相关论文: Hahn decomposition and Radon-Nikodym theorem with …
A compact space $K$ is Radon-Nikod\'{y}m if there is a lower semi-continuous metric fragmenting $K$. In this note, we show that, under $\diamondsuit (\mathrm{non}{\mathcal{M}})$, there is a Radon-Nikod\'{y}m compact space of weight…
Recently, the charge radius of the proton was extracted for the first time from muonic hydrogen. The value obtained is five standard deviations away from similar measurements of regular hydrogen. This talk discusses work done in…
The motion of a system of particles under electromagnetic interaction is considered. Under the assumption that the force acting on an electric charge is given by the sum of the electromagnetic fields produced by any other charged particles…
A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information…
On compact Riemannian manifolds, we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.
A charge-monopole theory is derived from simple and self-evident postulates. Charges and monopoles take an analogous theoretical structure. It is proved that charges interact with free waves emitted from monopoles but not with the…
We develop a Helmholtz-like theorem for differential forms in Euclidean space $E_{n}$ using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannian manifolds, $R_{n}$, which, by virtue of the…
This paper investigates Voevodsky's univalence axiom in intensional Martin-L\"of type theory. In particular, it looks at how univalence can be derived from simpler axioms. We first present some existing work, collected together from various…
The evolution of a hadronic system after its chemical decomposition is described through a model that conserves the hadronic multiplicities to their values at chemical freeze-out. The state of the system is found as function of temperature…
A quantum expectation is a positive linear functional of norm one on a non-commutative probability space (i.e., a C*-algebra). For a given pair of quantum expectations $\mu$ and $\lambda$ on a non-commutative probability space $A$, we…
We use Herbrand's theorem to give a new proof that Euclid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a…
Radar-holonomic congruences of wordlines are proposed as a weaker substitute for the too restrictive class of Born-rigid motions. The definition is expressed as a set of differential equations. Integrability conditions and Cauchy data are…
The recently proposed Partition Theory (PT) [J.Phys.Chem.A 111, 2229 (2007)] is illustrated on a simple one-dimensional model of a heteronuclear diatomic molecule. It is shown that a sharp definition for the charge of molecular fragments…
We report in this survey some new results concerning noncommutative Chern characters: construction and the cases when they are exactly computed. The major result indicates some clear relation of these noncommutative objects and their…
This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a…
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we…
Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are…
This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
We present a construction of the explicit Hodge decomposition for $\bar\partial$-equation on Riemann surfaces.
Introducing $h$- and $h'$-deformations of ${\mathbb Z}_2$-graded (1+2)- and (2+1)-spaces, denoted by ${\mathbb A}_h^{1|2}$ and ${\mathbb A}_{h'}^{2|1}$, a two-parameter first order differential calculus, de Rham complex, on ${\mathbb…