scholarly journals Orthogonal Operators: Applications, Origin and Outlook

Atoms ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 102
Author(s):  
Peter Uylings ◽  
Ton Raassen
Keyword(s):  
Transition Matrix ◽  
Transition Probabilities ◽  
Operator Approach ◽  
Intermediate Coupling ◽  
Orthogonal Operator ◽  
Pure Transition ◽  
Small Interactions

Orthogonal operators can successfully be used to calculate eigenvalues and eigenvector compositions in complex spectra. Orthogonality ensures least correlation between the operators and thereby more stability in the fit, even for small interactions. The resulting eigenvectors are used to transform the pure transition matrix into realistic intermediate coupling transition probabilities. Calculated transition probabilities for close lying levels illustrate the power of the complete orthogonal operator approach.

scholarly journals Orthogonal Operators: Applications, Origin and Outlook

2019 ◽  
Author(s):  
Peter Uylings ◽  
Ton Raassen
Keyword(s):  
Transition Matrix ◽  
Transition Probabilities ◽  
Operator Approach ◽  
Intermediate Coupling ◽  
Orthogonal Operator ◽  
Pure Transition ◽  
Small Interactions

Orthogonal operators can successfully be used to calculate eigenvalues and eigenvector compositions in complex spectra. Orthogonality ensures least correlation between the operators and thereby more stability in the fit, even for small interactions. The resulting eigenvectors are used to transform the pure transition matrix into realistic intermediate coupling transition probabilities. Calculated transition probabilities for close lying levels illustrate the power of the complete orthogonal operator approach.

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.

Relativistic oscillator strengths for np2 → np(n + 1)s transition array of SnI and PbI spectra in jj and intermediate coupling

1979 ◽  
Vol 57 (2) ◽  
pp. 147-151 ◽  
Author(s):  
J. Migdałek
Keyword(s):  
Transition Probabilities ◽  
Theoretical Data ◽  
Wave Functions ◽  
Oscillator Strengths ◽  
Intermediate Coupling ◽  
Hartree Fock ◽  
Semiempirical Approach ◽  
Exchange Effects ◽  
Relativistic Oscillator ◽  
Transition Array

The relativistic oscillator strengths for the np2 → np(n + 1)s transition array as well as the lifetimes of levels of the np(n + 1)s configuration in SnI and PbI spectra were calculated in jj and intermediate coupling. The relativistic radial integrals were computed employing the wave functions obtained by a semiempirical approach which allowed for exchange effects. The results obtained are compared with existing experimental and theoretical data. The significance of intermediate coupling for oscillator strengths computations is discussed. The agreement with experiment is for the present semiempirical results generally better (particularly for the PbI spectrum) than for oscillator strength deduced from 'Optimized Hartree–Fock–Slater' transition probabilities, which were published previously.

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.

scholarly journals Calculation of LTC Premiums Based on Direct Estimates of Transition Probabilities

2005 ◽  
Vol 35 (2) ◽  
pp. 455-469 ◽  
Author(s):  
Florian Helms ◽  
Claudia Czado ◽  
Susanne Gschlößl
Keyword(s):  
Life History ◽  
Generalized Estimating Equations ◽  
Transition Matrix ◽  
Transition Probabilities ◽  
State Model ◽  
Link Function ◽  
History Of ◽  
The Relationship ◽  
Pseudo Values ◽  
Almost Unbiased

In this paper we model the life-history of LTC-patients using a Markovian multi-state model in order to calculate premiums for a given LTC-plan. Instead of estimating the transition intensities in this model we use the approach suggested by Andersen et al. (2003) for a direct estimation of the transition probabilities. Based on the Aalen-Johansen estimator, an almost unbiased estimator for the transition matrix of a Markovian multi-state model, we calculate so-called pseudo-values, known from Jackknife methods. Further, we assume that the relationship between these pseudo-values and the covariates of our data are given by a GLM with the logit as link-function. Since the GLMs do not allow for correlation between successive observations we use instead the “Generalized Estimating Equations” (GEEs) to estimate the parameters of our regression model. The approach is illustrated using a representative sample from a German LTC portfolio.

scholarly journals On the Embedding Problem for Discrete-Time Markov Chains

2013 ◽  
Vol 50 (04) ◽  
pp. 918-930 ◽  
Author(s):  
Marie-Anne Guerry
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Discrete Time ◽  
Transition Matrix ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Embedding Problem ◽  
Time Intervals ◽  
Square Roots ◽  
Probability Matrices

When a discrete-time homogenous Markov chain is observed at time intervals that correspond to its time unit, then the transition probabilities of the chain can be estimated using known maximum likelihood estimators. In this paper we consider a situation when a Markov chain is observed on time intervals with length equal to twice the time unit of the Markov chain. The issue then arises of characterizing probability matrices whose square root(s) are also probability matrices. This characterization is referred to in the literature as the embedding problem for discrete time Markov chains. The probability matrix which has probability root(s) is called embeddable. In this paper for two-state Markov chains, necessary and sufficient conditions for embeddability are formulated and the probability square roots of the transition matrix are presented in analytic form. In finding conditions for the existence of probability square roots for (k x k) transition matrices, properties of row-normalized matrices are examined. Besides the existence of probability square roots, the uniqueness of these solutions is discussed: In the case of nonuniqueness, a procedure is introduced to identify a transition matrix that takes into account the specificity of the concrete context. In the case of nonexistence of a probability root, the concept of an approximate probability root is introduced as a solution of an optimization problem related to approximate nonnegative matrix factorization.

scholarly journals SPATIAL-TEMPORAL CONDITIONAL RANDOM FIELDS CROP CLASSIFICATION FROM TERRASAR-X IMAGES

2015 ◽  
Vol II-3/W4 ◽  
pp. 79-86 ◽  
Author(s):  
B. K. Kenduiywoa ◽  
D. Bargiel ◽  
U. Soergel
Keyword(s):  
Random Fields ◽  
Information Exchange ◽  
Transition Matrix ◽  
Markov Random Fields ◽  
Conditional Random Fields ◽  
Transition Probabilities ◽  
Arable Land ◽  
Security Measures ◽  
Crop Phenology ◽  
Novel Approach

The rapid increase in population in the world has propelled pressure on arable land. Consequently, the food basket has continuously declined while global demand for food has grown twofold. There is need to monitor and update agriculture land-cover to support food security measures. This study develops a spatial-temporal approach using conditional random fields (CRF) to classify co-registered images acquired in two epochs. We adopt random forest (RF) as CRF association potential and introduce a temporal potential for mutual crop phenology information exchange between spatially corresponding sites in two epochs. An important component of temporal potential is a transitional matrix that bears intra- and inter-class changes between considered epochs. Conventionally, one matrix has been used in the entire image thereby enforcing stationary transition probabilities in all sites. We introduce a site dependent transition matrix to incorporate phenology information from images. In our study, images are acquired within a vegetation season, thus perceived spectral changes are due to crop phenology. To exploit this phenomena, we develop a novel approach to determine site-wise transition matrix using conditional probabilities computed from two corresponding temporal sites. Conditional probability determines transitions between classes in different epochs and thus we used it to propagate crop phenology information. Classification results show that our approach improved crop discrimination in all epochs compared to state-of-the-art mono-temporal approaches (RF and CRF monotemporal) and existing multi-temporal markov random fields approach by Liu et al. (2008).

scholarly journals Allowed and Forbidden n = 2?2 Transitions of the Elements Kr and Mo

1984 ◽  
Vol 37 (6) ◽  
pp. 601
Author(s):  
R Glass
Keyword(s):  
Transition Probabilities ◽  
Relativistic Effects ◽  
Correlation Effect ◽  
Coupling Scheme ◽  
Intermediate Coupling ◽  
Transition Energies ◽  
Hartree Fock ◽  
Physical Assumption ◽  
Variational Process ◽  
Intermediate Coupling Scheme

Relativistic intermediate-coupling wavefunctions are used to evaluate transition energies, line strengths and transition probabilities for all allowed and forbidden n = 2-2 transitions for krypton and molybdenum beryllium-like ions. Our results are in very good agreement with those calculated using the relativistic multi-configuration Hartree-Fock approximation. These calculations were carried out under the same physical assumption that the dominant correlation effect is the n = 2 intra-shell correlation. We also discuss the importance of relativistic effects on the radial functions, the relativistic intermediate-coupling scheme in the variational process, the importance of radiative corrections for transition energies between states with different occupation of the 2s shell, and the relative importance of intra- versus inter-shell correlation effects.

Sign in / Sign up

Export Citation Format

Share Document