Sentence examples for introduced the equilibrium from inspiring English sources

In 1994, Blum and Oettli (see [1]) introduced the equilibrium problem (EP) which is to find x ¯ ∈ K, such that f ( x ¯, y ) ≥ 0, ∀ y ∈ K. (1.1).

In 1994, Blum and Oettli [5] introduced the equilibrium problem which is to find (xin C) such that begin{aligned} F x,y geq0 quadmbox{for all } yin C. end{aligned} (1.1) They denoted the solution set of problem (1.1) as (EP(F)).

The steady-state balance equation describing for n is then Solving for n and noting the rate of elongation is r= kt n yields where we have introduced the equilibrium dissociation constant, KD≡ koff/ kon.

We introduce the equilibrium problem to the optimization problem: min x ∈ C ζ ( x ), (4.1).

Before we introduce the equilibrium concepts of multiobjective noncooperative games, we give the following notation.

Therefore, we introduce the equilibrium point of SIR model to separate the forwarding process.

We introduce the equilibrium definition based on Wardrop's principles when there are some internal relationships between different kinds of goods which transported through the same traffic network.

In this paper, we introduce the equilibrium definition about this problem based on Wardrop's principles and propose a mathematical model about this traffic equilibrium problem in dynamic networks.

The model simplifies the full TMDD model by introducing the equilibrium constant, the total concentration of drug in the central compartment, and the total concentration of receptor into the model.

In 1999, Moudafi and Thèra [3] introduced the mixed equilibrium problem of finding (x^in C) such that Fbigl(x^,ybigr)+bigllangle Tbigl(x^bigr),y-x^bigrrangle geq0,quad forall yin C, (1.3) where (F Ctimes Clongrightarrowmathbb{R}) is a given bi-mapping with (F x,x =0), for all (xin C) and (T Clongrightarrow C) is a continuous mapping.

Remark 4.1 Recently, some authors introduced the following mixed equilibrium problem (MEP, for short) (see [15 17] and references therein) and generalized equilibrium problem (GEP, for short) (see [18 20] and references therein): (a) Mixed equilibrium problem [15 17]:  .