end{aligned} (25) We integrate this relation over (Btimes [0,t]), (tin [0,T)), and use the divergence theorem and equation (12) to obtain equation (19).
end{aligned} (17) We multiply (16) by (overline{f (x, lambda_{2} )}) and (17) by (f (x, lambda_{1} )), subtract the latter from the former, and finally integrate this relation according to x from 0 to ∞.
end{aligned} (22) We integrate this relation over (Btimes [0,t]), (tin [0,T)), and use the divergence theorem and equation (11) to obtain equation (18). We have frac{partial }{partial s} biggl{ frac{1}{2}frac{1}{theta_{0}}c theta^{2}(s) biggr} = theta (s)frac{1}{theta_{0}}c dot{theta }(s).
end{aligned} (27) We integrate this relation over (Btimes [0,t]), (tin [0,T)), and use the divergence theorem and equation (13) to obtain equation (20). □. Let us consider a solution of the initial boundary value problem corresponding to the external data (mathcal{D}).
This paper proposes a linguistic multiperson decision making model (LMDMM) based on linguistic preference relations, integrating fuzzy preference relations, different types of multiplicative preference relations and multigranular linguistic preference relations.
The key issue when dealing with multiple robots is to find the link between them, and to integrate these relations to maintain the overall geometric consistency; the events that introduce these links on the global graph are described in detail.
Integrating in relation (3.40) on and using Lemma 2.6, we deduce that.
Constitutive contact relations are obtained by integrating the force distance relation derived from the LJ potential with a finite element analysis of single-asperity adhesive contact.
Davidson integrates this response within a general account of causation and explanation, in which causation is an extensional relation that holds between coarse events, while explanation is an intensional relation that holds between the coarse events under a description.
Integrating the above relation, we obtain (3.5).
Multiplying both sides of (1.1) by Δu and integrating the resulting relation with respect to x over Ω, we have ∫ Ω u t Δ u d x + ∫ Ω div [ m ( u ) ( k ∇ Δ u − ∇ φ ( u ) ) ] Δ u d x = 0.
