Investigation of pH-dependent complex equilibria at low ligand to metal ratio by nonlinear least-squares fit to linear-sweep or cyclic voltammetric data

1987 ◽  
Vol 59 (20) ◽  
pp. 2456-2460 ◽  
Author(s):  
Harald. Gampp
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Linear Sweep ◽  
Cyclic Voltammetric ◽  
Complex Equilibria ◽  
Least Squares Fit ◽  
Metal Ratio ◽  
Ph Dependent

scholarly journals Near infrared nadir sounding of vertical column densities: methodology and application to SCIAMACHY

2011 ◽  
Vol 4 (3) ◽  
pp. 3685-3737
Author(s):  
S. Gimeno García ◽  
F. Schreier ◽  
G. Lichtenberg ◽  
S. Slijkhuis
Keyword(s):  
Least Squares ◽  
Near Infrared ◽  
Nonlinear Least Squares ◽  
Retrieval Algorithm ◽  
Atmospheric Gases ◽  
Vertical Column ◽  
Least Squares Fit ◽  
Least Squares Optimization ◽  
Shortwave Infrared ◽  
And Inversion

Abstract. Nadir observations with the shortwave infrared channels of SCIAMACHY onboard the ENVISAT satellite can be used to derive information on atmospheric gases such as CO, CH4, N2O, CO2, and H2O. For the operational level 1b–2 processing of SCIAMACHY data a new retrieval code BIRRA (Beer InfraRed Retrieval Algorithm) has been developed: BIRRA performs a nonlinear least squares fit of the measured radiance, where molecular concentration vertical profiles are scaled to fit the observed data. Here we present the forward modeling (radiative transfer) and inversion (least squares optimization) fundamentals of the code along with the further processing steps required to generate higher level products such as global distributions and time series. Moreover, various aspects of level 1 (observed spectra) and auxiliary input data relevant for successful retrievals are discussed. BIRRA is currently used for operational analysis of carbon monoxide vertical column densities from SCIAMACHY channel 8 observations, and is being prepared for methane retrievals using channel 6 spectra. A set of representative CO retrievals and first CH4 results are presented to demonstrate BIRRA's capabilities.

Molecular Parameters for the a3Πu and b3Σg− States in C2

1975 ◽  
Vol 53 (3) ◽  
pp. 299-302 ◽  
Author(s):  
L. Veseth
Keyword(s):  
Least Squares ◽  
Electronic Spectra ◽  
Nonlinear Least Squares ◽  
Experimental Information ◽  
Present Approach ◽  
Energy Separation ◽  
Molecular Parameters ◽  
Triplet Splitting ◽  
Least Squares Fit

Molecular parameters for the a3Πu and b3Σg− states in C2 (Ballik–Ramsay system) are determined by a nonlinear least squares fit directly to the observed wavelengths. No satellite lines are observed in the electronic spectra of C2, and the influence of nuclear statistics yields further restrictions with regard to observable lines. The present approach, however, yields accurate values of the various triplet splitting and Λ-doubling parameters in spite of this lack of experimental information. Finally a refined value of the triplet–singlet energy separation is obtained.

Easy-to-use indirect Fourier transformation routines for evaluation of slit-length-smeared SAXS curves of polystyrene in solution

1987 ◽  
Vol 20 (1) ◽  
pp. 41-47 ◽  
Author(s):  
O. Kube ◽  
J. Springer
Keyword(s):  
Least Squares ◽  
Fourier Transformation ◽  
Nonlinear Least Squares ◽  
Saxs Curve ◽  
Least Squares Fit ◽  
Non Linear ◽  
Slit Length

Two easy-to-use indirect Fourier-transformation routines for the evaluation of slit-length-smeared SAXS curves of polystyrene in solution are demonstrated. For approximation of the SAXS curve, analytically transformable Gaussian and Lorentzian functions are chosen. The nonlinear least-squares fit is transformed to a linear one by specifying fixed non-linear coefficients. The fit is constrained by allowing only positive linear coefficients. The range over which nonlinear coefficients have to be specified can be easily obtained from the SAXS curve. An exact specification of this range is unnecessary for the fit. The method allows direct and clear control of the indirect Fourier transformation.

A New Programmable Calculator Procedure for Individualizing Phenytoin Dosage

1983 ◽  
Vol 17 (12) ◽  
pp. 890-893 ◽  
Author(s):  
Andrea Messori ◽  
Tommaso Valenza ◽  
Gaetano Zaccara ◽  
Graziano Arnetoli ◽  
Carlo Bartoli ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Least Squares ◽  
Theoretical Approach ◽  
Nonlinear Least Squares ◽  
Computer Programs ◽  
Pharmacokinetic Data ◽  
Programmable Calculator ◽  
Model Parameter ◽  
Least Squares Fit ◽  
Programming Skill

A programmable calculator procedure allowing nonlinear least-squares fit to pharmacokinetic data conforming to the Michaelis-Menten model is described. Model parameter estimation is performed according to the iterative Gauss-Newton technique as modified by Hartley. This procedure thus employs the same theoretical approach used by most pharmacokinetic computer programs. No programming skill is needed to run the program described. The proposed procedure is discussed in detail and applied to some sets of pharmacokinetic data.

The three lowest ion-pair states of ICl

1984 ◽  
Vol 62 (12) ◽  
pp. 1941-1946 ◽  
Author(s):  
D. Bussières ◽  
A. R. Hoy
Keyword(s):  
Least Squares ◽  
Nonlinear Least Squares ◽  
Ion Pair ◽  
Matrix Elements ◽  
Coupling Matrix ◽  
Least Squares Fit ◽  
Vibrational Levels ◽  
Iodine Chloride ◽  
First Time ◽  
Chloride Molecule

The three lowest ion-pair states of the iodine chloride molecule, E(Ω = 0), β(Ω = 1), and D′(Ω = 2), form a coupled triad whose Te'S all lie within 50 cm−1. Transitions to low vibrational levels (ν = 0–2) of D′ are reported for the first time and the analysis of E and β at low ν is expanded considerably. By including the coupling matrix elements explicitly in a nonlinear least squares fit, values for the electronic matrix elements are found that are close to, but slightly less than, the pure precession values.

Mark IV "Grasshopper" grazing incidence monochromator for the Canadian Synchrotron Radiation Facility (CSRF)

1982 ◽  
Vol 60 (2) ◽  
pp. 131-136 ◽  
Author(s):  
K. H. Tan ◽  
G. M. Bancroft ◽  
L. L. Coatsworth ◽  
B. W. Yates
Keyword(s):  
Synchrotron Radiation ◽  
Least Squares ◽  
Radiation Source ◽  
Ultrahigh Vacuum ◽  
Nonlinear Least Squares ◽  
Grazing Incidence ◽  
Zero Order ◽  
Optical Characteristics ◽  
Least Squares Fit ◽  
Absorption Edges

The vacuum, mechanical, and optical characteristics of a "Grasshopper" grazing incidence monochromator, for use with a synchrotron radiation source in the 30–300 eV range, is described. The monochromator is compatible with ultrahigh vacuum (≤ 5 × 10−10 Torr throughout), and the motor driven scan mechanism is linear and reliable. The monochromator has been calibrated using several known absorption edges between 36 and 102 eV and a nonlinear least squares fit to the scan equation. These same absorption edges, plus a scan over zero order, show that the present resolution of the monochromator (with 10 and 16 μm exit and entrance slits respectively) is 0.16 Å (0.06 eV at the Al L2.3 edge). With 10 μm entrance and exit slits, the resolution will be very close to the theoretical Δλ = 0.083 Å.

NONLINEAR INVERSION OF PIEZOELECTRICAL TRANSDUCER IMPEDANCE DATA

2001 ◽  
Vol 09 (03) ◽  
pp. 899-910 ◽  
Author(s):  
LAURA CARCIONE ◽  
JOHN MOULD ◽  
V. PEREYRA ◽  
D. POWELL ◽  
G. WOJCIK
Keyword(s):  
Least Squares ◽  
Piezoelectric Materials ◽  
A Priori ◽  
Nonlinear Least Squares ◽  
Unconstrained Minimization ◽  
Electromagnetic Properties ◽  
Nonlinear Inversion ◽  
Inversion Algorithm ◽  
Bound Constraints ◽  
Least Squares Fit

We describe a nonlinear least squares inversion algorithm for obtaining elastic and electromagnetic properties for piezoelectric materials from measured impedances. Richard Brent's PRAXIS, a general unconstrained minimization code is used for the nonlinear least squares fit. No explicit derivatives of the goal functional are required by this code. Bound constraints are imposed in order to limit the variability of the parameters to physically meaningful values. Since PRAXIS is an unconstrained optimization code, these constraints are introduced via a novel change of independent variables. The forward modeling is achieved by using a coupled finite element time domain code for the elastic and electro-magnetic parts of the problem. We also describe how a linearized sensitivity analysis can be used to suggest a priori which parameters can be calculated from impedances measured on a given sample. Numerical results are included.

Sign in / Sign up

Export Citation Format

Share Document