The map H → H↓ assigns to each finite-dimensional space of smooth functions a homogeneous polynomial space of the same dimension. We discuss applications of this map in the areas of multivariate polynomial interpolation, box spline theory and polynomial ideals. §

In this paper we present new examples of homogeneous 2-nondegenerate CRmanifolds of dimension 5 and give, up to local CR-equivalence, a full classification of all CR-manifolds of this type.

We study the existence of multi-graphs which are immersed in E3(κ, τ), having constant mean curvatureH, where E3(κ, τ) is a homogeneous, simply connected 3-manifold whose isometry group has dimension 4.

Let α ≥ 1 and let (X, d, μ) be an α-homogeneous metric measure space with conformal Assouad dimension equal to α. Then there exists a weak tangent of (X, d, μ) with uniformly big 1-modulus.

Let A be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of A with coefficients in the bimodule A vanishes if and only if A is representation finite and simply connected (in the sense of Bongartz and Gabriel), if and only if the Euler characteristic of Q equals the number of indecomposable non uniserial projective injective A-mod...

We develop several results on hitting probabilities of random fields which highlight the role of the dimension of the parameter space. This yields upper and lower bounds in terms of Hausdorff measure and BesselRiesz capacity, respectively. We apply these results to a system of stochastic wave equations in spatial dimension k ≥ 1 driven by a d-dimensional spatially homogeneous additive Gaussian ...

We write a non-relativistic Lagrangian for a hierarchical universe. The equations of motion are solved numerically and the evolution of the fractal dimension is obtained for different initial conditions. We show that our model is homogeneous at the time of the last scattering, but evolves into a self-similar universe with a remarkably constant fractal dimension. We also show that the Hubble law...

We continue the classiication, begun in 11], 14] and 12], of quadratic Artin-Schelter regular algebras of global dimension 4 which map onto a twisted homogeneous coordinate ring of a quadric hypersurface in P 3. In this paper, we consider those cases where the quadric has rank 3. We also give suucient conditions for the point scheme of any quadratic regular algebra of global dimension 4 to be t...

We consider a topological class of germ complex analytic function in two variables which does not belong to its jacobian ideal. Such is quasi homogeneous. The 0-level such defines curve. Proceeding similarly the homogeneous case Genzmer and Paul (2011) (2016), we describe an algorithm computes dimension generic strata local moduli space curves.