Asymptotic distribution of integers with certain prime factorizations

Let $p_{1}<p_2<... <p_{\nu}<...$ be the sequence of prime numbers and let $m$ be a positive integer. We give a strong asymptotic formula for the distribution of the set of integers having prime factorizations of the form p_{m^{k_1}}p_{m^{k_{2}}...p_{m^{k_{n}}} with $k_{1}\le k_{2}\le...\le k_{n}$. Such integers originate in various combinatorial counting problems; when $m=2$, they arise as Matula numbers of certain rooted trees.Comment: 11 page

Doctor of Philosophy

dissertationA Uinta Basin bitumen was hydrotreated over a sulfided Ni-Mo on alumina commercial hydrodemetallation catalyst. The catalyst was on-stream continuously for more than 1,000 hours. The data were obtained with the reactor operating as a fixed bed reactor in the upflow mode to ensure complete wetting of the catalyst and nearly isothermal operation. The deactivation of the catalyst was monitored by the decline in the API gravity of the total liquid product with time-on-stream at a standard set of conditions. The primary process variables studied were reactor temperature (620-685 K; 656-775 °F), liquid weight hourly space velocity (0.24-1.38 h'1) and total reactor pressure (11.3-16.7 MPa; 1634-2423 psia). The hydrogen/oil ratio was fixed in all experiments at 890 m3/m3 (5000 scf H/bbl). The extent of heteroatom and metals removal, residuum (>1000 °F) conversion and molecular weight reduction were determined as a function of process operating variables. Simulated distillation of the hydrotreated total liquid products was used to compute residuum conversion and product distributions. Conradson carbon residue conversion and pour point reduction were also determined as functions of process operating conditions. Hydrodenitrogenation, hydrodesulfurization, hydrodemetallation and residuum conversion data were analyzed using a modified power rate law model. regression and ordinary differential equation solver techniques for the analysis of laboratory data. Simple first-order power rate law expressions for The apparent kinetic parameters were obtained by combined hydrodenitrogenation and hydrodesulfurization were obtained for bitumen hydrotreating over the hydrodemetallation catalyst. Higher than first-order kinetic data for residuum conversion and nickel removal were organized by invoking two parallel first-order reactions for the facile and refractory fractions. A molecular weight reduction model was proposed to examine the extent of residuum conversion to gas-oil, middle distillate and gases. The first-order rate constants were also determined. The hydrodemetallation catalyst was less active for nitrogen, sulfur and residuum conversion than the hydrodenitrogenation catalyst. Nitrogen, sulfur, and metals removal; residuum conversion; and product distributions are discussed for bitumen hydrotreating over the hydrodemetallation and hydrodenitrogenation catalysts

Strategies for the Synthesis of Nitrogeous Compounds : Aminal Radical Reaction and Pyridinium Oxide Cycloadditions

Pharmaceuticals, molecular catalysts, and secondary metabolites often contain nitrogen. The problems faced synthesizing compounds which contain nitrogen was because of the Lewis base reactivity of nitrogen lone pairs, and the acidic protons of some nitrogenous functional groups. We developed two methods for the synthesis of nitrogeous compounds. Additionally, we successfully constructed the heterotetracyclic core of himgaline. The aminal radicals were generated by reduction of the corresponding amidine or amidinium ion. The intermediate radicals participate in C−C bond- forming reactions to produce fully substituted aminal stereocenters. No toxic additives or reagents are required. The regioselectivity and diastereoselectivity was investigated in pyridinium oxide cycloadditions using complex substrates. The reaction is reversible under the reaction conditions. High levels of diastereoselectivity and regioselectivty are observed, which can be attributed to minimization of syn-pentane interactions in the products. The stereo- and region-selective intramoleculer pyridinium oxide cycloaddition successfully forms two bonds and builds four stereocenters in a single step. These key cycloaddition reactions are particularly suitable to the challenge of preparing multiple rings with control of stereochemistry. It has been shown that the new methodology replacing acid-base strategy would enhance the efficiency of alkaloid synthesis

Fundamentals of air pollution engineering

Analysis and abatement of air pollution involve a variety of technical disciplines. Formation of the most prevalent pollutants occurs during the combustion process, a tightly coupled system involving fluid flow, mass and energy transport, and chemical kinetics. Its complexity is exemplified by the fact that, in many respects, the simplest hydrocarbon combustion, the methane-oxygen flame, has been quantitatively modeled only within the last several years. Nonetheless, the development of combustion modifications aimed at minimizing the formation of the unwanted by-products of burning fuels requires an understanding of the combustion process. Fuel may be available in solid, liquid, or gaseous form; it may be mixed with the air ahead of time or only within the combustion chamber; the chamber itself may vary from the piston and cylinder arrangement in an automobile engine to a 10-story-high boiler in the largest power plant; the unwanted byproducts may remain as gases, or they may, upon cooling, form small particles. The only effective way to control air pollution is to prevent the release of pollutants at the source. Where pollutants are generated in combustion, modifications to the combustion process itself, for example in the manner in which the fuel and air are mixed, can be quite effective in reducing their formation. Most situations, whether a combustion or an industrial process, however, require some degree of treatment of the exhaust gases before they are released to the atmosphere. Such treatment can involve intimately contacting the effluent gases with liquids or solids capable of selectively removing gaseous pollutants or, in the case of particulate pollutants, directing the effluent flow through a device in which the particles are captured on surfaces. The study of the generation and control of air pollutants can be termed air pollution engineering and is the subject of this book. Our goal here is to present a rigorous and fundamental analysis of the production of air pollutants and their control. The book is intended for use at the senior or first-year graduate level in chemical, civil, environmental, and mechanical engineering curricula. We assume that the student has had basic first courses in thermodynamics, fluid mechanics, and heat transfer. The material treated in the book can serve as the subject of either a full-year or a one-term course, depending on the choice of topics covered. In the first chapter we introduce the concept of air pollution engineering and summarize those species classified as air pollutants. Chapter 1 also contains four appendices that present certain basic material that will be called upon later in the book. This material includes chemical kinetics, the basic equations of heat and mass transfer, and some elementary ideas from probability and turbulence. Chapter 2 is a basic treatment of combustion, including its chemistry and the role of mixing processes and flame structure. Building on the foundation laid in Chapter 2, we present in Chapter 3 a comprehensive analysis of the formation of gaseous pollutants in combustion. Continuing in this vein, Chapter 4 contains a thorough treatment of the internal combustion engine, including its principles of operation and the mechanisms of formation of pollutants therein. Control methods based on combustion modification are discussed in both Chapters 3 and 4. Particulate matter (aerosols) constitutes the second major category of air pollutants when classified on the basis of physical state. Chapter 5 is devoted to an introduction to aerosols and principles of aerosol behavior, including the mechanics of particles in flowing fluids, the migration of particles in external force fields, Brownian motion of small particles, size distributions, coagulation, and formation of new particles from the vapor by homogeneous nucleation. Chapter 6 then treats the formation of particles in combustion processes. Chapters 7 and 8 present the basic theories of the removal of particulate and gaseous pollutants, respectively, from effluent streams. We cover all the major air pollution control operations, such as gravitational and centrifugal deposition, electrostatic precipitation, filtration, wet scrubbing, gas absorption and adsorption, and chemical reaction methods. Our goal in these two chapters, above all, is to carefully derive the basic equations governing the design of the control methods. Limited attention is given to actual equipment specification, although with the material in Chapters 7 and 8 serving as a basis, one will be able to proceed to design handbooks for such specifications. Chapters 2 through 8 treat air pollution engineering from a process-by-process point of view. Chapter 9 views the air pollution control problem for an entire region or airshed. To comply with national ambient air quality standards that prescribe, on the basis of health effects, the maximum atmospheric concentration level to be attained in a region, it is necessary for the relevant governmental authority to specify the degree to which the emissions from each of the sources in the region must be controlled. Thus it is generally necessary to choose among many alternatives that may lead to the same total quantity of emission over the region. Chapter 9 establishes a framework by which an optimal air pollution control plan for an airshed may be determined. In short, we seek the least-cost combination of abatement measures that meets the necessary constraint that the total emissions not exceed those required to meet an ambient air quality standard. Once pollutants are released into the atmosphere, they are acted on by a variety of chemical and physical phenomena. The atmospheric chemistry and physics of air pollution is indeed a rich arena, encompassing the disciplines of chemistry, meteorology, fluid mechanics, and aerosol science. As noted above, the subject matter of the present book ends at the stack (or the tailpipe); those readers desiring a treatment of the atmospheric behavior of air pollutants are referred to J. H. Seinfeld, Atmospheric Chemistry and Physics of Air Pollution (Wiley-Interscience, New York, 1986). We wish to gratefully acknowledge David Huang, Carol Jones, Sonya Kreidenweis, Ranajit Sahu, and Ken Wolfenbarger for their assistance with calculations in the book. Finally, to Christina Conti, our secretary and copy editor, who, more than anyone else, kept safe the beauty and precision of language as an effective means of communication, we owe an enormous debt of gratitude. She nurtured this book as her own; through those times when the task seemed unending, she was always there to make the road a little smoother. R. C. Flagan J. H. Seinfel

Functional Coordination Polymers and Metal–Organic Frameworks

This book is a collection of contributions on the synthesis, characterization, and applications of Metal-Organic Frameworks (MOF) and Coordination Polymers (CP). Coordination Polymers (CP) and Metal–Organic Frameworks (MOF) are at the core of contemporary research on inorganic materials. The virtually infinite combination of their building blocks—inorganic metallic nodes (single ions or clusters) and organic polytopic linkers (polycarboxylates, bridging N-/S-/O-containing heterocycles)—generates solid air- and water-stable compounds. Interesting features from an applicative point of view are porosity, large surface area, and lattice flexibility (the “breathing” effect). These properties make them ubiquitous in several fields of materials science: gas storage and separation, luminescent sensing, heterogeneous catalysis, and magnetism

Stable Isotopes in Tree Rings

This Open Access volume highlights how tree ring stable isotopes have been used to address a range of environmental issues from paleoclimatology to forest management, and anthropogenic impacts on forest growth. It will further evaluate weaknesses and strengths of isotope applications in tree rings. In contrast to older tree ring studies, which predominantly applied a pure statistical approach this book will focus on physiological mechanisms that influence isotopic signals and reflect environmental impacts. Focusing on connections between physiological responses and drivers of isotope variation will also clarify why environmental impacts are not linearly reflected in isotope ratios and tree ring widths. This volume will be of interest to any researcher and educator who uses tree rings (and other organic matter proxies) to reconstruct paleoclimate as well as to understand contemporary functional processes and anthropogenic influences on native ecosystems. The use of stable isotopes in biogeochemical studies has expanded greatly in recent years, making this volume a valuable resource to a growing and vibrant community of researchers

Effect of the air pressure on electro-Fenton process

Electro-Fenton process is considered a very promising tool for the treatment of waste waters contaminated by organic pollutants refractant or toxic for microorganisms used in biological processes [1-6]. In these processes H2O2 is continuously supplied to an acidic aqueous solution contained in an electrolytic cell from the two-electron reduction of oxygen gas, directly injected as pure gas or bubbled air. Due to the poor solubility of O2 in aqueous solutions, two dimensional cheap graphite or carbon felt electrodes give quite slow generation of H2O2, thus resulting in a slow abatement of organics. In this context, we report here a series of studies [7-9] on the effect of air pressure on the electro-generation of H2O2 and the abatement of organic pollutants in water by electro-Fenton process. The effect of air pressure, current density, mixing and nature of the organic pollutant was evaluated. [1] E. Brillas, I. Sirés, M.A. Oturan, Chem. Rev., 109 (2009) 6570-6631. [2] C.A. Martínez-Huitle, M.A. Rodrigo, I. Sirés, O. Scialdone, Chem. Rev. 115 (2015) 13362–13407. [3] M. Panizza, G. Cerisola, Chem. Rev. 109 (2009) 6541–6569. [4] I. Sirés, E. Brillas, M.A. Oturan, M.A. Rodrigo, M. Panizza, Environ. Sci. Pollut. Res. 21 (2014) 8336–8367. [5] C.A. Martínez-Huitle, S. Ferro, Chem. Soc. Rev. 35 (2006) 1324–1340. [6] B.P.P. Chaplin, Environ. Sci. Process. Impacts. 16 (2014) 1182–1203. [7] O. Scialdone, A. Galia, C. Gattuso, S. Sabatino, B. Schiavo, Electrochim. Acta, 182 (2015) 775-780. [8] J.F. Pérez, A. Galia, M.A. Rodrigo, J. Llanos, S. Sabatino, C. Sáez, B. Schiavo, O. Scialdone, Electrochim. Acta, 248 (2017) 169-177. [9] A.H. Ltaïef, S. Sabatino, F. Proietto, A. Galia, O. Scialdone, O. 2018, Chemosphere, 202, 111-118

Pressurized CO2 Electrochemical Conversion to Formic Acid: From Theoretical Model to Experimental Results

To curb the severely rising levels of carbon dioxide in the atmosphere, new approaches to capture and utilize this greenhouse gas are currently being investigated. In the last few years, many researches have focused on the electrochemical conversion of CO2 to added-value products in aqueous electrolyte solutions. In this backdrop, the pressurized electroreduction of CO2 can be assumed an up-and-coming alternative process for the production of valuable organic chemicals [1-3]. In this work, the process was studied in an undivided cell with tin cathode in order to produce formic acid and develop a theoretical model, predicting the effect of several operative parameters. The model is based on the cathodic conversion of pressurized CO2 to HCOOH and it also accounts for its anodic oxidation. In particular, the electrochemical reduction of CO2 to formic acid was performed in pressurized filter press cell with a continuous recirculation of electrolytic solution (0.9 L) at a tin cathode (9 cm2) for a long time (charge passed 67’000 C). It was shown that it is possible to scale-up the process by maintaining good results in terms of faradaic efficiency and generating significantly high concentrations of HCOOH (about 0.4 M) [4]. It was also demonstrated that, for pressurized systems, the process is under the mixed kinetic control of mass transfer of CO2 and the reduction of adsorbed CO2 (described by the Langmuir equation), following our proposed reaction mechanism [5]. Moreover, the theoretical model is in good agreement with the experimental results collected and well describes the effect of several operating parameters, including current density, pressure, and the type of reactor used. 1. Ma, S., &amp; Kenis, P. J. (2013). Electrochemical conversion of CO2 to useful chemicals: current status, remaining challenges, and future opportunities. Current Opinion in Chemical Engineering, 2(2), 191-199. 2. Endrődi, B., Bencsik, G., Darvas, F., Jones, R., Rajeshwar, K., &amp; Janáky, C. (2017). Continuous-flow electroreduction of carbon dioxide. Progress in Energy and Combustion Science, 62, 133-154. 3. Dufek, E. J., Lister, T. E., Stone, S. G., &amp; McIlwain, M. E. (2012). Operation of a pressurized system for continuous reduction of CO2. Journal of The Electrochemical Society, 159(9), F514-F517. 4. Proietto, F., Schiavo, B., Galia, A., &amp; Scialdone, O. (2018). Electrochemical conversion of CO2 to HCOOH at tin cathode in a pressurized undivided filter-press cell. Electrochimica Acta, 277, 30-40. 5. Proietto, F., Galia, A., &amp; Scialdone, O. (2019) Electrochemical conversion of CO2 to HCOOH at tin cathode: development of a theoretical model and comparison with experimental results. ChemElectroChem, 6, 162-172

Bibliography of Lewis Research Center technical publications announced in 1987

This compilation of abstracts describes and indexes the technical reporting that resulted from the scientific and engineering work performed and managed by the Lewis Research Center in 1987. All the publications were announced in the 1987 issues of STAR (Scientific and Technical Aerospace Reports) and/or IAA (International Aerospace Abstracts). Included are research reports, journal articles, conference presentations, patents and patent applications, and theses

The influence of fuel molecular structure on particulate emission investigated with isotope tracing

This thesis is concerned with the formation of particulate matter, a topic of scientific and practical importance due to the toxicity of particulate emissions from automotive and other combustion sources. At present, fuels are predominantly derived from fossil sources, but as production technology improves, biofuels and synthetic fuels are expected to emerge as scalable long-term sources of liquid fuels. Efforts are being made to ensure that this next-generation of fuels is cleaner burning than the last. In order to inform the production and processing of cleaner burning fuels, more needs to be known about how molecular structure influences the formation of pollutant emissions. This thesis presents research that has been carried out in order to better understand the role of functional group chemistry on the conversion of carbon atoms in the fuel to the particulate matter (PM). In particular, the propensity of individual molecules or carbon atoms within molecules to form PM is reported quantitatively. To this end, a technique using carbon-13 (13C) labelled fuel molecules was used so to track the labelled carbon atoms in the fuel to PM. The technique required only very low levels of 13C enrichment, and isotope ratio mass spectrometry equipment (IRMS) was used as a means of 13C detection. Samples of particulate matter were formed using a tube reactor, and also in a compression ignition diesel engine. The tube reactor was designed and commissioned in order to study the pyrolysis of various fuel molecules under well-controlled, homogenous conditions. The contribution to PM of a number of molecules containing various functional groups was assessed, including: alcohols, esters, aromatics, double bonded carbon atoms, a ketone, and a carboxylic acid. Tests were conducted using single-component fuels, and blended in a binary mixture with n−heptane. The results show that the contribution of carbon atoms within molecules to PM, is not equal, but depends on the local molecular structure. For example, oxygenated molecules significantly reduced the contribution to PM of the carbon atoms directly attached to oxygen. The thesis presents one of only a handful of investigations that have been published on the conversion of specific carbon atoms of various molecules to soot and particulate. It advances the field of study by providing data for validation, at the sub-molecular level, for chemical kinetic models of soot formation, and advances fundamental understanding of how fuels convert to soot and particulates