Root-finding algorithmsIn mathematics and computing, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f, from the real numbers to real numbers or from the complex numbers to the complex numbers, is a number x such that f(x) = 0. As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form, root-finding algorithms provide approximations to zeros, expressed either as floating-point numbers or as small isolating intervals, or disks for complex roots (an interval or disk output being equivalent to an approximate output together with an error bound).
Direction findingDirection finding (DF), or radio direction finding (RDF), is - in accordance with International Telecommunication Union (ITU) - defined as radio location that uses the reception of radio waves to determine the direction in which a radio station or an object is located. This can refer to radio or other forms of wireless communication, including radar signals detection and monitoring (ELINT/ESM). By combining the direction information from two or more suitably spaced receivers (or a single mobile receiver), the source of a transmission may be located via triangulation.
Reuse of human excretaReuse of human excreta is the safe, beneficial use of treated human excreta after applying suitable treatment steps and risk management approaches that are customized for the intended reuse application. Beneficial uses of the treated excreta may focus on using the plant-available nutrients (mainly nitrogen, phosphorus and potassium) that are contained in the treated excreta. They may also make use of the organic matter and energy contained in the excreta.
ReuseReuse is the action or practice of using an item, whether for its original purpose (conventional reuse) or to fulfill a different function (creative reuse or repurposing). It should be distinguished from recycling, which is the breaking down of used items to make raw materials for the manufacture of new products. Reuse – by taking, but not reprocessing, previously used items – helps save time, money, energy and resources.
Waste hierarchyWaste hierarchy is a tool used in the evaluation of processes that protect the environment alongside resource and energy consumption from most favourable to least favourable actions. The hierarchy establishes preferred program priorities based on sustainability. To be sustainable, waste management cannot be solved only with technical end-of-pipe solutions and an integrated approach is necessary. The waste management hierarchy indicates an order of preference for action to reduce and manage waste, and is usually presented diagrammatically in the form of a pyramid.
High-frequency direction findingHigh-frequency direction finding, usually known by its abbreviation HF/DF or nickname huff-duff, is a type of radio direction finder (RDF) introduced in World War II. High frequency (HF) refers to a radio band that can effectively communicate over long distances; for example, between U-boats and their land-based headquarters. HF/DF was primarily used to catch enemy radios while they transmitted, although it was also used to locate friendly aircraft as a navigation aid.
Muller's methodMuller's method is a root-finding algorithm, a numerical method for solving equations of the form f(x) = 0. It was first presented by David E. Muller in 1956. Muller's method is based on the secant method, which constructs at every iteration a line through two points on the graph of f. Instead, Muller's method uses three points, constructs the parabola through these three points, and takes the intersection of the x-axis with the parabola to be the next approximation.
Secant methodIn numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method. However, the secant method predates Newton's method by over 3000 years. For finding a zero of a function f, the secant method is defined by the recurrence relation. As can be seen from this formula, two initial values x0 and x1 are required.
Reclaimed waterWater reclamation (also called wastewater reuse, water reuse or water recycling) is the process of converting municipal wastewater (sewage) or industrial wastewater into water that can be reused for a variety of purposes. Types of reuse include: urban reuse, agricultural reuse (irrigation), environmental reuse, industrial reuse, planned potable reuse, de facto wastewater reuse (unplanned potable reuse). For example, reuse may include irrigation of gardens and agricultural fields or replenishing surface water and groundwater (i.
Newton's methodIn numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a single-variable function f defined for a real variable x, the function's derivative f′, and an initial guess x0 for a root of f. If the function satisfies sufficient assumptions and the initial guess is close, then is a better approximation of the root than x0.
