scholarly journals Estimates on transition densities of subordinators with jumping density decaying in mixed polynomial orders

2021 ◽  
Author(s):  
Soobin Cho ◽  
Panki Kim
Keyword(s):  
Transition Densities

L 1 and L ∞ stability of transition densities of perturbed diffusions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ilya Bitter ◽  
Valentin Konakov
Keyword(s):  
Linear Growth ◽  
Stability Result ◽  
Regularity Conditions ◽  
Initial Condition ◽  
Weak Regularity ◽  
Transition Densities ◽  
The Stability ◽  
Drift Terms

Abstract In this paper, we derive a stability result for L 1 {L_{1}} and L ∞ {L_{\infty}} perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth, and the estimates reflect the transport of the initial condition by the unbounded drift through the corresponding flow. Our approach is based on the study of the distance in L 1 {L_{1}} - L 1 {L_{1}} metric between the transition densities of a given diffusion and the perturbed one using the McKean–Singer parametrix expansion. In the second part, we generalize the well-known result on the stability of diffusions with bounded coefficients to the case of at most linearly growing drift.

Helm model interpretation of 16O form factors: application to pion photoproduction and muon capture

1980 ◽  
Vol 58 (1) ◽  
pp. 48-62 ◽  
Author(s):  
R. D. Graves ◽  
B. A. Lamers ◽  
Anton Nagl ◽  
H. Überall ◽  
V. Devanathan ◽  
...  
Keyword(s):  
Form Factor ◽  
Electron Scattering ◽  
Form Factors ◽  
Muon Capture ◽  
Physical Parameters ◽  
Medium Energy ◽  
Model Interpretation ◽  
Charged Pions ◽  
Transition Densities ◽  
Energy Processes

The available experimental data for the form factors of the T = 1 levels in 16O, obtained from electron scattering at low (Darmstadt), medium (Tohoku), and high momentum transfer (Stanford), are interpreted by the generalized Helm model. This phenomenological model reduces the form factor description of each level to the listing of a few physical parameters, i.e., the radius and smearing width of the transition densities of charge (current) and magnetization, and their corresponding strength constants. Its parameters having been determined by the form factor fits, the model may then be used to predict the results of other medium energy processes; this is done here for the photoproduction of charged pions and for muon capture in16O.

scholarly journals Large-amplitude quadrupole shape mixing probed by the $(p,p^\prime)$ reaction: A model analysis

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Koichi Sato ◽  
Takenori Furumoto ◽  
Yuma Kikuchi ◽  
Kazuyuki Ogata ◽  
Yukinori Sakuragi
Keyword(s):  
Cross Sections ◽  
Large Amplitude ◽  
Model Parameters ◽  
Channel Calculation ◽  
Prolate Shape ◽  
Coupled Channel Calculation ◽  
Transition Densities ◽  
A Chain ◽  
Coupled Channel ◽  
Shape Phase Transition

Abstract To discuss a possible observation of large-amplitude nuclear shape mixing by nuclear reaction, we employ a simple collective model and evaluate the transition densities with which the differential cross sections are obtained through the microscopic coupled-channel calculation. Assuming the spherical-to-prolate shape transition, we focus on large-amplitude shape mixing associated with the softness of the collective potential in the $\beta$ direction. We introduce a simple model based on the five-dimensional quadrupole collective Hamiltonian, which simulates a chain of isotopes that exhibit spherical-to-prolate shape phase transition. Taking $^{154}$Sm as an example and controlling the model parameters, we study how the large-amplitude shape mixing affects the elastic and inelastic proton scatterings. The calculated results suggest that the inelastic cross section of the $2_2^+$ state shows us the important role of the quadrupole shape mixing.

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