A geometric formula for Haefliger knots

Haefliger has shown that a smooth embedding of the (4k−1)-sphere in the 6k-sphere can be knotted in the smooth sense. In this paper, we give a formula with which we can detect the isotopy class of such a Haefliger knot. The formula is expressed in terms of the geometric characteristics of an extension, analogous to a Seifert surface, of the given embedding. In particular, the Hopf invariant associated to the extension plays a crucial role. This leads us to a new characterisation of Haefliger knots.     

Synthesis and characterization of 6‐ and 12‐arm star polymers by nitroxide‐mediated radical polymerization of St and MA from dendritic TIPNO‐based hexafunctional and dodecafunctional macroinitiators

Dendritic multifunctional macroinitiators having six and 12 TIPNO‐based alkoxyamines, TIPNO‐6 and TIPNO‐12 , were synthesized and used in the living radical polymerization of styrene (St), methyl acrylate (MA), N,N‐dimethylacrylamide (DMAAm), and isoprene (IP). The polymerizations of St initiated with TIPNO‐6 gave 6‐arm star polymers with narrow polydispersities of 1.14–1.18. In the polymerizations of MA initiated with TIPNO‐6 and TIPNO‐12 , the influences of added TIPNO on the polydispersity indexes (PDIs) of the resulting star polymers were first investigated, and this led to the successful formation of poly(MA) star polymers with narrow polydispersities (1.10–1.18). Moreover, the polymerizations of DMAAm and IP from TIPNO‐6 in the presence or absence of TIPNO were briefly investigated. The benzyl ether bonds of the poly(St) and poly(MA) star polymers were cleaved by treating with Me₃SiI or Pd/C, and the resulting arm's parts were analyzed with SEC. The PDIs of the resulting arm parts were low (1.19–1.23), and the M_ns agreed with the M_n,theor, indicating that the poly(St) and poly(MA) star polymers had well‐controlled arms. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4364–4376, 2007     

Photo-initiated base-formation in a polymer matrix

It was found that amines were formed efficiently by the photolysis of O-acyloximes followed by hydrolysis in polystyrene films and the relationship between structures of O-acyloximes and yields of amines were investigated. O-phenylacetyl acetophenone oxime (PaApO), O-pivaloyl acetophenone oxime (PApO), and O-benzoyl acetophenone oxime (BApO) as monofunctional O-acyloximes and O,O′-succinyl diacetophenone oxime (SDApO) and O,O′-glutaryl diacetophenone oxime (GDApO) as bifunctional O-acyloximes were examined. The yields of amines for PaApO and SDApO under N₂ were ca. 70%, which was the highest among O-acyloximes examined in this experiment. On the other hand, the yields for PApO, BApO, and GDApO were less than 15% and it was verified that the hydrogen abstraction by imino radicals via 6-membered cyclic intermediates resulted in the lowering of yields. Although the effect of oxygen under photolysis on the yields of amine for PaApO was negligible under 50% conversion of PaApO, the yield decreased with further increase in the conversion and was 50% at 90% conversion. © 1994 John Wiley & Sons, Inc.     

Use of allyl, 2-tetrahydrofuryl, and 2-tetrahydropyranyl ethers as useful C3-, C4-, and C5-carbon sources: palladium-catalyzed allylation of aldehydes

Palladium-diethylzinc or palladium-triethylborane catalytically promotes self-allylation of 2-(allyloxy)tetrahydrofurans, 2-(allyloxy)tetrahydropyrans, and their hydroxy derivatives on the rings (ribose, glucose, mannose, deoxyribose, deoxyglucose). All the reactions proceed at room temperature and provide polyhydroxyl products, sharing a structural motif of a homoallyl alcohol, in good to excellent yields with high levels of stereoselectivity. Useful C3-unit elongation, which makes the best use of an allyl ether as a protecting group and a nucleophilic allylation agent, is demonstrated. Mechanisms for the umpolung reaction (of an allyl ether into an allylic anion) and stereoselectivity associated with allylation of aldehydes are discussed.     

Synthesis of block copolymer with polystyrene and nylon units

Bis-ε-aminocaproylaminocaproylhexamethylenediamine ( I ) was synthesized as an analog of 6-nylon pentamer diamine, and its incorporation into block copolymers was studied with the use of α,ω-dihydroxyl, α,ω-bisdimethylchlorosilyl, and α,ω-diepoxy polystyrene. In the course of the experiments, the stability and the reactivity of 4,4′-diphenylmethane diisocyanate and tetramethylene diisocyanate in aprotic dipolar solvents were examined by infrared spectroscopy. The only usable solvent, N-methylpyrrolidone, was found still inadequate for the synthesis involving I, diisocyanate, and α,ω-dihydroxyl polystyrene. A block copolymer having M _n = 18,000 was obtained by the reaction of I and α,ω-diepoxy polystyrene. All T_g values of the block copolymers were above 90°C, higher than for polystyrenes with corresponding molecular weight.     

Syntheses and spectrophotometric studies of 2-(2-thiazolylazo)- and 2-(2-benzothiazolylazo)-5-dimethylaminobenzoic acids as analytical reagents: Determination of nickel

2-(2-ThiazolyIazo)-5-dimethylaminobenzoic acid (TAMB) and 2-(2-benzothiazolylazo)-5-dimethylaminobenzoic acid (BTAMB) have been synthesized, and their potential for determinations of metals has been studied spectrophotometrically. Both are extremely sensitive chromogenic reagents for the determination of nickel. Molar absorptivities in aqueous methanol are 0.95 × 10⁵ (TAMB) and 1.2 × 10⁵ (BTAMB). In aqueous methanol, at apparent pH 5–9.5, the system conforms to Beer's law for 0.05–0.5 ppm nickel; Cu, Cr, Co, Pd and Fe interfere, but they can easily be masked.     

A new route to methyl (R,E)-(-)-tetradeca-2,4,5-trienoate (pheromone of Acanthoscelides obtectus) utilizing a palladium-catalyzed asymmetric allene formation reaction

[reaction: see text] A formal total synthesis of the sex attractant of male dried bean beetle, methyl (R,E)-(-)-tetradeca-2,4,5-trienoate, was achieved by a new efficient route utilizing the Pd-catalyzed asymmetric allene synthesis reaction. It was found that the atropisomeric biaryl bisphosphine (R)-segphos showed better enantioselectivity than (R)-binap in the Pd-catalyzed reaction for preparing alkyl-substituted axially chiral allenes.