FracSym: automated symbolic computation of Lie symmetries of fractional differential equations

In this paper, we present an algorithm for the systematic calculation of Lie point symmetries for fractional order differential equations (FDEs) using the method as described by Buckwar & Luchko (1998) and Gazizov, Kasatkin & Lukashchuk (2007, 2009, 2011). The method has been generalised here to allow for the determination of symmetries for FDEs with n independent variables and for systems of partial FDEs. The algorithm has been implemented in the new MAPLE package FracSym (Jefferson and Carminati 2013) which uses routines from the MAPLE symmetry packages DESOLVII (Vu, Jefferson and Carminati, 2012) and ASP (Jefferson and Carminati, 2013). We introduce FracSym by investigating the symmetries of a number of FDEs; specific forms of any arbitrary functions, which may extend the symmetry algebras, are also determined. For each of the FDEs discussed, selected invariant solutions are then presented. © 2013 Elsevier B.V. All rights reserved.

A comparative study of some computer algebra packages which determine the lie point symmetries of differential equations

The study seeks to determine which of five computer algebra packages is best at finding the Lie point symmetries of systems of partial differential equations with minimal user intervention. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. A series of systems of partial differential equations are used in the study. The paper concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie point symmetries of systems of partial differential equations.

Asymmetrical three-DOFs rotational-translational parallel-kinematics mechanisms based on lie group theory

The paper introduces four families of three-DOFs translational-rotational Parallel-Kinematics Mechanisms (PKMs) as well as the mobility analysis of such families using Lie group theory. Two of these families are mechanisms with one-rotational two-translational degrees of freedom (DOFs) and each of the other two has one-translational two-rotational DOFs. Four novel mechanisms are presented and discussed as representatives of these four families. Although these mechanisms are asymmetric, the components used to realise them are very similar and, hence, there is no great departure from the favourable modularity of parallel-kinematics mechanisms.

Growth performance, feed efficiency and fatty acid composition of juvenile Murray cod, Maccullochella peelii peelii, fed graded levels of canola and linseed oil

n two independent experiments, the effects of dietary inclusion of canola and linseed oil were evaluated in juvenile Murray cod (Maccullochella peelii peelii, Mitchell) over a 112-day period. In each experiment, fish received one of five semi-purified diets in which the dietary fish oil was replaced with canola oil (Experiment A) or linseed oil (Experiment B) in graded increments of 25% (0–100%). Murray cod receiving the graded canola and linseed oil diets ranged in final weight from 112.7 ± 7.6 to 73.8 ± 9.9 g and 93.9 ± 3.6 to 74.6 ± 2.2 g, respectively, and exhibited a negative trend in growth as the inclusion level increased. The fatty acid composition of the fillet and liver were modified extensively to reflect the fatty acid composition of the respective diets. Levels of oleic acid (18:1 n-9) and linoleic acid (18:2 n-6) increased with each level of canola oil inclusion while levels of α-linolenic acid (18:3 n-3) increased with each level of linseed oil inclusion. The concentration of n-3 highly unsaturated fatty acids in the fillet and liver decreased as the amount of vegetable oil in the diets increased. It is shown that the replacement of fish oil with vegetable oils in low fish meal diets for Murray cod is possible to a limited extent. Moreover, this study reaffirms the suggestion for the need to conduct ingredient substitution studies for longer periods and where possible to base the conclusions on regression analysis in addition to anova.

Fragmentation ; disjunction and unity : the lie of the land

The works presented interrogate a world in which lies have given us a set of metaphysical problems. The works deal with time, space and surfaces working together yet disrupted.

Lie symmetries of partial differential equations using symbolic computing

This study presents a theoretical basis for and outlines the method of finding the Lie point symmetries of systems of partial differential equations. It seeks to determine which of five computer algebra packages is best at finding these symmetries. The chosen packages are LIEPDE and DIMSYM for REDUCE, LIE and BIGLIE for MUMATH, DESOLV for MAPLE, and MATHLIE for MATHEMATICA. This work concludes that while all of the computer packages are useful, DESOLV appears to be the most successful system at determining the complete set of Lie symmetries. Also, the study describes REDUCEVAR, a new package for MAPLE, that reduces the number of independent variables in systems of partial differential equations, using particular Lie point symmetries. It outlines the results of some testing carried out on this package. It concludes that REDUCEVAR is a very useful tool in performing the reduction of independent variables according to Lie's theory and is highly accurate in identifying cases where the symmetries are not suitable for finding S/G equations.

The running lie

The thesis consists of a novel entitled, The Running Lie, and an exegesis of 10,000 words. The novel is based on themes of maturation and homosexuality.

Transient temperature distribution in functionally graded graphite/Polymer nanocomposites based on temperature dependent properties

Transient heat conduction in a functionally graded graphite/polymer nanocomposite (FGN) plate is analyzed using finite element method (FEM). Stepwise gradient structure consisted of four different nanocomposite layers with 0, 5, 10 and 20 wt% of graphite. Thermal conductivity and specific heat capacity of the individual layers were determined using C-Therm TCi Thermal Conductivity Analyzer (Canada) in temperature range of -20 to 100 °C. Temperature history and temperature distribution across the thickness of the plate with two different configurations for two positive and negative temperature gradients are presented.