We develop the theory of tamed spaces which are Dirichlet with distribution-valued lower bounds on Ricci curvature and investigate these from an Eulerian point view. To this end we analyze in detail singular perturbations form by a broad class distributions. The distributional bound is then formulated terms integrated version Bochner inequality using perturbed energy generalizing well-known Bak...

In the context of a strongly local Dirichlet space we show that if a function mapping the real line to itself (and fixing the origin) operates by composition on the left to map the Dirichlet space into itself, then the function is necessarily locally Lipschitz continuous. If, in addition, the Dirichlet space contains unbounded elements, then the function must be globally Lipschitz continuous. T...

Digital media tend to combine text and images to express richer information, especially on image hosting and online shopping websites. This trend presents a challenge in understanding the contents from different forms of information. Features representing visual information are usually sparse in high dimensional space, which makes the learning process intractable. In order to understand text an...

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Various studies highlighted that topicbased approaches give a powerful spoken content representation of documents. Nonetheless, these documents may contain more than one main theme, and their automatic transcription inevitably contains errors. In this study, we propose an original and promising framework based on a compact representation of a textual document, to solve issues related to topic s...

Inspired by a recent article on Fréchet spaces of ordinary Dirichlet series $$\sum a_n n^{-s}$$ due to J. Bonet, we study topological and geometrical properties certain scales general e^{-\lambda _n s}$$ focus the space $$\lambda $$ -Dirichlet which have limit functions bounded all half planes strictly smaller than right plane $$[{{\,\mathrm{Re}\,}}>0]$$ . We develop an abstract setting pre-Fré...