|
N-ary
-ary may refer to: * The arity of a function, operation, or relation ** -ary associativity, a specific rule attached to -ary functions *** -ary group, a generalization of group * The radix of a numerical representation system * The number of letters in an alphabet (formal languages) ** An -ary code *** An -ary Gray code *** An -ary Huffman code * An -ary tree See also * n- (other)#Mathematics, science and technology * Unary (other) * Binary (other) Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that ta ... * Ternary (other) {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arity
Arity () is the number of arguments or operands taken by a function, operation or relation in logic, mathematics, and computer science. In mathematics, arity may also be named ''rank'', but this word can have many other meanings in mathematics. In logic and philosophy, it is also called adicity and degree. In linguistics, it is usually named valency. Examples The term "arity" is rarely employed in everyday usage. For example, rather than saying "the arity of the addition operation is 2" or "addition is an operation of arity 2" one usually says "addition is a binary operation". In general, the naming of functions or operators with a given arity follows a convention similar to the one used for ''n''-based numeral systems such as binary and hexadecimal. One combines a Latin prefix with the -ary ending; for example: * A nullary function takes no arguments. ** Example: f()=2 * A unary function takes one argument. ** Example: f(x)=2x * A binary function takes two arguments. ** E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-ary Associativity
In algebra, ''n''-ary associativity is a generalization of the associative law In mathematics, the associative property is a property of some binary operations, which means that rearranging the parentheses in an expression will not change the result. In propositional logic, associativity is a valid rule of replacement f ... to ''n''-ary operations. Ternary associativity is : (''abc'')''de'' = ''a''(''bcd'')''e'' = ''ab''(''cde''), i.e. the string ''abcde'' with any three adjacent elements bracketed. ''n''-ary associativity is a string of length ''n'' + (''n'' − 1) with any ''n'' adjacent elements bracketed.. References Properties of binary operations {{algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-ary Group
In mathematics, and in particular universal algebra, the concept of an ''n''-ary group (also called ''n''-group or multiary group) is a generalization of the concept of a group to a set ''G'' with an ''n''-ary operation instead of a binary operation.. By an operation is meant any map ''f: Gn → G'' from the ''n''-th Cartesian power of ''G'' to ''G''. The axiom An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or f ...s for an group are defined in such a way that they reduce to those of a group in the case . The earliest work on these structures was done in 1904 by Kasner and in 1928 by Dörnte;W. Dörnte, Untersuchungen über einen verallgemeinerten Gruppenbegriff, ''Mathematische Zeitschrift'', vol. 29 (1928), pp. 1-19. the first systematic account of (what were then called) polya ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems In the system with radix 13, for example, a string of digits such as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alphabet (formal Languages)
In formal language theory, an alphabet is a non-empty set of symbols/glyphs, typically thought of as representing letters, characters, or digits but among other possibilities the "symbols" could also be a set of phonemes (sound units). Alphabets in this technical sense of a set are used in a diverse range of fields including logic, mathematics, computer science, and linguistics. An alphabet may have any cardinality ("size") and depending on its purpose maybe be finite (e.g., the alphabet of letters "a" through "z"), countable (e.g., \), or even uncountable (e.g., \). Strings, also known as "words", over an alphabet are defined as a sequence of the symbols from the alphabet set. For example, the alphabet of lowercase letters "a" through "z" can be used to form English words like "iceberg" while the alphabet of both upper and lower case letters can also be used to form proper names like "Wikipedia". A common alphabet is , the binary alphabet, and a "00101111" is an example of a bina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-ary Code
In telecommunication, an ''n''-ary code is a code that has ''n'' significant conditions, where ''n'' is a positive integer greater than 1. The integer substituted for ''n'' indicates the specific number of significant conditions, ''i.e.'', quantization states, in the code. For example, an 8-ary code has eight significant conditions and can convey three bits per code symbol. A prefix that indicates an integer, ''e.g.'', "bin", "tern," or "quatern", may be used in lieu of a numeral, to produce "binary", "ternary", or "quaternary" (2, 3, and 4 states respectively). See also * Arity Source: from Federal Standard 1037C and from MIL-STD-188 MIL-STD-188 is a series of U.S. military standards relating to telecommunications. Purpose Faced with "past technical deficiencies in telecommunications systems and equipment and software…that were traced to basic inadequacies in the applicat ... Line codes {{telecom-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-ary Gray Code
The reflected binary code (RBC), also known as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit). For example, the representation of the decimal value "1" in binary would normally be "" and "2" would be "". In Gray code, these values are represented as "" and "". That way, incrementing a value from 1 to 2 requires only one bit to change, instead of two. Gray codes are widely used to prevent spurious output from electromechanical switches and to facilitate error correction in digital communications such as digital terrestrial television and some cable TV systems. Motivation and name Many devices indicate position by closing and opening switches. If that device uses natural binary codes, positions 3 and 4 are next to each other but all three bits of the binary representation differ: : The problem with natural binary codes is that physical switches are not ideal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-ary Huffman Coding
In computer science and information theory, a Huffman code is a particular type of optimal prefix code that is commonly used for lossless data compression. The process of finding or using such a code proceeds by means of Huffman coding, an algorithm developed by David A. Huffman while he was a Sc.D. student at MIT, and published in the 1952 paper "A Method for the Construction of Minimum-Redundancy Codes". The output from Huffman's algorithm can be viewed as a variable-length code table for encoding a source symbol (such as a character in a file). The algorithm derives this table from the estimated probability or frequency of occurrence (''weight'') for each possible value of the source symbol. As in other entropy encoding methods, more common symbols are generally represented using fewer bits than less common symbols. Huffman's method can be efficiently implemented, finding a code in time linear to the number of input weights if these weights are sorted. However, although op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N-ary Tree
In graph theory, an ''m''-ary tree (also known as ''n''-ary, ''k''-ary or ''k''-way tree) is a rooted tree in which each node has no more than ''m'' children. A binary tree is the special case where ''m'' = 2, and a ternary tree is another case with ''m'' = 3 that limits its children to three. Types of ''m''-ary trees * A full ''m''-ary tree is an ''m''-ary tree where within each level every node has either 0 or ''m'' children. * A complete ''m''-ary tree is an ''m''-ary tree which is maximally space efficient. It must be completely filled on every level except for the last level. However, if the last level is not complete, then all nodes of the tree must be "as far left as possible". * A perfect ''m''-ary tree is a full ''m''-ary tree in which all leaf nodes are at the same depth. Properties of ''m''-ary trees * For an ''m''-ary tree with height ''h'', the upper bound for the maximum number of leaves is m^h. * The height ''h ''of an ''m''-ary tree does not include the ro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
N- (other)
Chemistry * ''n-'', a lowercase prefix in chemistry denoting the straight-chain form of an open-chain compound in contrast to its branched isomer * ''N-'', an uppercase prefix in chemistry denoting that the substituent is bonded to the nitrogen, as in amine In chemistry, amines (, ) are compounds and functional groups that contain a basic nitrogen atom with a lone pair. Amines are formally derivatives of ammonia (), wherein one or more hydrogen atoms have been replaced by a substituent ...s Mathematics, science and technology The italicized letter ''n'' is used in mathematics to denote an arbitrary number (usually a non-negative integer). * ''n''-ary associativity * ''n''-ary code * ''n''-ary group * ''n''-back * ''n''-body problem * ''n''-category * ''n''-category number * ''n''-connected space * ''n''-curve * ''n''-dimensional space * ''n''-dimensional sequential move puzzle * ''n''-electron valence state perturbation theory (NEVPT) * ''n''-entity * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unary (other)
{{Disambiguation ...
Unary may refer to: *Unary numeral system, the simplest numeral system to represent natural numbers *Unary function, a function that takes one argument; in computer science, a unary operator is a subset of unary function *Unary operation, a kind of mathematical operator that has only one operand *Unary relation, a mathematical relation that has one argument *Unary coding, an entropy encoding that represents a number ''n'' with n − 1 ones followed by a zero See also * Primary (other) * Binary (other) Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that ta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary (other)
Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that takes two arguments * Binary relation, a relation involving two elements * Binary-coded decimal, a method for encoding for decimal digits in binary sequences * Finger binary, a system for counting in binary numbers on the fingers of human hands Computing * Binary code, the digital representation of text and data * Bit, or binary digit, the basic unit of information in computers * Binary file, composed of something other than human-readable text ** Executable, a type of binary file that contains machine code for the computer to execute * Binary tree, a computer tree data structure in which each node has at most two children Astronomy * Binary star, a star system with two stars in it * Binary planet, two planetary bodies of comparable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
