?=?592.97(4) Å³, and Z?=?2. The asymmetric unit is composed of one-2,4-diammonium toluene cation and one [CdCl₄]^2? anion. The Cd atom is in a slightly distorted octahedra coordination environment. Its structure can be described by infinite chains of CdCl₆ octahedron linked to organic cations by a strong charge-assisted N–H???Cl interactions in order to build organic–inorganic layers staked along \( \left[ {0\overline 1 1} \right] \) direction. The solid state ¹³C CP-MAS-NMR spectra has shown seven isotropic resonances, confirming the existence of seven non-equivalent carbon atoms, which is consistent with crystal structure determined by X-ray diffraction. As for ¹¹¹Cd MAS-NMR, it has shown one cadmium site with isotropic chemical shift observed at 167.2 ppm. The complex impedance of the compound has been investigated in the temperature range of 403–460 K and in the frequency range of 200 Hz–5 MHz. The impedance plots have shown semicircle arcs at different temperatures and an electrical equivalent circuit has been proposed to explain the impedance results. The circuits consist of the parallel combination of bulk resistance R _p and constant phase elements.     

Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces

In this paper, we study the subcritical dissipative quasi-geostrophic equation. By using the Littlewood Paley theory, Fourier analysis and standard techniques we prove that there exists $v$ a unique global-in-time solution for small initial data belonging to the critical Fourier-Besov-Morrey spaces $ \mathcal{F} {\mathcal{N}}_{p, \lambda, q}^{3-2 \alpha+\frac{\lambda-2}{p}}$. Moreover, we show the asymptotic behavior of the global solution $v$. i.e., $\|v(t)\|_{ \mathcal{F} {\mathcal{N}}_{p, \lambda, q}^{3-2 \alpha+\frac{\lambda-2}{p}}}$ decays to zero as time goes to infinity.     

Free energy from molecular dynamics with multiple constraints

In molecular dynamics simulations of reacting systems, the key step to determining the equilibrium constant and the reaction rate is the calculation of the free energy as a function of the reaction coordinate. Intuitively the derivative of the free energy is equal to the average force needed to constrain the reaction coordinate to a constant value, but the metric tensor effect of the constraint on the sampled phase space distribution complicates this relation. The appropriately corrected expression for the potential of mean constraint force method (PMCF) for systems in which only the reaction coordinate is constrained was published recently. Here we will consider the general case of a system with multiple constraints. This situation arises when both the reaction coordinate and the ‘hard’ coordinates are constrained, and also in systems with several reaction coordinates. The obvious advantage of this method over the established thermodynamic integration and free energy perturbation methods is that it avoids the cumbersome introduction of a full set of generalized coordinates complementing the constrained coordinates. Simulations of n-butane and n-pentane in vacuum illustrate the method.     

PTFE/EP Reinforced MOF/SiO2 Composite as a Superior Mechanically Robust Superhydrophobic Agent towards Corrosion Protection,Self-Cleaning and Anti-Icing

Organic resin cross-linking ZIF-67/SiO₂ superhydrophobic (SHPB) multilayer coating was successfully fabricated on metal substrate. The perfluoro-octyl-triethoxy silane (POTS) modified ZIF-67 and SiO₂ coating was applied on primary coated polytetrafluoroethylene (PTFE) and epoxy resin (EP) via spray coating method. Here, we present that the robust superhydrophobicity can be realized by structuring surfaces at two different length scales, with a nanostructure design to provide water repellence and a microstructure design to provide durability. The as-fabricated multilayer coating displayed superior water-repellence (CA=167.4°), chemical robustness (pH=1–14) and mechanical durability undergoing 120th linear abrasion or 35th rotatory abrasion cycle. By applying different acidic and basic corrosive media and various weathering conditions, it can still maintain superior-hydrophobicity. To get a better insight of interaction between inhibitor molecules and metal surface, density functional theory (DFT) calculations were performed, showing lower energy gap and increased binding energy of ZPS/SiO₂/PTFE/EP (ZPS=ZIF-67+POTS) multilayer coating compared to the ZIF-67/SiO₂/PTFE/EP, thereby supporting the experimental findings. Additionally, such coatings may be useful for applications such as anti-corrosion, self-cleaning, and anti-icing multi-functionalities.     

An algorithm for the estimation of a regression function by continuous piecewise linear functions

The problem of the estimation of a regression function by continuous piecewise linear functions is formulated as a nonconvex, nonsmooth optimization problem. Estimates are defined by minimization of the empirical L ₂ risk over a class of functions, which are defined as maxima of minima of linear functions. An algorithm for finding continuous piecewise linear functions is presented. We observe that the objective function in the optimization problem is semismooth, quasidifferentiable and piecewise partially separable. The use of these properties allow us to design an efficient algorithm for approximation of subgradients of the objective function and to apply the discrete gradient method for its minimization. We present computational results with some simulated data and compare the new estimator with a number of existing ones.