We study p-harmonic functions on metric measure spaces, which are formulated as minimizers to certain energy functionals. For spaces supporting a p-Poincaré inequality, we show that such functions satisfy an infinitesmal Lipschitz condition almost everywhere. This result is essentially sharp, since there are examples of metric spaces and p-harmonic functions that fail to be locally Lipschitz co...

We present MH-MGT, a multivariate technique for sampling from twice-differentiable, log-concave probability density functions. MHMGT is Metropolis-Hastings sampling using asymmetric, multivariate Gaussian proposal functions constructed from Taylor-series expansion of the log-density function. The mean of the Gaussian proposal function represents the full Newton step, and thus MH-MGT is the stoc...

Abstract In this study, we prove equality for twice partially differentiable mappings involving the double generalized fractional integral. Using established identity, offer some Simpson’s type inequalities co-ordinated convex functions in a rectangle from plane $\mathbb{R} ^{2}$ R 2 </mml:msu...

This contribution extends learning vector quantization to the domain of graphs. For this, we first identify graphs with points in some orbifold, then derive a generalized differentiable intrinsic metric, and finally extend the update rule of LVQ for generalized differentiable distance metrics. First experiments indicate that the proposed approach can perform comparable to state-of-the-art metho...

To measure the fuzziness of fuzzy sets, this paper introduces a distance-based and a fuzzy entropybased measurements. Then these measurements are generalized to measure the fuzziness of fuzzy partition, namely partition fuzziness. According to the relationship between the validity of fuzzy partition and its partition fuzziness, a family of cluster validity functions is proposed based on the mod...

We deal with finite dimensional differentiable manifolds. All items are concerned with are differentiable as well. The class of differentiability is C∞. A metric structure in a vector bundle E is a constant rank symmetric bilinear vector bundle homomorphism of E × E in the trivial bundle line bundle. We address the question whether a given gauge structure in E is metric. That is the main concer...