Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.

Observable quantities in weyl gravity

Abstract: In this paper, the cosmological "constant" and the Hubble parameter are considered in the Weyl theory of gravity, by taking them as functions of r and t, respectively. Based on this theory and in the linear approximation, we obtain the values of H0 and Λ0 which are in good agreement with the known values of the parameters for the current state of the universe.

Quantum theory of a one-dimensional laser with output coupling: Linear approximation

Abstract: A simple model of a one-dimensional optical cavity having output coupling is used to develop a fully quantized linear laser theory. The present model and procedure, which work directly within the continuous spectrum, allow us to find a simple treatment that leads to explicit solutions for the field inside and outside the laser cavity. The threshold condition for laser light onset is obtained by assuming the field operating in a single collective mode and the usual adiabatic hypothesis. A development that removes this later restriction is also discussed and outlined.

Model selection and structure specification in ultra-high dimensional generalised semi-varying coefficient models

Abstract: In this paper, we study the model selection and structure specification for the generalised semi-varying coefficient models (GSVCMs), where the number of potential covariates is allowed to be larger than the sample size.We first propose a penalised likelihood method with the LASSO penalty function to obtain the preliminary estimates of the functional coefficients. Then, using the quadratic approximation for the local log-likelihood function and the adaptive group LASSO penalty (or the local linear approximation of the group SCAD penalty) with the help of the preliminary estimation of the functional coefficients, we introduce a novel penalised weighted least squares procedure to select the significant covariates and identify the constant coefficients among the coefficients of the selected covariates, which could thus specify the semiparametric modelling structure. The developed model selection and structure specification approach not only inherits many nice statistical properties from the local maximum likelihood estimation and nonconcave penalised likelihood method, but also computationally attractive thanks to the computational algorithm that is proposed to implement our method. Under some mild conditions, we establish the asymptotic properties for the proposed model selection and estimation procedure such as the sparsity and oracle property.We also conduct simulation studies to examine the finite sample performance of the proposed method, and finally apply the method to analyse a real data set, which leads to some interesting findings.

Characteristics analysis and stabilization of a planar 2R underactuated manipulator

Abstract: The weightless planar 2R underactuated manipulators with passive last joint are considered in this paper for investigating a feasible method to stabilize the system, which is a second-order nonholonomic-constraint mechanical system with drifts. The characteristics including the controllability of the linear approximation model, the minimum phase property, the Small Time Local Controllability (STLC), the differential flatness, and the exactly nilpotentizable properties, are analyzed. Unfortunately, these negative characteristics indicate that the simplest underactuated mechanical system is difficult to design a stable closed-loop control system. In this paper, nilpotent approximation and iterative steering methods are utilized to solve the problem. A globally effective nilpotent approximation model is developed and the parameterized polynomial input is adopted to stabilize the system to its non-singularity equilibrium configuration. In accordance with this scheme, it is shown that designing a stable closed-loop control system for the underactuated mechanical system can be ascribed to solving a set of nonlinear algebraic equations. If the nonlinear algebraic equations are solvable, then the controller is asymptotically stable. Some numerical simulations demonstrate the effectiveness of the presented approach.

On uniqueness and proportionality in multi-class equilibrium assignment

Abstract: Over the past few years, much attention has been paid to computing flows for multi-class network equilibrium models that exhibit uniqueness of the class flows and proportionality (Bar-Gera et al., 2012). Several new algorithms have been developed such as bush based methods of Bar-Gera (2002), Dial (2006), and Gentile (2012) that are able to obtain very fine solutions of network equilibrium models. These solutions can be post processed (Bar-Gera, 2006) in order to ensure proportionality and class uniqueness of the flows. Recently developed, the TAPAS, algorithm (Bar Gera, 2010) is able to produce solutions that have proportionality embedded, without requiring post processing. It was generally accepted that these methods for solving UE traffic assignment are the only way to obtain unique path and class link flows. The purpose of this paper is to show that the linear approximation method and some of its variants satisfy these conditions as well. In addition, some analytical results regarding the relation between steps of the linear approximation algorithm and the path flows entropy are presented.