Photoluminescence of Seven-Coordinate Zirconium and Hafnium Complexes with 2,2′-Pyridylpyrrolide Ligands

Luminescent seven-coordinated zirconium and hafnium complexes bearing three mono-anionic 2,2′-pyridylpyrrolide ligands and one chloride were synthesized. Solid-state structures and the dynamic behaviors in solution were probed by X-ray crystallography and variable temperature ¹H NMR experiments, respectively. Absorption spectroscopy and time-dependent density functional theory (TD-DFT) calculations supported a hybrid of ligand-to-metal charge transfer (LMCT)/ligand-to-ligand charge transfer (LLCT) for the visible light absorption band. The complexes (^MePMP^Me)₃MCl (M=Zr, Hf, ^MePMP^Me=3,5-dimethyl-2-(2-pyridyl)pyrrolide) are emissive in solution at room temperature upon irradiation with visible light due to a combination of phosphorescence and fluorescence characterized by excited state lifetimes in the μs and low to sub-ns timescale, respectively. Electrochemical experiments revealed that the zirconium complex possesses a reversible redox event under highly reducing condition (−2.29 V vs. Fc^+/0).     

A Study of Tate Homology via the Approximation Theory with Applications to the Depth Formula

Acta Mathematica Sinica, English Series - In this paper we are concerned with absolute, relative and Tate Tor modules. In the first part of the paper we generalize a result of Avramov and...     

An innovative extensional viscometer for low-viscosity and low-elasticity liquids

A spinline-type extensional viscometer is described in which an innovative method of tensile stress measurement is employed. A limited amount of liquid flows through a vertical capillary at a constant flow rate under the influence of a constant pressure head. The drainage time decreases when the liquid stream leaving the capillary is stretched by the application of vacuum. These drainage times are measured in a manner similar to that used for intrinsic viscosity measurements. The measured difference in drainage times, with and without stretching, is trivially related to the extensional stress at the capillary exit, and this provides a very simple method of accurately determining fluid stretching forces having a magnitude as low as 10^-4 N; stresses at other axial locations in the stretched liquid jet are obtained by means of a force balance in the usual manner. The validity of the proposed technique is demonstrated by obtaining the expected results for a Newtonian oil having a shear viscosity of 56.2 mPa-s. Also presented are preliminary data on polyethylene oxide-in-water solutions having an even lower shear viscosity.     

The effect of impurities on the viscoelastic response of polycarbonate reinforced with short glass fibers

Observations are reported in oscillatory torsion tests at room temperature on unfilled and fiber-reinforced polycarbonates melt-blended with impurities (acronitrile–butadiene–styrene, high-impact polystyrene, low-density polyethylene, poly(ethylene terephthalate) and Nylon 6,6). Constitutive equations are derived for the viscoelastic behavior of glassy polymers. With reference to the theory of cooperative relaxation, a polymer is treated as an ensemble of meso-regions with arbitrary shapes and sizes. The time-dependent response of the ensemble is attributed to rearrangement of meso-domains. The rearrangement events occur at random times, when meso-regions are excited by thermal fluctuations. Stress–strain relations are derived by using the laws of thermodynamics. The governing equations are determined by four adjustable parameters that are found by fitting the experimental data. Fair agreement is demonstrated between the observations and the results of numerical simulation. The study focuses on the effects of the concentration of impurities and glass fibers on material parameters.     

Cleaning Random d-Regular Graphs with Brooms

A model for cleaning a graph with brushes was recently introduced. Let α = (v ₁, v ₂, . . . , v _n ) be a permutation of the vertices of G; for each vertex v _i let ${N^+(v_i)=\{j: v_j v_i \in E {\rm and} j>\,i\}}${N^+(v_i)=\{j: v_j v_i \in E {\rm and} j>\,i\}} and N^-(v_i)={j: v_j v_i ? E and j <  i}{N^-(v_i)=\{j: v_j v_i \in E {\rm and} j<\,i\}} ; finally let b_a(G)=?_i=1ⁿ max{|N⁺(v_i)|-|N^-(v_i)|,0}{b_{\alpha}(G)=\sum_{i=1}^n {\rm max}\{|N^+(v_i)|-|N^-(v_i)|,0\}}. The Broom number is given by B(G) =  max _α b _α (G). We consider the Broom number of d-regular graphs, focusing on the asymptotic number for random d-regular graphs. Various lower and upper bounds are proposed. To get an asymptotically almost sure lower bound we use a degree-greedy algorithm to clean a random d-regular graph on n vertices (with dn even) and analyze it using the differential equations method (for fixed d). We further show that for any d-regular graph on n vertices there is a cleaning sequence such at least n(d + 1)/4 brushes are needed to clean a graph using this sequence. For an asymptotically almost sure upper bound, the pairing model is used to show that at most n(d+2?{d ln2})/4{n(d+2\sqrt{d \ln 2})/4} brushes can be used when a random d-regular graph is cleaned. This implies that for fixed large d, the Broom number of a random d-regular graph on n vertices is asymptotically almost surely \fracn4(d+Q(?d)){\frac{n}{4}(d+\Theta(\sqrt{d}))}.