Arc routingArc routing problems (ARP) are a category of general routing problems (GRP), which also includes node routing problems (NRP). The objective in ARPs and NRPs is to traverse the edges and nodes of a graph, respectively. The objective of arc routing problems involves minimizing the total distance and time, which often involves minimizing deadheading time, the time it takes to reach a destination.
Perturbation theoryIn mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter . The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of usually become smaller.
Special functionsSpecial functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defined by consensus, and thus lacks a general formal definition, but the list of mathematical functions contains functions that are commonly accepted as special. Many special functions appear as solutions of differential equations or integrals of elementary functions.
Competition (economics)In economics, competition is a scenario where different economic firms are in contention to obtain goods that are limited by varying the elements of the marketing mix: price, product, promotion and place. In classical economic thought, competition causes commercial firms to develop new products, services and technologies, which would give consumers greater selection and better products. The greater the selection of a good is in the market, the lower prices for the products typically are, compared to what the price would be if there was no competition (monopoly) or little competition (oligopoly).
Shortest path problemIn graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment.
State functionIn the thermodynamics of equilibrium, a state function, function of state, or point function for a thermodynamic system is a mathematical function relating several state variables or state quantities (that describe equilibrium states of a system) that depend only on the current equilibrium thermodynamic state of the system (e.g. gas, liquid, solid, crystal, or emulsion), not the path which the system has taken to reach that state. A state function describes equilibrium states of a system, thus also describing the type of system.
Battery recyclingBattery recycling is a recycling activity that aims to reduce the number of batteries being disposed as municipal solid waste. Batteries contain a number of heavy metals and toxic chemicals and disposing of them by the same process as regular household waste has raised concerns over soil contamination and water pollution. Most types of batteries can be recycled. However, some batteries are recycled more readily than others, such as lead–acid automotive batteries (nearly 90% are recycled) and button cells (because of the value and toxicity of their chemicals).
PathfindingPathfinding or pathing is the plotting, by a computer application, of the shortest route between two points. It is a more practical variant on solving mazes. This field of research is based heavily on Dijkstra's algorithm for finding the shortest path on a weighted graph. Pathfinding is closely related to the shortest path problem, within graph theory, which examines how to identify the path that best meets some criteria (shortest, cheapest, fastest, etc) between two points in a large network.
Knapsack problemThe knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.
State (polity)A state is a centralized political organization that imposes and enforces rules over a population within a territory. Definitions of a state are disputed. One widely used definition comes from the sociologist Max Weber: a "state" is a polity that maintains a monopoly on the legitimate use of violence, although other definitions are common. Absence of a state does not preclude the existence of a society, such as stateless societies like the Haudenosaunee Confederacy that "do not have either purely or even primarily political institutions or roles".
RegionIn geography, regions, otherwise referred to as areas, zones, lands or territories, are portions of the Earth's surface that are broadly divided by physical characteristics (physical geography), human impact characteristics (human geography), and the interaction of humanity and the environment (environmental geography). Geographic regions and sub-regions are mostly described by their imprecisely defined, and sometimes transitory boundaries, except in human geography, where jurisdiction areas such as national borders are defined in law.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
