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.

Descriptive Bond-Yield and Forward-Rate Models for the British Government Securities' Market: [forms Part Of: Report of the Fixed-Interest Working Group, B.A.J. 4, II Pg.213–383]

1998 ◽  
Vol 4 (2) ◽  
pp. 265-321 ◽  
Author(s):  
A.J.G. Cairns
Keyword(s):  
Least Squares ◽  
Working Group ◽  
Yield Curve ◽  
Securities Market ◽  
Rate Curve ◽  
Forward Rate ◽  
Bond Yield ◽  
Least Squares Fit ◽  
Curve Model ◽  
First Time

ABSTRACTThis paper discusses possible approaches to the construction of gilt yield indices published by the Financial Times. The existing method, described by Dobbie & Wilkie (1978) splits bonds into high, medium and low-coupon bands and fits separate yield curves to each. This method has been identified as susceptible to ‘catastrophic’ jumps when the least-squares fit jumps from one set of parameters to another set of quite different values. This problem is a result of non-linearities in the least-squares formula which can give rise to more than one local minimum. A desire to remove the risk of catastrophic changes prompted this research, which is being carried out as part of the work of the Fixed Interest Working Group.Recent changes in the taxation of bonds has, further, prompted the need for a review of the yield indices. Significantly, since the announcement of the new tax regime, the old coupon effect has been removed. This has made the use of a single forward-rate curve appropriate for the first time.A particular form of forward-rate curve is proposed as the basis for a revision of the gilt yield indices. This curve appears to give a significantly better fit than the present yield–curve model. It is also argued that the risk of catastrophic jumps has been reduced significantly.

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.

The Iodine Hvperfine Structure in the Microwave Spectrum of Ethyl Iodide: Nuclear Quadrupole and Spin Rotation Coupling

1988 ◽  
Vol 43 (11) ◽  
pp. 971-976 ◽  
Author(s):  
Joachim Gripp ◽  
Helmut Dreizler
Keyword(s):  
Fourier Transform ◽  
Microwave Spectrum ◽  
Spin Rotation ◽  
Ethyl Iodide ◽  
Hamiltonian Matrix ◽  
Matrix Elements ◽  
Coupling Matrix ◽  
Error Limit ◽  
Least Squares Fit ◽  
Nuclear Quadrupole

Abstract Some rotational transitions of ethyl iodide, CH3CH2I, have been reinvestigated by microwave Fourier transform (MWFT) spectroscopy. The iodine hyperfine structure splittings were first ana lyzed using a direct diagonalization procedure of the complete quadrupole Hamiltonian matrix. The results of this analysis showed deviations from our measurements up to 60 kHz. A new analysis using additional spin rotation coupling matrix elements reproduces our measurements within the experi­mental error limit and decreases the standard deviation of the least squares fit from 28 kHz to only 4 kHz.

Rotational analysis of the B2Σ+ – A2Πi system of the 12C16O+ molecule

1987 ◽  
Vol 65 (1) ◽  
pp. 94-100 ◽  
Author(s):  
Z. Jakubek ◽  
R. Kepa ◽  
A. Para ◽  
M. Rytel
Keyword(s):  
High Resolution ◽  
Least Squares ◽  
Least Squares Method ◽  
Nonlinear Least Squares ◽  
Spin Rotation ◽  
Spin Orbit ◽  
Rotational Analysis ◽  
Molecular Constants ◽  
Nonlinear Least Squares Method ◽  
First Time

The three bands (0–0, 1–0, 0–1) of the B2Σ+ – A2Πi system of the 12C16O+ molecule have been photographed at high resolution. In total, 824 lines were measured, from which 608 were fitted by a nonlinear least squares method to determine 33 molecular constants. The band-by-band results were merged to obtain 23 molecular constants for the B2Σ+, ν = 0 and 1, and A2Πi, ν = 0 and 1, states. The Λ-doubling constants and spin-orbit constants in the A2Πi, ν = 1 state and spin-rotation constants in the B2Σ+, ν = 0 and 1 states were obtained for the first time, and other constants were defined more precisely.

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.

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.

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