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N-tuple
In mathematics, a tuple is a finite sequence or ''ordered list'' of numbers or, more generally, mathematical objects, which are called the ''elements'' of the tuple. An -tuple is a tuple of elements, where is a non-negative integer. There is only one 0-tuple, called the ''empty tuple''. A 1-tuple and a 2-tuple are commonly called a singleton and an ordered pair, respectively. The term ''"infinite tuple"'' is occasionally used for ''"infinite sequences"''. Tuples are usually written by listing the elements within parentheses "" and separated by commas; for example, denotes a 5-tuple. Other types of brackets are sometimes used, although they may have a different meaning. An -tuple can be formally defined as the image of a function that has the set of the first natural numbers as its domain. Tuples may be also defined from ordered pairs by a recurrence starting from an ordered pair; indeed, an -tuple can be identified with the ordered pair of its first elements and its th e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recurrence Relation
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, F_n=F_+F_ where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Resource Description Framework
The Resource Description Framework (RDF) is a method to describe and exchange graph data. It was originally designed as a data model for metadata by the World Wide Web Consortium (W3C). It provides a variety of syntax notations and formats, of which the most widely used is Turtle ( Terse RDF Triple Language). RDF is a directed graph composed of triple statements. An RDF graph statement is represented by: (1) a node for the subject, (2) an arc from subject to object, representing a predicate, and (3) a node for the object. Each of these parts can be identified by a Uniform Resource Identifier (URI). An object can also be a literal value. This simple, flexible data model has a lot of expressive power to represent complex situations, relationships, and other things of interest, while also being appropriately abstract. RDF was adopted as a W3C recommendation in 1999. The RDF 1.0 specification was published in 2004, and the RDF 1.1 specification in 2014. SPARQL is a standard query ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantic Web
The Semantic Web, sometimes known as Web 3.0, is an extension of the World Wide Web through standards set by the World Wide Web Consortium (W3C). The goal of the Semantic Web is to make Internet data machine-readable. To enable the encoding of semantics with the data, technologies such as Resource Description Framework (RDF) and Web Ontology Language (OWL) are used. These technologies are used to formally represent metadata. For example, Ontology (information science), ontology can describe concepts, relationships between Entity–relationship model, entities, and categories of things. These embedded semantics offer significant advantages such as reasoning engine, reasoning over data and operating with heterogeneous data sources. These standards promote common data formats and exchange protocols on the Web, fundamentally the RDF. According to the W3C, "The Semantic Web provides a common framework that allows data to be shared and reused across application, enterprise, and commu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relational Algebra
In database theory, relational algebra is a theory that uses algebraic structures for modeling data and defining queries on it with well founded semantics (computer science), semantics. The theory was introduced by Edgar F. Codd. The main application of relational algebra is to provide a theoretical foundation for relational databases, particularly query languages for such databases, chief among which is SQL. Relational databases store tabular data represented as relation (database), relations. Queries over relational databases often likewise return tabular data represented as relations. The main purpose of relational algebra is to define Operator (mathematics), operators that transform one or more input relations to an output relation. Given that these operators accept relations as input and produce relations as output, they can be combined and used to express complex queries that transform multiple input relations (whose data are stored in the database) into a single output rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Row (database)
In a relational database, a row or " record" or " tuple", represents a single, implicitly structured data Data ( , ) are a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted for ... item in a table. A database table can be thought of as consisting of rows and columns. Cory Janssen, Techopedia, retrieved 27 June 2014 Each row in a table represents a set of related data, and every row in the table has the same structure. For example, in a table that represents companies, each row might represent a single company. Columns might represent things like company name, address, etc. In a table that represents ''the association'' of empl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relational Database
A relational database (RDB) is a database based on the relational model of data, as proposed by E. F. Codd in 1970. A Relational Database Management System (RDBMS) is a type of database management system that stores data in a structured format using rows and columns. Many relational database systems are equipped with the option of using SQL (Structured Query Language) for querying and updating the database. History The concept of relational database was defined by E. F. Codd at IBM in 1970. Codd introduced the term ''relational'' in his research paper "A Relational Model of Data for Large Shared Data Banks". In this paper and later papers, he defined what he meant by ''relation''. One well-known definition of what constitutes a relational database system is composed of Codd's 12 rules. However, no commercial implementations of the relational model conform to all of Codd's rules, so the term has gradually come to describe a broader class of database systems, which at a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Struct (C Programming Language)
In the C programming language, struct is the keyword used to define a composite, a.k.a. record, data type a named set of values that occupy a block of memory. It allows for the different values to be accessed via a single identifier, often a pointer. A struct can contain other data types so is used for mixed-data-type records. For example a bank customer struct might contains fields: name, address, telephone, balance. A struct occupies a ''contiguous block'' of memory, usually delimited (sized) by word-length boundaries. It corresponds to the similarly named feature available in some assemblers for Intel processors. Being a block of contiguous memory, each field within a struct is located at a certain fixed offset from the start. The sizeof operator results in the number of bytes needed to store a particular struct, just as it does for a primitive data type. The alignment of particular fields in the struct (with respect to word boundaries) is implementation-specific and may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Record (computer Science)
In computer science, a record (also called a structure, struct (C programming language), struct, or compound data type) is a composite data structure a collection of Field (computer science), fields, possibly of different data types, typically fixed in number and sequence. For example, a date could be stored as a record containing a Number, numeric year field, a month field represented as a string, and a numeric day-of-month field. A circle record might contain a numeric radius and a center that is a point record containing x and y coordinates. Notable applications include the programming language ''record type'' and for row-based storage, data organized as a sequence of records, such as a database table, spreadsheet or comma-separated values (CSV) file. In general, a record type value is stored in main memory, memory and row-based storage is in mass storage. A ''record type'' is a data type that describes such values and variables. Most modern programming languages allow the p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Assignment (computer Science)
In computer programming, an assignment statement sets and/or re-sets the value stored in the storage location(s) denoted by a variable name; in other words, it copies a value into the variable. In most imperative programming languages, the assignment statement (or expression) is a fundamental construct. Today, the most commonly used notation for this operation is ''x'' = ''expr'' (originally Superplan 1949–51, popularized by Fortran 1957 and C). The second most commonly used notation is ''x'' := ''expr'' (originally ALGOL 1958, popularised by Pascal). Many other notations are also in use. In some languages, the symbol used is regarded as an operator (meaning that the assignment statement as a whole returns a value). Other languages define assignment as a statement (meaning that it cannot be used in an expression). Assignments typically allow a variable to hold different values at different times during its life-span and scope. However, some languages (primarily stric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pattern Matching
In computer science, pattern matching is the act of checking a given sequence of tokens for the presence of the constituents of some pattern. In contrast to pattern recognition, the match usually must be exact: "either it will or will not be a match." The patterns generally have the form of either sequences or tree structures. Uses of pattern matching include outputting the locations (if any) of a pattern within a token sequence, to output some component of the matched pattern, and to substitute the matching pattern with some other token sequence (i.e., search and replace). Sequence patterns (e.g., a text string) are often described using regular expressions and matched using techniques such as backtracking. Tree patterns are used in some programming languages as a general tool to process data based on its structure, e.g. C#, F#, Haskell, Java, ML, Python, Ruby, Rust, Scala, Swift and the symbolic mathematics language Mathematica have special syntax for expressing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Data Type
In computer programming, especially functional programming and type theory, an algebraic data type (ADT) is a kind of composite data type, i.e., a data type formed by combining other types. Two common classes of algebraic types are product types (i.e., tuples, and records) and sum types (i.e., tagged or disjoint unions, coproduct types or ''variant types''). The values of a product type typically contain several values, called ''fields''. All values of that type have the same combination of field types. The set of all possible values of a product type is the set-theoretic product, i.e., the Cartesian product, of the sets of all possible values of its field types. The values of a sum type are typically grouped into several classes, called ''variants''. A value of a variant type is usually created with a quasi-functional entity called a ''constructor''. Each variant has its own constructor, which takes a specified number of arguments with specified types. The set of all po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
