The Lie-group formalism is applied to investigate the symmetries of the Dullin-Gottwald-Holm equation φt −αφxxt +2wφx +3φφx + γφxxx = α(2φxφxx +φφxxx), which describes the unidirectional propagation of two dimensional waves in shallow water over a flat bottom. We derived the infinitesimals that admit the classical symmetry group. The reduced ordinary differential equation is further studied and...

The observed properties of elliptical galaxies are compared to the predictions of models of hierarchical galaxy formation. While the models can explain some of the observed properties, the success of the models in producing a color-magnitude relation (dependence of stellar M=L on luminosity) while failing to produce the wavelength dependence of the slope of the Fundamental Plane correlations (d...

We use simple models (the Ising model in one and two dimensions, and the spherical model in arbitrary dimension) to put to the test some recent ideas on the slow dynamics of nonequilibrium systems. In this review the focus is on the temporal evolution of two-time quantities and on the violation of the fluctuation-dissipation theorem, with special emphasis given to nonequilibrium critical dynami...

Using structural geometry, Whiteley showed that a line drawing is a correct projection of a spherical polyhedron if and only if it has a cross-section compatible with it. We here enlarge the class of drawings to which this test applies, including those of polyhedral disks. Our proof is constructive, showing how to derive all spatial interpretations, it relies on elementary synthetic geometric a...

We give a new explicit construction of n × N matrices satisfying the Restricted Isometry Property (RIP). Namely, for some ε > 0, large N and any n satisfying N1−ε ≤ n ≤ N , we construct RIP matrices of order k ≥ n and constant δ−ε. This overcomes the natural barrier k = O(n) for proofs based on small coherence, which are used in all previous explicit constructions of RIP matrices. Key ingredien...

For the spherical model with nearest-neighbour interactions, the microcanonical entropy s(ε,m) is computed analytically in the thermodynamic limit for all accessible values of the energy ε and the magnetization m per spin. The entropy is found to be a concave function, implying that the microcanonical and the canonical ensemble are equivalent, despite the long-range nature of the spherical cons...

Rotation-invariant descriptions are required in many 3D volumetric image analysis tasks. The histogram-of-oriented-gradient (HOG) is widely used in 2D images and proves to be a very robust local description. This paper concentrates on how to use the HOG feature in 3D volumetric images when rotation-invariance is concerned. This is challenging because of the complexity of 3D rotations. We presen...

We demonstrate that the existence of a Noether symmetry in f (R) theories of gravity gives rise to an additional gravitational radius, besides the standard Schwarzschild one, determining the dynamics at galactic scales. By this feature, it is possible to explain the baryonic Tully-Fisher relation and the rotation curve of gas-rich galaxies without the dark matter hypothesis. Furthermore, under ...

We prove that the quantum stress tensor for a massless scalar field in two dimensional non-self-similar Tolman-Bondi dust collapse and Vaidya radiation collapse models diverges on the Cauchy horizon, if the latter exists. The two dimensional model is obtained by suppressing angular coordinates in the corresponding four dimensional spherical model.

Studies of the Fundamental Plane of early-type galaxies, from small to intermediate redshifts, are often carried out under the guiding principle that the Fundamental Plane reflects the existence of an underlying mass-luminosity relation for such galaxies, in a scenario where elliptical galaxies are homologous systems in dynamical equilibrium. Here I will re-examine the issue of whether empirica...