نتایج جستجو برای: differential forms

تعداد نتایج: 545161  

2008
ANNA WIENHARD

Various exotic cohomology groups can be defined by imposing boundedness conditions on cochains. This note discusses what happens if we impose boundedness conditions in the standard deRham complex of differential forms on a Riemannian manifold and surveys relations of the resulting bounded deRham cohomology to bounded cohomology and l∞-cohomology.

Journal: :Math. Comput. 2014
Douglas N. Arnold Gerard Awanou

We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the serendipity finite elements and the rectangular BDM elements. In three dimensions they include a recent generalization of the serendipity spaces, and new H(curl)...

2008
MIKHAIL BELISHEV VLADIMIR SHARAFUTDINOV

We define the Dirichlet to Neumann operator on exterior differential forms for a compact Riemannian manifold with boundary and prove that the real additive cohomology structure of the manifold is determined by the DN operator. In particular, an explicit formula is obtained which expresses Betti numbers of the manifold through the DN operator. We express also the Hilbert transform through the DN...

2009
Jürgen Mimkes

Econophysics is the transfer of methods from natural to socio-economic sciences. This concept has first been applied to finance, but it is now also used in various applications of economics and social sciences [2,3]. The present paper focuses on problems in macro economics and growth. 1. Neoclassical theory [4, 5] neglects the “ex post” property of income and growth. Income Y(K, L) is assumed t...

2016

In this thesis we study calculus of variations for differential forms. In the first part we develop the framework of direct methods of calculus of variations in the context of minimization problems for functionals of one or several differential forms of the type, ∫

Journal: :Foundations of Computational Mathematics 2011
Patrick Mullen Alexander McKenzie Dmitry Pavlov L. Durant Yiying Tong Eva Kanso Jerrold E. Marsden Mathieu Desbrun

In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan’s homotopy formula and a discret...

2008
ALEXANDRU DIMCA

We introduce in this paper a hypercohomology version of the resonance varieties and obtain some relations to the characteristic varieties of rank one local systems on a smooth quasi-projective complex variety M , see Theorem (3.1) and Corollaries (3.2) and (4.2). A logarithmic resonance variety is also considered in Proposition (4.5). As an application, we determine the first characteristic var...

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