On the Theory of Thermally Weighted Electron-Phonon Transition Probabilities

1980 ◽  
Vol 35 (9) ◽  
pp. 902-914
Author(s):  
J. Schupfner
Keyword(s):  
Transition Probabilities ◽  
Algebraic Method ◽  
Calculation Technique ◽  
Radiative Transitions ◽  
Special Cases ◽  
Explicit Formulae ◽  
The Common ◽  
Common Transition ◽  
Franck Condon ◽  
Refined Calculation

Abstract We present a refined calculation method for the phonon part (Franck-Condon Overlaps) of the transition probabilities of electron-phonon radiative and non-radiative transitions in crystals. The evaluation of the thermal averaged Franck-Condon integrals is a purely algebraic method and the transition probabilities we use are derived from first principles and completely atomistic. For the electronic transitions we take into account the frequency shift of the lattice and the change of the phonon normal coordinates. Explicit formulae of the phonon parts are derived and it is shown that the common transition probabilities used in literature are special cases of our functional calculation technique.

THEORETICAL TRANSITION PROBABILITIES FOR THE $\tilde{A}^{2}A_{1} -\tilde{X}^{2}B_{1}$ SYSTEM OF H2O+ AND D2O+ AND RELATED FRANCK–CONDON FACTORS BASED ON GLOBAL POTENTIAL ENERGY SURFACES

2005 ◽  
Vol 04 (01) ◽  
pp. 225-245 ◽  
Author(s):  
IKUO TOKUE ◽  
KATSUYOSHI YAMASAKI ◽  
SATOSHI MINAMINO ◽  
SHINKOH NANBU
Keyword(s):  
Potential Energy ◽  
Photoelectron Spectroscopy ◽  
Potential Energy Surfaces ◽  
Least Squares Method ◽  
Transition Probabilities ◽  
Three Dimensional ◽  
Equilibrium Geometry ◽  
Condon Factors ◽  
Energy Surfaces ◽  
Franck Condon

To elucidate the ionization dynamics, in particular the vibrational distribution, of H 2 O +(Ã) produced by photoionization and the Penning ionization of H 2 O and D 2 O with He *(2 3S) atoms, Franck–Condon factors (FCFs) were given for the [Formula: see text] ionization, and the transition probabilities were presented for the [Formula: see text] emission. The FCFs were obtained by quantum vibrational calculations using the three-dimensional potential energy surfaces (PESs) of [Formula: see text] and [Formula: see text] electronic states. The global PESs were determined by the multi-reference configuration interaction calculations with the Davidson correction and the interpolant moving least squares method combined with the Shepard interpolation. The obtained FCFs exhibit that the [Formula: see text] state primarily populates the vibrational ground state, as its equilibrium geometry is almost equal to that of [Formula: see text], while the bending mode (ν2) is strongly enhanced for the H 2 O +(Ã) state; the maximums in the population of H 2 O + and D 2 O + are approximately v2 = 11–12 and 15–17, respectively. These results are consistent with the distributions observed by photoelectron spectroscopy. Transition probabilities for the [Formula: see text] system of H 2 O + and D 2 O + show that the bending progressions consist primarily of the [Formula: see text] emission, with combination bands from the (1, v′2 = 4–8, 0) level being next most important.

EXPLICIT FUNCTIONS OF FUZZY CONTROL SYSTEMS

1996 ◽  
Vol 04 (06) ◽  
pp. 515-535 ◽  
Author(s):  
LÁSZLÓ T. KÓCZY ◽  
MICHIO SUGENO
Keyword(s):  
Computational Complexity ◽  
Fuzzy Control ◽  
Control Systems ◽  
Mathematical Description ◽  
Membership Functions ◽  
Mathematical Functions ◽  
Low Computational Complexity ◽  
Special Cases ◽  
Single Input ◽  
Explicit Formulae

Fuzzy control systems have proved their applicability in many areas. Their user-friend-liness and transparency certainly belong to their main advantages, and these two enable developing and tuning such controllers easily, without knowing their exact mathematical description. Nevertheless, it is of interest to know, what mathematical functions hide behind a set of fuzzy rules and an inference machine. For practical purposes it is necessary to consider real, implementable fuzzy control systems with reasonably low computational complexity. This paper discusses the problem of what types of functions are generated by realistic fuzzy control systems. In the paper the explicit formulae of the transference functions for practically important special cases are determined, controllers having rules with triangular and trapezoidal membership functions, and crisp consequents. Here we restrict our investigations to rules with a single input.

scholarly journals Generalising Exponential Distributions Using an Extended Marshall–Olkin Procedure

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 464
Author(s):  
Victoriano García ◽  
María Martel-Escobar ◽  
F.J. Vázquez-Polo
Keyword(s):  
Failure Rate ◽  
Real Data ◽  
Rate Function ◽  
Exponential Distributions ◽  
Symmetric Distributions ◽  
Failure Rate Function ◽  
Numerical Examples ◽  
Special Cases ◽  
The Common ◽  
Family Of Distributions

This paper presents a three-parameter family of distributions which includes the common exponential and the Marshall–Olkin exponential as special cases. This distribution exhibits a monotone failure rate function, which makes it appealing for practitioners interested in reliability, and means it can be included in the catalogue of appropriate non-symmetric distributions to model these issues, such as the gamma and Weibull three-parameter families. Given the lack of symmetry of this kind of distribution, various statistical and reliability properties of this model are examined. Numerical examples based on real data reflect the suitable behaviour of this distribution for modelling purposes.

scholarly journals Hitting Times and the Running Maximum of Markovian Growth-Collapse Processes

2011 ◽  
Vol 48 (02) ◽  
pp. 295-312 ◽  
Author(s):  
Andreas Löpker ◽  
Wolfgang Stadje
Keyword(s):  
Power Series Expansion ◽  
Inverse Function ◽  
Hitting Times ◽  
Asymptotic Results ◽  
Rapid Variation ◽  
State Dependent ◽  
Special Cases ◽  
The Laplace Transform ◽  
Running Maximum ◽  
Explicit Formulae

We consider the level hitting times τy= inf{t≥ 0 |Xt=y} and the running maximum processMt= sup{Xs| 0 ≤s≤t} of a growth-collapse process (Xt)t≥0, defined as a [0, ∞)-valued Markov process that grows linearly between random ‘collapse’ times at which downward jumps with state-dependent distributions occur. We show how the moments and the Laplace transform of τycan be determined in terms of the extended generator ofXtand give a power series expansion of the reciprocal of Ee−sτy. We prove asymptotic results for τyandMt: for example, ifm(y) = Eτyis of rapid variation thenMt/m-1(t) →w1 ast→ ∞, wherem-1is the inverse function ofm, while ifm(y) is of regular variation with indexa∈ (0, ∞) andXtis ergodic, thenMt/m-1(t) converges weakly to a Fréchet distribution with exponenta. In several special cases we provide explicit formulae.

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.

scholarly journals Extinction Probability in A Birth-Death Process with Killing

2005 ◽  
Vol 42 (01) ◽  
pp. 185-198 ◽  
Author(s):  
Erik A. Van Doorn ◽  
Alexander I. Zeifman
Keyword(s):  
Rate Of Convergence ◽  
Lower Bounds ◽  
Transition Probabilities ◽  
Upper And Lower Bounds ◽  
Death Process ◽  
Logarithmic Norm ◽  
Absorbing State ◽  
The Common ◽  
Absorption Probabilities ◽  
Birth Death

We study birth-death processes on the nonnegative integers, where {1, 2,…} is an irreducible class and 0 an absorbing state, with the additional feature that a transition to state 0 may occur from any state. We give a condition for absorption (extinction) to be certain and obtain the eventual absorption probabilities when absorption is not certain. We also study the rate of convergence, as t → ∞, of the probability of absorption at time t, and relate it to the common rate of convergence of the transition probabilities that do not involve state 0. Finally, we derive upper and lower bounds for the probability of absorption at time t by applying a technique that involves the logarithmic norm of an appropriately defined operator.

scholarly journals Stackelberg equilibria in a continuous-time vertical contracting model with uncertain demand and delayed information

2014 ◽  
Vol 51 (A) ◽  
pp. 213-226 ◽  
Author(s):  
Bernt Øksendal ◽  
Leif Sandal ◽  
Jan Ubøe
Keyword(s):  
Continuous Time ◽  
Variable Coefficients ◽  
Uncertain Demand ◽  
Uhlenbeck Process ◽  
Delayed Information ◽  
Equilibrium Prices ◽  
Special Cases ◽  
Explicit Formulae ◽  
Contracting Model ◽  
Vertical Contracting

We consider explicit formulae for equilibrium prices in a continuous-time vertical contracting model. A manufacturer sells goods to a retailer, and the objective of both parties is to maximize expected profits. Demand is an Itô-Lévy process, and to increase realism, information is delayed. We provide complete existence and uniqueness proofs for a series of special cases, including geometric Brownian motion and the Ornstein-Uhlenbeck process, both with time-variable coefficients. Moreover, explicit solution formulae are given, so these results are operational. An interesting finding is that information that is more precise may be a considerable disadvantage for the retailer.

scholarly journals Mstatecox: A Package for Simulating Transition Probabilities from Semiparametric Multistate Survival Models

2018 ◽  
Vol 18 (3) ◽  
pp. 533-563
Author(s):  
Shawna K. Metzger ◽  
Benjamin T. Jones
Keyword(s):  
Marrow Transplantation ◽  
Transition Probabilities ◽  
Duration Models ◽  
Survival Models ◽  
Duration Model ◽  
Multistate Models ◽  
Statistical Software ◽  
Blood And Marrow Transplantation ◽  
The Common ◽  
European Registry

Multistate duration models are a valuable tool used in multiple fields to examine how subjects move through a series of discrete phases and stages. The models themselves may be fit using common statistical software, but their broader adoption has been limited because of a lack of software to substantively interpret their results. Transition probabilities are the common postestimation quantity for interpreting multistate duration model results. De Wreede, Fiocco, and Putter's (2011, Journal of Statistical Software 38(7): 1–30) mstate package provides R with the functionality to estimate these quantities from semiparametric multistate models, yet no Stata equivalent exists for semiparametric models. We introduce a new set of Stata commands to meet this need. Our mstatecox suite calculates transition probabilities from semiparametric multistate duration models with simulation. It can accommodate any configuration of stages and also has the ability to accommodate time-interacted covariates. We demonstrate our package's functionality using de Wreede, Fiocco, and Putter‘s European Registry of Blood and Marrow Transplantation example dataset.

Structuralism? Functionalism? Behaviorism? Or mechanism? Looking for a better approach to AI

2008 ◽  
Vol 1 (3) ◽  
pp. 325-336 ◽  
Author(s):  
Yixin Zhong
Keyword(s):  
Intelligent System ◽  
New Approach ◽  
Content Type ◽  
Advantages And Disadvantages ◽  
Special Cases ◽  
Powerful Approach ◽  
Reasonable Approach ◽  
The Common ◽  
To Come ◽  
The One

PurposeResearch of artificial intelligence (AI), has aimed at making machines intelligent via the simulation of natural intelligence, particularly human intelligence. During the past decades, there have been three major approaches aimed at achieving this goal, namely structuralism, functionalism and behaviorism. Unfortunately, they work separately and contradictorily to a large extent. The purpose of this paper is to present a better and more unified approach.Design/methodology/approachThe paper analyses each of the three major approaches to AI, describing their advantages and disadvantages. There then follows an attempt to explore a new and more reasonable approach to AI. The new approach should be able to solve all the problems that the existing approaches can solve on one hand and can solve the problems that the existing approaches cannot solve on the other hand.FindingsIt was found that the more reasonable and more powerful approach is the one that directly touches the common and core mechanism of intelligence formation. This is due to the fact that the mechanism of intelligence formation is much more essential than other windows of an intelligent system, such as structure, function, or behavior. It was also found that the common and core mechanism of intelligence formation can be implemented through the information‐knowledge‐intelligence transformation. The third finding is that the three existing approaches are special cases of the mechanism approach under different conditions and can thus be harmoniously unified within the frame of the mechanism approach.Originality/valueThe three findings in the paper: the mechanism approach, the implementation of the mechanism approach, and the unification of the existed three major approaches, are important laws never found before in the literature. The breakthrough of the mechanism approach to AI will be of great significance to both theoretical and practical research in AI in the years to come.

Maximal and Minimal Ranks of the Common Solution of Some Linear Matrix Equations over an Arbitrary Division Ring with Applications

2009 ◽  
Vol 16 (02) ◽  
pp. 293-308 ◽  
Author(s):  
Qingwen Wang ◽  
Guangjing Song ◽  
Xin Liu
Keyword(s):  
Division Ring ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Equations ◽  
Common Solution ◽  
Special Cases ◽  
The Common ◽  
Necessary And Sufficient ◽  
Linear Matrix Equations

We establish the formulas of the maximal and minimal ranks of the common solution of certain linear matrix equations A1X = C1, XB2 = C2, A3XB3 = C3 and A4XB4 = C4 over an arbitrary division ring. Corresponding results in some special cases are given. As an application, necessary and sufficient conditions for the invariance of the rank of the common solution mentioned above are presented. Some previously known results can be regarded as special cases of our results.

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