A weak Asplund space whose dual is not weak fragmentable

Under the assumption that there exists in the unit interval an uncountable set with the property that every continuous mapping from a Baire metric space into is constant on some non-empty open subset of , we construct a Banach space such that belongs to Stegall's class but is not fragmentable.

     

A density theorem for matrix-valued radial basis functions

Recently a new class of customized radial basis functions (RBFs) was introduced. We revisit this class of RBFs and derive a density result guaranteeing that any sufficiently smooth divergence-free function can be approximated arbitrarily closely by a linear combination of members of this class. This result has potential applications to numerically solving differential equations, such as fluid flows, whose solution is divergence free. AMS subject classification 41Axx, 41A30, 41A35, 41A60Svenja Lowitzsch: The results are part of the authorss dissertation written at Texas A&M University, College Station, TX 77843, USA.     

Norm attaining functionals on

It is shown that for any infinite compact Hausdorff space , the Bishop-Phelps set in is of the first Baire category when has the supremum norm.

     

Ruthenium Oxidase Catalysis for Site‐Selective C–H Alkenylations with Ambient O2 as the Sole Oxidant

Ruthenium(II) oxidase catalysis by direct dioxygen‐coupled turnover enabled step‐economical oxidative C? H alkenylation reactions at ambient pressure. Versatile ruthenium(II) biscarboxylate catalysts displayed ample substrate scope and proved applicable to weakly coordinating and removable directing groups. The twofold C? H functionalization strategy was characterized by exceedingly mild reaction conditions as well as excellent positional selectivity.     

Conformational preferences and basicities of monofluorinated cyclopropyl amines in comparison to cyclopropylamine and 2-fluoroethylamine

Fluorine substituents in organic molecules do dramatically influence the electronic structure of neighbouring functional groups and the conformation of molecules. Hence the presence of fluorine in a compound changes its chemical reactivity and biological activity. On the basis of MP2 and SCS-MP2 calculations, we discuss the conformational preferences and basicity of the diastereoisomeric 2-fluorocyclopropylamines (cis-2 and trans-2) in comparison to those of cyclopropylamine (1) and 2-fluoroethylamine (3). 1 and 2 are viewed as model compounds for the antidepressant drug tranylcypromine (trans-2-phenylcyclopropylamine, 1a) and its fluorinated derivatives 2. The potential energy profile for the rotation of the amino group in cis-2 differs from that of trans-2 and 1 which have very similar rotational curves. For 2 the global minimum conformer is trans-2a and the lowest energy cis-conformer 2c is less stable by 2.57 kcal mol(-1). The calculated enthalpy differences between the conformers gauche-1b and s-trans-1a (2.0 kcal mol(-1)) as well as between gauche-3b and gauche-4a (0.2 kcal mol(-1)) agree well with the available experimental data of 2.0 kcal mol(-1) and 0.1 +/- 0.3 kcal mol(-1), respectively. The calculated gas phase proton affinities (PA) of 1 (217.6 kcal mol(-1)), cis-2c (215.6 kcal mol(-1)), and trans-2a (209.3 kcal mol(-1)) follow the trends of the pKa values measured in solution for the diastereomeric 2-phenylcyclopropylamines 1a and 1b and their fluorinated derivatives cis-2 and trans-2. It is shown that the conformational preferences and basicity of the investigated molecules are due to stereoelectronic effects from hyperconjugative interactions which lead to different local charge distributions and different hybridization of the nitrogen lone-pair. The basicity of gauche-3a (PA = 215.3 kcal mol(-1)) and anti-3b (PA = 210.1 kcal mol(-1)) is controlled by the charge of the nitrogen atom, while that of cis-2c and trans-2a is overlap controlled as a result of different hybridization of the nitrogen lone-pair [sp4.34 (cis-2c), sp4.07 (trans-2a)].     

Liposomal Enzyme Nanoreactors Based on Nanoconfinement for Efficient Antitumor Therapy

Enzymatic reactions can consume endogenous nutrients of tumors and produce cytotoxic species and are therefore promising tools for treating malignant tumors. Inspired by nature where enzymes are compartmentalized in membranes to achieve high reaction efficiency and separate biological processes with the environment, we develop liposomal nanoreactors that can perform enzymatic cascade reactions in the aqueous nanoconfinement of liposomes. The nanoreactors effectively inhibited tumor growth in vivo by consuming tumor nutrients (glucose and oxygen) and producing highly cytotoxic hydroxyl radicals (⋅OH). Co-compartmentalization of glucose oxidase (GOx) and horseradish peroxidase (HRP) in liposomes could increase local concentration of the intermediate product hydrogen peroxide (H₂O₂) as well as the acidity due to the generation of gluconic acid by GOx. Both H₂O₂ and acidity accelerate the second-step reaction by HRP, hence improving the overall efficiency of the cascade reaction. The biomimetic compartmentalization of enzymatic tandem reactions in biocompatible liposomes provides a promising direction for developing catalytic nanomedicines in antitumor therapy.     

Scanning tunneling microscopy and spectroscopy investigations of copper phthalocyanine adsorbed on Al2O3/Ni3Al(1 1 1)

Low temperature scanning tunneling microscopy (LT-STM) and scanning tunneling spectroscopy (STS) have been used to investigate adsorbed copper phthalocyanine (C₃₂H₁₆N₈Cu) molecules on an ordered ultrathin Al₂O₃ film on the Ni₃Al(1 1 1) surface as a function of coverage and annealing temperature. For sub-monolayer coverage and a deposition temperature of 140 K two different planar molecular adsorption configurations rotated by 30° with respect to each other were observed with submolecular resolution in the STM images. The template effect of the underlying oxide film on the CuPc orientation, however, is only weak and negligible at higher coverages. For θ_CuPc ≈ 1 ML, before completion of the first layer, the growth of a second layer was already observed. The measured spacing of 3.5 Å between first and second layer corresponds to the distance between the layers in the α-modification of crystalline CuPc. The molecules deposited at 140 K are thermally stable upon prolonged annealing to temperatures up to 250 K. By the use of STS the lowest unoccupied molecular orbital (LUMO) of the adsorbed copper phthalocyanine molecules has been identified at an energy of 1.2 eV above E_F. The lateral distribution of the electronic states of the CuPc has been analyzed and mapped by STS.     

Micellar Catalysis for Ruthenium(II)‐Catalyzed C−H Arylation: Weak‐Coordination‐Enabled C−H Activation in H2O

Chemoselective C?H arylations were accomplished through micellar catalysis by a versatile single‐component ruthenium catalyst. The strategy provided expedient access to C?H‐arylated ferrocenes with wide functional‐group tolerance and ample scope through weak chelation assistance. The sustainability of the C?H arylation was demonstrated by outstanding atom‐economy and recycling studies. Detailed computational studies provided support for a facile C?H activation through thioketone assistance.     

The Indigo Isomer Epindolidione as a Redox-Active Bridging Ligand for Diruthenium Complexes

Epindolidione (H₂L), a heteroatom-modified analogue of tetracene and a structural isomer of indigo, forms dinuclear complexes with [RuX₂]²⁺, X=bpy (2,2′-bipyridine, [ 1 ]²⁺) or pap (2-phenylazopyridine, [ 2 ]²⁺), in its doubly deprotonated bridging form μ-L²⁻. The dications in compounds meso-[ 1 ](ClO₄)₂ and meso-[ 2 ](ClO₄)₂, [X₂Ru(μ-L)RuX₂](ClO₄)₂, contain five-membered chelate rings N-C−C-O-Ru^II with π bridged metals at an intramolecular distance of 7.19 Å. Stepwise reversible oxidation and reduction is mainly ligand centered (oxidation: L²⁻; reduction: X), as deduced from EPR of one-electron oxidized and reduced intermediates and from UV/Vis/NIR spectroelectrochemistry, supported by TD-DFT calculation results. The results for [ 1 ](ClO₄)₂ and [ 2 ](ClO₄)₂ are qualitatively similar to the ones observed with the deprotonated indigo-bridged isomers with their six-membered chelate ring structures, confirming the suitability of both π systems for molecular electronics applications, low-energy absorptions, and multiple electron transfers.     

Light‐Induced Mechanistic Divergence in Gold(I) Catalysis: Revisiting the Reactivity of Diazonium Salts

In a systematic study of the Au‐catalyzed reaction of o‐alkynylphenols with aryldiazonium salts, we find that essentially the same reaction conditions lead to a change in mechanism when a light source is applied. If the reaction is carried out at room temperature using a Au^I catalyst, the diazonium salt undergoes electrophilic deauration of a vinyl Au^I intermediate and provides access to substituted azobenzofurans. If the reaction mixture is irradiated with blue LED light, C?C bond formation due to N₂‐extrusion from the diazonium salt is realized selectively, using the same starting materials without the need for an additional photo(redox) catalyst under aerobic conditions. We report a series of experiments demonstrating that the same vinyl Au^I intermediate is capable of producing the observed products under photolytic and thermal conditions. The finding that a vinyl Au^I complex can directly, without the need for an additional photo(redox) catalyst, result in C?C bond formation under photolytic conditions is contrary to the proposed mechanistic pathways suggested in the literature till date and highlights that the role of oxidation state changes in photoredox catalysis involving Au is thus far only poorly understood and may hold surprises for the future. Computational results indicate that photochemical activation can occur directly from a donor–acceptor complex formed between the vinyl Au^I intermediate and the diazonium salt.