The synthesis of single enantiomers of trans-alkene-containing mycolic acids

We report routes to single enantiomers of hydroxy and ketomycolic acids containing an α-methyl-trans-alkene unit.     

Truth versus validity in mathematical proof

In mathematics education, it is often said that mathematical statements are necessarily either true or false. It is also well known that this idea presents a great deal of difficulty for many students. Many authors as well as researchers in psychology and mathematics education emphasize the difference between common sense and mathematical logic. In this paper, we provide both epistemological and didactic arguments to reconsider this point of view, taking into account the distinction made in logic between truth and validity on one hand, and syntax and semantics on the other. In the first part, we provide epistemological arguments showing that a central concern for logicians working with a semantic approach has been finding an appropriate distance between common sense and their formal systems. In the second part, we turn from these epistemological considerations to a didactic analysis. Supported by empirical results, we argue for the relevance of the distinction and the relationship between truth and validity in mathematical proof for mathematics education.     

On the existence of almost periodic solutions for the impulsive Lasota–Wazewska model

By means of the Cauchy matrix we give sufficient conditions for the existence and exponential stability of almost periodic solutions for the delay impulsive Lasota–Wazewska model. The impulses are realized at fixed moments of time.     

Experimental and kinetic modeling study of tetralin: A naphtheno-aromatic fuel for gasoline,jet and diesel surrogates

Distillate fuels contain significant proportions of naphtheno-aromatic components and tetralin is a suitable surrogate component to represent this molecular moiety. The presence of aromatic and naphthyl rings makes kinetic modeling of tetralin very challenging. Primary radicals formed during the oxidation of tetralin can be aryl, benzylic or paraffinic in nature. Using available information on reaction paths and rate constants of naphthenes and alkyl-aromatics, a kinetic model of tetralin has been developed in the current study with emphasis on low-temperature chemistry and high-pressure conditions. Due to the lack of high-level quantum chemical calculations on reaction pathways of tetralin, analogous rates from ab-initio studies on benzylic and paraffinic radicals have been adopted here. Some modifications to the reaction rate rules are incorporated to account for the unique characteristics of tetralin's molecular structure. Important reaction channels have been identified using reaction path and brute force sensitivity analyses. In order to investigate the model performance at low temperatures, new experiments are carried out in a rapid compression machine on blends of tetralin and 3-methylpentane. Blending of low-reactivity tetralin with a high-reactivity alkane allowed the investigation of tetralin ignition at very low temperatures (665 – 856 K). The kinetic model developed in the current study is found to predict the current experiments and literature data adequately. The new model will aid in high-fidelity surrogate predictions at engine-relevant conditions.     

A class of transformed Markov processes

This paper considers some properties of a class of transformed Markov processes. The analogy with Whittle's relaxed Markov process is pointed out. Some applications of the transformed Markov processes to queueing networks are described     

Almost sure rates of mixing for i.i.d. unimodal maps

It has been known since the pioneering work of Jakobson and subsequent work by Benedicks and Carleson and others that a positive measure set of quadratic maps admit an absolutely continuous invariant measure. Young and Keller-Nowicki proved exponential decay of its correlation functions. Benedicks and Young [8], and Baladi and Viana [4] studied stability of the density and exponential rate of decay of the Markov chain associated to i.i.d. small perturbations. The almost sure statistical properties of the sample stationary measures of i.i.d. itineraries are more difficult to estimate than the “averaged statistics”. Adapting to random systems, on the one hand partitions associated to hyperbolic times due to Alves [1], and on the other a probabilistic coupling method introduced by Young [26] to study rates of mixing, we prove stretched exponential upper bounds for the almost sure rates of mixing.     

Synthesis of Furo[2,3‐d]pyridazin‐4(5H)‐one and Its N(5)‐Substituted Derivatives

We report the efficient preparation of furo[2,3‐d]pyridazin‐4(5H)‐one and its N‐substituted derivatives starting from methyl 2‐methylfuran‐3‐carboxylate. The Me group was converted to the aldehyde group, which was then condensed with hydrazine derivatives. Then, the ester functionalities were hydrolyzed to the corresponding acids, followed by treatment with SOCl₂ to give N‐substituted furopyridazinone derivatives.     

Low-temperature exfoliation of multilayer-graphene material from FeCl3 and CH3NO2 co-intercalated graphite compound

Microwave induced rapid decomposition of nitromethane at low temperature exfoliates the graphene sheets from the FeCl(3) and CH(3)NO(2) co-intercalated graphite compound without creating many defects and functional groups. This approach provides a scalable method for high-quality graphene materials via low-temperature exfoliation of graphite under mild chemical conditions.     

Euclidean algorithms are Gaussian

We obtain a central limit theorem for a general class of additive parameters (costs, observables) associated to three standard Euclidean algorithms, with optimal speed of convergence. We also provide very precise asymptotic estimates and error terms for the mean and variance of such parameters. For costs that are lattice (including the number of steps), we go further and establish a local limit theorem, with optimal speed of convergence. We view an algorithm as a dynamical system restricted to rational inputs, and combine tools imported from dynamics, such as transfer operators, with various other techniques: Dirichlet series, Perron's formula, quasi-powers theorems, and the saddle-point method. Such dynamical analyses had previously been used to perform the average-case analysis of algorithms. For the present (dynamical) analysis in distribution, we require estimates on transfer operators when a parameter varies along vertical lines in the complex plane. To prove them, we adapt techniques introduced recently by Dolgopyat in the context of continuous-time dynamics (Ann. Math. 147 (1998) 357).     

An integer linear programming approach for approximate string comparison

We introduce a problem called maximum common characters in blocks (MCCB), which arises in applications of approximate string comparison, particularly in the unification of possibly erroneous textual data coming from different sources. We show that this problem is NP-complete, but can nevertheless be solved satisfactorily using integer linear programming for instances of practical interest. Two integer linear formulations are proposed and compared in terms of their linear relaxations. We also compare the results of the approximate matching with other known measures such as the Levenshtein (edit) distance.