Sentence examples for system of operators from inspiring English sources

Then the system of operators ({mathcal {E}}^{g}_{s,t}[cdot]), (0leq sleq tleq T) is an ({mathcal {F}}_{t} -consistent nonlinear evaluation defined in ({mathcal {L}}({mathcal{F}}_{t} -consistent

end{aligned} (11) Thanks to Lemma 3.2, the corresponding coupled system of operators equations to coupled system (10) of integral equations is textstylebegin{cases} u(t)= mathcal{N}_{1}v t), v(t)= mathcal{N}_{2}u(t).

We obtain here some inequalities for the eigenvalues of Dirichlet and Neumann value problems for general classes of operators (or system of operators) acting inL2 (orL2(Ω, Cm)),Ω⊂Rd,d⩾1.

We thus define a system of operators: {mathcal{E}}^{g}_{s,t}[X]:Xin{mathcal{L}}({ mathcal{F}}_{t} mapsto {mathcal{L}}({mathcal{F}}_{s}), quad 0leq sleq tleq T. This system is completely determined by the above given function g.

Let Ω ⊂ R n be an open bounded domain with the infinitely smooth boundary ∂ Ω and the system of operators ( L u ) = ∑ | s | ≤ 2 m a s D s u , a s ∈ C, ( B j u ) = ∑ | s | ≤ m j b j, s D s u , b j, s ∈ C ∞ , j = 1, …, m. is regular elliptic (see e.g. [[13], Section 5.2.1]).

The element (p=(p_{1},p_{2}, ldots,p_{N})) is a solution of the system of operator equations (4.1).

Assume that ((X^{N}, |cdot|_)) is a uniformly smooth Banach space and the solution set of the system of operator equations (4.1) is nonempty.

An element ((x,y in Etimes E) is called a coupled mild solution of the system (4.1) if and only if it satisfies the following system of operator equations: textstylebegin{cases} x t)=(A_{1}x)(t)+(A_{2}y)(t),quad tin J, y(t)=(A_{1}y)(t)+(A_{2}x)(t),quad tin J. end{cases} (4.4).

The challenge is the economics have to work out in the mobile eco-system of operators, OEMs and the video service provider.

Notice that the system (2.1) of Urysohn integral equations has a unique common solution if and only if the system (2.2) of operators has a unique common fixed point.

Besides, any system of human operators could not possibly scale to accommodate the millions of drones expected in years to come.