Enhanced Low-Energy E2 Transitions in the Odd-A Isotopes of Sb, I, Cs, and Pr

1971 ◽  
Vol 49 (13) ◽  
pp. 1794-1797 ◽  
Author(s):  
I. V. Goldstein ◽  
A. G. de Pinho
Keyword(s):  
Transition Probabilities ◽  
Unified Model ◽  
Low Energy ◽  
Transition Rates ◽  
Intermediate Coupling

The intermediate coupling version of the unified model was used to calculate E2 transition rates in some odd-mass isotopes of Sb, I, Cs, and Pr. The observed enhancement of these transitions is reproduced and regular variations of the transition probabilities in groups of neighboring isotopes are explained.

Satellite dielectronic spectra created from autoionizing 2lnl' and 1s2lnl' states with n = 4–5

2000 ◽  
Vol 78 (12) ◽  
pp. 1055-1067 ◽  
Author(s):  
U I Safronova ◽  
A A Vasilyev ◽  
R K Smith
Keyword(s):  
Transition Probabilities ◽  
Relativistic Effects ◽  
Radiative Transition ◽  
Branching Ratios ◽  
Transition Rates ◽  
Correlation Effects ◽  
Coupling Coefficients ◽  
Energy Matrix ◽  
Asymptotic Dependence ◽  
Intermediate Coupling

The relative intensities of dielectronic satellite lines determined by radiative transition probabilities and autoionization rates are calculated for the transitions 2lnl' – 1snl'', 2lnl' – 1s2l (n = 4–5, l' = 0–3, l'' = 0–3, l = 0–1) in He-like ions and for the transitions 1s2lnl' – 1s2nl'', 1s2lnl' – 1s22l (n = 4–5, l' =0–3, l'' = 0–3, l = 0–1) in Li-like ions, for all Z = 5–54, using the perturbation theory method (Z-expansion). Relativistic effects are taken into account using the Breit–Pauli operators. The asymptotic dependence on n of the energy matrix is discussed for 2lnl' and 1s2lnl' autoionizing states. The intermediate coupling coefficients obtained after diagonalization of the energy matrices are also studied. It was observed that these coefficients change very sharply with n and Z due to a redistribution of the contributions of relativistic and correlation effects. As a result, all other atomic characteristics (radiative and nonradiative transition rates, branching ratios, and relative intensity factor) display nonmonotonic Z- and n-dependencies with maxima and minima. PACS Nos.: 32.80D, 31.20G, 31.30J, 31.50

Calculation of the Nuclear Properties of 53Cr by the Unified Model

1971 ◽  
Vol 49 (12) ◽  
pp. 1582-1588 ◽  
Author(s):  
M. Csürös ◽  
J. A. Cameron ◽  
Z. Zámori
Keyword(s):  
Unified Model ◽  
Low Energy ◽  
Intermediate Coupling ◽  
Coupling Approach

The results of a calculation based upon the intermediate coupling approach of the unified model are presented for the low energy nuclear properties of the 53Cr isotope.

A review of multistate modelling approaches in monitoring disease progression: Bayesian estimation using the Kolmogorov-Chapman forward equations

2021 ◽  
pp. 096228022199750
Author(s):  
Zvifadzo Matsena Zingoni ◽  
Tobias F Chirwa ◽  
Jim Todd ◽  
Eustasius Musenge
Keyword(s):  
Bayesian Estimation ◽  
Transition Probabilities ◽  
Markov Property ◽  
Likelihood Estimation ◽  
Single Individual ◽  
Transition Rates ◽  
Multistate Models ◽  
Time To Event ◽  
Modeling Framework ◽  
Forward Equations

There are numerous fields of science in which multistate models are used, including biomedical research and health economics. In biomedical studies, these stochastic continuous-time models are used to describe the time-to-event life history of an individual through a flexible framework for longitudinal data. The multistate framework can describe more than one possible time-to-event outcome for a single individual. The standard estimation quantities in multistate models are transition probabilities and transition rates which can be mapped through the Kolmogorov-Chapman forward equations from the Bayesian estimation perspective. Most multistate models assume the Markov property and time homogeneity; however, if these assumptions are violated, an extension to non-Markovian and time-varying transition rates is possible. This manuscript extends reviews in various types of multistate models, assumptions, methods of estimation and data features compatible with fitting multistate models. We highlight the contrast between the frequentist (maximum likelihood estimation) and the Bayesian estimation approaches in the multistate modeling framework and point out where the latter is advantageous. A partially observed and aggregated dataset from the Zimbabwe national ART program was used to illustrate the use of Kolmogorov-Chapman forward equations. The transition rates from a three-stage reversible multistate model based on viral load measurements in WinBUGS were reported.

scholarly journals Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Lianglin Xiong ◽  
Xiaobing Zhou ◽  
Jie Qiu ◽  
Jing Lei
Keyword(s):  
Partial Information ◽  
Transition Probabilities ◽  
Mixed Delays ◽  
Transition Rates ◽  
Neutral Systems ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Analysis Technique ◽  
Transition Rate Matrix ◽  
Delay Dependent

The delay-dependent stability problem is studied for Markovian jump neutral systems with partial information on transition probabilities, and the considered delays are mixed and model dependent. By constructing the new stochastic Lyapunov-Krasovskii functional, which combined the introduced free matrices with the analysis technique of matrix inequalities, a sufficient condition for the systems with fully known transition rates is firstly established. Then, making full use of the transition rate matrix, the results are obtained for the other case, and the uncertain neutral Markovian jump system with incomplete transition rates is also considered. Finally, to show the validity of the obtained results, three numerical examples are provided.

scholarly journals Infinitely divisible random transition probabilities with application to dependent Markov chains

1984 ◽  
Vol 25 (4) ◽  
pp. 463-472
Author(s):  
Peter L. Chesson
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
White Noise ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Transition Rates ◽  
Infinitely Divisible ◽  
Random Transition ◽  
Transition Probability Matrices ◽  
Probability Matrices

AbstractRandom transition probability matrices with stationary independent factors define “white noise” environment processes for Markov chains. Two examples are considered in detail. Such environment processes can be used to construct several Markov chains which are dependent, have the same transition probabilities and are jointly a Markov chain. Transition rates for such processes are evaluated. These results have application to the study of animal movements.

Optimal control of random walks, birth and death processes, and queues

1981 ◽  
Vol 13 (01) ◽  
pp. 61-83 ◽  
Author(s):  
Richard Serfozo
Keyword(s):  
Optimal Control ◽  
Random Walks ◽  
Queue Length ◽  
Transition Probabilities ◽  
Transition Rates ◽  
Average Reward ◽  
Birth And Death Processes ◽  
Optimal Policies ◽  
One Step ◽  
Increasing Functions

This is a study of simple random walks, birth and death processes, and M/M/s queues that have transition probabilities and rates that are sequentially controlled at jump times of the processes. Each control action yields a one-step reward depending on the chosen probabilities or transition rates and the state of the process. The aim is to find control policies that maximize the total discounted or average reward. Conditions are given for these processes to have certain natural monotone optimal policies. Under such a policy for the M/M/s queue, for example, the service and arrival rates are non-decreasing and non-increasing functions, respectively, of the queue length. Properties of these policies and a linear program for computing them are also discussed.

scholarly journals Developing a composite outcome measure for frailty prevention trials – rationale, derivation and sample size comparison with other candidate measures

2020 ◽  
Author(s):  
Miles D. Witham ◽  
James Wason ◽  
Richard M Dodds ◽  
Avan A Sayer
Keyword(s):  
Sample Size ◽  
Transition Probabilities ◽  
Adverse Outcomes ◽  
Transition Rates ◽  
Composite Outcome ◽  
Composite Measure ◽  
Sample Sizes ◽  
Loss To Follow Up ◽  
Prevention Trials

Abstract Introduction Frailty is the loss of ability to withstand a physiological stressor, and is associated with multiple adverse outcomes in older people. Trials to prevent or ameliorate frailty are in their infancy. A range of different outcome measures have been proposed, but current measures require either large sample sizes, long follow-up, or do not directly measure the construct of frailty. Methods We propose a composite outcome for frailty prevention trials, comprising progression to the frail state, death, or being too unwell to continue in a trial. To determine likely event rates, we used data from the English Longitudinal Study for Ageing, collected 4 years apart. We calculated transition rates between non-frail, prefrail, frail or loss to follow up due to death or illness. We used Markov state transition models to interpolate one- and two-year transition rates, and performed sample size calculations for a range of differences in transition rates using simple and composite outcomes. Results The frailty category was calculable for 4650 individuals at baseline (2226 non-frail, 1907 prefrail, 517 frail); at follow up, 1282 were non-frail, 1108 were prefrail, 318 were frail and 1936 had dropped out or were unable to complete all tests for frailty. Transition probabilities for those prefrail at baseline, measured at wave 4 were respectively 0.176, 0.286, 0.096 and 0.442 to non-frail, prefrail, frail and dead/dropped out. Interpolated transition probabilities were 0.159, 0.494, 0.113 and 0.234 at two years, and 0.108, 0.688, 0.087 and 0.117 at one year. Required sample sizes for a two-year outcome were between 1000 and 7200 for transition from prefrailty to frailty alone, 250 to 1600 for transition to the composite measure, and 75 to 350 using the composite measure with an ordinal logistic regression approach. Conclusion Use of a composite outcome for frailty trials offers reduced sample sizes and could ameliorate the effect of high loss to follow up inherent in such trials due to death and illness.

scholarly journals Developing a composite outcome measure for frailty prevention trials – rationale, derivation and sample size comparison with other candidate measures

2019 ◽  
Author(s):  
Miles D. Witham ◽  
James Wason ◽  
Richard M Dodds ◽  
Avan A Sayer
Keyword(s):  
Sample Size ◽  
Transition Probabilities ◽  
Adverse Outcomes ◽  
Transition Rates ◽  
Composite Outcome ◽  
Composite Measure ◽  
Sample Sizes ◽  
Loss To Follow Up ◽  
Prevention Trials

Abstract Introduction Frailty is the loss of ability to withstand a physiological stressor, and is associated with multiple adverse outcomes in older people. Trials to prevent or ameliorate frailty are in their infancy. A range of different outcome measures have been proposed, but current measures require either large sample sizes, long follow-up, or do not directly measure the construct of frailty. Methods We propose a composite outcome for frailty prevention trials, comprising progression to the frail state, death, or being too unwell to continue in a trial. To determine likely event rates, we used data from the English Longitudinal Study for Ageing, collected 4 years apart. We calculated transition rates between non-frail, prefrail, frail or loss to follow up due to death or illness. We used Markov state transition models to interpolate one- and two-year transition rates, and performed sample size calculations for a range of differences in transition rates using simple and composite outcomes. Results The frailty category was calculable for 4650 individuals at baseline (2226 non-frail, 1907 prefrail, 517 frail); at follow up, 1282 were non-frail, 1108 were prefrail, 318 were frail and 1936 had dropped out or were unable to complete all tests for frailty. Transition probabilities for those prefrail at baseline, measured at wave 4 were respectively 0.176, 0.286, 0.096 and 0.442 to non-frail, prefrail, frail and dead/dropped out. Interpolated transition probabilities were 0.159, 0.494, 0.113 and 0.234 at two years, and 0.108, 0.688, 0.087 and 0.117 at one year. Required sample sizes for a two-year outcome were between 1000 and 7200 for transition from prefrailty to frailty alone, 250 to 1600 for transition to the composite measure, and 75 to 350 using the composite measure with an ordinal logistic regression approach. Conclusion Use of a composite outcome for frailty trials offers reduced sample sizes and could ameliorate the effect of high loss to follow up inherent in such trials due to death and illness.

Study of High-spin States for 90,91,92Y Isotopes by Using Oxbash Code

2021 ◽  
Vol 14 (1) ◽  
pp. 25-33
Keyword(s):  
Experimental Data ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Model Space ◽  
Low Energy ◽  
Energy Spectra ◽  
Spin States ◽  
Nuclear Shell Model ◽  
High Spin States ◽  
Nuclear Shell

Abstract: In this paper, calculations of 90,91,92Y isotopes have been performed by application of nuclear shell model in the Gloeckner (Gl) model space for two different interactions (Gloeckner (Gl) and Gloeckner pulse bare G-Matrix (Glb) using Oxbash code. The energy levels are compared and discussed with experimental data and based on our results, many predictions about spins and parity were observed between experimental states, in addition to the predictions of low-energy spectra and B (E2; ↓) and B (M1; ↓)) transitional strengths in the isotopes 90,91,92Y. These predictions were not known in the experimental data. Keywords: Energy levels, Transition probabilities, Oxbash code.

scholarly journals Recombination Spectra of Planetary Nebulae

1983 ◽  
Vol 103 ◽  
pp. 514-516
Author(s):  
P.O. Bogdanovich ◽  
Z.B. Rudzikas ◽  
T. H. Feklistova ◽  
A.F. Kholtygin ◽  
A.A. Nikitin ◽  
...  
Keyword(s):  
Transition Probabilities ◽  
Planetary Nebulae ◽  
Dielectronic Recombination ◽  
Wave Functions ◽  
Energy Spectra ◽  
Coupling Scheme ◽  
Intermediate Coupling ◽  
Hartree Fock ◽  
Radiative Transitions ◽  
Intermediate Coupling Scheme

The lines of the transitions between the subordinate levels of the CIII, NIII etc. ions are observed in the spectra of planetary nebulae (PN) (1). Their theoretical intensities may be found by solving the stationarity equations and accounting for both the recombination and cascade radiative transitions. It is possible to calculate the recombination spectra in various approaches: the single- or multi-configuration approximations (SCA and MCA) making use of both the superposition of configurations (SC) or the multiconfigurational Hartree-Fock-Jucys equations (2), taking into consideration the contribution of the dielectronic recombination to the intensities of the recombination lines. The energy spectra, the transition probabilities etc., as a rule ought to be calculated in the intermediate coupling scheme (2). Both analytical or numerical (e.g. Hartree-Fock) wave functions may be adopted.

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