Sentence examples for exists an arbitrary from inspiring English sources

For the case where there exists an arbitrary constant reference signal, a distributed adaptive controller together with an internal model are presented to achieve output tracking in the sense that the subsystem outputs asymptotically follow a reference constant.

A function f is said to be a relative semi-convex function if and only if there exists an arbitrary function g : R n → R n such that f ( ( 1 − t ) g ( x ) + t g ( y ) ) ≤ ( 1 − t ) f ( x ) + t f ( y ), x, y ∈ M, t ∈ [ 0, 1 ].

A set M ⊆ R n is said to be a relative convex (g-convex) set if and only if there exists an arbitrary function g : R n → R n such that ( 1 − t ) g ( x ) + t g ( y ) ∈ M, ∀ x, y ∈ R n : g ( x ), g ( y ) ∈ M, t ∈ [ 0, 1 ].

Thus, in view of Lemma 4.2, it is enough to verify that there exists an arbitrary element u of L 2 ( 0, T ; V ) such that ( G + B 1 ) u = − p. By (2) of Lemma 2.3, B is pseudo-monotone and satisfies the condition (5) of Lemma 2.3.

Assume that it exists an arbitrary SU ℓ, such that it is the only SU in the spectrum i.e., x ℓ n =1, ∀n and if (R_{ell }^{min}> R_{ell }^{max}) then there is no solution and (mathcal {S}_{mathcal {F}}= emptyset ).

In view of (3.7), there exist an arbitrary (varepsilon >0) and (tau_{1}), (tau_{2}) with (0<tau_{1}<tau_{2}) such that F x,u leq varepsilon vert u vert ^{p} for every (xin Omega ) and every u with (vert u vert in [0, tau_{1}) cup (tau_{2}, +infty )). Since (F x,u)) is continuous on (Omega times mathbb{R}), it is bounded on (xin Omega ) and (vert u vert in [tau_{1},tau_{2}]).

If more than one best-match existed, an arbitrary assignment was made.

Due to the definition of the SRS, neither an analytical nor a unique inverse exists for an arbitrary function.

Thus if there exists an algorithm to solve an arbitrary diophantine equation of degree increasing type, then it can solve an arbitrary diophantine equation, which contradicts Matijasevič's result [10].

Then, for an arbitrary, there exists an element which belongs to the following sub-space of : (1.9).

It is also showed in the case (mu_{2} geqmu_{1}) that there exists a sequence of arbitrary small (or large) delays such that instabilities occur.