Rosin, P.L., A note on the least squares fitting of ellipses, Pattern Recognition Letters 14 (1993) 799-808. The characteristics of two normalisations for the general conic equation are investigated for use in least squares fitting: either setting F = 1 or A + C= 1. The normalisations vary in three main areas: curvature bias, singularities, transformational invariance. It is shown that setting ...

Dynamic model of continual process of contact and convective paper drying is recommended, as well as numerical procedure for its solution. Mathematical basis of the model suggested is partial differential equation of unsteady heat transfer by conduction, in direction perpendicular to paper surface. The equation has been solved with reference to two boundary conditions, one for each side of pape...

We report an experimental determination of the state-to-state rate constants of N2 in the vibrational ground state as a function of temperature, in the range 3,T,16 K. These rate constants were obtained by inversion of the master equation in a procedure not resorting to any particular fitting law. The coefficients of the master equation were obtained experimentally on the basis of Raman spectro...

The traditional Richards' equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards' equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scalin...

Introduction The Least Squares Fitting (LSF) is a computerized method of analysis of respiratory system mechanics. It is based on applying a regression analysis for every sample points of the loop of pressure, flow and volume by fitting the equation Paw = Rrs × V’ + VT/Crs + PEEPtot during inspiration [1]. This technique has been already validated in Controlled Mechanical Ventilation (CMV) and ...

Although algebraic or so-called “implicit polynomial” curves have been studied rather extensively for several decades, to the best of our knowledge, a dynamic formulation of them, similar to active contours, has not been done yet. This paper develops a dynamic formulation for implicit polynomial curves based on level set formalism. In particular, it is shown that utilization of an implicit poly...

We estimate a reduced-form model of credit risk that incorporates stochastic volatility in default intensity via stochastic time-change. Our Bayesian MCMC estimation method overcomes nonlinearity in the measurement equation and state-dependent volatility in the state equation. We implement on firm-level time-series of CDS spreads, and find strong in-sample evidence of stochastic volatility in t...

Although algebraic or so called “implicit polynomial” curves/surfaces have been studied rather extensively for several decades, to the best of our knowledge, a dynamic formulation of them, similar to active contours, has not been done yet. This paper proposes to use implicit polynomial functions instead of signed distance functions in classical level set formulation and shows potential of such ...