Homogeneous variable exponent Besov and Triebel–Lizorkin spaces

We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings.     

General non local boundary value problem for second order elliptic equation

In this paper we study a class of second order coefficient operators differential equation with general (possibly non local) boundary conditions. We obtain new results extending those given in a previous paper 1 . Existence, uniqueness and optimal regularity of the strict solution are proved in UMD spaces, using the well‐known Dore–Venni theorem.     

Synthesis of poly(isopropenylphenoxy propylene carbonate) and its facile side‐chain functionalization into hydroxy‐polyurethanes

4‐Isopropenyl phenol ( 4‐IPP ) is a versatile dual functional intermediate that can be prepared readily from bisphenol‐A ( BPA ). Through etherification with epichlorohydrin to the phenolic group of 4‐IPP , it can be converted into 4‐isopropenyl phenyl glycidyl ether ( IPGE ). On further reaction with carbon dioxide in the presence of tetra‐n‐butyl ammonium bromide ( TBAB ) as the catalyst, IPGE was transformed into 4‐isopropenylphenoxy propylene carbonate ( IPPC ) in 90% yield. Cationic polymerization of IPPC with strong acid such as trifluoromethanesulfonic acid or boron trifluoride diethyl etherate as the catalyst at ?40 °C gave a linear poly(isopropenylphenoxy propylene carbonate), poly( IPPC ), with multicyclic carbonate groups substituted uniformly at the side‐chains of the polymer. The cyclic carbonate groups of poly( IPPC ) were further reacted with different aliphatic amines and diamines resulting in formation of polymers with hydroxy‐polyurethane on side‐chains. Syntheses, characterizations of poly( IPPC ) and its conversion into hydroxy‐polyurethane crosslinked polymers were presented. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 802–808     

Arbitrage‐free call option surface construction using regression splines

In this work, we suggest a novel quadratic programming‐based algorithm to generate an arbitrage‐free call option surface. The empirical performance of the proposed method is evaluated using S&P 500 Index call options. Our results indicate that the proposed method provides a more precise fit to observed option prices than other alternative methodologies. Copyright © 2014 John Wiley & Sons, Ltd.     

Surface antimicrobial modification of polyamide by poly(hexamethylene guanidine) hydrochloride

Antimicrobial polyamide (PA) received much attention for the demand of packaging and biomedical fields. In this paper, an antimicrobial PA6 membrane was prepared via a surface chemical reaction. A highly effective antibacterial component (PHMG‐E) with terminal epoxy group was firstly synthesized via a reaction between polyhexamethylene guanidine hydrochloride (PHMG) and ethylene glycol diglycidyl ether (EGDE). Then, PHMG‐E was bonded on the surface of PA6 membrane with secondary amine reduced by borane‐tetrahydrofuran (BH₃‐THF). The antimicrobial rates of surface‐modified PA6 membrane (PA6‐PHMG) against Escherichia coli and Staphylococcus aureus were both higher than 99.99%, and the PHMG was non‐leaching due to the chemical bonding. The hydrophilicity of antibacterial PA6 membrane was also significantly improved and the mechanical performance became better.     

Non‐Covalent Functionalization of Graphene with Bisphenol A for High‐Performance Supercapacitors

The reduced graphene oxide (RGO)/bisphenol A (BPA) composites were prepared by an adsorption‐reduction method. The composites are characterized by X‐ray diffraction (XRD), UV‐vis, thermogravimetric (TG) analysis, field emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM). The results confirm that BPA is adsorbed on the basal plane of RGO by π‐π stacking interaction. Furthermore, the electrochemical behaviors were evaluated by cyclic voltammetry, galvanostatic charge/discharge techniques and electrochemical impedance spectroscopy (EIS). The results show that the RGO/BPA nanocomposites exhibit ultrahigh specific capacitance of 466 F·g^?1 at a current density of 1 A·g^?1, excellent rate capability (more than 81% retention at 10 A·g^?1 relative to 1 A·g^?1) and superior cycling stability (90% capacitance decay after 4000 cycles). Consequently, the RGO/BPA nanocomposites can be regarded as promising electrode materials for supercapacitor applications.     

Highly Stereoselective β‐Mannopyranosylation via the 1‐α‐Glycosyloxy‐isochromenylium‐4‐gold(I) Intermediates

While the gold(I)‐catalyzed glycosylation reaction with 4,6‐O‐benzylidene tethered mannosyl ortho‐alkynylbenzoates as donors falls squarely into the category of the Crich‐type β‐selective mannosylation when Ph₃PAuOTf is used as the catalyst, in that the mannosyl α‐triflates are invoked, replacement of the ^?OTf in the gold(I) complex with less nucleophilic counter anions (i.e., ^?NTf₂, ^?SbF₆, ^?BF₄, and ^?BAr₄^F) leads to complete loss of β‐selectivity with the mannosyl ortho‐alkynylbenzoate β‐donors. Nevertheless, with the α‐donors, the mannosylation reactions under the catalysis of Ph₃PAuBAr₄^F (BAr₄^F=tetrakis[3,5‐bis(trifluoromethyl)phenyl]borate) are especially highly β‐selective and accommodate a broad scope of substrates; these include glycosylation with mannosyl donors installed with a bulky TBS group at O3, donors bearing 4,6‐di‐O‐benzoyl groups, and acceptors known as sterically unmatched or hindered. For the ortho‐alkynylbenzoate β‐donors, an anomerization and glycosylation sequence can also ensure the highly β‐selective mannosylation. The 1‐α‐mannosyloxy‐isochromenylium‐4‐gold(I) complex ( Cα ), readily generated upon activation of the α‐mannosyl ortho‐alkynylbenzoate ( 1 α ) with Ph₃PAuBAr₄^F at ?35 °C, was well characterized by NMR spectroscopy; the occurrence of this species accounts for the high β‐selectivity in the present mannosylation.     

Mono‐ and Dinuclear Heteroleptic Cobalt Complexes with α‐Diimine and Polyarene Ligands

Reactions of the dimeric cobalt complex [(L^?Co)₂] ( 1 , L=[(2,6‐iPr₂C₆H₃)NC(Me)]₂) with polyarenes afforded a series of mononuclear and dinuclear complexes: [LCo(η⁴‐anthracene)] ( 2 ), [LCo(μ‐η⁴:η⁴‐naphthalene)CoL] ( 3 ), and [LCo(μ‐η⁴:η⁴‐phenanthrene)CoL] ( 4 ). The pyrene complexes [{Na₂(Et₂O)₂}{LCo(μ‐η³:η³‐pyrene)CoL}] ( 5 ) and [{Na₂(Et₂O)₃}{LCo(η³‐pyrene)}] ( 6 ) were obtained by treating precursor 1 with pyrene followed by reduction with Na metal. These complexes contain three potential redox active centers: the cobalt metal and both α‐diimine and polyarene ligands. Through a combination of X‐ray crystallography, EPR spectroscopy, magnetic susceptibility measurement, and DFT computations, the electronic configurations of these complexes were studied. It was determined that complexes 2 – 4 have a high‐spin Co^I center coupled with a radical α‐diimine ligand and a neutral polyarene ligand. Whereas, the ligand L in complexes 5 and 6 has been further reduced to the dianion, the cobalt remains in a formal (I) oxidation state, and the pyrene molecule is either neutral or monoanionic.     

Aromatic Interactions in Organocatalyst Design: Augmenting Selectivity Reversal in Iminium Ion Activation

Substituting N‐methylpyrrole for N‐methyindole in secondary‐amine‐catalysed Friedel–Crafts reactions leads to a curious erosion of enantioselectivity. In extreme cases, this substrate dependence can lead to an inversion in the sense of enantioinduction. Indeed, these closely similar transformations require two structurally distinct catalysts to obtain comparable selectivities. Herein a focussed molecular editing study is disclosed to illuminate the structural features responsible for this disparity, and thus identify lead catalyst structures to further exploit this selectivity reversal. Key to effective catalyst re‐engineering was delineating the non‐covalent interactions that manifest themselves in conformation. Herein we disclose preliminary validation that intermolecular aromatic (CH–π and cation–π) interactions between the incipient iminium cation and the indole ring system is key to rationalising selectivity reversal. This is absent in the N‐methylpyrrole alkylation, thus forming the basis of two competing enantio‐induction pathways. A simple L ‐valine catalyst has been developed that significantly augments this interaction.     

Mesoporous Silica Nanoparticles Decorated with Carbosilane Dendrons as New Non‐viral Oligonucleotide Delivery Carriers

A novel nanosystem based on mesoporous silica nanoparticles covered with carbosilane dendrons grafted on the external surface of the nanoparticles is reported. This system is able to transport single‐stranded oligonucleotide into cells, avoiding an electrostatic repulsion between the cell membrane and the negatively charged nucleic acids thanks to the cationic charge provided by the dendron coating under physiological conditions. Moreover, the presence of the highly ordered pore network inside the silica matrix would make possible to allocate other therapeutic agents within the mesopores with the aim of achieving a double delivery. First, carbosilane dendrons of second and third generation possessing ammonium or tertiary amine groups as peripheral functional groups were prepared. Hence, different strategies were tested in order to obtain their suitable grafting on the outer surface of the nanoparticles. As nucleic acid model, a single‐stranded DNA oligonucleotide tagged with a fluorescent Cy3 moiety was used to evaluate the DNA adsorption capacity. The hybrid material functionalised with the third generation of a neutral dendron showed excellent DNA binding properties. Finally, the cytotoxicity as well as the capability to deliver DNA into cells, was tested in vitro by using a human osteoblast‐like cell line, achieving good levels of internalisation of the vector DNA/carbosilane dendron‐functionalised material without affecting the cellular viability.