Purpose: To investigate the Lie groups of transformations (symmetries) approximately admitted by a finite difference discretization of a nonlinear advection equation on an unstructured mesh. Method: A recently developed technique of " approximate group analysis " is applied to a differential approximation (otherwise referred to as an equivalent differential equation) corresponding to the above ...

An expansion based on renormalization group methods for the spin correlation function in the z direction of the Heisenberg-Ising XY Z chain with an external magnetic field directed as the z axis is derived. Moreover, by using the hidden symmetries of the model, we show that the running coupling constants are small, if the coupling in the z direction is small enough, that a critical index appear...

In this chapter we show how to compute the Discrete Fourier Transform using a Fast Fourier Transform (FFT) algorithm, including not-so special case situations such as when the data to be transformed are real. In those situations, we speed up the transforms by about a factor of two by exploiting symmetries in the data and the coefficients. We end this chapter by showing how to approximate the de...

Comparison of properties of quark and leptons as well as understanding their similarities and differences is one of the milestones on the way to underlying physics. Several observations, if not accidental, can strongly affect the implications: (i) nearly tri-bimaximal character of lepton mixing, (ii) special neutrino symmetries, (iii) the QLC-relations. We consider possible connections between ...

We construct globally regular gravitating solutions, which possess only discrete symmetries. These solutions of Yang-Mills-dilaton theory may be viewed as exact (numerical) solutions of scalar gravity, by considering the dilaton as a kind of scalar graviton, or as approximate solutions of Einstein-Yang-Mills theory. We focus on platonic solutions with cubic symmetry, related to a rational map o...

By using the supersymmetry quantum mechanics method, we approximately solve the Dirac equation for the modiˇed Eckart and the modiˇed deformed Hylleraas potentials including the Coulomb-like tensor potential under spin and pseudospin symmetry. We obtain approximate energy eigenvalues and the corresponding wave functions in terms of the Jacobi polynomial under the spin and pseudospin symmetries ...

Dispersive deformations of the Monge equation uu = uux are studied using ideas originating from topological quantum field theory and the deformation quantization programme. It is shown that, to a high-order, the symmetries of the Monge equation may also be appropriately deformed, and that, if they exist at all orders, they are uniquely determined by the original deformation. This leads to eithe...

Low cost containerized shipping requires highquality stowage plans. Scalable stowage planning optimization algorithms have been developed recently. All of these algorithms, however, produce monolithic solutions that are hard for stowage coordinators to modify, which is necessary in practice due to the application of approximate optimization models. This paper introduces an approach for modifyin...

In this paper we propose the possible use of a new type of salient points we call CASS (Centers of Approximate Spherical Symmetry) that are extracted from the Multiscale Area Projection transform described in [GL12]. In particular, we show that it is possible to build graphs joining these points following maximal values of the MAPT (Radial Symmetry Graphs) and that these graphs can be used to e...

1 Restoration of chiral and U (1) A symmetries in excited hadrons. The effective restoration of SU(2) L × SU(2) R and U(1) A chiral symmetries of QCD in excited hadrons is reviewed. While the low-lying hadron spectrum is mostly shaped by the spontaneous breaking of chiral symmetry, in the high-lying hadrons the role of the quark con-densate of the vacuum becomes negligible and the chiral symmet...