We denote by b the upper bound of J and β the upper bound of J 0. Then either β = b or for all compact set K ⊂ O, there exists η < β such that: V ( t ) ∈ O | K, for all t ≥ η with t ∈ J 0 ⋅.
We show now that, for a suitable choice of the constant α o, there exists k o ∈ N such that for any k ≥ k o the coefficients d k verify also the last condition of (i1).
Then, we can write begin{aligned} y_iy_j = sum _{k = 1}^{ell ^2} c^k_{ij} y_k text{ with } c^k_{ij} in K. end{aligned} (1 Since (K) is the field of fractions of (mathcal O ), there exists (d in mathcal O ) such that (d c^k_{ij} in mathcal O ) for all (i, j) and (k).
The F-uniformity naturally determines a metrizable topology on S, called the strong topology or F-topology [9], a subset O of S is F-open if for every p ∈ O there exists t > 0 such that N p = { q ∈ S | F p q ( t ) > 1 − t } ⊂ O. Definition 2.1 [6].
Additionally, it is shown in [56, Theorem 1.13] that if X is any nonzero element in O n, then there exist A, B ∈ O n for which A X B = 1.
In each country in the presence of moral hazard, where θ j = θ, j≡(O, H), there exists a unique (q*) j, such that individuals enter into the complex sector if and only if q j > (q*) j.
In the oxide portion of the La Sr–O system there exist two intermediate phases, β with a certain homogeneity range centred around the stoichiometry La4SrO7 and a stoichiometric phase, La4Sr3O9.
Let η > 1 be a fixed constant, we say that f ∈ L loc 1 is in R B M O if there exists a constant such that 1 μ ( η Q ) ∫ Q | f ( y ) − m Q ˜ f | d μ ( y ) ≤ A (2.2). for any ball Q, and | m Q f − m R f | ≤ A K Q, R (2.3).
It reveals that there exists some O vacancy in the ZnO thin film.
The mean rotations for the two data sets under consideration will be denoted as M O and M P. For each observation in O 1,…,O n, there exists an axis A Oi such that a rotation by angle (arccos [!(text {trace}left (mathbf {M}_{O}^{T}mathbf {O}_{i}right -1)/2]) abO}_{i}right -1result in the meaboutO.
E is said to be an essential set of Ξ ( R ) if, for each open set O ⊃ E, there exists an open neighborhood U of R in M such that for any R ′ ∈ U with Ξ ( R ′ ) ∩ O ≠ ∅.
