Fixed points of some nonlinear operators in spaces of multifunctions and the Ulam stability

We prove a fixed point theorem for nonlinear operators, acting on some function spaces (of set-valued maps), which satisfy suitable inclusions. We also show some applications of it in the Ulam type stability.     

[11]Anthrahelicene on TiO2 surfaces

Helicenes are carbon-rich materials with an ordered structure that possess interesting and remarkable electronic, chiroptical, mechanical and magnetic properties either in bulk or as single molecule devices. We report on the first attempt to anchor and organize [11]anthrahelicene ([11]AH) molecules onto a metal oxide surface. Molecular structures obtained on the (110) and (011) faces of rutile titania are characterized using scanning probe microscopy. On the (110) surface, [11]AH molecules form islands that are comprised of small domains of two types that are mirror reflections of each other and have an ordered quasi-hexagonal lattice. In contrast, molecules form unordered clusters on the (011) surface. Single molecules on both faces are imaged with sub-molecular resolution.     

Effectiveness of the Oxygenation over Classical Protonolysis Reactions: A Case of Alkylzinc Complexes Incorporating an Aminoalcoholate Ligand

Alkylzinc aminoalcoholates have emerged as powerful catalysts in organic synthesis and polymerization processes. Despite extensive research, difficulties in the rational design of these catalytic systems and in-depth understanding of their modes of action have hitherto been encountered. Most of the major obstacles stem largely from the relatively limited knowledge of the structure-activity relationship of zinc catalysts. In fact, the key active species are often generated in situ via the protonolysis of the alkylzinc precursors, which precludes their isolation and detailed characterization. Herein, the effectiveness of the oxygenation over the classical protonolysis in the synthesis of zinc alkylperoxides stabilized by an aminoalcoholate ligand is demonstrated. The controlled oxygenation of a tert-butylzinc complex incorporating a pridinolum (prinol) ligand leads to well-defined a dinuclear adduct of a (prinol)ZnOOtBu moiety with the parent tBuZn(prinol) complex and a novel dimer [tBuOOZn(prinol)]₂ with terminal alkylperoxide groups. The observed reaction outcomes strongly depend on the reaction conditions. Although sparse examples of heteroleptic adducts of the [RZn(L)]_x[ROOZn(L)]_y-type are known, the herein reported homoleptic [ROOZn(L)]_x aggregate is unprecedented. Strikingly, comparative studies involving reactions between tBuZn(prinol) and tert-butylhydroperoxide or ethanol revealed that the respective seemingly simple zinc alkylperoxides, or zinc alkoxides, respectively, are not accessible via the classical alcoholysis. We believe that these game-changing results concerning multifaceted chemistry of organozinc aminoalcoholates should pave the way for more rational development of various Zn-based catalytic systems.     

Mathematical attitudes and semantic differentials

The semantic differential—one approach to attitude measurement— basically records a combination of a person's associations with a particular concept with a scaling procedure. This paper considers the implications of such a device for teachers of mathematics.     

Spatiotemporal Studies of the One-Dimensional Coordination Polymer [Fe(ebtz)2(C2H5CN)2](BF4)2: Tug of War between the Nitrile Reorientation Versus Crystal Lattice as a Tool for Tuning the Spin Crossover Properties**

Reaction of 1,2-di(tetrazol-2-yl)ethane (ebtz) with Fe(BF₄)₂⋅6 H₂O in different nitriles yields one-dimensional coordination polymers [Fe(ebtz)₂(RCN)₂](BF₄)₂⋅nRCN (n=2 for R=CH₃ ( 1 ) and n=0 for R=C₂H₅ ( 2 ) C₃H₇ ( 3 ), C₃H₅ ( 4 ), CH₂Cl ( 5 )) exhibiting spin crossover (SCO). SCO in 1 and 3 – 5 is complete and occurs above 160 K. In 2 , it is shifted to lower temperatures and is accompanied by wide hysteresis (T_1/2^↓=78 K, T_1/2^↑=123 K) and proceeds extremely slowly. Isothermal (80 K) time-resolved single-crystal X-ray diffraction studies revealed a complex nature for the HS→LS transition in 2 . An initial, slow stage is associated with shrinkage of polymeric chains and with reduction of volume at 77 % (in relation to the difference between cell volumes V_HS−V_LS) whereas only 16 % of iron(II) ions change spin state. In the second stage, an abrupt SCO occurs, associated with breathing of the crystal lattice along the direction of the Fe–nitrile bonds, while the nitriles reorient. HS→LS switching triggered by light (808 nm) reveals the coupling of spin state and nitrile orientation. The importance of this coupling was confirmed by studies of [Fe(ebtz)₂(C₂H₅CN/C₃H₇CN)₂](BF₄)₂ mixed crystals ( 2 a , 2 b ), showing a shift of T_1/2 to higher values and narrowing of the hysteresis loop concomitant with an increase of the fraction of butyronitrile. This increase reduces the capability of nitrile molecules to reorient. Density functional theory (DFT) studies of models of 1 – 5 suggest a particular possibility of 2 to adopt a low (140–145°) value of its Fe-N-C(propionitrile) angle.     

Unravelling Structural Mysteries of Simple Organozinc Alkoxides

Simple RZnOR’ alkoxides are among the first known organozinc compounds, and widespread interest in their multifaced chemistry has been driven by their fundamental significance and potential applications including various catalytic reactions. Nevertheless, their chemistry in solution and in the solid state remains both relatively poorly understood and a subject of constant debate. Herein, the synthesis and structural characterization of long-sought structural forms, a roof-like trimer [(tBuZn)₃(μ-OC(H)Ph₂)₂(μ₃-OC(H)Ph₂)] and a ladder-type tetramer [(PhZn)₄(μ-OC(H)Ph₂)₂(μ₃-OC(H)Ph₂)₂], incorporating diphenylmethanolate as a model alkoxide ligand, are reported. Both novel aggregates are robust in the solid state and resistant towards mechanical force. By using ¹H NMR and diffusion-order spectroscopy, it is demonstrated that new RZnOR’ alkoxides are kinetically labile in solution and readily undergo ligand scrambling, such as in the case of Schlenk equilibrium. The elucidated key structural issues, which have remained undiscovered for decades, significantly advance the chemistry of RZnOR’ alkoxides and should support the rational design of zinc alkoxide-based applications.     

Influence of the size and geometry of the anion binding pocket of sugar–urea anion receptors on chiral recognition

Three new chiral urea-type anion receptors were synthesized from aromatic diamines and 1-amino-1-deoxyglucose. The anion binding properties of these receptors were studied using chiral carboxylates derived from mandelic acid and three α-amino acids. We found that the size of the anion binding pocket played an important role in chiral recognition processes. The best results were obtained for 1,8-diaminoanthracene and α-amino acid anions.     

Identification of the Isomeric Dideutero p-Benzoquinones by 13C-H and 13C-D Coupling Constants

2,5- and 2,6-dideuterobenzoquinone-1,4 were prepared by a direct catalytic (NaBD₄/PdCl₂) exchange of bromine in the corresponding dibromo derivatives and the subsequent oxidation with Ag₂O. The structure of the products was unambiguously established by proton-carbon and deuteron-carbon splitting pattern of their NMR spectra.     

The Simple Synthesis of Chiral Polyazaoxacoronands Derived from α-Amino Acids

Abstract

Bisamidation of oxaloyl chloride using L-amino acid methyl ester hydrochlorides afforded chiral diesters. The following reactions of diesters with 2,2-(ethylene-dioxy)diethylamine, afforded tetramides possessing C₂ symmetry. Coupling of N-hydroxysuccinimide ester of N-benzyloxycarbonyl-L-alanine with 1,5-diamino-3-oxapentane, followed by cleavage of protecting groups, afforded an optically active diamine, which was transformed consequently into tetramide via the reaction with diglycolic acid dimethyl ester under high pressure conditions.