scholarly journals New function for representing IEC 61000-4-2 standard electrostatic discharge current

2014 ◽  
Vol 27 (4) ◽  
pp. 509-520 ◽  
Author(s):  
Vesna Javor
Keyword(s):  
Least Squares ◽  
Discharge Current ◽  
Least Squares Method ◽  
Electrostatic Discharge ◽  
First Derivative ◽  
Good Agreement

New function for representing electrostatic discharge (ESD) currents according to the IEC 61000-4-2 Standard current is proposed in this paper. Good agreement with the Standard defined parameters is obtained. This function is compared to other functions from literature. Its first derivative needed for field calculations is analyzed in the paper. Main advantages are simplified choice of parameters, possibility to obtain discontinuities in the decaying part, and zero value of the function first derivative at t=0+. Parameters of the function are obtained by using Least-squares method (LSQM).

Curve Shape Modification and Fairness Evaluation

2007 ◽  
Author(s):  
Tetsuzo Kuragano ◽  
Akira Yamaguchi
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Curvature Vector ◽  
Radius Of Curvature ◽  
Curve Shape ◽  
Linear Quadratic ◽  
Nurbs Curve ◽  
First Derivative ◽  
Curvature Distribution ◽  
The Given

A method to generate a quintic NURBS curve which passes through the given points is described. In this case, there are four more equations than there are positions of the control points. Therefore, four gradients which are the first derivative of a NURBS equation are assigned to the given points. In addition to this method, another method to generate a quintic NURBS curve which passes through the given points and which has the first derivative at these given points is described. In this case, a linear system will be underdetermined, determined or overdetermined depending on the number of given points with gradients. A method to modify NURBS curve shape according to the specified radius of curvature distribution to realize an aesthetically pleasing freeform curve is described. The differences between the NURBS curve radius of curvature and the specified radius of curvature is minimized by introducing the least-squares method. A criterion for a fair curve is proposed. Evaluation whether the designed curve is fair or not is accomplished by a comparison of the designed curve to a curve whose radius of curvature is monotone. The radius of curvature is specified by linear, quadratic, and cubic function using the least-squares method. A curve whose radius of curvature is reshaped by one of these algebraic functions is considered as a fair curve. The curvature vector of the curve is used to evaluate the fairness. The comparison of unit curvature vectors is used to evaluate the directional similarity of the curve. The comparison of the curvature is used to evaluate the similarity of the magnitude of curvature vectors. If the directional similarity of the designed curve is close to the fair curve, and also the similarity of the curvature is close to the fair curve, the designed curve can be judged as a fair curve.

scholarly journals THE MEASUREMENT OF INCIDENT AND REFLECTED SPECTRA USING A LEAST SQUARES METHOD

1980 ◽  
Vol 1 (17) ◽  
pp. 8 ◽  
Author(s):  
E.P.D. Mansard ◽  
E.R. Funke
Keyword(s):  
Wave Propagation ◽  
Least Squares ◽  
Simultaneous Measurement ◽  
Least Squares Method ◽  
Experimental Investigations ◽  
Side Channel ◽  
Line Parallel ◽  
The Waves ◽  
Good Agreement

A least squares method to separate the incident and reflected spectra from the measured co-existing spectra is presented. This method requires a simultaneous measurement of the waves at three positions in the flume which are in reasonable proximity to each other and are on a line parallel to the direction of wave propagation. Experimental investigations have shown that there is good agreement between the incident spectra calculated by the least squares method and the incident spectra measured concurrently in a side channel.

scholarly journals Resonance Parameters for Uranium 233

1967 ◽  
Vol 20 (6) ◽  
pp. 617 ◽  
Author(s):  
AR de L Musgrove
Keyword(s):  
Least Squares ◽  
Cross Sections ◽  
Least Squares Method ◽  
The Other ◽  
Resonance Parameters ◽  
Single Level ◽  
Channel Theory ◽  
Good Agreement

Single-level and multilevel resonance parameters are given for 233U below 11 e V_ The total and fission cross sections were fitted simultaneously and good agreement was obtained. Spin assignments determined by the least squares method support the prediction of the channel theory of fission that 233U has two level populations; one with predominantly large fission widths and the other with much narrower widths.

Schwingungsspektren und Kraftkonstanten einiger Tertiärbutylacetylene

1970 ◽  
Vol 25 (8-9) ◽  
pp. 1281-1291
Author(s):  
W. Hüttner ◽  
W. Zeil
Keyword(s):  
Force Field ◽  
Least Squares ◽  
Vibrational Spectra ◽  
Least Squares Method ◽  
Force Fields ◽  
Preceding Paper ◽  
Force Constants ◽  
Bond Properties ◽  
Tertiary Butyl ◽  
Good Agreement

Abstract A normal co-ordinate analysis of the vibrational spectra of the (CH3)3C-C = C-H, - D, -Cl, -Br and -J compounds has been carried out, and force constants of three slightly different simplified valence force fields have been obtained. Both the iteration procedure described in the preceding paper, and a well-known least-squares technique were used in the computations. The first method proved successful for all species and all force fields. The least-squares method yielded converging results in the case of tertiary butyl acetylene, when the two isotopic frequency sets were refined simultaneously and when a sufficient amount of constraint was introduced into the force field. The force constants belonging to the same force field as obtained by the two independent methods are in good agreement. The valence constants of the acetylenic chain seem to reveal some expected distinctions in the bond properties of the pure acetylene and the halogenated compounds.

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

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