Galois 2-extensions unramified outside 2

We classify quadratic, biquadratic and degree 4 cyclic 2-rational number fields. We also classify those quadratic number fields which are not 2-rational, but have a degree 2 extension, which is Galois over Q and is 2-rational. In this case we explicitly describe the Galois group of their maximal pro-2 extension unramified outside 2 and infinity using a result of Herfort-Ribes-Zalesskii on virtually free pro-p groups.     

Melting and crystallization of poly(butylene terephthalate) by temperature‐modulated and superfast calorimetry

Quantitative temperature‐modulated differential scanning calorimetry (TMDSC) and superfast thin‐film chip calorimetry (SFCC) are applied to poly(butylene terephthalate)s (PBT) of different thermal histories. The data are compared with those of earlier measured heat capacities of semicrystalline PBT by adiabatic calorimetry and standard DSC. The solid and liquid heat capacities, which were linked to the vibrational and conformational molecular motion, serve as references for the quantitative analyses. Using TMDSC, the thermodynamic and kinetic responses are separated between glass and melting temperature. The changes in crystallinity are evaluated, along with the mobile–amorphous and rigid–amorphous fractions with glass transitions centered at 314 and 375 K. The SFCC showed a surprising bimodal change in crystallization rates with temperature, which stretches down to 300 K. The earlier reported thermal activity at about 248 K was followed by SFCC and TMDSC and could be shown to be an irreversible endotherm and is not caused by a glass transition and rigid–amorphous fraction, as assumed earlier. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1364–1377, 2006     

Renewal of basic laws and principles for polar continuum theories (Ⅺ)—consistency problems

Some consistency problems existing in continuum field theories are briefly reviewed.Three arts of consistency problems are clarified based on the renewed basic laws for polar continua.The first art discusses the consistency problems between the basic laws for polar continua.The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua.The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body.The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them.In the meantime,these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories.     

Valuing finite-lived Russian options

This paper deals with the valuation of the Russian option with finite time horizon in the framework of the Black–Scholes–Merton model. On the basis of the PDE approach to a parabolic free boundary problem, we derive Laplace transforms of the option value, the early exercise boundary and some hedging parameters. Using Abelian theorems of Laplace transforms, we characterize the early exercise boundary at a time to close to expiration as well as the well-known perpetual case in a unified way. Furthermore, we obtain a symmetric relation in the perpetual early exercise boundary. Combining the Gaver–Stehfest inversion method and the Newton method, we develop a fast algorithm for computing both the option value and the early exercise boundary in the finite time horizon.     

Two-Dimensional Regular Shock Reflection for the Pressure Gradient System of Conservation Laws

We establish the existence of a global solution to a regular reflection of a shock hitting a ramp for the pressure gradient system of equations. The set-up of the reflection is the same as that of Mach＇s experiment for the compressible Euler system, i.e., a straight shock hitting a ramp. We assume that the angle of the ramp is close to 90 degrees. The solution has a reflected bow shock wave, called the diffraction of the planar shock at the compressive corner, which is mathematically regarded as a free boundary in the self-similar variable plane. The pressure gradient system of three equations is a subsystem, and an approximation, of the full Euler system, and we offer a couple of derivations.     

The Combination and Disproportionation of Ethyl,n-Propyl,and sec-Propyl Radicals: A DFT Study

Density functional theory (B3LYP) has been applied to the problem of free radical combination and disproportionation reactions. These have been examined for the ethyl, n-propyl, and sec-propyl radicals. For the combination reactions, the enthalpy of activation fell in the range of 5 to 7 kcal/mol, which is within the limits of computational error. The transition structure of disporportionation reaction each displayed a bent C...H...C angle for the transfer of the hydrogen in contrast to earlier reports done at the semiempirical level. The activation enthalpies for the hydrogen transfer process increased with the number of attached methyl groups on the donor radical.     

Free energy of nonideal two-component thermal plasma

The free energy of nonideal two-component thermal plasma is calculated using the Poisson-Boltzmann equation. The possibility of the existence of a metastable state is shown for a component of heavy multicharged particles with particle charge values bounded from below and plasma temperature values bounded from above. The component of oppositely-charged light singly-charged particles and plasma generally do not feature the metastable state.     

The exact solution for the free induction decay in a quasi-one-dimensional system in a multi-pulse NMR experiment

The exact solution for the free induction decay in a one-dimensional system in the multi-pulse experiment is obtained at both high and low temperatures in the approximation of nearest neighbor interactions. The experimental investigation is performed on a quasi-one-dimensional system of ¹⁹F nuclear spins in a single crystal of fluorapatite. The theoretical results are in a good agreement with the obtained experimental data.