The transitive closure of (mathcal{G} ) is defined as the digraph (R_{mathcal{G}}!=!(V, E_R)),where (E_R!=!{ v_i,v_j): exists ; text{ a} text{ journey}mathcal{J}(v_i,v_j)}).
end{aligned}By definition of (kappa ), the function (Z_kappa ) is nonnegative, and the set begin{aligned} Omega = {bar{x} in Sigma : text{ there } text{ exists } text{ a } text{ point } bar{y} in Sigma setminus {bar{x}} text{ such } text{ that } Z_kappa (bar{x},bar{y}) = 0} end{aligned}is non-empty.
"As if only this river existed," the text ends, "this wooden jetty, as if there were only this boat, only these rustling reeds, only this one day".
However, strict predefined selection and quality appraisal criteria were applied (see Additional files 1 and 2), and in cases where doubt existed, full-texts were assessed independently by the last author (MS).
In various Middle Eastern languages there also exist many texts dealing with celestial omens, though their sources and the question as to whether they are directly descended from a Mesopotamian tradition or are derived from Greek or Indian intermediaries is yet to be investigated.
Furthermore, we would like to note the importance of frost heave and freeze-thaw damage as a part of the family of moisture-induced damage mechanisms, which we have not included explicitly in this chapter, as there already exist comprehensive texts on these subjects.
– Strange text exists in Help text for Office Folder in Simplified Chinese language.
– Strange text exists in Help text for Games tile when in Chinese language.
After she won the Nobel Prize, in 1991, Gordimer's diary had filled up with endless lecturing obligations, and texts existed in a constellation of slightly different versions.
Literature exists as text, music as a score, but dance is created on living bodies and survives only as long as those bodies remember it and pass it on to others.
