Reactions of 29 Transition Metal Cations, in the Same Oxidation State and under the Same Gas-Phase Conditions, with Sulfur

A total of 29 transition metals (all except Tc), all as ions M(+), have been reacted with gaseous S(8). The reactivities and reaction products provide a unique set of comparative data on a fundamental reaction of the elements. The results underlie the interpretation of many other processes and compounds in condensed phases. Series of product ions [MS(y)()](+) are formed, with y generally starting at 4, and increasing with time through 8 up to 10, 12, 16, or 21 (for La(+)). A general mechanism is proposed, in which the first {MS(8)}(+) encounter complex is reactive and undergoes S-S bond scission and rearrangement around the metal, such that [MS(8)](+) is not an early product. The early transition metals react faster than later members of the series, and third row metals react about twice as fast as first row metals. The metals which are more chalcophilic in condensed-phase chemistry are apparently less so as M(+); Hg(+) does not form observable [HgS(y)()](+) (except for a very low yield of [HgS(3)](+)) and is remarkably less reactive with sulfur than most of the other metal ions. Simple electron transfer between M(+) and S(8) does not occur except possibly for Ir(+), but S(8)(+) is sometimes observed and is believed to be formed by electron transfer from S(8) to some [MS(y)()](+) complexes. Interpretation of the rates of reaction of the ions of groups 3, 4, and 5 with S(8) is complicated because they react with adventitious water in the cell forming oxo-species. The results are discussed in the context of condensed-phase metal polysulfide chemistry.     

Further studies on the application of vinylogous amides and β-halovinylaldehydes to the regiospecific synthesis of unsymmetrical,polyfunctionalized 2,3,4- and 1,2,3,4- substituted pyrroles

Highly functionalized pyrroles with appropriate regiochemical functionality represent an important class of marine natural products and potential drug candidates. We describe herein a detailed study of the reaction of α-aminoacid esters with vinylogous amides and also β-halovinylaldehydes for the regiospecific synthesis of 2,3,4-trisubstituted and 1,2,3,4-tetrasubstituted pyrroles. Since the vinylogous amides and β-halovinylaldehydes are readily available precursors, rapid access to a wide variety of unsymmetrically substituted pyrroles is accomplished via this methodology.     

Sub-ppt detection limits for copper ions with Gly-Gly-His modified electrodes

An electrochemical metal ion sensor has been developed with a detection limit of less than 0.2 ppt by the covalent attachment of the tripeptide Gly-Gly-His as a recognition element to a 3-mercaptopropionic acid modified gold electrode.     

Geometric lattice actions, entropy and fundamental groups

Let be a lattice in a noncompact simple Lie Group G, where . Suppose acts analytically and ergodically on a compact manifold M preserving a unimodular rigid geometric structure (e.g. a connection and a volume). We show that either the action is isometric or there exists a "large image" linear representation of . Under an additional assumption on the dynamics of the action, we associate to a virtual arithmetic quotient of full entropy. Received: December 14, 2000     

Resolving Extensions of Finitely Presented Systems

In this paper we extend certain central results of zero dimensional systems to higher dimensions. The first main result shows that if (Y,f) is a finitely presented system, then there exists a Smale space (X,F) and a u-resolving factor map π ₊:X→Y. If the finitely presented system is transitive, then we show there is a canonical minimal u-resolving Smale space extension. Additionally, we show that any finite-to-one factor map between transitive finitely presented systems lifts through u-resolving maps to an s-resolving map.     

Generalizations of Non-Commutative Neutrix Convolution Products of Functions

The non-commutative neutrix convolution product of the functions x ^r cos_–(x) and x ^s cos₊(x) is evaluated. Further similar non-commutative neutrix convolution products are evaluated and deduced.     

Sterling stirling play

In this paper we analyze a recently proposed impartial combinatorial ruleset that is played on a permutation of the set \(\left[ n\right] \). We call this ruleset Stirling Shave. A procedure utilizing the ordinal sum operation is given to determine the nim value of a given normal play position. Additionally, we enumerate the number of permutations of \(\left[ n\right] \) which are \(\mathcal {P}\)-positions. The formula given involves the Stirling numbers of the first-kind. We also give a complete analysis of the Misère version of Stirling Shave using Conway’s genus theory. An interesting by-product of this analysis is insight into how the ordinal sum operation behaves in Misère Play.     

Interactive optimization

Optimization algorithms or heuristics in which the user interacts significantly either during the solution process or as part of post-optimality analysis are becoming increasingly popular. An important underlying premise of such man/machine systems is that there are some steps in solving a problem in which the computer has an advantage and other steps in which a human has an advantage. This paper first discusses how man/machine systems can be useful in facilitating model specification and revision, coping with aspects of a problem that are difficult to quantify and assisting in the solution process. We then survey successful systems that have been developed in the areas of vehicle scheduling, location problems, job shop scheduling, course scheduling, and planning language-based optimization.     

Surface-enhanced emission from single semiconductor nanocrystals

The fluorescence behavior of single CdSe(ZnS) core-shell nanocrystal (NC) quantum dots is dramatically affected by electromagnetic interactions with a rough metal film. Observed changes include a fivefold increase in the observed fluorescence intensity of single NCs, a striking reduction in their fluorescence blinking behavior, complete conversion of the emission polarization to linear, and single NC exciton lifetimes that are >10(3) times faster. The enhanced excited state decay process for NCs coupled to rough metal substrates effectively competes with the Auger relaxation process, allowing us to observe both charged and neutral exciton emission from these NC quantum dots.