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

Oscillations and stability of numerical solutions of the heat conduction equation

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform

Loop space homology associated with the mod 2 Dickson invariants

Peer reviewedPublisher PD

Evaluating Judges and Judicial Institutions: Reorienting the Perspective

Empirical scholarship on judges, judging, and judicial institutions, a staple in political science, is becoming increasingly popular in law schools. We propose that this scholarship can be improved and enhanced by greater collaboration between empirical scholars, legal theorists, and the primary subjects of the research, the judges. We recently hosted a workshop that attempted to move away from the conventional mode of involving judges and theorists in empirical research, where they serve as commentators on empirical studies that they often see as reductionist and mis-focused. Instead, we had the judges and theorists set the discussion agenda for the empiricists by describing topics that they thought were worthy of inquiry. In this essay, we explain why we think collaboration of this sort should be encouraged and draw on the workshop experience to offer suggestions for improving the quality and utility of empirical research in this area

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

Multiscale expansion and integrability properties of the lattice potential KdV equation

We apply the discrete multiscale expansion to the Lax pair and to the first few symmetries of the lattice potential Korteweg-de Vries equation. From these calculations we show that, like the lowest order secularity conditions give a nonlinear Schroedinger equation, the Lax pair gives at the same order the Zakharov and Shabat spectral problem and the symmetries the hierarchy of point and generalized symmetries of the nonlinear Schroedinger equation.Comment: 10 pages, contribution to the proceedings of the NEEDS 2007 Conferenc

Asymptotically AdS Magnetic Branes in (n+1)-dimensional Dilaton Gravity

We present a new class of asymptotically AdS magnetic solutions in ($n+1$)-dimensional dilaton gravity in the presence of an appropriate combination of three Liouville-type potentials. This class of solutions is asymptotically AdS in six and higher dimensions and yields a spacetime with longitudinal magnetic field generated by a static brane. These solutions have no curvature singularity and no horizons but have a conic geometry with a deficit angle. We find that the brane tension depends on the dilaton field and approaches a constant as the coupling constant of dilaton field goes to infinity. We generalize this class of solutions to the case of spinning magnetic solutions and find that, when one or more rotation parameters are nonzero, the brane has a net electric charge which is proportional to the magnitude of the rotation parameters. Finally, we use the counterterm method inspired by AdS/CFT correspondence and compute the conserved quantities of these spacetimes. We found that the conserved quantities do not depend on the dilaton field, which is evident from the fact that the dilaton field vanishes on the boundary at infinity.Comment: 15 page

Wild Stallion Distortion Pedal

The Wild Stallion Distortion Pedal project encompasses the research, design, implementation, PCB layout, and packaging of a distortion effect pedal for the electric guitar. This project aims to use analog circuitry in order to replicate the effect of vintage tube amplifiers to create a distortion effect. The procedure includes research, design, simulations, and prototype testing in order to produce a quality distortion effect built as a stomp pedal for the electric guitar