we study the notion of harmonicity in the sense of symplectic geometry, and investigate the geometric properties of harmonic thom forms and distributional thom currents, dual to different types of submanifolds. we show that the harmonic thom form associated to a symplectic submanifold is nowhere vanishing. we also construct symplectic smoothing operators which preserve the harmonicity of distri...

We study fine properties of currents in the framework of geometric measure theory on metric spaces developed by Ambrosio and Kirchheim, and we prove a rectifiability criterion for flat currents of finite mass. We apply these tools to study the structure of the distributional Jacobians of functions in the space BnV, defined by Jerrard and Soner. We define the subspace of special functions of bou...

We show that the de Rham theorem, interpreted as the isomorphism between distributional de Rham cohomology and simplicial homology in the dual dimension for a simplicial decomposition of a compact oriented manifold, is a straightforward consequence of elementary properties of currents. The explicit construction of this isomorphism extends to other cases, such as relative and absolute cohomology...

Cephalopods (nautiluses, cuttlefishes, squids and octopuses) exhibit direct development and display two major developmental modes: planktonic and benthic. Planktonic hatchlings are small and go through some degree of morphological changes during the planktonic phase, which can last from days to months, with ocean currents enhancing their dispersal capacity. Benthic hatchlings are usually large,...

Over the last decades the research on monetary policy has largely concentrated on the impact of monetary authorities’ decisions on inflation and the fine-tuning of the macroeconomic, so that distributional effects of monetary policy which are non-trivial has been ignored. A view that has become increasingly popular since the financial crisis 2008 is that expansionary monetary policy can exacerb...

in the present paper, measure differential equations involving the distributional henstock-kurzweil integral are investigated. theorems on the existence and structure of the set of solutions are established by using schauder$^prime s$ fixed point theorem and vidossich theorem. two examples of the main results paper are presented. the new results are generalizations of some previous results in t...

The purpose of this article is to survey recent results on distributional properties of random binary search trees. In particular we consider the profile and the height.