Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measure-preserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac ...

It is shown that delta hedging provides the optimal trading strategy in terms of minimal required initial capital to replicate a given terminal payoff in a continuous-time Markovian context. This holds true in market models where no equivalent local martingale measure exists but only a square-integrable market price of risk. A new probability measure is constructed, which takes the place of an ...

Let the invariant probability measures for an orientation-reversing weakly expanding map of the interval [0, 1] be partially ordered by majorization. The minimal elements of the resulting poset are shown to be convex combinations of Dirac measures supported on two adjacent fixed points. A consequence is that if f : [0, 1] → R is strictly convex, then either its minimizing measure is unique and ...

Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl–Titchmarsh–Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac operator up to a gauge transformation. Our result applies in particular to radial Dirac operators and extends the classical results for Dirac operators with one...

in this paper we introduce the concept of dirac structures on (hermitian) modules and vectorbundles and deduce some of their properties. among other things we prove that there is a one to onecorrespondence between the set of all dirac structures on a (hermitian) module and the group of allautomorphisms of the module. this correspondence enables us to represent dirac structures on (hermitian)mod...

In this paper. (1) We determine the complex-valued solutions of the following variant of Van Vleck's functional equation $$int_{S}f(sigma(y)xt)dmu(t)-int_{S}f(xyt)dmu(t) = 2f(x)f(y), ;x,yin S,$$ where $S$ is a semigroup, $sigma$ is an involutive morphism of $S$, and $mu$ is a complex measure that is linear combinations of Dirac measures $(delta_{z_{i}})_{iin I}$, such that for all $iin I$, $z_{...

A class of translation bounded complex measures, which have the form of weighted Dirac combs, on locally compact Abelian groups is investigated. Given such a Dirac comb, we are interested in its diffraction spectrum which emerges as the Fourier transform of the autocorrelation measure. We present a sufficient set of conditions to ensure that the diffraction measure is a pure point measure. Simu...

For the subshift of finite type Σ = {0, 1, 2}N we study the convergence and the selection at temperature zero of the Gibbs measure associated to a non-locally constant Hölder potential which admits exactly two maximizing ergodic measures. These measures are Dirac measures at two different fixed points and the potential is flatter at one of these two fixed points. We prove that there always is c...

we assume that each valence quark in a nucleon is in a phenomenological modified harmonic oscillator potential of the form: ( l+yo) (ar +br+cr +dr ), where a, b, c and d are constants and ? is one of the dirac matrices. then by making use of a suitable ansatz, the dirac equation has a very simple solution which is exact. we then have calculated the static properties of the nucleon in the ground...

The GSReg package allows to analyze pathways based on the variability of the expression of sets of genes that are targets of those pathways. Basing this set statistic on variability enables inference of dysregulated pathways in diseases, including notably cancers. The first set statistic for gene variability was in the work of Eddy and his colleagues (see [1]) which used a ranked based methodol...