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More significant, however, was his use of algebra in developing 'analytic' geometry as it came to be called, which allowed geometrical problems to be transformed into arithmetical ones and more easily solved.
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In addition, MISQP accepts black-box problems and, thus, does not require the problem to be transformed into an algebraic form, a typical requirement of most MINLP methods.
The method utilizes the ARMAX canonical form and block-pulse function spectral representations, through which the problem is shown to be transformed into that of estimating an induced and special-form discrete stochastic system from spectral data.
It is well known that optimization problems can be transformed to the problems of the existence of a best proximity point.
Therefore almost all existence results for boundary value problems with state-dependent impulses have been reached for periodic problems which can be transformed to fixed point problems of corresponding Poincaré maps in R n.
They satisfy the KKT optimality conditions of (36) for P. Therefore, according to the rate-WMMSE relationship (35) and the common rate transformation c=−x, problem (36) can be transformed to problem (15).
Lack of any mobility problem should be transformed to a value of one (equivalent to no change to access), whilst maximum mobility disadvantage should be transformed to a value significantly less than one which results in a decreased population catchment size.
Substituting ϕ u to the first equation of the problem (1.1), then the problem can be transformed to a one variable equation.
To simply the calculation, the random variables approximate to a set of discrete values so that the TSP problem can be transformed to a linear programming model.
Therefore, for a specific t, Problem P11 can be transformed to Problem P12 through introducing new variables T k : Problem P12 (for a specific t): max W k, P k S, P k R, T k R W k, P k S, P k R, T k = ∑ k = 1 K T k (42).
A uniformity approach is used to deal with the evidence variables, through which the original reliability problem can be transformed to a traditional reliability problem with only random uncertainty.
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