The weak conjecture on spherical classes

Let be the mod 2 Steenrod algebra. We construct a chain-level representation of the dual of Singer's algebraic transfer, which maps Singer's invariant-theoretic model of the dual of the Lambda algebra, , to and is the inclusion of the Dickson algebra, , into . This chain-level representation allows us to confirm the weak conjecture on spherical classes (see [9]), assuming the truth of (1) either the conjecture that the Dickson invariants of at least k = 3 variables are homologically zero in }, (2) or a conjecture on ${\mathcal{A}}$ -decomposability of the Dickson algebra in $\Gamma_k^{\wedge}$. We prove the conjecture in item (1) for k = 3 and also show a weak form of the conjecture in item (2). Received November 27, 1996; in final form March 6, 1998     

Morphology study of Nafion membranes prepared by solutions casting

The structures of Nafion membranes prepared by solutions casting from low aliphatic alcohols/water mixture solvents and N,N′‐dimethyl formamide (DMF) solvent were investigated using differential scanning calorimeter and small angle X‐ray scattering. The aggregation behavior of Nafion molecules in the casting solutions was also investigated using dynamic light scattering. We show that the morphology of membranes was strongly influenced by the conformations of Nafion molecules in the solutions. In aliphatic alcohol/water mixture solvents, which have a worse compatibility with Nafion backbones, the Nafion molecules aggregate and form fringed rod‐like structures. These primary rod‐like structures then aggregate again through fringed side chains to form secondary ionic aggregations. In DMF solvent, owing to its better compatibility with Nafion backbones, less Nafion molecules aggregate. The high degree of Nafion molecular aggregations in aliphatic alcohol/water mixture solvents leads to a high degree of hydrophobic and hydrophilic phase separation for membranes prepared by casting from Nafion/aliphatic alcohol/water solutions. However, the lower degree of molecular aggregations in DMF solvent results in a lower degree of hydrophobic and hydrophilic phase separation for membranes prepared by casting from Nafion/DMF solution. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3044–3057, 2005     

Inducing anisotropy in bulk Nd-Fe-Co-Al-B nanocrystalline alloys by quenching in magnetic field

We have observed magnetic anisotropy in bulk Nd_55−xCo_xFe₃₀Al₁₀B₅ (x=10, 15 and 20) alloys prepared by copper mold suction casting method with a presence of external magnetic field (quenching field) μ₀H=0.25 T. By changing direction of the measuring field from perpendicular to parallel one in comparison with that of the quenching field, coercive force of the alloys slightly decreases while remanent magnetization and squareness of hysteresis loop increase more clearly. It is also found that the higher Co-concentration in the alloys the larger magnetic anisotropy is induced. The structure analyses manifest nanocrystalline particles embedded in residual amorphous matrix of the alloys. The size of the particles is in range of 10-30 nm and their crystalline phases consist of Nd₂(Fe,Co)₁₄B, Nd₃Co, Nd₃Al, NdAl₂ and Nd.     

Site-selective Suzuki cross-coupling reactions of 2,3-dibromobenzofuran

The Suzuki-Miyaura reaction of 2,3-dibromobenzofuran with two equivalents of boronic acids gave 2,3-diarylbenzofurans. The reaction with one equivalent of arylboronic acids resulted in site-selective formation of 2-aryl-3-bromobenzofurans. 2,3-Diarylbenzofurans containing two different aryl groups were prepared from 2,3-dibromobenzofuran in a one-pot protocol by sequential addition of two different boronic acids.     

Synthesis and computational oxidation mechanism study of novel organosoluble aramids with high modulus by low‐temperature solution polycondensation

A series of highly organosoluble polyamides with high modulus having propeller‐shaped triarylamine were synthesized using aromatic diacid chlorides by low‐temperature solution polycondensation. The polyamide films had strong, tough, flexible, and amorphous properties. These polymers revealed electrochromic characteristics both in the visible range and near‐infrared (NIR) region, with a color change from pale yellowish at its neutral state to green and blue at its oxidized state at applied potentials ranging from 0.00 to 1.35 V. Cyclic voltammetry (CV) of the polymer films cast onto an indium tin oxide (ITO)‐coated glass substrate exhibited two reversible redox couples at potentials of 0.80–0.87 V and 1.19–1.25 V, respectively, vs. Ag/Ag⁺ in acetonitrile solution. From the combination of the experimental and computational study, we proposed an oxidation mechanism based on molecular orbital (MO) theory, which well explains the CV experimental result. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Modulation versus Templating: Fine‐Tuning of Hierarchally Porous PCN‐250 Using Fatty Acids To Engineer Guest Adsorption

Modulation and templating are two synthetic techniques that have garnered significant attention over the last several years for the preparation of hierarchically porous metal–organic frameworks (HP‐MOFs). In this study, by using fatty acids with different lengths and concentrations as dual‐functional modulators/templates, we were able to obtain HP‐MOFs with tunable mesopores that exhibit different pore diameters and locations. We found that the length and concentration of the fatty acids can determine if micelle formation occurs, which in turn dictates the porosity of the resulting HP‐MOFs. The HP‐MOFs with different mesopores differed in their performance in gas uptake and dye adsorption, and the structure–performance relationships were ascribed to the pore diameters and locations. This approach could provide a potentially universal method to efficiently introduce hierarchal mesopores into existing microporous MOF adsorbents with tunable properties.     

Carboxyboronate: A Versatile C1 Building Block

The synthesis and applications of carboxy‐MIDA‐boronate, a novel C1 building block, are described. This molecule is accessible via a ruthenium tetraoxide‐mediated cleavage of commercially available ethynyl‐MIDA‐boronate. In the course of this study, carboxy‐MIDA‐boronate was found to possess ambident reactivity towards nucleophiles. Carboxylic acid derivatization produces a broad range of previously unknown carbamoyl‐, oxycarbo‐ and thiocarboboronates. Carboxy‐MIDA‐boronate and its derivatives undergo condensations to access borylated heterocycles with boron at positions that are difficult to access using alternate methods. The resulting heterocycles participate in the Suzuki–Miyaura cross‐coupling reaction, enabling entry into diverse bis(heteroaryl) motifs. The carbon monoxide‐releasing capacity of carboxy‐MIDA‐boronate was also examined and applied in palladium‐catalyzed carbonylation.     

Solvent‐Induced Cluster‐to‐Cluster Transformation of Homoleptic Gold(I) Thiolates between Catenane and Ring‐in‐Ring Structures

Supramolecular ensembles adopting ring‐in‐ring structures are less developed compared with catenanes featuring interlocked rings. While catenanes with inter‐ring closed‐shell metallophilic interactions, such as d¹⁰–d¹⁰ Au^I–Au^I interactions, have been well‐documented, the ring‐in‐ring complexes featuring such metallophilic interactions remain underdeveloped. Herein is described an unprecedented ring‐in‐ring structure of a Au^I‐thiolate Au₁₂ cluster formed by recrystallization of a Au^I‐thiolate Au₁₀ [2]catenane from alkane solvents such as hexane, with use of a bulky dibutylfluorene‐2‐thiolate ligand. The ring‐in‐ring Au^I‐thiolate Au₁₂ cluster features inter‐ring Au^I–Au^I interactions and underwent cluster core change to form the thermodynamically more stable Au₁₀ [2]catenane structure upon dissolving in, or recrystallization from, other solvents such as CH₂Cl₂, CHCl₃, and CH₂Cl₂/MeCN. The cluster‐to‐cluster transformation process was monitored by ¹H NMR and ESI‐MS measurements. Density functional theory (DFT) calculations were performed to provide insight into the mechanism of the “ring‐in‐ring? [2]catenane” interconversions.