A database
of 140 diesel fuels having cetane numbers in the range
of 10–70 points; densities at 15 °C; and distillation
characteristics according to ASTM D-86 T
10%, T
50%, and T
90% was used to develop new procedures for predicting diesel cetane
numbers by application of the least-squares method (LSM) using MAPLE
software and an artificial neural network (ANN) using MATLAB. The
existing standard methods of determining cetane-index values, ASTM
D-976 and ASTM D-4737, which are correlations of the cetane number,
confirmed the earlier conclusions that these methods predict the cetane
number with a large variation. The four-variable ASTM D-4737 method
was found to better approximate the diesel cetane number than the
two-variable ASTM D-976 method. The developed four cetane-index models
(one LSM and three ANN models) were found to better approximate the
middle-distillate cetane numbers. Between 4% and 5% of the selected
database of 140 middle distillates were samples with differences between
their measured cetane numbers and the cetane-index values predicted
by the four new procedures was higher than the specified reproducibility
limit in the standard for measuring cetane number, ASTM D-613. In
contrast, the cetane-index values calculated in accordance with standards
ASTM D-976 and ASTM D-4737 demonstrated that 18% and 16% of the selected
database of 140 middle distillates, respectively, were samples with
differences between their measured cetane numbers and predicted cetane-index
values higher than the specified reproducibility limit in standard
ASTM D-613. The ASTM D-4737 method, LSM, and three ANN models were
tested against 22 middle distillates not included in the database
of 140 diesel fuels. The LSM cetane index showed the best cetane-number
prediction capability among all of the models tested.
In this article we introduce some impulsive models of tumor growth based on classical models as inhibition model, Piantadosi model, and autostimulation model. The basic goal is to describe the medical interventions during the treatment of the cancer process.The used technique is based on the theory of impulsive differential equations.
In this article, some properties of matrices of moving least-squares approximation have been proven. The used technique is based on singular-value decomposition and inequalities for singular-values. Some inequalities for the norm of coefficientsvector of the linear approximation have been proven.2010 Mathematics Subject Classification. 93E24.
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