[reaction: see text] The highly diastereoselective oxy-Michael addition of the "naked" anion of (6S)-methyl delta lactol to alkylidiene-, arylidene-, and heteroarylidenemalonate derivatives leading to the direct formation of THP-protected beta-hydroxy ester derivatives is described. Subsequent acid-mediated deprotection affords the enantioenriched aldol products in quantitative yields.

The "naked" anion of (S)-6-methyl delta lactol undergoes efficient oxy-Michael addition to alpha,beta-disubstituted nitro olefins to give the THP* protected Henry products with excellent (95-->98% de) stereocontrol at the beta-position and moderate (up to 3 : 1) stereocontrol at the alpha-position in favour of the syn-diastereoisomer. Nitro group reduction with in situN-Boc protection and THP* removal provides alpha,beta-disubstituted ethanolamine derivatives, while treatment with tetrapropylammonium perruthenate gives THP* protected alpha-hydroxy ketone derivatives in high diasteromeric excess.

The abundance of bioactive natural and unnatural products that contain the 1,2-amino alcohol motif continues to stimulate the development of new methods for their efficient asymmetric synthesis. Whereas 1,2-amino alcohols derived from proteinogenic amino acids are readily accessible, nonproteinogenic amino acid derived amino alcohols require efficient enantioselective routes.[1] Methods for the asymmetric synthesis of 1,2-amino alcohols with a stereogenic hydroxy-substituted carbon center are relatively uncommon, even though these materials and their derivatives are widespread in nature and routinely exploited in asymmetric synthesis. [2] Stimulated by the utility of 1,2-amino alcohols and encouraged by the lack of a general synthetic approach to such compounds, we recently became interested in developing asymmetric methods for their synthesis. Although a logical retrosynthetic disconnection is based on an asymmetric nitroaldol reaction, [3] our approach relies on the stereoselective Michael addition of a chiral water equivalent 1 to readily available nitroalkenes 2. As in many asymmetric catalytic processes, the levels of asymmetric induction in the nitroaldol reaction are substrate dependent, and in the worst cases there is no way of increasing the enantiopurity of the product. In the oxy-Michael addition approach the chirality in the nucleophile allows the separation of the diastereomeric products 3 and hence the isolation of enantiopure material after auxiliary removal. However, ideally the chirality of the nucleophile will induce high levels of stereoselectivity in the formation of the stereogenic center b to N, and subsequent nitro-group manipulation and nondestructive removal of the auxiliary will free the deprotected oxy-Michael product 4 (Scheme 1).The strength of this concept was recognized previously by Enders et al., [4] who used the sodium salt of N-formylnor-[*] Dr.

The exact expression is derived for the average stationary cost of a (Q,R) inventory system with lost sales, unit Poisson demands, Erlang-distributed lead times, fixed order cost, fixed cost per unit lost sale, linear holding cost per unit time, and a maximum of one order outstanding. Explicit expressions for the state probabilities and a fast method of calculating them are obtained for the case of Q greater than R . Exponential lead times are analyzed as a special case. A simple cyclic coordinate search procedure is used to locate the minimum cost policy. Examples of the effect of lead time variability on costs are given.

The abundance of bioactive natural and unnatural products that contain the 1,2-amino alcohol motif continues to stimulate the development of new methods for their efficient asymmetric synthesis. Whereas 1,2-amino alcohols derived from proteinogenic amino acids are readily accessible, nonproteinogenic amino acid derived amino alcohols require efficient enantioselective routes.[1] Methods for the asymmetric synthesis of 1,2-amino alcohols with a stereogenic hydroxy-substituted carbon center are relatively uncommon, even though these materials and their derivatives are widespread in nature and routinely exploited in asymmetric synthesis. [2] Stimulated by the utility of 1,2-amino alcohols and encouraged by the lack of a general synthetic approach to such compounds, we recently became interested in developing asymmetric methods for their synthesis. Although a logical retrosynthetic disconnection is based on an asymmetric nitroaldol reaction, [3] our approach relies on the stereoselective Michael addition of a chiral water equivalent 1 to readily available nitroalkenes 2. As in many asymmetric catalytic processes, the levels of asymmetric induction in the nitroaldol reaction are substrate dependent, and in the worst cases there is no way of increasing the enantiopurity of the product. In the oxy-Michael addition approach the chirality in the nucleophile allows the separation of the diastereomeric products 3 and hence the isolation of enantiopure material after auxiliary removal. However, ideally the chirality of the nucleophile will induce high levels of stereoselectivity in the formation of the stereogenic center b to N, and subsequent nitro-group manipulation and nondestructive removal of the auxiliary will free the deprotected oxy-Michael product 4 (Scheme 1).The strength of this concept was recognized previously by Enders et al., [4] who used the sodium salt of N-formylnor-[*] Dr.