The Euler equations for inviscid incompressible fluid flow have a Hamiltonian structure in Eulerian coordinates, the Hamiltonian operator, though, depending on the vorticity. Conservation laws arise from two sources. One parameter symmetry groups, which are completely classified, yield

This thesis is concerned with the construction of new one-parameter symmetry groups and similarity solutions for a generalisation of the one-dimensional thin film equation by the method of symmetry-enhancing constraints involving judicious equation-splitting. Firstly by Lie classical analysis we

On the occasion of Richard Hamilton’s nth birthday Abstract. We provide a detailed description of solutions of Curve Shortening in R n that are invariant under some one-parameter symmetry group of the equation, paying particular attention to geometric properties of the curves, and the asymptotic

On the occasion of Richard Hamilton’s nth birthday Abstract. We provide a detailed description of solutions of Curve Shortening in Rn that are invariant under some one-parameter symmetry group of the equation, paying particular attention to geometric properties of the curves, and the asymptotic

distributions, often leads to nonsensical answers. This is due to the so-called “labelswitching” problem, which is caused by symmetry in the likelihood of the model parameters. A frequent response to this problem is to remove the symmetry using artificial identifiability constraints. We demonstrate

model for the strong N-N interaction, one defines seven weak meson-nucleon couplings for π, ρ, and ω exchanges and according the change in isospin. These seven weak meson-nucleon couplings or another set of seven parameters in another theoretical framework characterize the hadronic weak interaction

submonoid which contains as its maximal subgroup the set of conformal transformations. We find the necessary and sufficient conditions for a vector field ξ to be the infinitesimal generator of a one-parameter submonoid of pure causal symmetries. We speculate about possible applications to gravitation

This work is concerned with branes and differential equations for one–parameter Calabi–Yau hypersurfaces in weighted projective spaces. For a certain class of B–branes we derive the inhomogeneous Picard–Fuchs equations satisfied by the brane superpotential. In this way we arrive at a prediction

Since order parameter of the chiral symmetry breaking Green Functions are a useful link between the OPE expansion and χPT we perform a calculation to the NLO in αs, working in the chiral limit, for all the 2 and 3 point ones. These Green Functions have no perturbative term in the chiral limit

We consider AF flows, i.e., one-parameter automorphism groups of a unital simple AF C ∗-algebra which leave invariant the dense union of an increasing sequence of finite-dimensional *-subalgebras, and derive two properties for these; an absence of continuous symmetry breaking and a kind of real