Reflectionless measures and the Mattila-Melnikov-Verdera uniform rectifiability theorem

A new proof is given of the Mattila-Melnikov-Verdera theorem on the uniform rectifiability of an Ahlfors-David regular measure whose associated Cauchy transform operator is bounded.Comment: 31 pages, 5 figure

An Iterative Abstraction Algorithm for Reactive Correct-by-Construction Controller Synthesis

In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a Finite Transition System (FTS) and thus convert the problem into a two player game between the environment and the system on the FTS. The controller design problem can then be solved using synthesis tools for general linear temporal logic or generalized reactivity(1) specifications. In this article, we propose a new abstraction algorithm. Instead of generating a single FTS to represent the system, we generate two FTSs, which are under- and over-approximations of the original dynamical system. We further develop an iterative abstraction scheme by exploiting the concept of winning sets, i.e., the sets of states for which there exists a winning strategy for the system. Finally, the efficiency of the new abstraction algorithm is illustrated by numerical examples.Comment: A shorter version has been accepted for publication in the 54th IEEE Conference on Decision and Control (held Tuesday through Friday, December 15-18, 2015 at the Osaka International Convention Center, Osaka, Japan

Using chemical ionization mass spectrometry to probe indoor and outdoor atmospheric chemistry

2021 Spring.Includes bibliographical references.People spend the majority of their time in indoor environments. Knowledge of the sources, sinks, and chemistry of indoor pollutants is therefore imperative to indoor air quality and human health. We studied the indoor chemistry of cooking and cleaning at the House Observations of Microbial and Environmental Chemistry (HOMEChem) field campaign during summer 2018 at the University of Texas test house (UTest house) in Austin, TX. We performed measurements of several gas-phase cooking- and cleaning-related analytes using a fast (1 Hz), online chemical ionization mass spectrometry (CIMS) measurement technique utilizing iodide reagent ions. Combining these and other measurements of gas-phase analytes and particulate matter present in indoor air during HOMEChem enables us to piece together a holistic story of the indoor chemistry of cooking and cleaning. We observed enhanced levels of several chlorinated and nitrogenated compounds when cleaning indoors with a commercial bleach solution during HOMEChem. We observed production of several inorganic chlorinated and nitrogenated pollutants from bleaching, including hypochlorous acid, chlorine gas, and chloramines. Levels of hypochlorous acid and nitrogen trichloride observed during cleaning are likely detrimental to human health. Bleach cleaning indoors also lead to the production of secondary organic aerosol—a common outdoor atmospheric pollutant associated with respiratory and cardiovascular issues—as well as potentially harmful organic isocyanates, cyanogen chloride, and chlorocarbons. These results collectively demonstrate bleach cleaning as a source of indoor pollution which impacts indoor air quality and occupant health. We characterized indoor reactive organic carbon (ROC) emissions from cooking and cleaning during HOMEChem, and directly compared resultant chemical complexity of indoor air to outdoors. Cooking indoors greatly impacts ROC concentrations and physiochemical properties, and thus carbon reactivities and lifetimes. Cleaning indoors yielded relatively insubstantial changes. Consistently higher indoor ROC concentrations compared to outdoors demonstrated that indoor emissions were a net source of reactive carbon to the outdoor atmosphere, following their removal by ventilation. ROC dominated indoor and outdoor oxidant reactivity compared to other atmospheric carbon species, thereby greatly influencing secondary pollutant formation, including carbon dioxide, ozone, and secondary particulate matter. Most oxidation chemistry to produce these secondary pollutants likely took place outdoors following the ventilation of ROC species, given the low oxidant levels typical of indoor environments. Moving outdoors, we demonstrated the efficacy of a CIMS instrument utilizing acetate ionization toward quantifying various gas-phase acids in the troposphere. Here, we performed measurements during the Front Range Air Pollution and Photochemistry Experiment (FRAPPE) field campaign in summer 2014. Diurnal increases in mixing ratios were consistent with photochemical sources of nitric, isocyanic, formic, propionic, butyric, valeric, and pyruvic acid. Vertical profiles taken on the 300 m Boulder Atmospheric Observatory tower demonstrated net surface-level emissions of alkanoic acids, but net surface deposition of nitric and pyruvic acid. Nearby traffic emissions and agricultural activity were a primary source of propionic, butyric, and valeric acids, and likely contributed photochemical precursors to nitric and isocyanic acids. The combined diel and vertical profiles of the alkanoic acids and isocyanic acid were inconsistent with dry deposition and photochemical losses being the only sinks, suggesting additional loss mechanisms

Super star clusters and Supernovae in interacting LIRGs unmasked by NIR adaptive optics

We report on an on-going near-IR adaptive optics survey targeting interacting luminous IR galaxies. High-spatial resolution NIR data are crucial to enable interpretation of kinematic, dynamical and star formation (SF) properties of these very dusty objects. Whole progenitor nuclei in the interactions can be missed if only optical HST imaging is used. Here we specifically present the latest results regarding core-collapse supernovae found within the highly extincted nuclear regions of these galaxies. Direct detection and study of such highly obscured CCSNe is crucial for revising the optically-derived SN rates used for providing an independent measurement of the SF history of the Universe. We also present thus-far the first NIR luminosity functions of super star cluster (SSC) candidates. The LFs can then be used to constrain the formation and evolution of SSCs via constraints based on initial mass functions and cluster disruption models.Comment: 6 pages. To appear in proceedings of 'Galaxies and their Masks' (Namibia, April 2010), published by Springer, New York, eds. D.L. Block, K.C. Freeman, I. Puerar

Progenitor's signatures in Type Ia supernova remnants

The remnants of Type Ia supernovae can provide important clues about their progenitor-histories. We discuss two well-observed supernova remnants (SNRs) that are believed to result from a Type Ia SN and use various tools to shed light on the possible progenitor history. We find that Kepler's SNR is consistent with a symbiotic binary progenitor consisted of a white dwarf and an AGB star. Our hydrosimulations can reproduce the observed kinematic and morphological properties. For Tycho's remnant we use the characteristics of the X-ray spectrum and the kinematics to show that the ejecta has likely interacted with dense circumstellar gas.Comment: 4 pages, 9 figures, proceedings for IAU Symposium 281, Padova, July 201