A metric space of A. H. Stone and an example concerning -minimal bases

In this paper we use a metric space due to A. H. Stone and one of its completions to construct a linearly ordered topological space that is \v{C}ech complete, has a -closed-discrete dense subset, is perfect, hereditarily paracompact, first-countable, and has the property that each of its subspaces has a -minimal base for its relative topology. However, is not metrizable and is not quasi-developable. The construction of is a point-splitting process that is familiar in ordered spaces, and an orderability theorem of Herrlich is the link between Stone's metric space and our construction.

     

An efficient approximation algorithm for the survivable network design problem

The survivable network design problem (SNDP) is to construct a minimum-cost subgraph satisfying certain given edge-connectivity requirements. The first polynomial-time approximation algorithm was given by Williamson et al. (Combinatorica 15 (1995) 435–454). This paper gives an improved version that is more efficient. Consider a graph ofn vertices and connectivity requirements that are at mostk. Both algorithms find a solution that is within a factor 2k – 1 of optimal fork 2 and a factor 2 of optimal fork = 1. Our algorithm improves the time from O(k ³n⁴) to O ). Our algorithm shares features with those of Williamson et al. (Combinatorica 15 (1995) 435–454) but also differs from it at a high level, necessitating a different analysis of correctness and accuracy; our analysis is based on a combinatorial characterization of the redundant edges. Several other ideas are introduced to gain efficiency. These include a generalization of Padberg and Rao's characterization of minimum odd cuts, use of a representation of all minimum (s, t) cuts in a network, and a new priority queue system. The latter also improves the efficiency of the approximation algorithm of Goemans and Williamson (SIAM Journal on Computing 24 (1995) 296–317) for constrained forest problems such as minimum-weight matching, generalized Steiner trees and others. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.A preliminary version of this paper has appeared in the Proceedings of the Third Mathematical Programming Society Conference on Integer Programming and Combinatorial Optimization, 1993, pp. 57–74.Research supported in part by NSF Grant No. CCR-9215199 and AT & T Bell Laboratories.Research supported in part by Air Force contracts AFOSR-89-0271 and F49620-92-J-0125 and DARPA contracts N00014-89-J-1988 and N00014-92-1799.This research was performed while the author was a graduate student at MIT. Research supported by an NSF Graduate Fellowship, Air Force contract F49620-92-J-0125, DARPA contracts N00014-89-J-1988 and N00014-92-J-1799, and AT & T Bell Laboratories.     

De Rham cohomology of manifolds containing the points of infinite type,and Sobolev estimates for the\bar \partial - Neumann problem

We consider smooth bounded pseudoconvex domains Ω in Cⁿ whose boundary points of infinite type are contained in a smooth submanifoldM (with or without boundary) of the boundary having its (real) tangent space at each point contained in the null space of the Levi form ofbΩ at the point. (In particular, complex submanifolds satisfy this condition.) We consider a certain one-form α onbΩ and show that it represents a De Rham cohomology class on submanifolds of the kind described. We prove that if α represents the trivial cohomology class onM, then the Bergman projection and the \(\bar \partial - Neumann\) operator on Ω are continuous in Sobolev norms. This happens, in particular, ifM has trivial first De Rham cohomology, for instance, ifM is simply connected.     

Pattern recognition in the prediction of protein structure. II. Chain conformation from a probability-directed search procedure

A procedure that finds the most probable conformational states of a protein chain is described. Single-residue conformations are represented in terms of four conformational states, α, ?, α*, and ?*. The conformation of the entire chain is represented by a sequence of single-residue conformational states; the distinct conformations in this representation are called “chain-states.” The first article in this series described a procedure that computes tripeptide conformational probabilities from the amino acid sequence using pattern recognition techniques. The procedure described in this article uses the tripeptide probabilities to estimate the probabilities of the chain-states. The chain-state probability estimator is a product of conditional and marginal probabilities (obtained from the tripeptide probabilities), with a penalty factor to eliminate conformations containing α-helices and ?-strands of excessive length. The probability estimator considers short-range conformational information, medium-range sequence information and some simple long-range information (through the restrictions on helix and strand lengths). Energy minimization calculations can be carried out in the region of conformational space corresponding to a particular chain-state. By selecting the most probable chain-states, the search can be focused on the most probable, or “important,” regions of the conformational space. These energy calculations are described in the third article of the series. The complete procedure described by the three articles is called PRISM, for pattern recognition-based importance sampling minimization.     

A convenient one-pot synthesis of 4-, 6-, and 7-azaindoles from aminopyridines

A one-pot synthesis of a variety of substituted 4-, 6-, and 7-azaindoles from commercially available aminopyridines in moderate to good yields is described.     

Squaric acid: Reactions with certain metals

The metals which were exposed to the action of aqueous squaric acid formed salts of comparatively low solubility. At room temperatures the solubility of magnesium squarate dihydrate, for example, was in the 0.5% range. Of the metals investigated only magnesium and zinc could be said to react rapidly. Under the conditions imposed some of the metals, such as nickel, aluminum, and indium, required many hours, or even days, to react sufficiently to yield precipitates. The activity of certain metals could be increased by placing in intimate contact with metallic copper. Predictably, only iron, cobalt, and nickel formed colored squarates. In general the salt of a given metal appeared in several different forms. Although there was some similarity in the crystalline forms of the various squarates, there was a tendency for those of several metals, such as aluminum and lead, to be restricted to smaller dimensions than others, such as zinc and cadmium. An interesting property of the product formed by tin was that the spontaneous evaporation of part of the moisture from the reaction mixture yielded a gel, in which the original crystalline forms could no longer be detected. This property was not observed in connection with any of the other metals studied.     

Attempts to prepare a pyramidal carbocation with an apical fluorine substituent

Gem-difluorides $\text{7}$ and $\text{8}$, different only in the location of a methyl substituent and each a potential precursor of the same pyramidal carbocation $\text{9}$, ionize instead to give allylic carbocation $\text{13}$ and homotropylium ion $\text{20}$ respectively.     

7-N-(mercaptoalkyl)mitomycins: implications of cyclization for drug function

The Kyowa Hakko Kogyo and Bristol-Myers Squibb companies reported that select mitomycin C(7) aminoethylene disulfides displayed improved pharmacological profiles compared with mitomycin C (1). Mechanisms have been advanced for these mitomycins that differ from 1. Central to many of these hypotheses is the intermediate generation of 7-N-(2-mercaptoethyl)mitomycin C (5). Thiol 5 has been neither isolated nor characterized. Two efficient methods were developed for mitomycin (porfiromycin) C(7)-substituted thiols. In the first method, the thiol was produced by a thiol-mediated disulfide exchange process using an activated mixed mitomycin disulfide. In the second route, the thiol was generated by base-mediated cleavage of a porfiromycin C(7)-substituted thiol ester. We selected four thiols, 7-N-(2-mercaptoethyl)mitomycin C (5), 7-N-(2-mercaptoethyl)porfiromycin (12), 7-N-(2-mercapto-2-methylpropyl)mitomycin C (13), and 7-N-(3-mercaptopropyl)porfiromycin (14), for study. Thiols 5 and 12-14 differed in the composition of the alkyl linker that bridged the thiol with the mitomycin (porfiromycin) C(7) amino substituent. Thiol generation was documented by HPLC and spectroscopic studies and by thiol-trapping experiments. The linker affected the structure of the thiol species and the stability of the thiol. We observed that thiols 5 and 12 existed largely as their cyclic isomers. Evidence is presented that cyclization predominantly occurred at the mitomycin C(7) position. Correspondingly, alkyl linker substitution (13) or extension of the linker to three carbons (14) led to enhanced thiol stability and the predominant formation of the free thiol species. The dominant reaction of thiols 5 and 12-14 or their isomers was dimerization, and we found no evidence that thiol formation led to mitosene production and aziridine ring-opening. These findings indicated that thiol generation was not sufficient for mitomycin ring activation. The potential pharmacological advantages of mitomycin C(7) aminoethylene disulfides compared with 1 is discussed in light of the observed thiol cyclization pathway.     

Die Bestimmung von Spuren von Quecksilber

Ohne Zusammenfassung