Morse-Palais lemma for nonsmooth functionals on normed spaces

Using elementary differential calculus we get a version of the Morse-Palais lemma. Since we do not use powerful tools in functional analysis such as the implicit theorem or flows and deformations in Banach spaces, our result does not require the -smoothness of functions nor the completeness of spaces. Therefore it is stronger than the classical one but its proof is very simple.

     

A universal kinetic equation for characterising the fractal nature of delignification of lignocellulosic materials

A kinetic model was developed, based on the power law of growth and Avrami’s nuclei growth concepts, to describe the heterogeneous nature of pulping kinetics, taking into account the effects of chemical concentration and temperature. The general form of the kinetic equation is first order with a time-dependent rate coefficient. The model was statistically tested using published data obtained from delignification of lignocellulosic materials (hemp woody core, giant reed, wheat straw, cottonwood, bamboo and flax fibres). The activation energies of the delignification range from 71 to 136 kJ/mol. The p-values obtained from the regression analysis are significantly small indicating that all the estimates of the model parameters were significant with very high levels of confidence. The correlation coefficients R ² for these models range from 0.76 to 0.98.     

Nuclear partition functions in the random phase approximation and the temperature dependence of collective states

Green functions techniques at finite temperature are used to calculate nuclear partition functions in the random phase approximation. The theory is shown to yield corrections to the results of functional methods neglecting exchange terms. We discuss the special case of a schematic model for which the level density and the temperature dependence of collective states can be worked out explicitly.     

General theory of optimal trajectory for rocket flight in a resisting medium

This paper considers the problem of optimizing the flight trajectory of a rocket vehicle moving in a resisting medium and in a general gravitational force field. General control laws for the lift, the bank angle, and the thrusting program are obtained in terms of the primer vector, the adjoint vector associated to the velocity vector. Additional relations for the case of variable thrusting and integrals of motion for flight at maximum lift-to-drag ratio and flight in a constant gravitational field are obtained.This work was supported by Air Force Grant No. AFOSR-71-2129.     

Optimum maneuvers of a skip vehicle with bounded lift constraints

This paper presents the analytical solutions of the problem of optimum maneuvering of a glide vehicle flying in the hypervelocity regime. The investigation is based on the approximation of Allen and Eggers; namely, that along the fundamental part of a reentry or ascent trajectory, the aerodynamic forces greatly exceed the components of the gravitational force in the directions tangent and normal to the flight path.The problem consists of finding an optimal control law for the lift such that the final velocity or the final altitude is maximized. This problem can be viewed as bringing the vehicle to the best condition for interception, penetration, or making an evasive maneuver.If the range is free, the optimal lift control is obtained in closed form. If the lift control is bounded, then bounded control is optimal whenever it is reached. The switching sequences for different cases are discussed, and it is shown that there are at most two switchings. Bounded lift control is always at the ends of the optimal trajectory; for the case of two switchings, the optimal trajectory has an inflection point.The authors wish to thank the National Aeronautics and Space Administration for the Grant No. NGR-06-003-033 under which this work was carried out.     

Photo-oxidation of polymers—III: Molecular weight changes in the photolysis and photo-oxidation of polystyrene

Changes of molecular weight distribution resulting from vacuum photolysis and photo-oxidation of polystyrene have been determined by gel permeation chromatography. On irradiation at 253.7 nm, crosslinking is predominant in vacuo; in the presence of oxygen, crosslinking and main chain scission occur simultaneously because of light absorption by two or more different chromophores. Main chain scission is more important than crosslinking in the photolysis and photo-oxidation of polystyrene containing cumene hydroperoxide irradiated at 313 nm or containing benzophenone irradiated in the range 320–420 nm. In this last case, main chain scission and crosslinking are both strongly inhibited if the sample contains napthalene which acts as quencher of the excited triplet state of benzophenone. Only moderate inhibition is observed in the presence of 2,6-di-t-butyl-4 methylphenol.     

New strong convergence theorem of the inertial projection and contraction method for variational inequality problems

Numerical Algorithms - In this paper, we introduce a new algorithm which combines the inertial projection and contraction method and the viscosity method for solving monotone variational inequality...     

Robust and data-driven approaches to call centers

We propose both robust and data-driven approaches to a fluid model of call centers that incorporates random arrival rates with abandonment to determine staff levels and dynamic routing policies. We test the resulting models with real data obtained from the call center of a US bank. Computational results show that the robust fluid model is significantly more tractable as compared to the data-driven one and produces overall better solutions to call centers in most experiments.     

On the role of secondary interactions in the production of bremsstrahlung spectra from a thick target

Bremsstrahlung emission, or radiation loss, is the dominant mechanism of energy dissipation of electrons at relativistic energies greater than a few MeV when it is subjected to acceleration in the field of the nucleus or of the electrons. In this study, the Monte Carlo calculations for bremsstrahlung spectra have been described for the case of a thick tungsten target with incident electron beams from 10 to 50 MeV, where secondary interactions induced by the electrons and photons in the target, such as energy loss, absorption, scattering, and (e ⁺, e ⁻)-pair production effects, were taken into account. The text was submitted by the authors in English.