Carleman Estimates for Parabolic Equations with Nonhomogeneous Boundary Conditions

The authors prove a new Carleman estimate for general linear second order parabolic equation with nonhomogeneous boundary conditions. On the basis of this estimate, improved Carleman estimates for the Stokes system and for a system of parabolic equations with a penalty term are obtained. This system can be viewed as an approximation of the Stokes system.     

Novel Copolymers of Styrene and Alkyl and Alkoxy Ring‐Trisubstituted Methyl 2‐Cyano‐3‐phenyl‐2‐propenoates

Electrophilic trisubstituted ethylene monomers, akyl and alkoxy ring‐trisubstituted methyl 2‐cyano‐3‐phenyl‐2‐propenoates, RC₆H₂CH[dbnd]C(CN)CO₂CH_3, (where R is 2,3‐dimethyl‐4‐methoxy, 2,5‐dimethyl‐4‐methoxy‐, 2,3,4‐trimethoxy‐, 2,4,5‐trimethoxy, 2,4,6‐trimethoxy, and 2,4‐dimethoxy‐3‐methyl), were synthesized by the piperidine catalyzed Knoevenagel condensation of ring‐substituted benzaldehydes and methyl cyanoacetate, and characterized by CHN elemental analysis, IR, ¹H‐ and ¹³C‐NMR. Novel copolymers of the ethylenes and styrene were prepared at equimolar monomer feed composition by solution copolymerization in the presence of a radical initiator (AIBN) at 70°C. The composition of the copolymers was calculated from nitrogen analysis, and the structures were analyzed by IR, ¹H and ¹³C NMR, GPC, DSC, and TGA. High T_g of the copolymers in comparison with that of polystyrene indicates a substantial decrease in chain mobility of the copolymer due to the high dipolar character of the trisubstituted ethylene monomer unit. The gravimetric analysis indicated that the copolymers decompose in the 283–306°C range.     

First Synthesis of 1,3-Alternate 25,27-Dialkyloxy-5,17-diarylcalix[4]arenes-crown-6 as New Cesium Selective Extractants by Suzuki Cross-coupling Reaction

The synthesis of new 25,27-dialkyloxy-5,17-diarylcalix[4]arenes-crown-6 1a–f in 1,3-alternate conformation by Suzuki cross-coupling reaction is reported. Their conformation was determined using ¹H, ¹³C, 2D NMR and ROESY analysis, and X-ray crystallography. Extraction experiments using a two-phase solvent method involving sodium, potassium or cesium picrate showed good extraction of the cesium cation. The X-ray crystal structures of 1,3-alternate 25,27-dipropoxy-5,17-diphenylcalix[4]arene-crown-6 ether 1a and its cesium picrate complex were established. Solid-state data were used to determine the complexation behavior of these new ligands. The efficiency of calixarenes 1a–f for cesium ion extraction could be ascribed to the rigidity and flatness linkages caused by the aryl groups at the lower rim of the aromatic moieties in the calixarene skeleton. In addition, the introduction of these aromatic moieties in positions 5 and 17 enhanced the solubility of the metal complexes in organic media.     

From Pyranosuloses and Pyranosenuloses to Deoxy Hydroxyamino Sugars

Abstract

Deoxy hydroxyamino sugars represent a potentially useful series of sugar analogs owing mainly to the fact that they oxidize spontaneously to nitroxide free radicals to give spin-labeled sugar derivatives whose structure is very close to that of the parent sugar.₃ We describe herin two synthetic pathways towards these compounds, reduction of sugar oximes and conjugate addition to enolones derivatives, both in the pyranose series.     

Longitudinal Relaxation Enhancement in 1H NMR Spectroscopy of Tissue Metabolites via Spectrally Selective Excitation

Nuclear magnetic resonance spectroscopy is governed by longitudinal (T₁) relaxation. For protein and nucleic acid experiments in solutions, it is well established that apparent T₁ values can be enhanced by selective excitation of targeted resonances. The present study explores such longitudinal relaxation enhancement (LRE) effects for molecules residing in biological tissues. The longitudinal relaxation recovery of tissue resonances positioned both down‐ and upfield of the water peak were measured by spectrally selective excitation/refocusing pulses, and compared with conventional water‐suppressed, broadband‐excited counterparts at 9.4 T. Marked LRE effects with up to threefold reductions in apparent T₁ values were observed as expected for resonances in the 6–9 ppm region; remarkably, statistically significant LRE effects were also found for several non‐exchanging metabolite resonances in the 1–4 ppm region, encompassing 30–50 % decreases in apparent T₁ values. These LRE effects suggest a novel means of increasing the sensitivity of tissue‐oriented experiments, and open new vistas to investigate the nature of interactions among metabolites, water and macromolecules at a molecular level.     

Nickel‐Catalyzed Arylation,Alkenylation, and Alkynylation of Unprotected Thioglycosides at Room Temperature

Unprotected thioglycosides were effective nucleophiles for Ni⁰‐catalyzed C? S bond‐forming reaction with functionalized (hetero)aryl, alkenyl, and alkynyl halides. The functional‐group tolerance on the electrophilic partner was typically high and the anomeric selectivities of the thioglycosides were high in all cases. The efficiency of this general procedure was well‐demonstrated by the synthesis of 4‐methyl‐7‐thioumbelliferyl‐β‐D ‐cellobioside (MUS‐CB).     

High‐Yield Formation of Substituted Tetracyanobutadienes from Reaction of Ynamides with Tetracyanoethylene

A high‐yielding sequence of [2+2] cycloaddition–retroelectrocyclization of ynamides with tetracyanoethylene (TCNE) is described. The reaction provided tetracyanobutadiene (TCBD) species, which were characterized by various techniques. DFT and TD‐DFT calculations were also performed to complement experimental findings.     

Bright White‐Light Emission from a Single Organic Compound in the Solid State

White‐light‐emitting materials and devices have attracted enormous interest because of their great potential for various lighting applications. We herein describe the light‐emitting properties of a series of new difunctional organic molecules of remarkably simple structure consisting of two terminal 4‐pyridone push–pull subunits separated by a polymethylene chain. They were found to emit almost “pure” white light as a single organic compound in the solid state, as well as when incorporated in a polymer film. To the best of our knowledge, they are the simplest white‐light‐emitting organic molecules reported to date.