On quantitative aspects of the unit sum number problem

We investigate the function u _K,S (n; q) which counts the number of representations of algebraic integers α with |N_{K/\mathbb Q}(a)| ￡ q{|N_{K/{\mathbb Q}}(\alpha)| \leq q} for some real positive q that can be written as sums of exactly n S-units of the number field K.     

Structural changes in data communication in wireless sensor networks

Wireless sensor networks are an important technology for making distributed autonomous measures in hostile or inaccessible environments. Among the challenges they pose, the way data travel among them is a relevant issue since their structure is quite dynamic. The operational topology of such devices can often be described by complex networks. In this work, we assess the variation of measures commonly employed in the complex networks literature applied to wireless sensor networks. Four data communication strategies were considered: geometric, random, small-world, and scale-free models, along with the shortest path length measure. The sensitivity of this measure was analyzed with respect to the following perturbations: insertion and removal of nodes in the geometric strategy; and insertion, removal and rewiring of links in the other models. The assessment was performed using the normalized Kullback-Leibler divergence and Hellinger distance quantifiers, both deriving from the Information Theory framework. The results reveal that the shortest path length is sensitive to perturbations.     

Atmospheric chemistry of isopropyl formate and tert‐butyl formate

Formates are produced in the atmosphere as a result of the oxidation of a number of species, notably dialkyl ethers and vinyl ethers. This work describes experiments to define the oxidation mechanisms of isopropyl formate, HC(O)OCH(CH₃)₂, and tert‐butyl formate, HC(O)OC(CH₃)₃. Product distributions are reported from both Cl‐ and OH‐initiated oxidation, and reaction mechanisms are proposed to account for the observed products. The proposed mechanisms include examples of the α‐ester rearrangement reaction, novel isomerization pathways, and chemically activated intermediates. The atmospheric oxidation of isopropyl formate by OH radicals gives the following products (molar yields): acetic formic anhydride (43%), acetone (43%), and HCOOH (15–20%). The OH radical initiated oxidation of tert‐butyl formate gives acetone, formaldehyde, and CO₂ as major products. IR absorption cross sections were derived for two acylperoxy nitrates derived from the title compounds. Rate coefficients are derived for the kinetics of the reactions of isopropyl formate with OH (2.4 ± 0.6) × 10^?12, and with Cl (1.75 ± 0.35) × 10^?11, and for tert‐butyl formate with Cl (1.45 ± 0.30) × 10^?11 cm³ molecule^?1 s^?1. Simple group additivity rules fail to explain the observed distribution of sites of H‐atom abstraction for simple formates. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 479–498, 2010     

Untersuchung von Mehl

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Jodzahl

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