The separability of the Gauss map and the reflexivity for a projective surface

It is known that if a projective variety X in P ^N is reflexive with respect to the projective dual, then the Gauss map of X defined by embedded tangent spaces is separable, and moreover that the converse is not true in general. We prove that the converse holds under the assumption that X is of dimension two. Explaining the subtleness of the problem, we present an example of smooth projective surfaces in arbitrary positive characteristic, which gives a negative answer to a question raised by S. Kleiman and R. Piene on the inseparability of the Gauss map.      

Constraints on four-Fermi contact interactions from low-energy electroweak experiments

We investigate the constraints on four-Fermi contact interactions from low-energy lepton-quark and lepton-lepton scattering experiments – polarization asymmetries in electron (muon)-nucleon scattering experiments, cesium and thallium atom parity violation measurements, neutrino-nuclei and neutrino-electron scattering experiments. These constraints are then combined by assuming the lepton and quark universalities and gauge invariance of the contact interaction, which leave independent six lepton-quark and three pure-leptonic interactions. Impacts of these constraints on models with an additional -boson are briefly discussed. We also present updates of the low-energy constraints on the and parameters. Received: 28 November 1997 / Published online: 26 February 1998     

Hyperfine interaction of13O and23Mg implanted in Pt

The spin relaxation timeT ₁ for short-lived beta emitters¹³O and²³Mg implanted in Pt have been measured for the first time;T ₁T¹³O) = 2.90 ±0.65 Ks andT ₁ T(²³Mg) = 1665 ±140 Ks. The Knight shift for¹³O in Pt was measured at 300 K to beK(¹³O) = +(4.23 ±0.14) × 10^–3. In the case of¹³O, the Knight shift is unusually large and the relaxation time is unusually fast compared with other interstitial impurities in Pt. A KKR band-structure calculation reproduces the present large Knight shift fairly well.     

Locally sulfonated poly(ether sulfone)s with highly sulfonated units as proton exchange membrane

Novel locally sulfonated poly(ether sulfone)s with highly sulfonated units were successfully synthesized for fuel cell applications. Poly(ether sulfone)s were prepared by the nucleophilic substitution of bis(4‐fluorophenyl) sulfone with 1,2,4,5‐tetrakis([1,1′‐biphenyl]‐2‐oxy)‐3,6‐bis(4‐hydroxyphenoxy)benzene and bis(4‐hydroxyphenyl) sulfide, followed by oxidation using m‐chloroperoxybenzoic acid. The desired highly sulfonated units were easily introduced by postsulfonation and each one had ten sulfonic acid groups. The sulfonated polymers gave tough, flexible, and transparent membranes by solvent casting. The high contrast in polarity between highly sulfonated units and hydrophobic poly(ether sulfone) units enabled the formation of defined phase‐separated structures and well‐connected proton paths. The sulfonated polymers exhibited excellent proton conductivity over a wide range of relative humidities. The proton conductivity of the sulfonated polymer with an ion exchange capacity value of 2.38 mequiv/g was comparable to that of Nafion 117 even at 30% relative humidity. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3444–3453, 2009     

Radical polymerization of alkyl crotonates as 1,2-disubstituted ethylenes leading to thermally stable substituted polymethylene

Radical polymerization of several alkyl crotonates (RCr) was carried out in bulk or in benzene in the presence of radical initiators. Homopolymerization of RCr bearing bulky ester alkyl groups, e.g. tert-butyl (tBCr), 1-adamantyl (AdCr), and 3,5-dimethyl-1-adamantyl crotonate (DMAdCr) proceeded to give a polymer with molecular weight of several thousands despite of the steric hindrance and chain transfer by the presence of the β-methyl group, while the methyl and ethyl esters gave no polymer. The kinetics of the polymerization was examined in detail and absolute rate constants were evaluated by means of electron spin resonance spectroscopy. The propagation rate constants of RCr were 0.41–1.0 L/mol s, being much smaller than those of the corresponding methacrylates (530–570 L/mol s). The termination rate constants were also determined from the analyses of steady state and non-steady state polymerizations. Radical copolymerizations of AdCr (M₂) with several vinyl monomers (M₁) were carried out in bulk at 60°C and the rate constants for cross propagations were calculated to examine reactivities of the monomer and its polymer radical. The structure and thermal properties of the resulting poly (AdCr) were also investigated. Onset temperature of decomposition and glass transition temperature of poly(AdCr) were revealed to be much high as 302 and 234°C, respectively. © 1994 John Wiley & Sons, Inc.     

Isopropenyldihydrofuran derivatives. Preparation and reactions of some isopropenyldihydrofurandicarboxylates

Diethyl 5-isopropenyl-4,5-dihydrofuran-2,3-dicarboxylate 1a and methyl 5-isopropenyl-3-methoxy-carbonyl-4,5-dihydrofuran-2-acetate 2a were prepared by cylization of diethyl 2-oxosuccinate or dimethyl 3-oxoglutarate with (E)-1,4-dibromo-2-methyl-2-butene. Their chemical properties were studied.     

The reaction of perfluorobicyclic ethers and perfluorospiro-ethers with anhydrous aluminum chloride

Perfluorobicyclic ethers and perfluorospiroethers, all containing an oxolane skeleton, were treated with AlCl₃ in a heterogeneous manner to give the corresponding α,α,α′-trichlorinated and α,α-dichlorinated products, respectively. From perfluoroacetal compounds, for example, perfluoro(8-methoxy-7-oxabicyclo- [4.3.0]nonane), mono- and di-chlorinated products, i.e. perfluoro- (8-chloro-8-methoxy-7-oxabicyclo[4.3.0]nonane) and perfluoro- (8,8-dichloro-7-oxabicyclo[4.3.0]nonane) were obtained in good yields. The action of fuming sulfuric acid on these polychlorinated products led to the formation of the corresponding lactones. Perfluoro(6-chloro-7-oxa-8-oxobicyclo[4.3.0]nonane) was treated with (CH₃)₂NLi to give N,N-dimethylundecafluoro-2-oxocyclohexyl- acetamide.     

Errata to “A revised taxonomy of the ammonoid genus Desmoceras from Japan and southern Sakhalin”: [Proc. Jpn. Acad., Ser. B 80, No. 5, 225–229 (2004)]

Based on the stratigraphically well sorted material from Japan and southern Sakhalin, the ammonoid species belonging to the genus Desmoceras are classified as follows in ascending order: D. latidorsatum (Michelin) (Middle to mid-Upper Albian), D. dawsoni shikokuense (Yabe and Shimizu) (Upper Albian), D. kossmati Matsumoto (uppermost Albian–Lower Cenomanian), D. japonicum Yabe (uppermost Albian–Cenomanian), and D. ezoanum Matsumoto (mid-Upper Cenomanian–mid-Lower Turonian). D. japonicum can be subdivided into the earlier and later subspecies. D. poronaicum Yabe is a junior synonym of D. japonicum. Despite the scarcely ornamented shell, each taxon can be defined by its own characters.     

Millimeter-Wave over Fiber Systems Using Hybrid OCDM/WDM Transmission

In this paper, we propose and simulate 2 OCDM × 4 WDM transmission system for a millimeter-wave (60 GHz) over fiber system to be used in broadband wireless access networks (BWANs). The general system setup is devised and the necessary building blocks identified. Results gathered (for a 155 Mbit/s per user system) under worst case parameter specifications and settings suggest indicate that system performance is severely limited by optical multiuser interference (OMUI) penalties. Several methods to reduce the OMUI limitations are described. These methods should ensure that this transmission scheme possible wavelength-reuse option for future MMW BWANs.