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In fact, Proclus, in his commentary on Euclid, Elements i, preserves many examples of attempts to prove theorems for a finite universe.
The independence of formula B from formula A is established by a matrix that (i) preserves the validity of the rules of the system and that (ii) under an interpretation σ assigns to A but not to B a designated value.
Assume that A p i preserves the grading of the Clifford algebra and converges to A p ( x, ξ ) uniformly on compact subset of R n. Suppose that u i ∈ W 1, p i ( Ω, C ℓ n k ) is the weak solution to the following K ψ f, p i ( Ω, C ℓ n k ) -obstacle problem ∫ Ω 〈 A p i ( x, D u i ), D v − D u i 〉 d x ≥ 0 (24).
Similarly, in osteoblasts, extracellular matrix (collagen type I) preserves CpG-methylation of the Fas promoter via MAPK1 and DNMT1, thus preventing apoptosis of proliferating osteoblasts [19].
Similar(56)
How do I preserve them?
I preserve my energies".
"I preserved my honor," he said.
"I preserved the capacity to evolve," he told me.
"I preserve things that are significant to me," he said.
'I preserved that picture by tearing it out.
So I preserved the wood-beam construction because of what it can do for your body".
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