Dupin cyclides osculating surfaces

We study the order of tangency of surfaces and Dupin cyclides. We show that generically the maximal tangency order equals 4 and provide a number of examples.     

White Light Emissive DyIII Single‐Molecule Magnets Sensitized by Diamagnetic [CoIII(CN)6]3− Linkers

The self‐assembly of Dy^III–3‐hydroxypyridine (3‐OHpy) complexes with hexacyanidocobaltate(III) anions in water produces cyanido‐bridged {[Dy^III(3‐OHpy)₂(H₂O)₄] [Co^III(CN)₆]}?H₂O ( 1 ) chains. They reveal a single‐molecule magnet (SMM) behavior with a large zero direct current (dc) field energy barrier, ΔE=266(12) cm^?1 (≈385 K), originating from the single‐ion property of eight‐coordinated Dy^III of an elongated dodecahedral geometry, which are embedded with diamagnetic [Co^III(CN)₆]^3? ions into zig‐zag coordination chains. The SMM character is enhanced by the external dc magnetic field, which results in the ΔE of 320(23) cm^?1 (≈460 K) at H_dc=1 kOe, and the opening of a butterfly hysteresis loop below 6 K. Complex 1 exhibits white Dy^III‐based emission realized by energy transfer from Co^III and 3‐OHpy to Dy^III. Low temperature emission spectra were correlated with SMM property giving the estimation of the zero field ΔE. 1 is a unique example of bifunctional magneto‐luminescent material combining white emission and slow magnetic relaxation with a large energy barrier, both controlled by rich structural and electronic interplay between Dy^III, 3‐OHpy, and [Co^III(CN)₆]^3?.     

A family of Group 4 metal alkoxo complexes with an M3(mu3-O) core relevant to Ziegler-Natta catalyst intermediates

Reactions of [Mg(thffo)(2)] (1) or [Ca(thffo)(2)] (2) with ZrCl(4) or HfCl(4) in a CH(2)Cl(2)/THF/CH(3)CN mixture give thermally stable neutral heterobimetallic tetranuclear complexes [M(3)M'(mu(x)-O)(mu,eta(2)-thffo)(6)(Cl)(6)] (thffo=tetrahydrofurfuroxide; M/M'/x: 3, Zr/Mg/3; 4, Hf/Mg/3; 5, Zr/Ca/4; 6, Hf/Ca/4) as colorless crystals in 75-82 % yield. X-ray diffraction studies show complexes 3-5 to contain oxo-bridged M(3) triangles that are capped by an alkaline earth metal-containing moiety to form species of C(3) symmetry. Reactions of ZrCl(4) and HfCl(4) with pure tetrahydrofurfuryl alcohol in EtOH and MeOH provide ionic complexes [M(3)(mu(3)-O)(mu,eta(2)-thffo)(3)(L)(3)(Cl)(6)]Cl (M/L: 8, Zr/EtOH; 9, Hf/EtOH; 10, Zr/MeOH) in 66-79 % yield. Complexes 8-10 consist of M(3) triangles that are analogous to those in 3-6 and possess similar overall symmetry, as shown by X-ray crystallography. Changes in the reaction conditions afforded the asymmetric neutral dimer [Zr(2)(mu-thffo)(2)(thffoH)(Cl)(6)] (7) and the homometallic [Zr(3)(mu(3)-O)(mu,eta(2)-thp)(3)(thf)(2)(Cl)(7)] (11).     

Monge–Ampère Operator on Four Dimensional Almost Complex Manifolds

We define the Monge–Ampère operator \({(i\partial {\bar{\partial }}u)^{2}}\) for continuous J-plurisubharmonic functions on four dimensional almost complex manifolds.     

A homospin iron(II) single chain magnet

Synthetic, structural and magnetic studies of a new Fe(II) single chain magnet are reported.     

Descriptive properties of families of autohomeomorphisms of the unit interval

Let H⊂C[0,1] stand for the Polish space of all increasing autohomeomorphisms of [0,1]. We show that the family of all strictly singular autohomeomorphisms is -complete. This confirms a suggestion of Graf, Mauldin and Williams. Some related results are also included.     

On boundary blow-up problems for the complex Monge-Ampère equation

We prove the regularity for some complex Monge-Ampère equations with boundary data equal to .

     

On structure of upper semicontinuity

The refinement of a Choquet theorem on (strong) upper semi-continuity and its relation to the Vainstein lemma are dealt with here. Relevance of subcontinuity is discussed. Consequently, an improvement of a characterization theorem of Dolecki and Rolewicz is achieved.     

Lactic acid derived aziridinyl alcohols as highly effective catalysts for asymmetric additions of an organozinc species to aldehydes

A straightforward synthetic route to a series of new catalysts bearing secondary hydroxyl and aziridine moieties as nucleophilic centers built on the chiral skeleton of (S)-(+)-lactic acid is described. All of the new compounds have been tested in the enantioselective addition of diethyl- and phenylethynylzinc to aryl and alkyl aldehydes, yielding the corresponding chiral alcohols in high chemical yields (up to 85%) and good ee’s of approximately 85%. The influence of the stereogenic center located at the aziridine subunit on the stereochemical outcome is also discussed.