Photochemical smog in greater Cape Town

Bibliography: leaves 124-131.Photochemical smog is the name given to a complex sequence of chemical reactions that occurs in the presence of sunlight. These reactions comprise a mix of organic and inorganic compounds, including a number of toxic secondary pollutants such as ozone (O3) and peroxyacetyl nitrate. These substances are commonly referred to as oxidants and are the result of numerous reactions of primary pollutants or precursors (including nitrogen oxides (NOx) and non- methane hydrocarbons (NHHC)) emitted from vehicle exhausts and to some extent industry, O3 is the major constituent of the photochemical oxidants, and its concentration is often used to determine the severity of photochemical smog. Limited research on photochemical smog in Cape Town has been undertaken, and this study has concentrated on providing a more detailed understanding of photochemical precursor and oxidant levels in the urban atmosphere of Greater Cape Town. This was approached by the investigation and assessment of the spatial and temporal behaviour of photochemical pollutants, making use of automatic monitor data collected from 1984 to 1986, and supplemented by data collected during a spatial survey in April and Hay of 1987. Precursor levels were found to be strongly influenced by the seasonal cycle of the weather and were highest in winter when stable atmospheric conditions prevailed, particularly during morning rush hours, O3 behaviour was complex and lacked any definite relationship to season or to selected meteorological variables, although the limited data indicated high levels during the early spring months. Peak levels were generally experienced on fair weather days during the early afternoon hours at the time of maximum ultraviolet radiation, O3 levels did not exceed the USEPA 1-hour standard of 0.12ppm during 1985 and 1986. The spatial distribution of precursor and oxidant concentrations showed the NOx levels to be spatially dependent, following the major arterial roads. NHHC levels were spatially less well defined than NOx, and O3 levels were spatially relatively uniform, exhibiting depletion due to scavenging by nitric oxide (NO) in areas close to main traffic routes. High NOx levels were experienced predominantly in the city centre, while the suburbs tended to experience the higher O3 levels. Cape Town was not considered to have a photochemical smog problem of the same magnitude as Los Angeles or Sydney, ( due to a number of factors which contributed to the complex situation (such as high NO levels, relatively low NMHC levels and strong winds in summer). However in the Northern Suburbs, the absence of high NO levels together with additional NMHC emissions from nearby industry led to the recognition of this area as one of potential photochemical smog formation

Polynomial Constraints for Sets with Cardinality Bounds

Logics that can reason about sets and their cardinality bounds are useful in program analysis, program verification, databases, and knowledge bases. This paper presents a class of constraints on sets and their cardinalities for which the satisfiability and the entailment problems are computable in polynomial time. Our class of constraints, based on tree-shaped formulas, is unique in being simultaneously tractable and able to express 1) that a set is a union of other sets, 2) that sets are disjoint, and 3) that a set has cardinality within a given range. As the main result we present a polynomial-time algorithm for checking entailment of our constraints

An Algorithm for Deciding BAPA: Boolean Algebra with Presburger Arithmetic

We describe an algorithm for deciding the first-order multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmetic operations (PA). BAPA can express the relationship between integer variables and cardinalities of sets, and supports arbitrary quantification over both sets and integers.Our motivation for BAPA is deciding verification conditions that arise in the static analysis of data structure consistency properties. Data structures often use an integer variable to keep track of the number of elements they store; an invariant of such a data structure is that the value of the integer variable is equal to the number of elements stored in the data structure. When the data structure content is represented by a set, the resulting constraints can be captured in BAPA. BAPA formulas with quantifier alternations arise when annotations contain quantifiers themselves, or when proving simulation relation conditions for refinement and equivalence of program fragments. Furthermore, BAPA constraints can be used to extend the techniques for proving the termination of integer programs to programs that manipulate data structures, and have applications in constraint databases.We give a formal description of a decision procedure for BAPA, which implies the decidability of the satisfiability and validity problems for BAPA. We analyze our algorithm and obtain an elementary upper bound on the running time, thereby giving the first complexity bound for BAPA. Because it works by a reduction to PA, our algorithm yields the decidability of a combination of sets of uninterpreted elements with any decidable extension of PA. Our algorithm can also be used to yield an optimal decision procedure for BA though a reduction to PA with bounded quantifiers.We have implemented our algorithm and used it to discharge verification conditions in the Jahob system for data structure consistency checking of Java programs; our experience with the algorithm is promising