20,297 research outputs found
-symmetries for discrete equations
Following the usual definition of -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
are considered
according to their Lie point symmetry groups. The set represents the
point 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
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