The Impact of European Elections on their Stock Markets

This paper seeks to provide insight on changes in the European political landscape and how these changes may affect the financial markets in Europe. By analyzing market trends in eight different European countries—Belgium, Austria, France, Germany, Netherlands, Great Britain, Switzerland and Greece—since 1990, this paper attempts to identify any significant relationships between the results of an election and the performances of the major stock indices of these countries. By comparing country index returns starting one hundred days before and ending one hundred days after each election date to a global index, this paper explores the amount of risk in each country’s stock index at times of a political change. It examines the difference in the volatility of stock markets before and after an election occurs both in the short term of five days around the event and over a longer term of one hundred days. It also investigates the impact of the implementation of the Euro on the country indices during a time of an election. The final aspect considered is the effect when there is a switch in political ideology from the controlling party before the election to the incumbent party post-election. By examining these effects around election dates through a regression model, insight is provided into the performances of markets and what investors can expect around upcoming elections

Transforming opacity verification to nonblocking verification in modular systems

We consider the verification of current-state and K-step opacity for systems modeled as interacting non-deterministic finite-state automata. We describe a new methodology for compositional opacity verification that employs abstraction, in the form of a notion called opaque observation equivalence, and that leverages existing compositional nonblocking verification algorithms. The compositional approach is based on a transformation of the system, where the transformed system is nonblocking if and only if the original one is current-state opaque. Furthermore, we prove that $K$-step opacity can also be inferred if the transformed system is nonblocking. We provide experimental results where current-state opacity is verified efficiently for a large scaled-up system

The Gambier Mapping, Revisited

We examine critically the Gambier equation and show that it is the generic linearisable equation containing, as reductions, all the second-order equations which are integrable through linearisation. We then introduce the general discrete form of this equation, the Gambier mapping, and present conditions for its integrability. Finally, we obtain the reductions of the Gambier mapping, identify their integrable forms and compute their continuous limits.Comment: 11 pages, no figures, to be published in Physica

Stability analysis for combustion fronts traveling in hydraulically resistant porous media

We study front solutions of a system that models combustion in highly hydraulically resistant porous media. The spectral stability of the fronts is tackled by a combination of energy estimates and numerical Evans function computations. Our results suggest that there is a parameter regime for which there are no unstable eigenvalues. We use recent works about partially parabolic systems to prove that in the absence of unstable eigenvalues the fronts are convectively stable.Comment: 21 pages, 4 figure

Symmetry Classification of Diatomic Molecular Chains

A symmetry classification of possible interactions in a diatomic molecular chain is provided. For nonlinear interactions the group of Lie point transformations, leaving the lattice invariant and taking solutions into solutions, is at most five-dimensional. An example is considered in which subgroups of the symmetry group are used to reduce the dynamical differential-difference equations to purely difference ones.Comment: 27 pages, one figur

When is negativity not a problem for the ultra-discrete limit?

The `ultra-discrete limit' has provided a link between integrable difference equations and cellular automata displaying soliton like solutions. In particular, this procedure generally turns strictly positive solutions of algebraic difference equations with positive coefficients into corresponding solutions to equations involving the "Max" operator. Although it certainly is the case that dropping these positivity conditions creates potential difficulties, it is still possible for solutions to persist under the ultra-discrete limit even in their absence. To recognize when this will occur, one must consider whether a certain expression, involving a measure of the rates of convergence of different terms in the difference equation and their coefficients, is equal to zero. Applications discussed include the solution of elementary ordinary difference equations, a discretization of the Hirota Bilinear Difference Equation and the identification of integrals of motion for ultra-discrete equations

Discrete and Continuous Linearizable Equations

We study the projective systems in both continuous and discrete settings. These systems are linearizable by construction and thus, obviously, integrable. We show that in the continuous case it is possible to eliminate all variables but one and reduce the system to a single differential equation. This equation is of the form of those singled-out by Painlev\'e in his quest for integrable forms. In the discrete case, we extend previous results of ours showing that, again by elimination of variables, the general projective system can be written as a mapping for a single variable. We show that this mapping is a member of the family of multilinear systems (which is not integrable in general). The continuous limit of multilinear mappings is also discussed.Comment: Plain Tex file, 14 pages, no figur