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A-optimal chemical balance weighing design with correlated errors, and
BronisLaw Ceranka,MaLgorzata Graczyk 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-
In this paper we study the estimation problem of individual weights of objects using an A-optimal chemical balance weighing design. We assume that in this model errors are correlated and they have the same variances. The lower bound of tr(X0G−1X)−1 is obtained and a necessary and sufficient condition for this lower bound to be attained is given. There is given new construction method of A-optimal chemical balance weighing design.
A-OPTIMAL CHEMICAL BALANCE WEIGHING DESIGN WITH CORRELATED ERRORS
Ceranka, Bronislaw,Graczyk, Malgorzata 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.1
In this paper we study the estimation problem of individual weights of objects using an A-optimal chemical balance weighing design. We assume that in this model errors are correlated and they have the same variances. The lower bound of tr$(X'G^{-1}X)^{-1}$ is obtained and a necessary and sufficient condition for this lower bound to be attained is given. There is given new construction method of A-optimal chemical balance weighing design.
Bayda, Malgorzata,Hug, Gordon L.,Lukaszewicz, Jakub,Majchrzak, Mariusz,Marciniec, Bogdan,Marciniak, Bronislaw Korean Society of Photoscience 2009 Photochemical & photobiological sciences Vol.8 No.12
The kinetics scheme for directly excited, photoreversible reactions is solved exactly under the assumptions of no irreversible side reactions and constant excitation intensity for the duration of the reaction. The advantages of the methodology over the extrapolation-to-zero-time and the back-reaction correction methods are (i) that the quantum yields of both the forward and reverse photoreactions can be obtained starting from either pure reactant or pure product and (ii) the conversion percentage is not limited to a narrow domain in the neighborhood of small conversions. Examples of E-Z photoisomerizations are given to illustrate the fitting procedures required. The results from these examples are compared to the photoisomerization method of extrapolating the empirical quantum yields to zero time and the back-reaction correction. The exact equations are used to justify the extrapolation-to-zero-time method and to establish criteria on extrapolation ranges for the conversion percentage of starting material.