scholarly journals Crystal shapes and phase equilibria: A common mathematical basis

1996 ◽  
Vol 27 (6) ◽  
pp. 1431-1440 ◽  
Author(s):  
J. W. Cahn ◽  
W. C. Carter
Keyword(s):  
Phase Equilibria ◽  
Mathematical Basis ◽  
Crystal Shapes

On the Mathematical Basis of Zelen’s Prerandomized Designs

1985 ◽  
Vol 24 (03) ◽  
pp. 120-130 ◽  
Author(s):  
E. Brunner ◽  
N. Neumann
Keyword(s):  
Clinical Trial ◽  
Normal Distribution ◽  
Random Variables ◽  
Small Samples ◽  
Selection Effects ◽  
Sample Sizes ◽  
Mathematical Basis ◽  
Additional Assumptions

SummaryThe mathematical basis of Zelen’s suggestion [4] of pre randomizing patients in a clinical trial and then asking them for their consent is investigated. The first problem is to estimate the therapy and selection effects. In the simple prerandomized design (PRD) this is possible without any problems. Similar observations have been made by Anbar [1] and McHugh [3]. However, for the double PRD additional assumptions are needed in order to render therapy and selection effects estimable. The second problem is to determine the distribution of the statistics. It has to be taken into consideration that the sample sizes are random variables in the PRDs. This is why the distribution of the statistics can only be determined asymptotically, even under the assumption of normal distribution. The behaviour of the statistics for small samples is investigated by means of simulations, where the statistics considered in the present paper are compared with the statistics suggested by Ihm [2]. It turns out that the statistics suggested in [2] may lead to anticonservative decisions, whereas the “canonical statistics” suggested by Zelen [4] and considered in the present paper keep the level quite well or may lead to slightly conservative decisions, if there are considerable selection effects.

Comparison of Rheumatological Diagnoses by a Bayesian Program and by Physicians

1991 ◽  
Vol 30 (03) ◽  
pp. 187-193 ◽  
Author(s):  
H. J. Moens ◽  
J. K. van der Korst
Keyword(s):  
Receiver Operating Characteristics ◽  
Bayesian Decision ◽  
Operating Characteristics ◽  
Likelihood Ratios ◽  
Improve Performance ◽  
Mathematical Basis ◽  
Human Expert ◽  
Test Population ◽  
Sensitivity Specificity ◽  
Diagnostic Outcome

AbstractA Bayesian decision support system was developed for the diagnosis of rheumatic disorders. Knowledge in this system is represented as evidential weights of findings. Simple weights were calculated as the logarithm of likelihood ratios on the basis of 1,000 consecutive patients from a rheumatological clinic. The effect of various methods to improve performance of the system by modification of the weights was studied. Three methods had a mathematical basis; a fourth consisted of weights adapted by a human expert, which allowed inclusion of diagnostic rules such as defined in widely accepted criteria sets. The system’s performance was measured in a test population of 570 different cases from the same clinic and compared with predictions of diagnostic outcome made by rheumatologists. The weights from a human expert gave optimal results (sensitivity 65% and specificity 96%), that were close to the physicians’ predictions (sensitivity 64% and specificity 98%). The methods to measure the performance of the various models used in this study emphasize sensitivity, specificity and the use of receiver operating characteristics.

Phase equilibria in partially open systems under pressure: the decomposition of stoichiometric GeO2 oxide

2003 ◽  
Vol 173 (12) ◽  
pp. 1359 ◽  
Author(s):  
Vadim V. Brazhkin ◽  
Roman N. Voloshin ◽  
A.G. Lyapin ◽  
Svetlana V. Popova
Keyword(s):  
Phase Equilibria ◽  
Open Systems

Mathematical basis of an algorithm for the formation of space equipment complex for a scientific and applied RSE program

2002 ◽  
Vol 8 (2-3) ◽  
pp. 73-76
Author(s):  
O.D. Fedorovskyi ◽  
◽  
V.P. Zubko ◽  
V.G. Yakimchuk ◽  
◽  
...  
Keyword(s):  
Mathematical Basis ◽  
Equipment Complex

VAN LAAR EQUATION AND UNIFAC TO CORRELATE THE DATA LIQUID PHASE EQUILIBRIA FOR THE EXTRACTION OF PHENOLIC COMPOUNDS FROM MODEL COAL TAR

2016 ◽  
Vol 72 (9) ◽  
Author(s):  
Dewi Selvia Fardhyanti ◽  
Wahyudi B. Sediawan ◽  
Panut Mulyono ◽  
Muslikhin Hidayat
Keyword(s):  
Phenolic Compounds ◽  
Liquid Phase ◽  
Phase Equilibria ◽  
Coal Tar ◽  
Van Laar Equation
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