Lefschetz fixed-point theoremIn mathematics, the Lefschetz fixed-point theorem is a formula that counts the fixed points of a continuous mapping from a compact topological space to itself by means of traces of the induced mappings on the homology groups of . It is named after Solomon Lefschetz, who first stated it in 1926. The counting is subject to an imputed multiplicity at a fixed point called the fixed-point index. A weak version of the theorem is enough to show that a mapping without any fixed point must have rather special topological properties (like a rotation of a circle).
Controlled-access highwayA controlled-access highway is a type of highway that has been designed for high-speed vehicular traffic, with all traffic flow—ingress and egress—regulated. Common English terms are freeway, motorway and expressway. Other similar terms include throughway (or thruway) and parkway. Some of these may be limited-access highways, although this term can also refer to a class of highways with somewhat less isolation from other traffic. In countries following the Vienna convention, the motorway qualification implies that walking and parking are forbidden.
CommutingCommuting is periodically recurring travel between one's place of residence and place of work or study, where the traveler, referred to as a commuter, leaves the boundary of their home community. By extension, it can sometimes be any regular or often repeated travel between locations, even when not work-related. The modes of travel, time taken and distance traveled in commuting varies widely across the globe. Most people in least-developed countries continue to walk to work.
Emissions tradingEmissions trading is a market-based approach to controlling pollution by providing economic incentives for reducing the emissions of pollutants. The concept is also known as cap and trade (CAT) or emissions trading scheme (ETS). Carbon emission trading for and other greenhouse gases has been introduced in China, the European Union and other countries as a key tool for climate change mitigation. Other schemes include sulfur dioxide and other pollutants.
Marginal costIn economics, the marginal cost is the change in the total cost that arises when the quantity produced is incremented, the cost of producing additional quantity. In some contexts, it refers to an increment of one unit of output, and in others it refers to the rate of change of total cost as output is increased by an infinitesimal amount. As Figure 1 shows, the marginal cost is measured in dollars per unit, whereas total cost is in dollars, and the marginal cost is the slope of the total cost, the rate at which it increases with output.
Brouwer fixed-point theoremBrouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function mapping a nonempty compact convex set to itself there is a point such that . The simplest forms of Brouwer's theorem are for continuous functions from a closed interval in the real numbers to itself or from a closed disk to itself. A more general form than the latter is for continuous functions from a nonempty convex compact subset of Euclidean space to itself.
Three-phase traffic theoryThree-phase traffic theory is a theory of traffic flow developed by Boris Kerner between 1996 and 2002. It focuses mainly on the explanation of the physics of traffic breakdown and resulting congested traffic on highways. Kerner describes three phases of traffic, while the classical theories based on the fundamental diagram of traffic flow have two phases: free flow and congested traffic.
Social costSocial cost in neoclassical economics is the sum of the private costs resulting from a transaction and the costs imposed on the consumers as a consequence of being exposed to the transaction for which they are not compensated or charged. In other words, it is the sum of private and external costs. This might be applied to any number of economic problems: for example, social cost of carbon has been explored to better understand the costs of carbon emissions for proposed economic solutions such as a carbon tax.
Greenhouse gas emissionsGreenhouse gas emissions (abbreviated as GHG emissions) from human activities strengthen the greenhouse effect, contributing to climate change. Carbon dioxide (), from burning fossil fuels such as coal, oil, and natural gas, is one of the most important factors in causing climate change. The largest emitters are China followed by the US, although the United States has higher emissions per capita. The main producers fueling the emissions globally are large oil and gas companies.
Fixed-point theorems in infinite-dimensional spacesIn mathematics, a number of fixed-point theorems in infinite-dimensional spaces generalise the Brouwer fixed-point theorem. They have applications, for example, to the proof of existence theorems for partial differential equations. The first result in the field was the Schauder fixed-point theorem, proved in 1930 by Juliusz Schauder (a previous result in a different vein, the Banach fixed-point theorem for contraction mappings in complete metric spaces was proved in 1922). Quite a number of further results followed.
