The Antoine equation is a semi-empirical equation which expresses vapour pressure as a function of temperature. A new, rapid and highly accurate method for obtaining its three constants from experimental data is presented and applied to ethanol, water and 14 anaesthetic substances. Alternative vapour pressure equations are discussed and references for original temperature--vapour pressure data ...

We begin by reviewing the derivation of generalized Maxwell equations from an operational definition of the electromagnetic field and the most basic notions of what constitutes a dynamical field theory. These equations encompass the familiar Maxwell equations as a special case but, in other cases, can predict birefringence, charge non-conservation, wave damping and other effects that the famili...

In this paper we give a proof of the Wilks theorem for the empirical likelihood ratio test for the right censored data, when the hypothesis are formulated in terms of p estimating equations or mean functions. In particular we show that the empirical likelihood ratio test statistic is equal to a quadratic form similar to a Hotelling’s T 2 statistic, plus a small error. The least favorable distri...

The generalized empirical likelihood (GEL) method produces a class of estimators of parameters defined via general estimating equations. This class includes several important estimators, such as empirical likelihood (EL), exponential tilting (ET), and continuous updating estimators (CUE). We examine the information geometric structure of GEL estimators. We introduce a class of estimators closel...

The scarf framework as presented [2] offers the basic equations for training SCRFs. We propose to extend the framework with Empirical Bayes Risk training or Empirical Training Error optimization, which are better correlated with the error metric one seeks to optimize, than the conditional log-likelihood normally used. Second, SCRFs are (marginalized) exponential models over segmented sequences....

Flow over a downstream-facing step is predicted using the F.E.M. A two-equation model of turbulence is employed where the transport of turbulence kinetic energy and dissipation rate are depicted using transport-type equations, i.e. the two-equation model of turbulence. The results obtained are compared with other models and experimental results. Generally, the model was found to be under-predic...

A formant analyser is interpreted probabilistically via a noisy channel model. This leads to a robust method of incorporating formant features into hiddenMarkov models for automatic speech recognition. Recognition equations follow trivially, and Baum-Welch style re-estimation equations are derived. Experimental results are presented which provide empirical proof of convergence, and demonstrate ...

Attenuation relation (Ground-motion prediction equation) The term “attenuation relation” is a former short-hand notation in earthquake engineering for “empirical ground-motion attenuation relationship”, now referred to as “ground-motion prediction equation” (GMPE). Attenuation relations represent empirical scaling equations that relate observed ground-motion intensity measures to parameters of ...

Conventional work on scienti c discovery such as BACON derives empirical law equations from experimental data. In recent years, SDS introducing mathematical admissibility constraints has been proposed to discover rst principle based law equations, and it has been further extended to discover law equations from passively observed data. Furthermore, SSF has been proposed to discover the structure...

This paper proposes a new perspective for solving systems of nonlinear equations. A system of equations can be viewed as a multiobjective optimization problem: every equation represents an objective function whose goal is to minimize difference between the right and left term of the corresponding equation in the system. We used an evolutionary computation technique to solve the problem obtained...