Equilibrium relationships for non-equilibrium chemical dependencies

In contrast to common opinion, it is shown that equilibrium constants determine the time-dependent behavior of particular ratios of concentrations for any system of reversible first-order reactions. Indeed, some special ratios actually coincide with the equilibrium constant at any moment in time. This is established for batch reactors, and similar relations hold for steady-state plug-flow reactors, replacing astronomic time by residence time. Such relationships can be termed time invariants of chemical kinetics

The switching point between kinetic and thermodynamic control

In organic chemistry, the switching point between the kinetic and thermodynamic control regimes of two competitive, parallel reactions is widely studied. A new definition for this switching point is proposed: the time at which the rates of formation of the competing products are equal. According to this definition, the kinetic control regime is present from the beginning of the reaction, and is valid as long as the rate of formation of the kinetic product is larger than the rate of formation of the thermodynamic product. On the switching point, both rates of formation are equal, so, from this switching point the thermodynamic product has a larger rate of formation, and the thermodynamic control remains until the end of the reaction. A closed form expression is given for the proposed time of the switching point, as a function of the direct and inverse kinetic constants of both competing reactions, as well as the initial concentrations of the starting reagent and the competing products. The concept of competing control regimes is extended also to the case where the reactions start from two competitive reagents which decompose to produce a single product. (C) 2016 Elsevier Ltd. All rights reserved

Saks vs. Macys: (r-1) marches on in New York City department stores

Labov\u27s 1963 study of /r/ in New York City department stores had three principal findings: 1) social stratification: use of consonantal /r/ in coda position (r-1) was correlated with the status of the store, i.e. more (r-1) in Saks than Macys 2) an age distribution suggesting ongoing \u27change from above\u27 towards increased (r-1) use 3) linguistic conditioning: more (r-1) in word-final position and emphatic repetitions. These observations have subsequently been reinvestigated, in 1986 by Fowler, and in 2009 by Mather, effectively providing a real-time trend series by replicating the original methodology. In this paper we replicate Labov’s methodology. The results indicate continuing progression in the direction Labov predicted. This is a unique case in variationist studies of change in progress; no other change has been so frequently sampled with controlled methodology across so long a time frame. The present study extends the duration of this series to 54 years. The original study investigated three department stores that were socially stratified by price level and target clientele: Saks, Macys and S. Klein. Klein, the low-end store, closed in 1976, but the other two still operate in their original locations in Manhattan and were investigated for the present study using Labov\u27s original methodology. 160 speakers were observed in each store. The results show continued advance of (r-1) in real time. The percentage of speakers using all (r-1) has increased by a factor of 2.8 in both stores since Labov’s study, but the rate of change has accelerated considerably since Mather’s 2009 data collection. Social stratification of the variable is still apparent: Saks, the high-end store, continues to show higher rates of (r-1) than Macys. In Labov’s apparent time results, (r-1) use increased among younger speakers at Saks, but was higher among older speakers at Macys, suggesting that the change originated among higher status speakers, and spread to lower status speakers by diffusion in adult life. In the current study, this pattern has shifted. The age distribution at Saks is flattening out at a high level (speaker groups under age 50 all produce over 80% (r-1) tokens), while Macys now shows a conventional apparent time pattern, with (r-1) advancing among younger speakers. The linguistic conditioning on the process is moderating as the change approaches completion: Macys speakers showed moderate increases in (r-1) of about 7% between internal (\u27fourth\u27) and final position (\u27floor\u27), and between non-emphatic and emphatic productions, but Saks employees are essentially uniform across all conditions

Optimal Distributed Covering Algorithms

We present a time-optimal deterministic distributed algorithm for approximating a minimum weight vertex cover in hypergraphs of rank f. This problem is equivalent to the Minimum Weight Set Cover problem in which the frequency of every element is bounded by f. The approximation factor of our algorithm is (f+epsilon). Let Delta denote the maximum degree in the hypergraph. Our algorithm runs in the congest model and requires O(log{Delta} / log log Delta) rounds, for constants epsilon in (0,1] and f in N^+. This is the first distributed algorithm for this problem whose running time does not depend on the vertex weights nor the number of vertices. Thus adding another member to the exclusive family of provably optimal distributed algorithms. For constant values of f and epsilon, our algorithm improves over the (f+epsilon)-approximation algorithm of [Fabian Kuhn et al., 2006] whose running time is O(log Delta + log W), where W is the ratio between the largest and smallest vertex weights in the graph. Our algorithm also achieves an f-approximation for the problem in O(f log n) rounds, improving over the classical result of [Samir Khuller et al., 1994] that achieves a running time of O(f log^2 n). Finally, for weighted vertex cover (f=2) our algorithm achieves a deterministic running time of O(log n), matching the randomized previously best result of [Koufogiannakis and Young, 2011]. We also show that integer covering-programs can be reduced to the Minimum Weight Set Cover problem in the distributed setting. This allows us to achieve an (f+epsilon)-approximate integral solution in O((1+f/log n)* ((log Delta)/(log log Delta) + (f * log M)^{1.01}* log epsilon^{-1}* (log Delta)^{0.01})) rounds, where f bounds the number of variables in a constraint, Delta bounds the number of constraints a variable appears in, and M=max {1, ceil[1/a_{min}]}, where a_{min} is the smallest normalized constraint coefficient. This improves over the results of [Fabian Kuhn et al., 2006] for the integral case, which combined with rounding achieves the same guarantees in O(epsilon^{-4}* f^4 * log f * log(M * Delta)) rounds

The Effect of Salience on Co-variation in Brazilian Portuguese

This paper analyzes cross-correlations among six variables of Brazilian Portuguese (the pronunciation of nasal /e/, coda r-retroflexion, coda r-deletion, NP agreement, 3rd person plural subject-verb agreement, and 1st person plural subject-verb agreement), with the objective of identifying constraints that promote the co-occurrence of sociolinguistic variants in individual speakers’ speech. We focus on the perspective of structural cohesion, and show that co-variability is conditioned not only by structural similarities among dependent variables (such as agreement processes or coda weakening), but also by general linguistic constraints that operate across multiple variables, such as phonic salience (Naro 1981, Scherre 1988, Naro et al. 1999). Finally, we suggest that markedness may be a more general linguistic principle underlying co-variation