Pythagorean Theorem & Curvature with Lower or Upper Bound*

In this paper, the authors give a comparison version of Pythagorean theorem to judge the lower or upper bound of the curvature of Alexandrov spaces(including Riemannian manifolds).     

Completely positive module maps and completely positive extreme maps

Let be unital -algebras and be the set of all completely positive linear maps of into . In this article we characterize the extreme elements in , for all , and pure elements in in terms of a self-dual Hilbert module structure induced by each in . Let be the subset of consisting of -module maps for a von Neumann algebra . We characterize normal elements in to be extreme. Results here generalize various earlier results by Choi, Paschke and Lin.

     

Total synthesis and initial structure-function analysis of the potent V-ATPase inhibitors salicylihalamide A and related compounds

Salicylihalamide A is the first member of a growing class of macrocyclic salicylate natural products that induce a variety of interesting phenotypes in cultured mammalian cells. Salicylihalamide A was reported to be a unique and highly differential cytotoxin and a potent inhibitor of the mammalian vacuolar (H(+))-ATPase. The total synthesis of both enantiomers of salicylihalamide A, a revision of the absolute configuration assigned to the natural product, and extensive structure-function studies with synthetic salicylihalamide variants are reported. These studies were possible only due to a highly efficient synthetic strategy that features (1) a remarkably E-selective ring-closing olefin metathesis to construct the 12-membered benzolactone skeleton 29, (2) a mild stereocontrolled elaboration to E-alkenyl isocyanate 41, and (3) addition of carbon, oxygen, and sulfur nucleophiles to isocyanate 41 to obtain salicylihalamide A and congeners. We demonstrate for the first time that salicylihalamide A is a potent inhibitor of fully purified reconstituted V-ATPase from bovine brain, and have identified several similarly potent side chain modified derivatives, including salicylihalamide dimers 43-45. In combination, these studies have laid the foundation for ongoing studies aimed at a comprehensive understanding of salicylihalamide's mode-of-action, of potential relevance to the development of lead compounds for the treatment of osteoporosis and cancer.     

Development of an enantioselective synthetic route to neocarzinostatin chromophore and its use for multiple radioisotopic incorporation

A convergent, enantioselective synthetic route to the natural product neocarzinostatin chromophore (1) is described. Synthesis of the chromophore aglycon (2) was targeted initially. Chemistry previously developed for the synthesis of a neocarzinostatin core model (4) failed in the requisite 1,3-transposition of an allylic silyl ether when applied toward the preparation of 2 with use of the more highly oxygenated substrates 27 and 54. An alternative synthetic plan was therefore developed, based upon a proposed reduction of the epoxy alcohol 58 to form the aglycon 2, a transformation that was achieved in a novel manner, using a combination of the reagents triphenylphosphine, iodine, and imidazole. The successful route to 1 and 2 began with the convergent coupling of the epoxydiyne 15, obtained in 9 steps (43% overall yield) from D-glyceraldehyde acetonide, and the cyclopentenone (+)-14, prepared in one step (75-85% yield) from the prostaglandin intermediate (+)-16, affording the alcohol 22 in 80% yield and with > or =20:1 diastereoselectivity. The alcohol 22 was then converted into the epoxy alcohol 58 in 17 steps with an average yield of 92% and an overall yield of 22%. Key features of this sequence include the diastereoselective Sharpless asymmetric epoxidation of allylic alcohol 81 (98% yield); intramolecular acetylide addition within the epoxy aldehyde 82, using Masamune's lithium diphenyltetramethyldisilazide base (85% yield); selective esterification of the diol 84 with the naphthoic acid 13 followed by selective cleavage of the chloroacetate protective group in situ to furnish the naphthoic acid ester 85 in 80% yield; and elimination of the tertiary hydroxyl group within intermediate 88 using the Martin sulfurane reagent (79% yield). Reductive transposition of the product epoxy alcohol (58) then formed neocarzinostatin chromophore aglycon (2, 71% yield). Studies directed toward the glycosylation of 2 focused initially on the preparation of the N-methylamino --> hydroxyl replacement analogue 3, an alpha-D-fucose derivative of neocarzinostatin chromophore, formed in 42% yield by a two-step Schmidt glycosylation-deprotection sequence. For the synthesis of 1, an extensive search for a suitable 2'-N-methylfucosamine glycosyl donor led to the discovery that the reaction of 2 with the trichloroacetimidate 108, containing a free N-methylamino group, formed the alpha-glycoside 114 selectively in the presence of boron trifluoride diethyl etherate. Subsequent deprotection of 114 under mildly acidic conditions then furnished the labile chromophore (1). The synthetic route was readily modified for the preparation of singly and doubly (3)H- and (14)C-labeled 1, compounds unavailable by other means, for studies of the mechanism of action of neocarzinostatin in vivo.     

假四面体(C2v)钴(Ⅱ)配合物电子光谱的强场处理

钴(Ⅱ)的假四面体(C_(2v))配合物 CoL_2X_2的配体场光谱一般显示出两组谱带,分别对应于基态~4A_2对两个~4T_1谱项的三个低对称性分量~4B_1,~4A_2和~4B_2的跃迁。前人对这类光谱的处理多采用弱场近似,模型多采用点电荷模型,结果得到的跃迁能和实测值相差较大。Menzel等指出:简单点电荷模型的固有弊病使得它不可能对此类共价配合物的光谱作出理想的处理。他们对点电荷模型作了适当的修改,应用弱场近似取得了满意的结果。本文应用强场近似处理这类配合物的光谱,和修改的点电荷模型相比较我们的结果更为满意。