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The first algorithm is designed with the prior knowledge of the Lipschitz-type constant of bifunction. This means that the Lipschitz-type constant is an input parameter of the algorithm while the next two algorithms are modified such that they can work without any information of the Lipschitz-...
The chief problem with supply-demand analysis is that it requires a strictceteris-paribusassumption, so that everything but the price and the quantity of the good under analysis remains constant. For many reasons, that assumption can’t literally be true. If the price of the good rises (falls...
The combined use of coarse-graining and neural operators is of primary importance. On the one hand, the mere application of neural operators does not resolve the high-dimensionality problem, as it is not straightforward to design and train an efficient surrogate for thousands of coupled differential...
The equilibrium solutions of problem [4.14–4.18] are determined, in the case where the external forces are constant, by solving the following system, generalizing the method presented in Chapter 4: [4.19](1+c2)u1t+csu1n−u2t=F1t+R1t,csu1t+(1+s2)u1n=F1n+R1n,−u1t+(1+c2)u2t...
Fig. 1. Example of inverse chemical equilibrium problem for the determination of the equilibrium constant of a mineral dissolution/ precipitation reaction at a given temperature and pressure. Note that in each of these examples, at least one forward input variable is unknown, which can include not...
The proposed method replaces the classical grid-based solution by a near continuous-time solution based on piecewise linear/constant functions that removes a lot of disadvantage of discretization. The testing shows that the precision of the solution can be easily driven by a few approximation ...
This collection of problem sets and problems focus on the methods used to determine factors that affect the rate of a reaction and upon the use of an equilibrium constant to determine the equilibrium position of a reversible reaction system.
We find that, although we are able to solve many equations of this form, we can learn much about the behavior of solutions without actually solving the differential equation. An equilibrium solution of the autonomous first order equation dy/dt=f(y) is a constant solution of the ODE: a ...
If Π(𝜔) is constant across all 𝜔∈𝛺 and 𝑣𝐽=∑𝑖∈𝐽𝑢𝑖 for all 𝐽⊆ℐ, then an agency equilibrium is a (Bayesian) Coalitional Equilibrium [19]. The cited paper shows that, if utility is transferable, then there exists a mechanism of transfers between individuals...