Euler Integration of Gaussian Random Fields and Persistent Homology

In this paper we extend the notion of the Euler characteristic to persistent homology and give the relationship between the Euler integral of a function and the Euler characteristic of the function's persistent homology. We then proceed to compute the expected Euler integral of a Gaussian random field using the Gaussian kinematic formula and obtain a simple closed form expression. This results in the first explicitly computable mean of a quantitative descriptor for the persistent homology of a Gaussian random field.Comment: 21 pages, 1 figur

Cosine families and semigroups really differ

We reveal three surprising properties of cosine families, distinguishing them from semigroups of operators: (1) A single trajectory of a cosine family is either strongly continuous or not measurable. (2) Pointwise convergence of a sequence of equibounded cosine families implies that the convergence is almost uniform for time in the entire real line; in particular, cosine families cannot be perturbed in a singular way. (3) A non-constant trajectory of a bounded cosine family does not have a limit at infinity; in particular, the rich theory of asymptotic behaviour of semigroups does not have a counterpart for cosine families. In addition, we show that equibounded cosine families that converge strongly and almost uniformly in time may fail to converge uniformly.Adam Bobrowski and Wojciech Chojnack

Quantification of the depletion of ozone in the plume of Mount Etna

Volcanoes are an important source of inorganic halogen species into the atmosphere. Chemical processing of these species generates oxidised, highly reactive, halogen species which catalyse considerable O3 destruction within volcanic plumes. A campaign of ground-based in situ O3, SO2 and meteorology measurements was undertaken at the summit of Mount Etna volcano in July/August 2012. At the same time, spectroscopic measurements were made of BrO and SO2 columns in the plume downwind. Depletions of ozone were seen at all in-plume measurement locations, with average O3 depletions ranging from 11–35 nmol mol 1 (15–45 %). Atmospheric processing times of the plume were estimated to be between 1 and 4 min. A 1-D numerical model of early plume evolution was also used. It was found that in the early plume O3 was destroyed at an approximately constant rate relative to an inert plume tracer. This is ascribed to reactive halogen chemistry, and the data suggests the majority of the reactive halogen that destroys O3 in the early plume is generated within the crater, including a substantial proportion generated in a high-temperature “effective source region” immediately after emission. The model could approximately reproduce the main measured features of the ozone chemistry. Model results show a strong dependence of the near-vent bromine chemistry on the presence or absence of volcanic NOx emissions and suggest that near-vent ozone measurements can be used as a qualitative indicator of NOx emission

Emission of polycyclic aromatic hydrocarbons (PAHs) and benzene, toluene, ethylbenzene and xylene (BTEX) from the furan moulding sands with addition of the reclaim

In this paper, the results of decomposition of a moulding sand with furfuryl resin also on a quartz matrix and with additions of a reclaimed material, under industrial conditions, are presented. Investigations of the gases emission in the test foundry plant were performed according to the original method developed in the Faculty of Foundry Engineering, AGH UST. The dependence of the emitted PAHs and BTEX group substances and ignition losses on the reclaim fraction in a moulding sand are of a linear character of a very high correlation coefficient R2. On the bases of the derived equations, it is possible to determine the amount of the emitted hazardous substances from the moulding sand containing the known fraction of the reclaim

Neškodljivost kalupnih pjesaka sa bentonitom i svijetlećim nositeljima ugljika

Procedures have been developed to determine the volume, rate and composition (particularly BTEX: benzene, toluene, ethylbenzene and xylenes and PAHs (polycyclic aromatic hydrocarbons)) of gas evolution from moulds and cores prepared with various binders as a means of harmfulness of moulding sands. The rate of gas evolution from green sands with four different lustrous carbon carrier and BTEX content were determined. The gas evolution rates are highest in the range of about 20 to 30 s after contact with molten metal. In practice during the first 200-250 s the total emission of gases generated in investigated samples occurred. The main emitted component from the BTEX group was benzene.Postupci su razvijeni za određivanje volumena, brzine i sastava (posebice BTEX: benzen, toluen, etilbenzen, xilana) i PAH (policiklički automatski hidrokarbonati) plina koji nastaje iz kalupa i jezgri na različitim nosačima u težnji za neškodljivost kalupnih pijesaka. Brzine nastajanja plina iz pripravljenih pijesaka sa 4 različita svijetleća nositelja ugljika i sadržajem BTEX su određeni. Brzine nastajanja plina su najveće u razini 20 do 30 s poslije dodira sa rastopljenim metalom. Praktično, tijekom prvih 200-250 s ostvaruje se ukupna emisija stvorenih plinova u istraživanim uzorcima. Iz BTEX skupine, benzen je glavna emitirajuća komponenta

Reply to comment from Liotta and Rizzo on “Evolution of CO2 , SO2 , HCl and HNO3 in the volcanic plumes from Etna” by Voigt et al. [Geophys. Res. Lett.; 41, doi:10.1002/2013GL058974]

Editor’s Note: The following comment and reply arise from an article published in Geophysical Research Letters by Voigt et al. (2014). The article addresses a volcanology topic, and the commenters take issue with some conclusions and offer an analysis of their own. Voigt and co-authors have responded. Why is this comment-and-reply being published in the Bulletin? It is because Geophysical Research Letters is one of a number of journals that do not offer any published forum for discussion of the papers they publish. This is a matter of editorial policy and a decision for each journal. The Bulletin of Volcanology does provide a forum for discussion of articles published. When contacted by Marcello Liotta with the request that the Bulletin consider hosting a discussion of the Voigt et al. volcanology article in GRL, I agreed to do so if the GRL authors were willing to engage with the comment. Voigt and co-authors were willing to do so and have been allowed a small amount of additional space to summarize for Bulletin readers the key points of the GRL paper under discussion before responding directly to the comment from Liotta and Rizzo. I hope that Bulletin readers find the discussion and reply of interest

Reactive halogen chemistry in volcanic plumes

Bromine monoxide (BrO) and sulphur dioxide (SO2) abundances as a function of the distance from the source were measured by ground-based scattered-light Multi AXis Differential Optical Absorption Spectroscopy (MAX-DOAS) in the volcanic plumes of Mt. Etna on Sicily, Italy in August-October 2004 and May 2005 and Villarica in Chile in November 2004. BrO and SO2 spatial distributions in a cross section of Mt. Etna’s plume were also determined by Imaging DOAS. We observed an increase in the BrO/SO2 ratio in the plume from below the detection limit near the vent to about 4.5 x 10-4 at 19 km (Mt. Etna) and to about 1.3 x 10-4 at 3 km (Villarica) distance, respectively. Additional attempts were undertaken to evaluate the compositions of individual vents on Mt. Etna. Furthermore, we detected the halogen species ClO and OClO. This is the first time that OClO could be detected in a volcanic plume. Using calculated thermodynamic equilibrium compositions as input data for a one–dimensional photochemical model, we could reproduce the observed BrO and SO2 vertical columns in the plume and their ratio as function of distance from the volcano as well as vertical BrO and SO2 profiles across the plume with current knowledge of multiphase halogen chemistry, but only when we assumed the existence of an ”effective source region”, where volcanic volatiles and ambient air are mixed at about 600°C (in the proportions of 60% and 40%, respectively

Assessment of harmfulness of phenolic resins hardened by CO2 in an aspect of emission of substances from BTEX and PAH groups

Abstract Out of moulding sands used in the foundry industry, sands with organic binders deserve a special attention. These binders are based on synthetic resins, which ensure obtaining the proper technological properties and sound castings, however, they negatively influence the environment. If in the initial state these resins are not very dangerous for people and for the environment, thus under an influence of high temperatures they generate very harmful products, being the result of their thermal decomposition. Depending on the kind of the applied resin under an influence of a temperature such compounds as: furfuryl alcohol, formaldehyde, phenol, BTEX group (benzene, toluene, ethylobenzene, xylenes), and also polycyclic aromatic hydrocarbons (PAHs) can be formed and released