Fibre products, non-positive curvature, and decision problems

We give a criterion for fibre products to be finitely presented and use it as the basis of a construction that encodes the pathologies of finite group presentations into pairs of groups where G is a product of hyperbolic groups and P is a finitely presented subgroup. This enables us to prove that there is a finitely presented subgroup P in a biautomatic group G such that the generalized word problem for is unsolvable and P has an unsolvable conjugacy problem. An additional construction shows that there exists a compact non-positively curved polyhedron X such that is biautomatic and there is no algorithm to decide isomorphism among the finitely presented subgroups of . Received: October 7, 1999.     

Summation of series

Three approaches are considered to the summation of some ‘standard’ series: an elementary analysis, an approach based on residues, and a technique employing the digamma function and partial fractions. This last procedure is the most convenient to use, but all three techniques have their limitations.     

The effect of positive ion energy on plasma polymerization: a comparison between acrylic and propionic acids

Using a novel RF biasing technique, the energy of positive ions at a depositing substrate is controlled, independently of other parameters. Under bias conditions which gave the maximum and minimum ion energies, plasmas of propionic and acrylic acid were investigated using mass spectrometry, an ion flux probe, quartz crystal microbalance, and X-ray photoelectron spectroscopy (XPS). For both compounds investigated, the ion energy affects the deposition rate but leaves the neutral gas-phase chemistry and positive ion fluxes unchanged. The chemistry of the polymer deposit for acrylic acid is unaffected by the change in ion energy, but the chemistry of the propionic acid plasma polymer changes markedly. We argue that the results presented are consistent with the hypothesis that, under the plasma conditions explored, the carbon-carbon double bond present in acrylic acid plays a significant role in the formation of the polymer. Conversely, the absence of this bond in propionic acid leads us to conclude that positive ions contribute significantly to film formation for this compound.     

The reducibility of Ru,Pt/Ru and Pt oxide electrocatalysts as measured by temperature-programmed reduction and cyclic voltammetry

The electrochemical reduction of alkaline cryptates (222, M)⁺ has been studied on mercury electrode by normal pulse polarography, potentiostatic coulometry and cyclic voltammetry in propylene carbonate as solvent. The corresponding kinetic parameters have been calculated and compared with those obtained on solvated alkaline cations in the same medium. A more detailed study of the electrochemical reduction mechanism of the cryptate (222, K)⁺ shows that the primary product of the reduction is the unstable (222, K^o), and that the final stable products are the free ligand (222) and the amalgam K^o (Hg). The alkaline cations, when complexed by the same (222) ligand, exhibit close values of the polarographic diffusion coefficients. The specific polarographic behaviour of the cryptate (222, Cs)⁺ is described and its stability constant calculated in propylene carbonate. An analytical application of the electrochemical reduction of cryptates is also proposed.     

Ionisation corrections in the determination of impurities in solids by means of the M.S.7 mass spectrometer

Determinations on the M.S.7 mass spectrometer of a number of trace elements have been made on standard samples, whose composition had previously been determined by independent techniques and which had been tested for homogeneity. From the ratios of the apparent contents, as determined on the M.S.7, to the true contents, a correction factor is obtained. This factor depends largely on ionisation phenomena at the source, but also includes other errors. It has been shown that for a number of elements such factors depart significantly from unity and that the value for a particular impurity depends on the matrix element. The variation of the factors showed no direct connection with the electrical parameter of the source. Cooling of the electrodes produced a significant reduction in the magnitude of the correction factor in the cases of only very few elements. In the absence of independent standards of similar composition to the sample, any figures obtained by mass spectrometry must be treated with caution unless the ionisation factor for the particular impurity in the particular matrix is known. This is especially the case for certain elements (e.g., S, Zn, Pb) known to be liable to give high factors.     

Synthesis and characterization of some new polymeric peroxycarbamates

The synthesis and characterization of several polymeric peroxycarbamates prepared by successive reaction of poly(ethylene oxides), first, with diisocyanates, and then with hydroperoxides, are described in detail for bis(2,5-dimethyl-2-hydroperoxyhexane peroxycarbamate) polyethers, the chain-extended analogs of these peroxycarbamyl polyethers and for bis(α-cumyl peroxycarbamate) polyether. The polymerization of styrene with this last initiator was studied at 60, 80, and 100°C. Both low- and high-conversion polymerizations were studied. The relationship between the rates of initiation and the inverse degree of polymerization was determined.     

A PHOTORECEPTOR SYSTEM REGULATING in vivo AND in vitro PHOSPHORYLATION OF A PEA PLASMA MEMBRANE PROTEIN*

Abstract— We have continued to characterize the blue light-regulated phosphorylation of a 120 kDa pea plasma membrane protein thought to be involved in sensory transduction for phototropism (Short and Briggs, 1990, Plant Physiol. 92 , 179–185). By incubating pea stem sections in ³²P-phosphate, we show that the 120 kDa protein is phosphorylated in vivo only after blue light irradiation and that the photosensitive fluence range matches that for phototropism. Blue light induces phosphorylation of the protein in vitro as well, but the fluences required to elicit the response are at least 30-fold higher. Triton solubilization of the plasma membrane vesicles does not further alter the fluence-response relationship. Very little turnover was detected over 20 min phosphorylation time courses or by pulse-chase experiments on unirradiated, blue light pulse-irradiated, or continuously irradiated membranes. Experiments with a dark period intervening between irradiation and addition of adenosine triphosphate show the light-induced change to persist for several minutes at 30°c. Agents that disrupt the normal photochemistry of flavins preferentially inhibit the light-induced enhancement of phosphorylation, suggesting a flavin chromophore. However, exogenous free flavins do not affect the sensitivity of the response. Staphylococcus aureus V-8 proteolysis of the phosphorylated protein from membranes subjected to a range of fluences before phosphorylation shows that the radiolabel on each of three peptides increases in proportion to the phosphorylation level of the undigested polypeptide. These studies may be valuable for assessing the nature of the photoreceptor and for unravelling the early sensory transduction steps in phototropism.     

Use of region II of the a/q stability diagram for fast scanning of a linear quadrupole mass spectrometer

For evaluation as a detector for high-speed gas chromatography, a linear quadrupole mass spectrometer was operated in rf only mode by using Region II (a = 0; 7.514 < q < 7.580) of the Mathieu a/q stability diagram. The available power supply and the diameter of the quadrupole rods of the mass spectrometer placed an upper mass limit of ～ m/z 93. Scan rates of 1000 scans/s were obtained with mass spectral peaks resolved over an 80-u range The m/z 91 and 92 ions produced from the electron ionization of toluene are resolved with an R _1/2 of 135. A potential difference between the source and the quadruple mass filter of up to 1000 V was used to accelerate ions into the quadrupole. Broadening of mass-to-charge ratio peaks results from the time constant of the signal amplification rather than the small number of rf cycles the ions experience. The expected loss of sensitivity relative to Region I is observed, and the problem of mass aliasing is discussed.