Automorphisms of p-local compact groups

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λ\lambda-symmetries for discrete equations

Following the usual definition of $\lambda$-symmetries of differential equations, we introduce the analogous concept for difference equations and apply it to some examples.Comment: 10 page

Factors Affecting Retention of Transfer Students at Linfield College

Building on the work of Tyler (2011), this paper analyzes the factors that affect the decision by transfer students at Linfield College to return for a second year. Data was obtained for transfer students from the Department of Institutional Research at Linfield College from 2009 to 2013. We estimate the logit probabilities of retention likelihood as a function of academic ability, net price, curricular engagement, extra-curricular engagement, choice of major and demographic characteristics. We find that academic ability, curricular engagement, institutional commitment, and choice of major variables may be significant factors in the retention of transfer students at Linfield College. The estimated effects and the resulting conclusions must be interpreted cautiously due to our small sample size. However, a discussion of the results shows that Linfield may be able to improve retention of transfer students through increased curricular engagement and greater departmental awareness

A Lattice Simulation of the SU(2) Vacuum Structure

In this article we analyze the vacuum structure of pure SU(2) Yang-Mills using non-perturbative techniques. Monte Carlo simulations are performed for the lattice gauge theory with external sources to obtain the effective potential. Evidence from the lattice gauge theory indicating the presence of the unstable mode in the effective potential is reported.Comment: 12 pages, latex with revtex style, figures avalable by e-mail: [email protected]

On the construction of partial difference schemes II: discrete variables and Schwarzian lattices

In the process of constructing invariant difference schemes which approximate partial differential equations we write down a procedure for discretizing an arbitrary partial differential equation on an arbitrary lattice. An open problem is the meaning of a lattice which does not satisfy the Clairaut--Schwarz--Young theorem. To analyze it we apply the procedure on a simple example, the potential Burgers equation with two different lattices, an orthogonal lattice which is invariant under the symmetries of the equation and satisfies the commutativity of the partial difference operators and an exponential lattice which is not invariant and does not satisfy the Clairaut--Schwarz--Young theorem. A discussion on the numerical results is also presented showing the different behavior of both schemes for two different exact solutions and their numerical approximations.Comment: 14 pages, 4 figure

Lie Symmetries and Exact Solutions of First Order Difference Schemes

We show that any first order ordinary differential equation with a known Lie point symmetry group can be discretized into a difference scheme with the same symmetry group. In general, the lattices are not regular ones, but must be adapted to the symmetries considered. The invariant difference schemes can be so chosen that their solutions coincide exactly with those of the original differential equation.Comment: Minor changes and journal-re

Difference schemes with point symmetries and their numerical tests

Symmetry preserving difference schemes approximating second and third order ordinary differential equations are presented. They have the same three or four-dimensional symmetry groups as the original differential equations. The new difference schemes are tested as numerical methods. The obtained numerical solutions are shown to be much more accurate than those obtained by standard methods without an increase in cost. For an example involving a solution with a singularity in the integration region the symmetry preserving scheme, contrary to standard ones, provides solutions valid beyond the singular point.Comment: 26 pages 7 figure

Lie discrete symmetries of lattice equations

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differential-difference equations. As an example of the application of the methods, we construct the discrete symmetries of the discrete Painlev\'e I equation and of the Toda lattice equation

Symmetries of differential-difference dynamical systems in a two-dimensional lattice

Classification of differential-difference equation of the form $\ddot{u}_{nm}=F_{nm}\big(t, \{u_{pq}\}|_{(p,q)\in \Gamma}\big)$ are considered according to their Lie point symmetry groups. The set $\Gamma$ represents the point $(n,m)$ and its six nearest neighbors in a two-dimensional triangular lattice. It is shown that the symmetry group can be at most 12-dimensional for abelian symmetry algebras and 13-dimensional for nonsolvable symmetry algebras.Comment: 24 pages, 1 figur