Almost linearity of -bi-Lipschitz maps between real Banach spaces

Let and be real Banach spaces. A map between and is called an -bi-Lipschitz map if for all . In this note we show that if is an -bi-Lipschitz map with from onto , then is almost linear. We also show that if is a surjective -bi-Lipschitz map with , then there exists a linear isomorphism such that

where as and .

     

Exact solutions for Belousov-Zhabotinskii reaction-diffusion system

Abstract. We consider the following simplified model for the Belousou-Zhabotinskii(B-Z)reaction:     

Incremental backprojection algorithm: modification of the searching flow scheme and utilization of the relationship among projection views

A two-dimensional (2-D) search flow scheme is proposed for the incremental backprojection algorithm. In this scheme, the searching direction in a beam is determined only by the distance from the current pixel to the corresponding ray; no pixels outside the beam are involved in the procedure. In addition, the geometrical relationships between the image grids and the projection rays in different views are fully exploited to further reduce the search operations. It is found that backprojection of four views can be performed at the same time, and the search operation is only required for one of them if the number of views is even. Thus, backprojection is accomplished on a quartet-by-quartet of views basis as well as on beam-by-beam basis. These approaches not only minimize the number of search operations but also possess a simple algorithm structure. Implementation results obtained with an AST-386 computer for the incremental backprojection algorithm using this search flow scheme and the relationship among projection views show that the processing time can be reduced by a factor of about 2.     

Thermal reaction of HNCO with NO2 at moderate temperatures

The thermal reaction of HNCO with NO₂ has been studied in the temperature range of 623 to 773 K by FTIR spectrometry. Major products measured are CO₂ and NO with a small amount of N₂O. Kinetic modeling of the time resolved concentration profiles of the reactants and products, aided by the thermochemical data of various likely reactive intermediates computed by means of the BAC-MP4 method, allows us to conclude that the reaction is initiated exclusively by a new bimolecular process: with a rate constant, k₁ = 2.5 × 10¹²e^?13,100/T cm³/mols. The well-known bimolecular reaction is the only strong competitive process in this important reactive system throughout the temperature range studied. Kinetic modeling of NO formation and NO₂ decay rates gave rise to values of k₁₀ which were in close agreement with literature data. © 1993 John Wiley & Sons, Inc.     

An Electrostatic Bond Energy Model for Enthalpies of Formation of Chloroalkanes in Gaseous States

An electrostatic bond energy model is formulated to fit the enthalpies of formation and dipole moments of the alkanes and chloroalkanes. In this model, the charge distributions are calculated by an electrostatic approach similar to the "MSE" method, and the enthalpy of formation of a molecule is the sum of the bond energy terms plus the electrostatic energy of the interactions between the charges on all atoms. All parameters of this model are obtained by parameterization. The calculated dipole moments for 13 chloroalkanes and enthalpies of formation for 19 alkanes and non-geminal chloroalkanes agree with the determined values very well. To calculate the enthalpies of formation of geminal chloroalkanes, a correction mainly attributed to the van der Waals interactions in the geminal substituted group, about 24 kJ/mol per pair of geminal chlorine atoms, is introduced.