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About 10,000 papers for “Dynamic equation”

Dynamic Structural Equation Models

Tihomir Asparouhov, Ellen L. Hamaker, Bengt Muthén · Structural Equation Modeling A Multidisciplinary Journal · 2017

This article presents dynamic structural equation modeling (DSEM), which can be used to study the evolution of observed and latent variables as well as the structural equation models over time. DSEM is suitable for analyzing intensive longitudinal data where observations from multiple individuals are collected at many points in time. The modeling framework encompasses previously published DSEM models and is a comprehensive attempt to combine time-series modeling with structural equation modeling. DSEM is estimated with Bayesian methods using the Markov chain Monte Carlo Gibbs sampler and the Metropolis–Hastings sampler. We provide a detailed description of the estimation algorithm as implemented in the Mplus software package. DSEM can be used for longitudinal analysis of any duration and with any number of observations across time. Simulation studies are used to illustrate the framework and study the performance of the estimation method. Methods for evaluating model fit are also discussed.

Cited by 915

On the dynamic vacuum equation

Fischer, E, Jones, E, Lewin, G · CERN Document Server (European Organization for Nuclear Research) · 1971

Cited by 0Open access

Bellman Equation in Dynamic Programming

K. Vinotha · 2015

The unifying purpose of this paper to introduces basic ideas and methods of dynamic programming. It sets out the basic elements of a recursive optimization problem, describes Bellman's Principle of Optimality, the Bellman equation, and presents three methods for solving the Bellman equation with example.

Cited by 0

dsem: Dynamic Structural Equation Models

James T. Thorson · 2023

Applies dynamic structural equation models to time-series data with generic and simplified specification for simultaneous and lagged effects. Methods are described in Thorson et al. (2024) "Dynamic structural equation models synthesize ecosystem dynamics constrained by ecological mechanisms."

Cited by 0Open access

The Beverton–Holt dynamic equation

Martin Böhner, Howard Warth · Applicable Analysis · 2007

The Cushing–Henson conjectures on time scales are presented and verified. The central part of these conjectures asserts that based on a model using the dynamic Beverton–Holt equation, a periodic environment is deleterious for the population. The proof technique is as follows. First, the Beverton–Holt equation is identified as a logistic dynamic equation. The usual substitution transforms this equation into a linear equation. Then the proof is completed using a recently established dynamic version of the generalized Jensen inequality.

Cited by 48

Dynamic disquantization of Dirac equation

Yuri A. Rylov · ArXiv.org · 2001

Classical model S_dc of Dirac particle S_D is constructed. S_D is the dynamic system described by the Dirac equation. Its classical analog S_dc is described by a system of ordinary differential equations, containing the quantum constant h as a parameter. Dynamic equations for S_dc are determined by the Dirac equation uniquely. Both dynamic systems S_D and S_dc appear to be nonrelativistic. One succeeded in transforming nonrelativistic dynamic system S_dc into relativistic one S_dcr. The dynamic system S_dcr appears to be a two-particle structure (special case of a relativistic rotator). It explains freely such properties of S_D as spin and magnetic moment, which are strange for pointlike structure. The rigidity function f_r(a), describing rotational part of total mass as a function of the radius $a$ of rotator, has been calculated for S_dcr. For investigation of S_D and construction of S_dc one uses new dynamic methods: dynamic quantization and dynamic disquantization. These relativistic pure dynamic procedures do not use principles of quantum mechanics (QM). They generalize and replace conventional quantization and transition to classical approximation. Totality of these methods forms the model conception of quantum phenomena (MCQP). Technique of MCQP is more subtle and effective, than conventional methods of QM. MCQP relates to conventional QM, much as the statistical physics relates to thermodynamics.

Cited by 13Open access

THE DYNAMIC EQUATION OF ACCOUNTING.

Lawrence Lipkin · The Accounting Review · 1959

Abstract This article says that the equation A = L+P is often termed the basic of fundamental equation of accounting. There is no question as to the validity of this equation. There is, however, a question as to whether or not this equation should be termed the basic equation of accounting, implying that it fully describes the accounting and economic processes of the firm. A much more useful equation to describe the accounting process and accounting relationships can be readily developed wherein it is not necessary to qualify P by definition, implication, or otherwise. This dynamic equation can be extremely useful in teaching elementary accounting, for the instructor can explain much theory and some of the mechanics of accounting quite easily with the help of this equation. Another excellent use of the dynamic equation is in explaining the theory of closing the books. All too often this becomes a rather mechanical process for the student doesn't really understand what he is trying to accomplish. It can also be pointed out that the dynamic equation represents the general ledger because it includes all categories of accounts.

Cited by 0

Equation-free Dynamic Renormalization of a KPZ-type Equation

Kessler, David A., Kevrekidis, Ioannis G., Chen, Ligang · arXiv (Cornell University) · 2005

In the context of equation-free computation, we devise and implement a procedure for using short-time direct simulations of a KPZ type equation to calculate the self-similar solution for its ensemble averaged correlation function. The method involves "lifting" from candidate pair-correlation functions to consistent realization ensembles, short bursts of KPZ-type evolution, and appropriate rescaling of the resulting averaged pair correlation functions. Both the self-similar shapes and their similarity exponents are obtained at a computational cost significantly reduced to that required to reach saturation in such systems.

Cited by 0Open access

Dynamic Structural Equation Modeling with Cycles

Muthén, Bengt, Asparouhov, Tihomir, Keijsers, Loes · Figshare · 2024

Cyclical phenomena are commonly observed in many areas of repeated measurements, especially with intensive longitudinal data. A typical example is circadian (24-hour) rhythm of physical measures such as blood pressure, heart rate, glucose level, and alertness. This paper focuses on positive affect, which is a common measure in psychological studies and for which circadian rhythm has been observed but not analyzed by modern statistical methods. The paper demonstrates that a large new analysis arsenal is available for analysis of cyclical features in intensive longitudinal data. This can help researchers extract more information from their data to get more valid estimates of coupled processes and to get new theoretical insights into circadian rhythms of mood. To assist in this effort, the analyses are based on general models with a rich set of features while still being accessible without an unduly steep learning curve. Scripts for the Mplus software are available for all the analyses presented.

Cited by 0Open access

Relativistic Dynamic Equation in Invariant Form

Yaakov Friedman · 2002

Abstract In some dynamical systems boosts and rotations occur synchronically. Usually in analysis of such systems we separate these two types of motion. Unfortunately, the result of such analysis depends on the order in which operations are performed.

Cited by 0

Dynamic of the extended Mandelbrots equation

Berezowski, Marek · arXiv (Cornell University) · 2016

The paper deals with the mathematical - numerical analysis of the Mandelbrot equation extended by the dynamic continuous term. The possibilities of generation of fractal patterns with the mathematical form, defined in such a manner, were investigated. The decay of fractal structure with time was demonstrated.

Cited by 0Open access

Dynamic Structural Equation Modeling with Cycles

Bengt Muthén, Tihomir Asparouhov, Loes Keijsers · Structural Equation Modeling A Multidisciplinary Journal · 2024

Cyclical phenomena are commonly observed in many areas of repeated measurements, especially with intensive longitudinal data. A typical example is circadian (24-hour) rhythm of physical measures such as blood pressure, heart rate, glucose level, and alertness. This paper focuses on positive affect, which is a common measure in psychological studies and for which circadian rhythm has been observed but not analyzed by modern statistical methods. The paper demonstrates that a large new analysis arsenal is available for analysis of cyclical features in intensive longitudinal data. This can help researchers extract more information from their data to get more valid estimates of coupled processes and to get new theoretical insights into circadian rhythms of mood. To assist in this effort, the analyses are based on general models with a rich set of features while still being accessible without an unduly steep learning curve. Scripts for the Mplus software are available for all the analyses presented.

Cited by 14Open access

Equation Balance and Dynamic Political Modeling

Matthew Lebo, Grant, Taylor · Harvard Dataverse · 2015

The papers in this symposium agree on several points. In this paper we sort through some remaining areas of disagreement and discuss some of the practical issues of time series modeling we think deserve further explanation. In particular, we have five points: (1) clarifying our stance on the GECM in light of the comments in this issue; (2) clarifying equation balance and discussing how bounded series affects our thinking about stationarity, balance, and modeling choices; (3) answering lingering questions about our Monte Carlo simulations and exploring potential problems in the inferences drawn from long-run multipliers; (4) reviewing and defending fractional integration methods in light of the questions raised in this symposium and elsewhere, and (5) providing a short practical guide to estimating a multivariate ARFIMA model with or without an error correction term.

Cited by 1Open access

Dynamic Economic Analysis from Difference Equation

Nand Kishor Kumar · International Journal of Humanities Education and Social Sciences · 2025

Dynamic economic analysis often involves understanding how economic variables evolve over time. One approach to modeling these dynamics is through the application of difference equations. Difference equations provide a framework for describing the evolution of economic variables in discrete time periods, making them particularly useful for analyzing time series data and economic processes that unfold in steps. In dynamic economic analysis, difference equations are an effective tool for modeling and comprehending how economic variables change with time. These difference equations are used by to study the behavior with economic systems and forecast future trends. Examples of these systems include market dynamics in the cobweb model and capital accumulation in the Solow growth model. Understanding the long-term behavior of complex systems is further aided by stability analysis, which guarantees that the models offer insightful information about economic processes. Stability analysis further aids in understanding the long-term behavior of these systems, ensuring that the models provide meaningful insights into economic processes.

Cited by 0Open access