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When the Hashin failure criteria are applied, the DV of each failure mode is expressed by the following equivalent displacement: {d}_I=frac{X_{eq}^{If}left({X}_{eq}^I-{X}_{eq}^{Ii}right)}{X_{eq}^Ileft({X}_{eq}^{If}-{X}_{eq}^{Ii}right)} left(I= Lt, Lc, Yt, Yc, Zt, Zcright).
By contrast, by evaluating the outage probability, P out, at a fixed source transmission rate, i.e. (R_{S_{0}}) (bits/s/Hz), throughput in the delay-sensitive mode is expressed as tau = left({1 - alpha} right)R_{S_{0}}left({1 - {P_{text{out}}}} right).
The sum of microgrid total costs and PHEVs charging cost in the first mode is expressed as C_{Dc1}^{M} = C_{Dc0}^{M} + sumlimits_{k = 1}^{S} {sumlimits_{t = 1}^{24} {P_{1k,t}^{text{PHEV}} } } B_{t}^{text{Grid}} (9 where ( P_{1k,t}^{text{PHEV}} ) is charging power of k th PHEV at hour t in the first mode; S is the number of PHEVs.
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The three charging modes are expressed as follows.
(21)–(24), the equivalent stress ( {sigma}_{eq}^I ) and the equivalent displacement ( {X}_{eq}^I ) associated to different failure modes are expressed in Table 3.
Phase velocities for these propagation modes are expressed in terms of five elasticity constants needed to describe a general TI material, and also in terms of three constants after the application of two constraints that hold in the limit of an incompressible material.
The AHP method uses an additive aggregation with normalization of the sum of the local priorities, which is referred to as distributive mode and is expressed as: P_{i} = mathop sum limits_{i} w_{j} * p_{ij}where P i is the global priority of alternative i, p ij is the alternative's local priority with regard to criterion j, and w j is the criterion j with regard to the goal.
The general solution of the mode shape equation is expressed as the superposition of four linearly independent functions.
Isaacs argued that 'every impulse, every feeling, every mode of defence is expressed and experienced in such a specific phantasy, which gives it mental life and shows its specific direction and purpose' (Isaacs, 1991[1943]: 277 8).
The general solution of the mode shape differential equation is expressed as the superposition of four converging polynomial functions.
The solution to the mode shape differential equation is expressed as the superposition of four independent functions.
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