Structural diversity through ligand flexibility: two novel metal-organic nets via ligand-to-ligand cross-linking of "paddlewheels"

Solvothermal reaction of a partially flexible ligand, H(4)L, and Cu(NO(3))(2)·2.5H(2)O afforded two cross-linked Kagomé lattices of formula [Cu(2)(L)](n): an acs net sustained by novel trigonal prismatic supermolecular building blocks (SBBs) and the first example of a partially pillared Kagomé net.     

Sterically Less‐Hindered Half‐Titanocene(IV) Phenoxides: Ancillary‐Ligand Effect on Mono‐, Bis‐, and Tris(2‐Alkyl‐/arylphenoxy) Titanium(IV) Chloride Complexes

A series of mono‐, bis‐, and tris(phenoxy)–titanium(IV) chlorides of the type [Cp*Ti(2‐R? PhO)_nCl_3?n] (n=1–3; Cp*=pentamethylcyclopentadienyl) was prepared, in which R=Me, iPr, tBu, and Ph. The formation of each mono‐, bis‐, and tris(2‐alkyl‐/arylphenoxy) series was authenticated by structural studies on representative examples of the phenyl series including [Cp*Ti(2‐Ph? PhO)Cl₂] ( 1 PhCl2 ), [Cp*Ti(2‐Ph? PhO)₂Cl] ( 2 PhCl ), and [Cp*Ti(2‐Ph? PhO)₃] ( 3 Ph ). The metal‐coordination geometry of each compound is best described as pseudotetrahedral with the Cp* ring and the 2‐Ph? PhO and chloride ligands occupying three leg positions in a piano‐stool geometry. The mean Ti? O distances, observed with an increasing number of 2‐Ph? PhO groups, are 1.784(3), 1.802(4), and 1.799(3) Å for 1 PhCl2 , 2 PhCl , and 3 Ph , respectively. All four alkyl/aryl series with Me, iPr, tBu, and Ph substituents were tested for ethylene homopolymerization after activation with Ph₃C⁺[B(C₆F₅)₄]^? and modified methyaluminoxane (7% aluminum in isopar E; mMAO‐7) at 140 °C. The phenyl series showed much higher catalytic activity, which ranged from 43.2 and 65.4 kg (mmol of Ti?h)^?1, than the Me, iPr, and tBu series (19.2 and 36.6 kg (mmol of Ti?h)^?1). Among the phenyl series, the bis(phenoxide) complex of 2 PhCl showed the highest activity of 65.4 kg (mmol of Ti?h)^?1. Therefore, the catalyst precursors of the phenyl series were examined by treating them with a variety of alkylating reagents, such as trimethylaluminum (TMA), triisobutylaluminum (TIBA), and methylaluminoxane (MAO). In all cases, 2 PhCl produced the most catalytically active alkylated species, [Cp*Ti(2‐Ph? PhO)MeCl]. This enhancement was further supported by DFT calculations based on the simplified model with TMA.     

Influence of some crosslinking agents on thermal and mechanical properties of electron beam irradiated polylactide

The aim of this article was to determine and compare the influence of trimethylopropane trimethacylate (TMPTA) and trially isocyanurate (TAIC) crosslinking agents on thermal and mechanical properties of electron beam irradiated polylactide (PLA). The blends were made of PLA mixed with 3 wt% of TMPTA (PLA/TMPTA), and PLA mixed with 3 wt% of TAIC (PLA/TAIC). Injection moulded samples were irradiated with the use of high energy (10 MeV) electron beam at various radiation doses to crosslinking PLA macromolecules. Thermal and mechanical properties were investigated by means of differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), tensile strength, and impact strength measurements. The samples were also characterized by Fourier transform infrared spectroscopy (FTIR). It was found that under the influence of electron irradiation PLA/TMPTA samples underwent degradation while PLA/TAIC samples became crosslinked. Tensile and impact strengths of PLA/TMPTA samples decreased with increasing radiation dose while an enhancement of these properties for PLA/TAIC samples was observed.     

Collapsibility and Vanishing of Top Homology in Random Simplicial Complexes

Let $\Delta _{n-1}$ denote the $(n-1)$ -dimensional simplex. Let $Y$ be a random $d$ -dimensional subcomplex of $\Delta _{n-1}$ obtained by starting with the full $(d-1)$ -dimensional skeleton of $\Delta _{n-1}$ and then adding each $d$ -simplex independently with probability $p=\frac{c}{n}$ . We compute an explicit constant $\gamma _d$ , with $\gamma _2 \simeq 2.45$ , $\gamma _3 \simeq 3.5$ , and $\gamma _d=\Theta (\log d)$ as $d \rightarrow \infty $ , so that for $c < \gamma _d$ such a random simplicial complex either collapses to a $(d-1)$ -dimensional subcomplex or it contains $\partial \Delta _{d+1}$ , the boundary of a $(d+1)$ -dimensional simplex. We conjecture this bound to be sharp. In addition, we show that there exists a constant $\gamma _d< c_d <d+1$ such that for any $c>c_d$ and a fixed field $\mathbb{F }$ , asymptotically almost surely $H_d(Y;\mathbb{F }) \ne 0$ .     

Random attractors for stochastic 2D-Navier–Stokes equations in some unbounded domains

We show that the stochastic flow generated by the 2-dimensional Stochastic Navier–Stokes equations with rough noise on a Poincaré-like domain has a unique random attractor. One of the technical problems associated with the rough noise is overcomed by the use of the corresponding Cameron–Martin (or reproducing kernel Hilbert) space. Our results complement the result by Brze?niak and Li (2006) [10] who showed that the corresponding flow is asymptotically compact and also generalize Caraballo et al. (2006) [12] who proved existence of a unique attractor for the time-dependent deterministic Navier–Stokes equations.     

On the Sharpness of Mockenhaupt’s Restriction Theorem

We prove that the range of exponents in Mockenhaupt’s restriction theorem for Salem sets (Geom Funct Anal 10:1579–1587, 2000), with the endpoint estimate due to Bak and Seeger (Math Res Lett 18:767–781, 2011), is optimal.     

CLTs and Asymptotic Variance of Time-Sampled Markov Chains

For a Markov transition kernel P and a probability distribution μ on nonnegative integers, a time-sampled Markov chain evolves according to the transition kernel $P_{\mu} = \sum_k \mu(k)P^k.$ In this note we obtain CLT conditions for time-sampled Markov chains and derive a spectral formula for the asymptotic variance. Using these results we compare efficiency of Barker’s and Metropolis algorithms in terms of asymptotic variance.     

Nystatin in Langmuir monolayers at the air/water interface

The paper presents a thorough characteristics of Langmuir monolayers formed at the air/water interface by a polyene macrolide antibiotic-nystatin. The investigations are based on the analysis of pi/A isotherms recorded for monolayers formed by this antibiotic at different experimental conditions. A significant part of this work is devoted to the stability and relaxation phenomena. It has been found that nystatin forms at the air/water interface monolayers of the LE state. A plateau region, observed during the course of the isotherm compression, is suggested to be due to the orientational change of nystatin molecules from horizontal to vertical position. Quantitative analysis of the desorption of the monolayer material into bulk water indicates that the solubility of nystatin monolayers increases with surface pressure. At low surface pressures, the desorption of nystatin from a monolayer is controlled both by dissolution and by diffusion. However, at the plateau and in the post-plateau region, the desorption does not achieve a steady state and the monolayer is less stable than in the pre-plateau region. However, the presence of membrane lipids, even at a low mole fraction, considerably increases the stability of nystatin monolayers. This enables the application of the Langmuir monolayer technique to study nystatin in mixture with cellular membrane components, aiming at verifying its mode of action and the mechanism of toxicity.