2 resultados para B-Riesz Potential
em CaltechTHESIS
Resumo:
The ritterazine and cephalostatin natural products have biological activities and structures that are interesting to synthetic organic chemists. These products have been found to exhibit significant cytotoxicity against P388 murine leukemia cells, and therefore have the potential to be used as anticancer drugs. The ritterazines and cephalostatins are steroidal dimers joined by a central pyrazine ring. Given that the steroid halves are unsymmetrical and highly oxygenated, there are several challenges in synthesizing these compounds in an organic laboratory.
Ritterazine B is the most potent derivative in the ritterazine family. Its biological activity is comparable to drugs that are being used to treat cancer today. For this reason, and the fact that there are no reported syntheses of ritterazine B to date, our lab set out to synthesize this natural product.
Herein, efforts toward the synthesis of the western fragment of ritterazine B are described. Two different routes are explored to access a common intermediate. An alkyne conjugate addition reaction was initially investigated due to the success of this key reaction in the synthesis of the eastern fragment. However, it has been found that a propargylation reaction has greater reactivity and yields, and has the potential to reduce the step count of the synthesis of the western fragment of ritterazine B.
Resumo:
A Riesz space with a Hausdorff, locally convex topology determined by Riesz seminorms is called a locally convex Riesz space. A sequence {xn} in a locally convex Riesz space L is said to converge locally to x ϵ L if for some topologically bounded set B and every real r ˃ 0 there exists N (r) and n ≥ N (r) implies x – xn ϵ rb. Local Cauchy sequences are defined analogously, and L is said to be locally complete if every local Cauchy sequence converges locally. Then L is locally complete if and only if every monotone local Cauchy sequence has a least upper bound. This is a somewhat more general form of the completeness criterion for Riesz – normed Riesz spaces given by Luxemburg and Zaanen. Locally complete, bound, locally convex Riesz spaces are barrelled. If the space is metrizable, local completeness and topological completeness are equivalent.
Two measures of the non-archimedean character of a non-archimedean Riesz space L are the smallest ideal Ao (L) such that quotient space is Archimedean and the ideal I (L) = { x ϵ L: for some 0 ≤ v ϵ L, n |x| ≤ v for n = 1, 2, …}. In general Ao (L) ᴝ I (L). If L is itself a quotient space, a necessary and sufficient condition that Ao (L) = I (L) is given. There is an example where Ao (L) ≠ I (L).
A necessary and sufficient condition that a Riesz space L have every quotient space Archimedean is that for every 0 ≤ u, v ϵ L there exist u1 = sup (inf (n v, u): n = 1, 2, …), and real numbers m1 and m2 such that m1 u1 ≥ v1 and m2 v1 ≥ u1. If, in addition, L is Dedekind σ – complete, then L may be represented as the space of all functions which vanish off finite subsets of some non-empty set.