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It is clear that the graph G x is connected for all x ∈ X.
In survivable routing, the goal is to find a Route and Wavelength Assignment (RWA) such that the logical topology remains connected for all single link failures.
Since X is connected, for all x ∈ X the geometric fibers H x ¯ are reductive group schemes of the same "type" [41, XXII, 2.3].
Each individual preference relation $R_{i}$ is assumed to be connected (for all alternatives $x$ and $y$, either $xR_{i}y$, or $yR_{i}x$, or both) and transitive (for all $x$, $y$ and $z$, if $xR_{i}y$ and $yR_{i}z$, then $xR_{i}z$).
Then, by Lemma 3, (Omega _u eta )) is connected for all (eta in [eta _0,1[). Choose (0
} end{aligned} (21 where ({varvec{I}}) is the identity matrix, and (|N_i|) is the cardinality of the neighbour set of node i. Assume there exists a positive constant m such that for the sequence (left{ k,k+1,dots,k+mright}) the graph associated with the matrix (prod limits _{l=k}^{k+m} {varvec{P}}^{(l)}) is fully connected for all k.
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Batista then connected for an insurance run.
It is easy to imagine two sides locked in pitched battle over Internet freedom: The democracies, embracing the freedom to connect for all, and the dictatorships, who censor, monitor, and disrupt.
But people connect for all kinds of reasons, both sexual and emotional, and relationships can look a lot different from the outside than the inside.
For example, I dream about being able to navigate the Internet, because I believe in all these years I haven't been connected for even one hour reading all the information that interests me.
Certainly those are all connected for me.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com