Search results for "Differential equation"
showing 10 items of 759 documents
The body-mind problem from a personality relativity theory approach: (Relativity of personality)
2012
The body-mind problem is here posed fromthe General Factor of Personality Theory and mathematically presented as a relativity theory: 1. A two-level-invariant model; 2. The transformation equation between both levels. On a hand, the investigation of personality dynamicsas a consequenceof a stimulant drug provides a system of two coupled differential equations, which adapts to both biological (body) and psychological (mind)levels ofdescription. On the other hand, a system of two coupled partial differential equations is here deduced as the transformation model between the biological and psychological levels. Both models are presented and validated in this paper. The experimental design to va…
Supply chain modelling and analysis: an application of Latin square to a repeated coupling of non-linear differential equations
2011
In the last 50 years, Forrester’s system dynamics techniques have been adopted to analyse problems and find solutions for global supply chains. An important topic in production-inventory system modelling is the design of experiment. The aim of this paper is to present an application of a statistical technique of design of experiment, the Latin Square Design, to set a combination of input values for the initial-value problem of non-linear repeated coupling of first-order differential equations modelling a production-inventory system. This design permits to reduce the number of experiments while allowing statistical analysis for testing the significance of the studied parameters.
Spatial seismic point pattern analysis with Integrated Nested Laplace Approximation
2020
This paper proposes the use of Integrated Nested Laplace Approximation (Rue et al., 2009) to describe the spatial displacement of earthquake data. Specifying a hiechical structure of the data and parameters, an inhomogeneuos Log-Gaussian Cox Processes model is applied for describing seismic events occurred in Greece, an area of seismic hazard. In this way, the dependence of the spatial point process on external covariates can be taken into account, as well as the interaction among points, through the estimation of the parameters of the covariance of the Gaussian Random Field, with a computationally efficient approach.
Energy and Personality: A Bridge between Physics and Psychology
2021
[EN] The objective of this paper is to present a mathematical formalism that states a bridge between physics and psychology, concretely between analytical dynamics and personality theory, in order to open new insights in this theory. In this formalism, energy plays a central role. First, the short-term personality dynamics can be measured by the General Factor of Personality (GFP) response to an arbitrary stimulus. This GFP dynamical response is modeled by a stimulus¿response model: an integro-differential equation. The bridge between physics and psychology appears when the stimulus¿response model can be formulated as a linear second order differential equation and, subsequently, reformulat…
Analysis of a slow–fast system near a cusp singularity
2016
This paper studies a slow fast system whose principal characteristic is that the slow manifold is given by the critical set of the cusp catastrophe. Our analysis consists of two main parts: first, we recall a formal normal form suitable for systems as the one studied here; afterwards, taking advantage of this normal form, we investigate the transition near the cusp singularity by means of the blow up technique. Our contribution relies heavily in the usage of normal form theory, allowing us to refine previous results. (C) 2015 Elsevier Inc. All rights reserved.
Indefinite integrals involving Jacobi polynomials from integrating factors
2020
A method was presented recently for deriving integrals of special functions using two kinds of integrating factor for the homogeneous second-order linear differential equations which many special f...
Indefinite integrals of special functions from hybrid equations
2019
Elementary linear first and second order differential equations can always be constructed for twice differentiable functions by explicitly including the function's derivatives in the definition of ...
Indefinite integrals of Lommel functions from an inhomogeneous Euler–Lagrange method
2015
ABSTRACTA method given recently for deriving indefinite integrals of special functions which satisfy homogeneous second-order linear differential equations has been extended to include functions which obey inhomogeneous equations. The extended method has been applied to derive indefinite integrals for the Lommel functions, which obey an inhomogeneous Bessel equation. The method allows integrals to be derived for the inhomogeneous equation in a manner which closely parallels the homogeneous case, and a number of new Lommel integrals are derived which have well-known Bessel analogues. Results will be presented separately for other special functions which obey inhomogeneous second-order linear…
A generalized integration formula for indefinite integrals of special functions
2020
An integration formula for generating indefinite integrals which was presented in Conway JT [A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec...
A third integrating factor for indefinite integrals of special functions
2020
An integrating factor f ~ x is presented involving the terms in y ′ ′ x and q x y x of the general homogenous second-order linear ordinary differential equation. The new integrating factors obey se...