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When we carry out the method of moving planes on equation (1.4), we derive the fact (c_{i}=0) and consequently obtain the equivalence.

With the knowledge about the classes of individual samples we determine the clusters in the projection plane and consequently obtain the coordinates of the centroid (gravity point) of a particular cluster.

These force displacement relationships are then used to derive the incremental stiffnesses at the grain-scale, and consequently, obtain the sample-scale stress strain relationship of a representative volume of the material.

It should be noted that ΔGR values depend on how reaction 19 is written; some previous workers [84] write the reaction to produce one mole of SO42−, rather than ¼ mole, and consequently obtain ΔGR values four times larger.

An important advantage of working in symbolic mode (i.e., of introducing parameters in the computations) is the possibility to work with unknowns (that represent network improvement goals) and consequently obtain the time improvement required in a line in order to fulfil a network specific improvement goal.

The total Hamiltonian becomes H = H 0 + H int + H ac. By minimizing the action functional of such a Q1 D system, we get the equation of motion and consequently obtain the non-local charge conductivity using the linear response theory: (9).

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An efficient, rapid and reliable delivery system is essential for gaining customer loyalty online and consequently obtaining profitability [12].

If p i =p3, then it invokes A with input v3, and consequently obtains v3 from it, by validity property of edge convergence.

I manually detected the start point and end point for each motion segment after the annotation task, and consequently obtained datasets of the motion segments and their descriptive sentences.

Building the radix-4 algorithm can be done starting from the DFT formula in (1) which can be rewritten in a decomposed form and consequently obtaining the DIF radix-4 butterfly description.

If p i is either p1 or p2, it invokes B with input v i, and consequently obtains v i from B, by validity of graph convergence; and hence p i invokes A with v i and obtains v i as well, for the same reason, therefore it returns i.

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