This second version shows that the current example of hybridization, as conducted in Set-Set, yields a symmetric generalized consequence relation.[10]) Let us note in view of the recent reference to ⊢∧ ∩ ⊢∨, there has been an interest in how one might form something like the union rather than the intersection of the two consequence relations involved here.
We conclude this discussion on the quantitative Sobolev inequality for (1<p<n) by noting that, in view of the results of [16, 75], the question arises of the optimal exponent (alpha ) in equality (6.9).
Note that, in view of the oddness of f, we have f ( − x ) = − f ( x ) for all x ∈ X.
Note that, in view of the periodicity of coefficients, if is a solution of (1.10), then is also a solution of (1.10).
It is interesting to note that in view of Theorem 2.21, Proposition 2.3 and Definition 2.6, it is possible to introduce another concept of changing-periodic time scales.
First of all we note that in view of the short time existence result in the Riemannian setting we can assume that locally (u_epsilon ) are smooth both in time and space.
Note that, in view of (Karatzas and Shreve 1998, Appendix A), ess inf i∈I X i ∧n and ess sup i∈I X i ∧n are well defined, so that ess inf i∈I X i is well defined.
Note that, in view of (2), the mrl function of (X z)) is given by m xmid z)= int_{x}^{infty}frac{bar{F} u e^{-uz}}{bar {F}(x e^{-xz}},du,quad x,zgeq0.
Note that in view of the updates (12), (23), (32), and (36), the origin of the local coordinate system at time i is at xk,iand the direction of the x-axis is the same as vk,i(see Figure 10).
Note that in view of construction for g-splines (G_{r,n,f,a}(t)), functions (Delta(t)) and (G_{r,n,f,a}(t)) have not less than (n+r) sign changes ((G_{r,n,f,a}(t)) has exactly (n+r) sign changes); functions (Delta ^{(r)}(t)) and (G^{(r)}_{r,n,f,a}(t)) can have sign changes only in the knots of the g-spline (G_{r,n,f,a}(t)), and hence not more than n sign changes.
