If [U.sub.d]([??]), [??] [member of] h[Z.sup.m], is a function of a

discrete variable, then we call it "discrete function".

Black knot is used to define

discrete variable and quantum operations, variable significance represented by any black knot being discrete form of sum transformation of all variables, being in the knot, according to a certain rate.

A library was populated containing airfoil element coordinates, and an integer value applied to each airfoil; the non-linear optimization solver could select the geometry of each element via

discrete variable selection.

The next set of chi-square tests evaluated the relationship between the triadic element of fire setting and each

discrete variable of parental abuse.

As is determined as a

discrete variable and must be chosen from the following list: As = [6.0, 6.16, 6.32, 6.6, 7.0, 7.11, 7.2, 7.8, 7.9, 8.0, 8.4] in2; b is determined as an integer variable: b = [28, 29, 30, ...

There are many different techniques proposed to solve this problem, such as (1) utilizing a binary-coded technique to handle

discrete variables (Datta and Figueira 2011 [30], Datta and Figueira 2013 [31]), (2) replacing the continuous variables by the closest

discrete variables, (3) transforming the design variable X to [log.sub.10]X and carrying out the algorithm operation on [log.sub.10]X, (4) representing each

discrete variable by an integer in ascending order and performing the algorithm operation on the integer (Ho-Huu et al.

However, when we analyze and model the data, we can meet the explanatory variable Y is not a continuous variable, but a

discrete variable. Because the variable is discrete, this kind of regression model is called the discrete choice model.

For the stochastic

discrete variable X whose values represent the states of a certain information system, and with the distribution: [p.sub.k] [greater than or equal to] 0, we refer to information energy as delineated by Onicescu, IE and, in accordance with the stochastic discrete distribution of the variable X, the following formula is used [7]:

In this paper, in order to optimize the weight of the truss, the complex variable crosses section as a

discrete variable. And the location of nodes truss design as a continuous variable, selected the desired constraints, limitations and restrictions of stresses and displacements are satisfied.

Furthermore, a

discrete variable, say [Y.sub.t] can be generated based upon the [Y.sup.*.sub.t] values and then the [Y.sub.t] can be utilized as a dependent variable in the ordered probit model.

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are functions of

discrete variable x = 0, 1, 2, ..., M - 1, [16-18].

The first three chapters cover initial-value problems, and boundary-value problems solved using

discrete variable methods or finite element methods, for ordinary differential equations.