Sentence examples for formulation is given by from inspiring English sources
The proposed formulation is given by the following pure IP problem.
The mathematical model formulation is given by the following (Schiling 1980): {text{Maximize }}sumlimits_{i} {h_{it} Y_{it} } quadforall t = 1,2, ldots,T (17).
Indeed, for a simplified version, whose formulation is given by a degenerate problem on a rectangle, the existence and uniqueness of a solution under proper assumptions on the data can be proven.
Based on this generative model, our proposed Singular Spectrum Matrix Completion (SS-MC) formulation is given by: begin{array}{*{20}l} & underset{mathbf{L}}{text{minimize}} ~~ rank(mathbf{L}) notag & text{subject to} ~~ mathcal{P}_{Omega}(mathbf{M}) = mathcal{P}_{Omega}({mathbf{DL}}) end{array} (8).
The new problem formulation is given by: begin{array}{*{20}l} {{text{min}};left( { - F_{{{text{gas}}}},F_{{{text{dhc}}}},F_{{text{a}}},F_{{{text{ele5}}}} } right)} hfill {{text{s}}.{text{t}}. F_{{{text{ele6}}}} le 1} hfill end{array} (42 The resultant Pareto-optimal front obtained by (42) is projected into the original eight-objective space in Fig. 5 with red lines.
Hence, a new problem formulation is given by: begin{array}{*{20}l} {{text{min}}{mkern 1mu} left( { - F_{{{text{gas}}}},F_{{{text{dhc}}}},F_{{text{a}}},F_{{{text{ele4}}}},F_{{{text{ele5}}}} } right)} hfill {{mkern 1mu} {text{s}}.{text{t}}. F_{{{text{ele6}}}} le 1} hfill end{array} (41 Solving this new model in (41) leads to the Pareto-optimal front plotted in Fig. 5 with light blue lines.
The second is also present in some sense in the works of Plato (at least on some readings of those works), but its first modern formulation was given by Frege (1884, 1892, 1893-1903, 1919); I will call this the singular term argument, and unlike the One Over Many, it can be used in connection with all the different kinds of abstract objects, i.e., numbers, properties, propositions, and so on.
For the convenience of the computational derivation and implementation, the material formulation is given in the unrotated intermediate configuration mapped by the plastic part of the deformation gradient.
The integrated variational formulation is given, based on which the numerical equation is derived by using the mode summation approach.
