Linear algebraLinear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis, a branch of mathematical analysis, may be viewed as the application of linear algebra to spaces of functions.
Linear programmingLinear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
Optimizing compilerIn computing, an optimizing compiler is a compiler that tries to minimize or maximize some attributes of an executable computer program. Common requirements are to minimize a program's execution time, memory footprint, storage size, and power consumption (the last three being popular for portable computers). Compiler optimization is generally implemented using a sequence of optimizing transformations, algorithms which take a program and transform it to produce a semantically equivalent output program that uses fewer resources or executes faster.
1 − 2 + 4 − 8 + ⋯In mathematics, 1 − 2 + 4 − 8 + ⋯ is the infinite series whose terms are the successive powers of two with alternating signs. As a geometric series, it is characterized by its first term, 1, and its common ratio, −2. As a series of real numbers it diverges, so in the usual sense it has no sum. In a much broader sense, the series is associated with another value besides ∞, namely 1/3, which is the limit of the series using the 2-adic metric. Gottfried Leibniz considered the divergent alternating series 1 − 2 + 4 − 8 + 16 − ⋯ as early as 1673.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Object code optimizerAn object code optimizer, sometimes also known as a post pass optimizer or, for small sections of code, peephole optimizer, forms part of a software compiler. It takes the output from the source language compile step - the object code or - and tries to replace identifiable sections of the code with replacement code that is more algorithmically efficient (usually improved speed). The earliest "COBOL Optimizer" was developed by Capex Corporation in the mid 1970s for COBOL.
Urban renewalUrban renewal (also called urban regeneration in the United Kingdom and urban redevelopment in the United States) is a program of land redevelopment often used to address urban decay in cities. Urban renewal involves the clearing out of blighted areas in inner cities to clear out slums and create opportunities for higher class housing, businesses, and other developments. A primary purpose of urban renewal is to restore economic viability to a given area by attracting external private and public investment and by encouraging business start-ups and survival.
1 − 2 + 3 − 4 + ⋯In mathematics, 1 − 2 + 3 − 4 + ··· is an infinite series whose terms are the successive positive integers, given alternating signs. Using sigma summation notation the sum of the first m terms of the series can be expressed as The infinite series diverges, meaning that its sequence of partial sums, (1, −1, 2, −2, 3, ...), does not tend towards any finite limit. Nonetheless, in the mid-18th century, Leonhard Euler wrote what he admitted to be a paradoxical equation: A rigorous explanation of this equation would not arrive until much later.
Urban decayUrban decay (also known as urban rot, urban death or urban blight) is the sociological process by which a previously functioning city, or part of a city, falls into disrepair and decrepitude. There is no single process that leads to urban decay. Urban decay can include the following aspects: Industrialization Deindustrialization Gentrification Population decline or overpopulation Counterurbanization Economic Restructuring Multiculturalism Abandoned buildings or infrastructure High local unemployment Increased poverty Fragmented families Low overall living standards or quality of life Political disenfranchisement Crime (e.
Urban reforestationUrban reforestation is the practice of planting trees, typically on a large scale, in urban environments. It may also include urban horticulture and urban farming. Reasons for practicing urban reforestation include urban beautification; increasing shade; modifying the urban climate; improving air quality, such as by sequestering carbon dioxide; and restoration of urban forests after a natural disaster. Increased shade from urban reforestation can also lead to decreased energy costs, as heat from the sun is blocked from heating structures that use air conditioning.
