Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains

Using three different notions of the generalized principal eigenvalue of linear second‐order elliptic operators in unbounded domains, we derive necessary and sufficient conditions for the validity of the maximum principle, as well as for the existence of positive eigenfunctions for the Dirichlet problem. Relations between these principal eigenvalues, their simplicity, and several other properties are further discussed. © 2015 Wiley Periodicals, Inc.     

Thermal and structural investigation of random ethylene/1-hexene copolymers with high 1-hexene content

Random ethylene/1-hexene copolymers with the 1-hexene content in the range from 2 to 28 mol% were produced with a novel post-metallocene catalyst and analyzed by three techniques, FTIR, ¹³C NMR, and DSC. The 1-hexene content and the sequence distribution in the copolymers were determined by means of FTIR-M and ¹³C NMR. The crystallization behavior of the copolymers was studied by DSC under dynamic and isothermal conditions; the Avrami model was used to analyze the crystallization kinetics. It was found that both the 1-hexene content and the crystallization temperature affect the relative crystallinity. The bulk crystallization rate decreases with the 1-hexene content and reduces exponentially with an increase of T _c. The melting behavior of isothermally crystallized samples was also investigated and it was found that the melting temperatures of the copolymers under equilibrium conditions were related to the composition.     

Transfer Hydrogenation of Ketones Catalyzed by Surface‐Active Ruthenium and Rhodium Complexes in Water

An improved, high‐yield, one‐pot synthetic procedure for water‐soluble ligands functionalized with trialkyl ammonium side groups H₂N(CH₂)₂NHSO₂‐p‐C₆H₄CH₂[NMe₂(C_nH_2n+1)]⁺ ( [HL ⁿ ]⁺ ; n=8, 16) was developed. The corresponding new surface‐active complexes [(p‐cymene)RuCl( L ⁿ )] and [Cp*RhCl( L ⁿ )] (Cp*=η⁵‐C₅Me₅) were prepared and characterized. For n=16 micelles are formed in water at concentrations as low as 0.6 mM , as demonstrated by surface‐tension measurements. The complexes were used for catalytic transfer hydrogenation of ketones with formate in water. Highly active catalyst systems were obtained in the case of complexes bearing C₁₆ tails due to their ability to be adsorbed at the water/substrate interface. The scope of these catalyst systems in aqueous solutions was extended from partially water soluble aryl alkyl ketones (acetophenone, butyrophenone) to hydrophobic dialkyl ketones (2‐dodecanone).     

Solvent‐Dependent Cation Exchange in Metal–Organic Frameworks

We investigated which factors govern the critical steps of cation exchange in metal–organic frameworks by studying the effect of various solvents on the insertion of Ni²⁺ into MOF‐5 and Co²⁺ into MFU‐4l. After plotting the extent of cation insertion versus different solvent parameters, trends emerge that offer insight into the exchange processes for both systems. This approach establishes a method for understanding critical aspects of cation exchange in different MOFs and other materials.     

Rollover‐Assisted C(sp2)C(sp3) Bond Formation

Rollover cyclometalation involves bidentate heterocyclic donors, unusually acting as cyclometalated ligands. The resulting products, possessing a free donor atom, react differently from the classical cyclometalated complexes. Taking advantage of a “rollover”/“retro‐rollover” reaction sequence, a succession of oxidative addition and reductive elimination in a series of platinum(II) complexes [Pt(N,C)(Me)(PR₃)] resulted in a rare C(sp²)?C(sp³) bond formation to give the bidentate nitrogen ligands 3‐methyl‐2,2′‐bipyridine, 3,6‐dimethyl‐2,2′‐bipyridine, and 3‐methyl‐2‐(2′‐pyridyl)‐quinoline, which were isolated and characterized. The nature of the phosphane PR₃ is essential to the outcome of the reaction. This route constitutes a new method for the activation and functionalization of C?H bond in the C(3) position of bidentate heterocyclic compounds, a position usually difficult to functionalize.     

gem‐Difluorocarbadisaccharides: Restoring the exo‐Anomeric Effect

Molecular mimicry is an essential part of the development of drugs and molecular probes. In the chemical glycobiology field, although many glycomimetics have been developed in the past years, it has been considered that many failures in their use are related to the lack of the anomeric effects in these analogues. Additionally, the origin of the anomeric effects is still the subject of virulent scientific debates. Herein, by combining chemical synthesis, NMR methods, and theoretical calculations, we show that it is possible to restore the anomeric effect for an acetal when replacing one of the oxygen atoms by a CF₂ group. This result provides key findings in chemical sciences. On the one hand, it strongly suggests the key relevance of the stereoelectronic component of the anomeric effect. On the other hand, the CF₂ analogue adopts the natural glycoside conformation, which might provide new avenues for sugar‐based drug design.     

Controlled Generation of 9-Boratriptycene by Lewis Adduct Dissociation: Accessing a Non-Planar Triarylborane

A highly bent triarylborane, 9-boratriptycene, was generated in solution by selective protodeboronation of the corresponding tetra-aryl boron ate complex with the strong Brønsted acid HNTf₂. The iptycene core confers enhanced Lewis acidity to 9-boratriptycene, making it unique in terms of structure and reactivity. We studied the stereoelectronic properties of 9-boratriptycene by quantifying its association with small N- and O-centered Lewis bases, as well as with sterically hindered phosphines. The resultant Lewis adducts exhibited unique structural, spectroscopic, and photophysical properties. Beyond the high pyramidalization of the 9-boratriptycene scaffold and its low reorganization energy upon Lewis base coordination, quantum chemical calculations revealed that the absence of π donation from the triptycene aryl rings to the boron vacant p_z orbital is one of the main reasons for its high Lewis acidity.     

Mono- and Di-Fucosylated Glycans of the Parasitic Worm S. mansoni are Recognized Differently by the Innate Immune Receptor DC-SIGN

The parasitic worm, Schistosoma mansoni, expresses unusual fucosylated glycans in a stage-dependent manner that can be recognized by the human innate immune receptor DC-SIGN, thereby shaping host immune responses. We have developed a synthetic approach for mono- and bis-fucosylated LacdiNAc (LDN-F and LDN-DF, respectively), which are epitopes expressed on glycolipids and glycoproteins of S. mansoni. It is based on the use of monosaccharide building blocks having carefully selected amino-protecting groups, facilitating high yielding and stereoselective glycosylations. The molecular interaction between the synthetic glycans and DC-SIGN was studied by NMR and molecular modeling, which demonstrated that the α1,3-fucoside of LDN-F can coordinate with the Ca²⁺-ion of the canonical binding site of DC-SIGN allowing for additional interactions with the underlying LDN backbone. The 1,2-fucoside of LDN-DF can be complexed in a similar manner, however, in this binding mode GlcNAc and GalNAc of the LDN backbone are placed away from the protein surface resulting in a substantially lower binding affinity. Glycan microarray binding studies showed that the avidity and selectivity of binding is greatly enhanced when the glycans are presented multivalently, and in this format Le^x and LDN-F gave strong responsiveness, whereas no binding was detected for LDN-DF. The data indicates that S. mansoni has developed a strategy to avoid detection by DC-SIGN in a stage-dependent manner by the addition of a fucoside to a number of its ligands.