Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDistributions associated to homogeneous distributions
209
0
0.0
(
0
)
Authors
A.V.Kosyak
Ask ChatGPT about the research
No Arabic abstract
In this paper we continue to study {it quasi associated homogeneous distributions rm{(}generalized functionsrm{)}} which were introduced in the paper by V.M. Shelkovich, Associated and quasi associated homogeneous distributions (generalized functions), J. Math. An. Appl., {bf 338}, (2008), 48-70. [arXiv:math/0608669]. For the multidimensional case we give the characterization of these distributions in the terms of the dilatation operator $U_{a}$ (defined as $U_{a}f(x)=f(ax)$, $xin bR^n$, $a >0$) and its generator $sum_{j=1}^{n}x_jfrac{partial}{partial x_j}$. It is proved that $f_kin {cD}(bR^n)$ is a quasi associated homogeneous distribution of degree $lambda$ and of order $k$ if and only if $bigl(sum_{j=1}^{n}x_jfrac{partial}{partial x_j}-lambdabigr)^{k+1}f_{k}(x)=0$, or if and only if $bigl(U_a-a^lambda Ibigr)^{k+1}f_k(x)=0$, $forall , a>0$, where $I$ is a unit operator. The structure of a quasi associated homogeneous distribution is described.
rate research
Read More
We give a bijection between a quotient space of the parameters and the space of moments for any $A$-hypergeometric distribution. An algorithmic method to compute the inverse image of the map is proposed utilizing the holonomic gradient method and an asymptotic equivalence of the map and the iterative proportional scaling. The algorithm gives a method to solve a conditional maximum likelihood estimation problem in statistics. Our interplay between the theory of hypergeometric functions and statistics gives some new formulas of $A$-hypergeometric polynomials.
We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g_{alpha}(x), 0 leq x < infty, 0 < alpha < 1. We demonstrate that the knowledge of one such a distribution g_{alpha}(x) suffices to obtain exactly g_{alpha^{p}}(x), p=2, 3,... Similarly, from known g_{alpha}(x) and g_{beta}(x), 0 < alpha, beta < 1, we obtain g_{alpha beta}(x). The method is based on the construction of the integral operator, called Levy transform, which implements the above operations. For alpha rational, alpha = l/k with l < k, we reproduce in this manner many of the recently obtained exact results for g_{l/k}(x). This approach can be also recast as an application of the Efros theorem for generalized Laplace convolutions. It relies solely on efficient definite integration.
We investigate unpolarized and polarized gluon distributions and their applications to the Ioffe-time distributions, which are related to lattice QCD calculations of parton distribution functions. Guided by the counting rules based on the perturbative QCD at large momentum fraction $x$ and the color coherence of gluon couplings at small $x$, we parametrize gluon distributions in the helicity basis. By fitting the unpolarized gluon distribution, the inferred polarized gluon distribution from our parametrization agrees with the one from global analysis. A simultaneous fit to both unpolarized and polarized gluon distributions is also performed to explore the model uncertainty. The agreement with the global analysis supports the $(1-x)$ power suppression of the helicity-antialigned distribution relative to the helicity-aligned distribution. The corresponding Ioffe-time distributions and their asymptotic expansions are calculated from the gluon distributions. Our results of the Ioffe-time distributions can provide guidance to the extrapolation of lattice QCD data to the region lacking precise gluonic matrix elements. Therefore, they can help regulate the ill-posed inverse problem associated with extracting the gluon distributions from discrete data from first-principle calculations, which are available in a limited range of the nucleon momentum and the spatial separation between the gluonic currents. Given various limitations in obtaining lattice QCD data at large Ioffe time, phenomenological approaches can provide important complementary information to extract the gluon distributions in the entire $x$ region. The possibility of investigating higher-twist effects and other systematic uncertainties in the contemporary first-principle calculations of parton distributions from phenomenologically well-determined Ioffe-time distributions in the large Ioffe-time region is also discussed.
Emission line observations together with photoionization models provide important information about the ionization mechanisms, densities, temperatures, and metallicities in AGN-ionized gas. Photoionization models usually assume Maxwell-Boltzmann (M-B) electron energy distributions (EED), but it has been suggested that using kappa distributions may be more appropriate and could potentially solve the discrepancies in temperatures and abundances found in HII regions and Planetary Nebulae (PNe). We consider the impact of the presence of kappa distributions in photoionized nebulae associated with AGN and study how this might affect spectral modelling and abundance analyses for such regions. Using the photoionization code MAPPINGS 1e we compute models adopting M-B and kappa distributions of electron energies, and compare the behaviour of emission line ratios for different values of kappa, gas metallicity, density, ionization parameter and SED slope. We find that the choice of EED can have a large impact on some UV and optical emission lines emitted by photoionized nebulae associated with AGN, and that the impact of adopting a kappa distribution is strongly dependent on gas metallicity and ionization parameter. We compile a sample of line ratios for 143 type 2 AGN and compare our models against the observed line ratios. We find that for 98 objects kappa distributions provide a better fit to the observed line ratios than M-B distributions. In addition, we find that adopting kappa-distributed electron energies results in significant changes in the inferred gas metallicity and ionization parameter in a significant fraction of objects.
We derive one-loop matching relations for the Ioffe-time distributions related to the pion distribution amplitude (DA) and generalized parton distributions (GPDs). They are obtained from a universal expression for the one-loop correction in an operator form, and will be used in the ongoing lattice calculations of the pion DA and GPDs based on the parton pseudo-distributions approach.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
