We assume that a tubular surface [M.sub.1] is a linear Weingarten surface in [E.sup.3.sub.1], such that, it satisfies the linear equation
[ak.sub.1] + [bk.sub.2] = c.
The formalism with nth-order linear differential equations is developed for obtaining equivalent differential systems of n first-order linear equations
. The solution existence and uniqueness are addressed through the use of the iterative Picard's method for construction of the solution and Lipschitz's condition.
This matrix equation is equivalent to the set of linear equations
This is obtained by solving three linear equations
with three unknowns, a, b and c as seen below.
Thus, we have that the fuzzy linear equation
(5) has a nonnegative strong LR complex fuzzy minimal solution by Definition 8.
That is, given ([x.sub.1], [f.sub.1]) and ([x.sub.2], [f.sub.2]), ([x.sub.n], [f.sub.n]) is able to be predicted through the linear equations
. As shown in Figure 6, after contour information of lung is extracted in the nth and n + 1th slices of chest CT images, the coordinates similar to the actual contours coordinates can be obtained if the outline of the results of the n + 2th second installment is predicted through the linear equation
A linear equation
of the slope angles ([theta]) of all the potential vertical line components is estimated using a LLS(linear least squares) as the dotted regression line in Fig.
The linear equation
for calculating the temperature from the results of measuring of the sensor type LM35A No 7 output voltage of sensor takes the form
The equation coefficients' significance of the linear equation
was tested with the help of the Student test.
 A M Ikotun, A T Akinwale, O T Arogundade, Parameter Variation For Linear Equation
Solver Using Genetic Algorithm, Journal Of Natural Sciences Engineering And Technology, 15/2, 2016
In various fields of sciences, in solving real-life problems, where the system of linear equations
is noticed, there are situations where the values of the parameters cannot be stated exactly, but their estimation or some bounds on them can be measured.
To have a mathematical relation for temperature drop in terms of depth of cross section, a linear equation
or more accurately a fourth-degree polynomial is the most suitable choice after testing different curve fittings.