Group Analysis of Nonlinear Fin Equations

Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further applications of them. The derived Lie symmetries are used to construct exact solutions of truly nonlinear equations for the class under consideration. Nonclassical symmetries of the fin equations are discussed. Adduced results amend and essentially generalize recent works on the subject [M. Pakdemirli and A.Z. Sahin, Appl. Math. Lett., 2006, V.19, 378-384; A.H. Bokhari, A.H. Kara and F.D. Zaman, Appl. Math. Lett., 2006, V.19, 1356-1340].Comment: 6 page

Exact Solutions of a Remarkable Fin Equation

A model "remarkable" fin equation is singled out from a class of nonlinear (1+1)-dimensional fin equations. For this equation a number of exact solutions are constructed by means of using both classical Lie algorithm and different modern techniques (functional separation of variables, generalized conditional symmetries, hidden symmetries etc).Comment: 6 page

Blow up Analysis for Anomalous Granular Gases

We investigate in this article the long-time behaviour of the solutions to the energy-dependant, spatially-homogeneous, inelastic Boltzmann equation for hard spheres. This model describes a diluted gas composed of hard spheres under statistical description, that dissipates energy during collisions. We assume that the gas is "anomalous", in the sense that energy dissipation increases when temperature decreases. This allows the gas to cool down in finite time. We study existence and uniqueness of blow up profiles for this model, together with the trend to equilibrium and the cooling law associated, generalizing the classical Haff's Law for granular gases. To this end, we investigate the asymptotic behaviour of the inelastic Boltzmann equation with and without drift term by introducing new strongly "nonlinear" self-similar variables.Comment: 20

Power-law behaviour evaluation from foreign exchange market data using a wavelet transform method

Numerous studies in the literature have shown that the dynamics of many time series including observations in foreign exchange markets exhibit scaling behaviours. A simple new statistical approach, derived from the concept of the continuous wavelet transform correlation function (WTCF), is proposed for the evaluation of power-law properties from observed data. The new method reveals that foreign exchange rates obey power-laws and thus belong to the class of self-similarity processes. (C) 2009 Elsevier B.V. All rights reserved

Exact Soliton-like Solutions of the Radial Gross-Pitaevskii Equation

We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e., radial) Gross- Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the solutions can take the form of stationary dark or bright rings whose time dependence is in the phase dynamics only, or oscillating and bouncing solutions, related to the second Painlev\'e transcendent. In each case the potential can be chosen to be time-independent.Comment: 8 pages, 7 figures. Version 2: stability analysis of the dark solutio

The present status and the future of missile aerodynamics

Some recent developments in the state of the art in missile aerodynamics are reviewed. Among the subjects covered are: (1) tri-service/NASA data base, (2) wing-body interference, (3) nonlinear controls, (4) hypersonic transition, (5) vortex interference, (6) airbreathers, supersonic inlets, (7) store separation problems, (8) correlation of missile data, (9) CFD codes for complete configurations, (10) engineering prediction methods, and (11) future configurations. Suggestions are made for future research and development to advance the state of the art of missile aerodynamics