Search results for "equation"
showing 10 items of 4219 documents
The shadow economy in three Mediterranean countries: France, Spain and Greece. A MIMIC approach
2007
This paper offers estimations of the evolution of the shadow economy in three Mediterranean countries, namely France, Spain and Greece. A multiple indicators and multiple causes model based on the latent variable structural theory has been applied. As established by Giles (Working paper on monitoring the health of the tax system, 1995), filtered data to solve the non-stationary problems are used. The model includes the tax burden (both as a whole and disaggregated into direct taxes, indirect taxes and social security contributions), a proxy of regulation burden, theu nemployment rate and self-employment as causes of the shadow economy and the GDP growth rate, the labour force participation …
Splitting the dynamics of large biochemical interaction networks
2003
This article is inscribed in the general motivation of understanding the dynamics on biochemical networks including metabolic and genetic interactions. Our approach is continuous modeling by differential equations. We address the problem of the huge size of those systems. We present a mathematical tool for reducing the size of the model, master-slave synchronization, and fit it to the biochemical context.
Phase separation in multi-component mixtures: the four-component case
2002
Abstract Calculation of ternary phase diagrams for several mixtures formed by two salts and a neutral component is presented here. The phase diagrams are obtained by inspection of the shape of the Gibbs free energy of mixing surface (Gmix) as a function of the composition at constant temperature and pressure. The Gmix surface is calculated by the mean spherical approximation (MSA). The model for the mixtures is represented by hard spheres, with the charged components interacting via a Coulomb potential. The results are interpreted in terms of a thermodynamic analysis of the contributions to the Gibbs free energy of mixing, i.e., the configurational energy, the volume and the entropy of mixi…
Relaxation of Electron Spin during High-Field Transport in GaAs Bulk
2011
A semiclassical Monte Carlo approach is adopted to study the multivalley spin depolarization of drifting electrons in a doped n-type GaAs bulk semiconductor, in a wide range of lattice temperature ($40<T_L<300$ K) and doping density ($10^{13}<n<10^{16}$cm$^{-3}$). The decay of the initial non-equilibrium spin polarization of the conduction electrons is investigated as a function of the amplitude of the driving static electric field, ranging between 0.1 and 6 kV/cm, by considering the spin dynamics of electrons in both the $\Gamma$ and the upper valleys of the semiconductor. Doping density considerably affects spin relaxation at low temperature and weak intensity of the driving electric fiel…
Distribution of oxygen partial pressure in a two-dimensional tissue supplied by capillary meshes and concurrent and countercurrent systems
1969
Abstract For the calculations of oxygen partial pressure in a two-dimensional tissue model supplied by a capillary network (inhomogeneously perfused tissue), two differential equations are given that describe the process in the tissue and capillaries. The differential equations are coupled by the boundary conditions. Results obtained by using the method of successive displacements are given for the two-dimensional problem. This method exhibits a satisfactory convergence. The accuracy of the results is about ±5% based on the initial concentration. The results for the network model are compared with those for equivalent concurrent and countercurrent systems. Equivalence means in this connecti…
Mass-flux-based outlet boundary conditions for the lattice Boltzmann method
2009
We present outlet boundary conditions for the lattice Boltzmann method. These boundary conditions are constructed with a mass-flux-based approach. Conceptually, the mass-flux-based approach provides a mathematical framework from which specific boundary conditions can be derived by enforcing given physical conditions. The object here is, in particular, to explain the mass-flux-based approach. Furthermore, we illustrate, transparently, how boundary conditions can be derived from the emerging mathematical framework. For this purpose, we derive and present explicitly three outlet boundary conditions. By construction, these boundary conditions have an apparent physical interpretation which is fu…
Exponential and bayesian conjugate families: Review and extensions
1997
The notion of a conjugate family of distributions plays a very important role in the Bayesian approach to parametric inference. One of the main features of such a family is that it is closed under sampling, but a conjugate family often provides prior distributions which are tractable in various other respects. This paper is concerned with the properties of conjugate families for exponential family models. Special attention is given to the class of natural exponential families having a quadratic variance function, for which the theory is particularly fruitful. Several classes of conjugate families have been considered in the literature and here we describe some of their most interesting feat…
Minimax estimation with additional linear restrictions - a simulation study
1988
Let the parameter vector of the ordinary regression model be constrained by linear equations and in addition known to lie in a given ellipsoid. Provided the weight matrix A of the risk function has rank one, a restricted minimax estimator exists which combines both types of prior information. For general n.n.d. A two estimators as alternatives to the unfeasible exact minimax estimator are developed by minimizing an upper and a lower bound of the maximal risk instead. The simulation study compares the proposed estimators with competing least-squares estimators where remaining unknown parameters are replaced by suitable estimates.
Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit
2011
In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. Electron. J. Probab. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there exists a unique symmetric limit measure associated to the set of invariant measures in the small-noise limit. The aim of this study is essentially to point out that this statement leads to the existence, as the noise intensity is small, of one unique…
Comprehensive estimation of input signals and dynamics in biochemical reaction networks
2012
Abstract Motivation: Cellular information processing can be described mathematically using differential equations. Often, external stimulation of cells by compounds such as drugs or hormones leading to activation has to be considered. Mathematically, the stimulus is represented by a time-dependent input function. Parameters such as rate constants of the molecular interactions are often unknown and need to be estimated from experimental data, e.g. by maximum likelihood estimation. For this purpose, the input function has to be defined for all times of the integration interval. This is usually achieved by approximating the input by interpolation or smoothing of the measured data. This procedu…