A Program for Linear Regression with a Common Point of Intersection:  The Isokinetic Relationship

2001 ◽  
Vol 41 (5) ◽  
pp. 1141-1144 ◽  
Author(s):  
Carole Ouvrard ◽  
Michel Berthelot ◽  
Thierry Lamer ◽  
Otto Exner
Keyword(s):  
Linear Regression ◽  
Common Point ◽  
Isokinetic Relationship ◽  
Point Of Intersection

Concerning the Problem of the Isokinetic Relationship. IV. The Evaluation of the Isosubstituent Hammett Parameter by Means of Isokinetic and Isoequilibrium Temperatures

1986 ◽  
Vol 39 (2) ◽  
pp. 199 ◽  
Author(s):  
W Linert
Keyword(s):  
Temperature Dependence ◽  
Activation Parameters ◽  
Common Point ◽  
Isokinetic Temperature ◽  
Benzoic Acids ◽  
Reaction Series ◽  
Isokinetic Relationship ◽  
The Common ◽  
Point Of Intersection ◽  
Hammett Parameter

The interrelation between the isosubstituent and the isokinetic relationship is developed and tested for several Hammett reaction series. Two methods of approach to relate the temperature dependence of Arrhenius and Hammett plots are given, one utilizing the isoequilibrium temperature of the ionization of benzoic acids and the other the isokinetic temperature of the respective Hammett reaction series. The efficiency of the approaches for the evaluation of the coordinates of the common point of intersection in the Hammett plot, i.e. the characteristics of the isosubstituent relationship, are compared with each other and with experimental results. With the former approach, by using the activation parameters of only one (commonly the unsubstituted ) member of the series, the temperature dependence of a Hammett line can be predicted provided that the isokinetic temperature of the Hammett series does not approach the experimental temperature range. Otherwise the latter approach must be used which, however, needs the temperature dependence of at least two (or better more) members of the reaction series.

A result of resonant energy exchange between reactants and their chemical surrounding: The isokinetic relationship

1990 ◽  
Vol 55 (1) ◽  
pp. 21-31 ◽  
Author(s):  
Wolfgang Linert
Keyword(s):  
Energy Transfer ◽  
Energy Exchange ◽  
Equilibrium Constants ◽  
Heat Bath ◽  
Common Point ◽  
Isokinetic Temperature ◽  
Isokinetic Relationship ◽  
Resonant Energy ◽  
Point Of Intersection

Many homologous series of reactions exhibit a common point of intersection in the ln k versus 1/T plots. This can be taken as a profound basis for the appearance of the isokinetic relationship (IKR) defining a temperature where rate (or equilibrium) constants of the series show a minimum in selectivity. The theoretically derived relationship describing the IKR and yielding a correlation between the isokinetic temperature and the frequencies available in an ideal heat bath is examined for real systems. It is shown that the role of the solvent in chemical reactions that exhibit isokinetic relationship is not only due to chemical interactions but also to energy transfer between reactants and solvents and vice versa.

On estimating the common point of intersection of curves

2001 ◽  
Vol 135 (2) ◽  
pp. 350-360 ◽  
Author(s):  
Shaul P Ladany ◽  
Israel David
Keyword(s):  
Common Point ◽  
The Common ◽  
Point Of Intersection

Concerning the Problem of the Isokinetic Relationship. III. The Temperature-Dependance of the hammett Equation

1985 ◽  
Vol 38 (5) ◽  
pp. 677 ◽  
Author(s):  
W Linert ◽  
R Schmid ◽  
AB Kudrjawtsev
Keyword(s):  
Benzoic Acid ◽  
Hammett Equation ◽  
Reaction Series ◽  
Temperature Dependent ◽  
Isokinetic Relationship ◽  
A Value ◽  
The Common ◽  
Point Of Intersection ◽  
Temperature Dependance ◽  
The Relationship

It is shown that the temperature-dependence of the Hammett equation is, in contrast to tradition, both physically and experimentally better described by means of temperature-dependent σ and temperature- independent ρ (termed ρo). The relationship between ρo and the customary (temperature dependent) ρ is ρT = ρo(1/T-1/Tbiso)/(1/T-1/Tbiso) where Tbiso , is the isoequilibrium temperature of the benzoic acid ionization, for which the present analysis suggests a value of -255 K, and T is 298 K. In these terms, the temperature variation of the Hammett equation can be evaluated by supplying merely E(u)a (the activation energy for the reaction of the unsubstituted reactant) and ρo, in that the σ value for the isokinetic substituent , i.e., the abscissa of the common point of intersection in the Hammett plot, is σiso = (1/T-1/Tbiso)E(u)a/(2.303Rρo) = E(u)a/(2630po) Further, ρo I related to energies ρo = E(u)a/(ΔH°u-ΔH°s(iso))where ΔH°u and ΔH°s(iso) are the ionization enthalpies of the parent benzoic acid and that bearing the isokinetic substituent , respectively. Analogous equations apply to thermodynamic reaction series when substituting E(u)a for ΔH°u(series). Along these lines the interpretation of the customary Hammett plot is advanced.

The Use Of Prior Information In Linear Regression Analysis

1975 ◽  
Vol 4 (6) ◽  
pp. 497-517
Author(s):  
R. L. Anderson ◽  
E. L. Battiste
Keyword(s):  
Regression Analysis ◽  
Linear Regression ◽  
Prior Information ◽  
Linear Regression Analysis

Review of An Introduction to Linear Regression and Correlation. 2nd ed.

1985 ◽  
Vol 30 (10) ◽  
pp. 824-824
Author(s):  
William L. Hays
Keyword(s):  
Linear Regression

Prothrombin Time Standardization: Report of the Expert Panel on Oral Anticoagulant Control

1979 ◽  
Vol 42 (04) ◽  
pp. 1073-1114 ◽  
Keyword(s):  
Prothrombin Time ◽  
Expert Panel ◽  
The Other ◽  
Rabbit Brain ◽  
Calibration Constant ◽  
Freeze Dried ◽  
The Mean ◽  
Point Of Intersection ◽  
And Control ◽  
Standardization Report

SummaryIn collaborative experiments in 199 laboratories, nine commercial thromboplastins, four thromboplastins held by the National Institute for Biological Standards and Control (NIBS & C), London and the British Comparative Thromboplastin were tested on fresh normal and coumarin plasmas, and on three series of freeze-dried plasmas. One of these was made from coumarin plasmas and the other two were prepared from normal plasmas; in each series, one plasma was normal and the other two represented different degrees of coumarin defect.Each thromboplastin was calibrated against NIBS&C rabbit brain 70/178, from the slope of the line joining the origin to the point of intersection of the mean ratios of coumarin/normal prothrombin times when the ratios obtained with the two thromboplastins on the same fresh plasmas were plotted against each other. From previous evidence, the slopes were calculated which would have been obtained against the NIBS&C “research standard” thromboplastin 67/40, and termed the “calibration constant” of each thromboplastin. Values obtained from the freeze-dried coumarin plasmas gave generally similar results to those from fresh plasmas for all thromboplastins, whereas values from the artificial plasmas agreed with those from fresh plasmas only when similar thromboplastins were being compared.Taking into account the slopes of the calibration lines and the variation between laboratories, precision in obtaining a patient’s prothrombin time was similar for all thromboplastins.

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