相关论文: Hahn decomposition and Radon-Nikodym theorem with …

In this short paper we generalise a theorem due to Kani and Rosen on decomposition of Jacobian varieties of Riemann surfaces with group action. This generalisation extends the set of Jacobians for which it is possible to obtain an isogeny…

We discuss arithmetic and Hodge-theoretic properties of the isomorphisms appearing in the decomposition theorem for quantum cohomology of blowups. These properties underpin the application to the rationality questions by…

The Hohenberg-Kohn theorem plays a fundamental role in density functional theory, which has become a basic tool for the study of electronic structure of matter. In this article, we study the Hohenberg-Kohn theorem for a class of external…

A maxitive measure is the analogue of a finitely additive measure or charge, in which the usual addition is replaced by the supremum operation. Contrarily to charges, maxitive measures often have a density. We show that maxitive measures…

Hanner's theorem is a classical theorem in the theory of retracts and extensors in topological spaces, which states that a local ANE is an ANE. While Hanner's original proof of the theorem is quite simple for separable spaces, it is rather…

Recently, many nucleon spin decompositions have been proposed in the literature, creating a lot of confusion. This revived in particular old controversies regarding the measurability of theoretically defined quantities. We propose a brief…

The Born effective charge, Z*, that describes the polarization created by collective atomic displacements, can be computed from first-principles following different techniques. We establish the connections existing between these different…

We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable $G$-flat chain admits a decomposition in set-indecomposable sub-chains. This generalizes the decomposition of sets of finite…

Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…

We provide a suitable generalisation of Pansu's differentiability theorem to general Radon measures on Carnot groups and we show that if Lipschitz maps between Carnot groups are Pansu-differentiable almost everywhere for some Radon measures…

Weak radiative hyperon decays present us with a long-standing puzzle, namely the question of validity of a hadron-level theorem proved by Hara. We briefly discuss the conflict between expectations based on Hara's theorem and experiment as…

We study eigenvalue problems for the de Rham complex on varying three dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed boundary conditions and non-constant coefficients. We provide…

The connections between the objects mentioned in the title are used to give a short proof of the Cartan--Helgason theorem and a natural construction of the compactifications.

We prove conformal versions of the local decomposition theorems of de Rham and Hiepko of a Riemannian manifold as a Riemannian or a warped product of Riemannian manifolds. Namely, we give necessary and sufficient conditions for a Riemannian…

We provide a compactness principle which is applicable to different formulations of Plateau's problem in codimension one and which is exclusively based on the theory of Radon measures and elementary comparison arguments. Exploiting some…

These notes are not intended to substitute for a course in linear algebra on reduction of endomorphisms nor an exhaustive presentation of the Dunford's decomposition. We will limit ourselves to the case where the base is R or C, and the…

A Hamilton cycle in a graph $\Gamma$ is a cycle passing through every vertex of $\Gamma$. A Hamiltonian decomposition of $\Gamma$ is a partition of its edge set into disjoint Hamilton cycles. One of the oldest results in graph theory is…

We study the computational content of the Radon-Nokodym theorem from measure theory in the framework of the representation approach to computable analysis. We define computable measurable spaces and canonical representations of the measures…

We show that if K is Rosenthal compact which can be represented by functions with countably many discontinuities then every Radon measure on K is countably determined. We also present an alternative proof of the result stating that every…

A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…