THE QUALITATIVE CONTENT OF RENEWABLE RESOURCE MODELS

This paper analyzes the extent to which standard dynamic renewable resource models possess refutable implications. Both the steady state comparative static and local comparative dynamic properties of the standard model are studied. A unified framework is developed which enables one to analyze the qualitative properties of any standard renewable resource model. This is achieved by explicitly linking the local stability, steady state comparative static, and local comparative dynamic properties of the model.     

A note on tilde algebras

A closed setE is constructed so thatA∼(E) is an inseparable Banach space but its maximal ideal space isE. Supported in part by the National Science Foundation.     

On the Limiting Steady Configurations of a Model Plasma

A model equation describing the configuration of a simple plasma maintained by external radiation is studied. A branch of steady solutions of the equation was found by Eckhaus et al. to terminate at a finite critical value of the power of the external source, and this is attributed to the discontinuous nature of a nonlinear term in the governing equation. On introducing a small parameter to render the term continuous, a second branch of solutions is constructed in a neighborhood of the termination point of the original branch. This suggests that the termination point is formed as the limit of a subcritical fold in the surface of the steady solution branch.     

L'ensemble des algèbres de Lie algébriques n'est pas Zariski-dense dans la variété des algèbres de Lie de dimensionM≧9

Sans résumé     

Observation of the nonlinear effect in relativistic Thomson scattering of electron and laser beams

Thomson scattering of high-power laser and electron beams is a good test of electrodynamics in the high-field region. We demonstrated production of high-intensity X-rays in the head-on collision of a CO₂ laser and 60-MeV electron beams at Brookhaven National Laboratory, Accelerator Test Facility. The energy of an X-ray photon was limited at 6.5 keV in the linear (lowest order) Thomson scattering, but the nonlinear (higher order) process produces higher energy X-rays. We measured the angular distribution of the high-energy X-rays and confirmed that it agrees with theoretical predictions.     

Advantages of NIR radiation use for optical determination of skin horny layer thickness with embedded TiO2 nanoparticles during tape stripping procedure

The tape stripping technique is an experimental method frequently used for reconstruction of the in-depth distribution of various topically administered substances within the horny layer of human skin, e.g., compounds contained in sunscreens. Titanium dioxide (TiO₂) nanoparticles (25–200 nm in diameter) are one such compound. Optical techniques which apply blue light are found to be suitable for reconstruction. However, the presence of particles affects the light propagation within the skin and therefore causes incorrect determination of strip thickness, leading to an improper reconstructed distribution of nanoparticle concentration revealed from the experimental data. This study evaluates the errors emerging from the use of blue (400 nm) and NIR (800 nm) radiation and finds the use of longer wavelength light more advantageous. Particles of different diameters are considered, and it is revealed that the application of small particles (25–60 nm) results in the lowest rate of error.     

On construction of symmetries from integrals of hyperbolic partial differential systems

An algorithm is proposed which allows one to construct higher symmetries of arbitrary order for some special classes of hyperbolic systems possessing integrals. The Pohlmeyer-Lund-Regge system and the open two-dimensional Toda lattices are shown to belong to the class of systems where our algorithm is applicable. __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 1, Geometry of Integrable Models, 2004.     

The study and applications of photochemical-dynamical gravity wave model I

A two-dimensional, nonlinear, compressible, diabatic, nonhydrostatic photochemical-dynamical gravity wave model has been advanced. The model includes diabetic process produced by photochemistry and the effect of gravity wave on atmospheric chemical species. In the horizontal direction, the pseudospectral method is used. The finite difference approximations are used in vertical direction z and time t. The FICE method is used to solve the model. The model results on small amplitude fluctuation are very close to those of linear theory, which demonstrates the correctness of the model.