The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing (Riemannian) metric that favors regions of high local density. The resulting locally adaptive normal distribution (LAND) is a generalization of the normal distributio...

Parameterization of 3D manifold mesh data involves embedding the mesh in some natural parametric domain, such as the plane or the sphere. Parameterization is important for many applications in geometry processing, including texture mapping, remeshing and morphing. The main objective is to generate a bijective mapping between the mesh surface and the parametric domain, which minimizes the distor...

The volumes of the surfaces of 3-dimensional Euclidean Space which are traced by a fixed point as a trajectory surface during 3-parametric motions are given by H. R. Müller [3], [4], [5] and W. Blaschke [1]. In this paper, the volumes of the trajectory surfaces of fixed points under 3-parametric homothetic motions are computed. Also, using a certain pseudo-Euclidean metric we generalized the we...

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lischitz and upper Hölder type, respectively, hold. Furthermore, we apply the a...

We present a first experimental test of the existence of Spontaneus Para-metric Up Conversion predicted in Ref. [3]. The measurement has been made using a ccd camera on the emission of a LiIO 3 crystal pumped by a 351 nm and/or a 789 nm lasers. We obtain an upper limit of 160 times on the ratio between intensity of Spontaneus Parametric Up Conversion and Spontaneous Parametric Down conversion.

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lipschitz and upper Hölder type, respectively, hold. Furthermore, we apply the ...

We consider examples of the H-type groups with the natural horizontal distribution generated by the commutation relations of the group. In the contrast with the previous studies we furnish the horizontal distribution with the Lorentzian metric, which is nondegenerate metric of index 1 instead of a positive definite quadratic form. The causal character is defined. We study the reachable set by t...

We i n vestigate the cosmological perturbation of two-scalar eld model during the reheating phase after innation. Using the exact solution of the perturbation in long-wavelength limit, which is expressed in terms of the background quantities, we analyze the behavior of the metric perturbation. The oscillating innaton eld gives rise to the parametric resonance of the massless scalar eld and this...