Post's theoremIn computability theory Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees. Arithmetical hierarchy#Relation to Turing machines The statement of Post's theorem uses several concepts relating to definability and recursion theory. This section gives a brief overview of these concepts, which are covered in depth in their respective articles. The arithmetical hierarchy classifies certain sets of natural numbers that are definable in the language of Peano arithmetic.
Halting problemIn computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. The halting problem is undecidable, meaning that no general algorithm exists that solves the halting problem for all possible program–input pairs. A key part of the formal statement of the problem is a mathematical definition of a computer and program, usually via a Turing machine.
Mass productionMass production, also known as flow production or continuous production, is the production of substantial amounts of standardized products in a constant flow, including and especially on assembly lines. Together with job production and batch production, it is one of the three main production methods. The term mass production was popularized by a 1926 article in the Encyclopædia Britannica supplement that was written based on correspondence with Ford Motor Company.
AnalysisAnalysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development. The word comes from the Ancient Greek ἀνάλυσις (analysis, "a breaking-up" or "an untying;" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses.
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.
Fractional Fourier transformIn mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate domain between time and frequency. Its applications range from filter design and signal analysis to phase retrieval and pattern recognition.
Factors of productionIn economics, factors of production, resources, or inputs are what is used in the production process to produce output—that is, goods and services. The utilized amounts of the various inputs determine the quantity of output according to the relationship called the production function. There are four basic resources or factors of production: land, labour, capital and entrepreneur (or enterprise). The factors are also frequently labeled "producer goods or services" to distinguish them from the goods or services purchased by consumers, which are frequently labeled "consumer goods".
Word problem for groupsIn mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group G is the algorithmic problem of deciding whether two words in the generators represent the same element. More precisely, if A is a finite set of generators for G then the word problem is the membership problem for the formal language of all words in A and a formal set of inverses that map to the identity under the natural map from the free monoid with involution on A to the group G.
Data analysisData analysis is the process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, encompassing diverse techniques under a variety of names, and is used in different business, science, and social science domains. In today's business world, data analysis plays a role in making decisions more scientific and helping businesses operate more effectively.
Cutting stock problemIn operations research, the cutting-stock problem is the problem of cutting standard-sized pieces of stock material, such as paper rolls or sheet metal, into pieces of specified sizes while minimizing material wasted. It is an optimization problem in mathematics that arises from applications in industry. In terms of computational complexity, the problem is an NP-hard problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem.
