ChemInform Abstract: YCa3(CrO)3(BO3)4: A Cr3+ Kagome Lattice Compound Showing No Magnetic Order Down to 2 K.

Polycrystalline gaudefroyite‐type YCa₃(CrO)₃(BO₃)₄ with Cr³⁺ ions (3d³, S = 3/2) forming an undistorted Kagome lattice is prepared by reaction of a stoichiometric mixture of Y₂O₃, CaCO₃, Cr₂O₃, H₃BO₃ in a KCl flux (Al₂O₃ crucible, 1000 °C, 1 d) followed by re‐grinding and further annealing (1000 °C, 2 d, 95% yield).     

Synthesis,Cytotoxicity and Antibacterial Studies of Novel Symmetrically and Nonsymmetrically 4‐(Methoxycarbonyl)benzyl‐Substituted N‐Heterocyclic Carbene–Silver Acetate Complexes

From the reaction of 1H‐imidazole ( 1a ), 4,5‐dichloro‐1H‐imidazole ( 1b ), 1H‐benzimidazole ( 1c ), 1‐methyl‐1H‐imidazole ( 1d ), and 1‐methyl‐1H‐benzimidazole ( 1f ) with methyl 4‐(bromomethyl)benzoate ( 2 ), symmetrically and nonsymmetrically 4‐(methoxycarbonyl)benzyl‐substituted N‐heterocyclic carbene (NHC) precursors, 3a – 3f , were synthesized. These NHC precursors were then reacted with silver(I) acetate (AgOAc) to yield the NHC–silver acetate complexes (acetato‐κO){1,3‐bis[4‐(methoxycarbonyl)benzyl]imidazol‐2‐ylidene}silver ( 4a ), (acetato‐κO){4,5‐dichloro‐1,3‐bis[4‐(methoxycarbonyl)benzyl]‐2,3‐dihydro‐1H‐imidazol‐2‐yl}silver ( 4b ), (acetato‐κO){1,3‐bis[4‐(methoxycarbonyl)benzyl]‐2,3‐dihydro‐1H‐benzimidazol‐2‐yl}silver ( 4c ), (acetato‐κO){1‐[4‐(methoxycarbonyl)benzyl]‐3‐methyl‐2,3‐dihydro‐1H‐imidazol‐2‐yl}silver ( 4d ), (acetato‐κO){4,5‐dichloro‐1‐[4‐(methoxycarbonyl)benzyl]‐3‐methyl‐2,3‐dihydro‐1H‐imidazol‐2‐yl}silver ( 4e ), and (acetato‐κO){1‐[4‐(methoxycarbonyl)benzyl]‐3‐methyl‐2,3‐dihydro‐1H‐benzimidazol‐2‐yl}silver ( 4f ), respectively. The three NHC–AgOAc complexes 4a, 4c , and 4d were characterized by single‐crystal X‐ray diffraction. All compounds studied in this work were preliminarily screened for their antimicrobial activities in vitro against Gram‐positive bacteria Staphylococcus aureus, and Gram‐negative bacteria Escherichia coli using the qualitative disk‐diffusion method. All NHC–AgOAc complexes exhibited weak‐to‐medium antibacterial activity with areas of clearance ranging from 4 to 7 mm at the highest amount used, while the NHC precursors showed significantly lower activity. In addition, NHC–AgOAc complexes 4a and 4b , and 4d – 4f exhibited in preliminary cytotoxicity tests on the human renal‐cancer cell line Caki‐1 medium‐to‐high cytotoxicities with IC₅₀ values ranging from 3.3±0.4 to 68.3±1 μM .     

Cation disorder in NaW2O6+δ·nH2−zO post-ion exchange with K, Rb, Sr, and Cs

The structure of the defect pyrochlore NaW₂O_6+δ·nH_2−zO after ion exchange with K, Rb, Sr or Cs for Na has been investigated using thermal analysis, solid-state nuclear magnetic resonance, laboratory X-ray and neutron diffraction methods. Neutron diffraction studies show that both the A-type cations (Na⁺, K⁺, Rb⁺, and/or Cs⁺) and the water molecules reside within the channels that form in the 111 direction of the W₂O₆ framework and that these strongly interact. The analytical results suggest that the water and A-type cations compete for space in the tunnels within the W₂O₆ pyrochlore framework, with the total number of water molecules and cations being approximately constant in the six samples investigated. The interplay between the cations and water explains the non-linear dependence of the a lattice parameter on the choice of cation. It appears that the ion-exchange capacity of the material will be controlled by the amount of water initially present in the sample.     

Loss analysis and increasing of the fabrication tolerance of resonant coupling by tapering the mode beating section

The film mode matching method was used to analyze the inter waveguide coupling losses in a passive asymmetric twin waveguide caused by waveguide width and refractive index variation for both resonant and adiabatic coupling at a wavelength of 1,550 nm. The reasons for power losses are shown. It is demonstrated that tapering the mode beating section of the resonant coupler can increase the fabrication tolerance of resonant coupling without increasing the coupling length.     

Embedding pointed curves in K3 surfaces

Mathematische Zeitschrift - We analyze morphisms from pointed curves to K3 surfaces with a distinguished rational curve, such that the marked points are taken to the rational curve, perhaps with...     

Asymptotically liberating sequences of random unitary matrices

A fundamental result of free probability theory due to Voiculescu and subsequently refined by many authors states that conjugation by independent Haar-distributed random unitary matrices delivers asymptotic freeness. In this paper we exhibit many other systems of random unitary matrices that, when used for conjugation, lead to freeness. We do so by first proving a general result asserting “asymptotic liberation” under quite mild conditions, and then we explain how to specialize these general results in a striking way by exploiting Hadamard matrices. In particular, we recover and generalize results of the second-named author and of Tulino, Caire, Shamai and Verdú.