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.

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.

Algebra skills and traps and diagnostic teaching for the future

Explores on some research about teaching and learning algebra and related classroom issues. Diagnostic instruments that may be used by senior secondary teachers in teaching algebra to senior classes; Strategies for remediating algebraic difficulties and misconceptions; Impact of technology on the algebra curriculum; Usefulness of copying algebraic expressions while using Computer Algebra Systems or mathematics processing software in a calculus class.

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.

Algebra concepts and skills survey - a draft

Presents questions adapted from the 'Group Review of Algebra Topics' (ACER 1991) that form a draft survey test of 24 items ranging across aspects of algebra and secondary algebra instruction.

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.

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.

Finding higher symmetries of differential equations using the MAPLE package DESOLVII

We present and describe, with illustrative examples, the MAPLE computer algebra package DESOLVII, which is a major upgrade of DESOLV. DESOLVII now includes new routines allowing the determination of higher symmetries (contact and Lie-Backlund) for systems of both ordinary and partial differential equations.

Hedgehog partial agonism drives warburg-lie metabolism in muscle and brown fat

Diabetes, obesity, and cancer affect upward of 15% of the world’s population. Interestingly, all three diseases juxtapose dysregulated intracellular signaling with altered metabolic state. Exactly which genetic factors define stable metabolic set points in vivo remains poorly understood. Here, we show that hedgehog signaling rewires cellular metabolism. We identify a cilium-dependent Smo-Ca2+-Ampk axis that triggers rapid Warburg-like metabolic reprogramming within minutes of activation and is required for proper metabolic selectivity and flexibility. We show that Smo modulators can uncouple the Smo-Ampk axis from canonical signaling and identify cyclopamine as one of a new class of “selective partial agonists,” capable of concomitant inhibition of canonical and activation of noncanonical hedgehog signaling. Intriguingly, activation of the Smo-Ampk axis in vivo drives robust insulin-independent glucose uptake in muscle and brown adipose tissue. These data identify multiple noncanonical endpoints that are pivotal for rational design of hedgehog modulators and provide a new therapeutic avenue for obesity and diabetes.