Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to either of the editors-in-chief, Chandler Davis or Marjorie Senechal.     

Differential inhibition of postnatal brain,spinal cord and body growth by a growth hormone antagonist

Background  

Growth hormone (GH) plays an incompletely understood role in the development of the central nervous system (CNS). In this study, we use transgenic mice expressing a growth hormone antagonist (GHA) to explore the role of GH in regulating postnatal brain, spinal cord and body growth into adulthood. The GHA transgene encodes a protein that inhibits the binding of GH to its receptor, specifically antagonizing the trophic effects of endogenous GH.     

Experimental evidence for a reduction in electron thermal diffusion due to trapped particles

New high time resolution measurements of the electron thermal diffusion χ(e) throughout the sawtooth cycle of the Madison Symmetric Torus reversed-field pinch have been made by utilizing the enhanced capabilities of the upgraded multipoint, multipulse Thomson scattering system. These measurements are compared to the χ(e) due to magnetic diffusion predicted by using information from a new high spectral resolution zero-β nonlinear resistive magnetohydrodynamic simulation performed, for the first time, at the Lundquist number of high current Madison Symmetric Torus plasmas (S≈4×10(6)). Agreement between the measured and predicted values is found only if the reduction in thermal diffusion due to trapped particles is taken into account.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

用红外光谱法研究麦秸各层面的化学组成

本文以麦秸为例 ,用红外OMNI采样器研究了麦秸各层面红外光谱的差异 ,并进一步研究了麦草表面在不同的处理条件下 ,表面化学成分的变化规律。实验结果表明 :麦秸表面聚积着大量的SiO2 (～ 1 0 70cm- 1 ～ 80 0cm- 1 ) ,麦秸表皮层脂类物质含量高 (νCO =1 733cm- 1 )。麦秸表面的羟基 (～ 330 0cm- 1 )物质很少。麦秸的中层和内层主要是木素 ( 1 731 ,1 65 0 ,1 5 95 ,1 5 0 5 1 ,1 45 5 ,1 42 5 ,1 2 34,1 0 39和 835cm- 1 )和纤维素类物质 ( 335 0 ,2 935 ,2 85 0 ,1 65 0 ,1 45 5 ,1 430 ,1 367,1 31 7,1 1 60 ,1 0 34和 891cm- 1 )。木素的含量由外向里逐渐减少。麦秸表面的SiO2 是人造板制造中麦草不易粘接的主要原因。用热水处理后 ,表面仅有部分简单的碳水化合物和少量脂类物质溶出 ,而用NaOH处理麦草 ,可使表面的脂类物质和SiO2 溶出 ,便于人造板加工。     

Theoretical study of substituent and solvent effects on the thermodynamics for <Emphasis Type="Italic">cis</Emphasis>/<Emphasis Type="Italic">trans</Emphasis> isomerization and intramolecular rearrangements of 2,2′-diphenoquinones

Enthalpies (Δ_isom H _(g)^o), Gibbs free energies (Δ_isom G _(g)^o), and equilibrium constants (log K _isom) for the trans → cis isomerization of various 3,3′-, 4,4′-, and 5,5′- disubstituted 2,2′-diphenoquinones with a range of electron withdrawing and releasing moieties (methyl, fluoro, chloro, bromo, trifluoromethyl, and amino) were calculated in the gas phase and in the solvent phase (n-hexane, benzene, n-octanol, acetonitrile, and water). In the gas phase, the trans isomer of the parent and all substituted 2,2′-diphenoquinones is predicted to be more thermodynamically stable than the cis configuration, with log K _isom ranging from −2.8 to −7.0. For all compounds, increasing solvent polarity/proticity progressively favors shifting the cis/trans equilibrium towards greater contributions of the cis configuration and substantially increases the log K _isom by up to 5.1 units relative to the gas phase. In polar protic and polar aprotic solvents, the estimated log K _isom ranges as low as −0.4, indicating significant populations of the cis isomers should be present. The findings support the polar solvent phase mechanistic predictions for a cis configuration of 2,2′-diphenoquinones participating in the thermal transformation of trans-2,2′-diphenoquinones to oxepino[2,3-b]benzofurans. With limited exceptions for some amino derivatives, the cis-2,2′-diphenoquinone to oxepino[2,3-b]benzofuran isomerization is expected to be thermodynamically favorable for all substituents/phases under consideration. The cis-2,2′-diphenoquinone to oxepino[2,3-b]benzofuran rearrangement is predicted to become less thermodynamically favored with increasing solvent polarity/proticity.     

Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua

This work elaborates upon two robust models of gradient elasticity and gradient plasticity, and one gradient model of heat transfer, as originally advocated by the second author in the 1980’s. The objective is, after recalling the links between these models and existing generalized continuum theories as developed in the 1960’s and subsequently, to apply the same methodology to the case of diffusion with a view to establishing generalized transport equations. Aifantis double diffusivity and conductivity theory that provides generalized mass or heat transfer equations is compared to micromorphic-type hyper-temperature and micro-entropy proposals. The double temperature and the micromorphic thermal models are shown to lead to equations more general that Cattaneo’s. The sign of the coefficient of the second time-derivative of temperature is found to differ according to both approaches. The double temperature model contains a fourth space derivative term not present in the micromorphic models. Such generalized equations can be useful, for example, in the interpretation of recent femtosecond laser experiments on metals.