UnicodeUnicode, formally The Unicode Standard, is an information technology standard for the consistent encoding, representation, and handling of text expressed in most of the world's writing systems. The standard, which is maintained by the Unicode Consortium, defines as of the current version (15.0) 149,186 characters covering 161 modern and historic scripts, as well as symbols, thousands of emoji (including in colours), and non-visual control and formatting codes.
Character encodingCharacter encoding is the process of assigning numbers to graphical characters, especially the written characters of human language, allowing them to be stored, transmitted, and transformed using digital computers. The numerical values that make up a character encoding are known as "code points" and collectively comprise a "code space", a "code page", or a "character map". Early character codes associated with the optical or electrical telegraph could only represent a subset of the characters used in written languages, sometimes restricted to upper case letters, numerals and some punctuation only.
ASCIIASCII (ˈæskiː ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of technical limitations of computer systems at the time it was invented, ASCII has just 128 code points, of which only 95 are , which severely limited its scope. Many computer systems instead use Unicode, which has millions of code points, but the first 128 of these are the same as the ASCII set.
Character theoryIn mathematics, more specifically in group theory, the character of a group representation is a function on the group that associates to each group element the trace of the corresponding matrix. The character carries the essential information about the representation in a more condensed form. Georg Frobenius initially developed representation theory of finite groups entirely based on the characters, and without any explicit matrix realization of representations themselves.
Modular representation theoryModular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime number. As well as having applications to group theory, modular representations arise naturally in other branches of mathematics, such as algebraic geometry, coding theory, combinatorics and number theory.
ISO/IEC 8859-1ISO/IEC 8859-1:1998, Information technology — 8-bit single-byte coded graphic character sets — Part 1: Latin alphabet No. 1, is part of the ISO/IEC 8859 series of ASCII-based standard character encodings, first edition published in 1987. ISO/IEC 8859-1 encodes what it refers to as "Latin alphabet no. 1", consisting of 191 characters from the Latin script. This character-encoding scheme is used throughout the Americas, Western Europe, Oceania, and much of Africa.
ASCII artASCII art is a graphic design technique that uses computers for presentation and consists of pictures pieced together from the 95 printable (from a total of 128) characters defined by the ASCII Standard from 1963 and ASCII compliant character sets with proprietary extended characters (beyond the 128 characters of standard 7-bit ASCII). The term is also loosely used to refer to text-based visual art in general. ASCII art can be created with any text editor, and is often used with free-form languages.
Extended ASCIIExtended ASCII is a repertoire of character encodings that include (most of) the original 96 ASCII character set, plus up to 128 additional characters. There is no formal definition of "extended ASCII", and even use of the term is sometimes criticized, because it can be mistakenly interpreted to mean that the American National Standards Institute (ANSI) had updated its standard to include more characters, or that the term identifies a single unambiguous encoding, neither of which is the case.
Representation theoryRepresentation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essence, a representation makes an abstract algebraic object more concrete by describing its elements by matrices and their algebraic operations (for example, matrix addition, matrix multiplication).
Unicode ConsortiumThe Unicode Consortium (legally Unicode, Inc.) is a 501(c)(3) non-profit organization incorporated and based in Mountain View, California. Its primary purpose is to maintain and publish the Unicode Standard which was developed with the intention of replacing existing character encoding schemes which are limited in size and scope, and are incompatible with multilingual environments. The consortium describes its overall purpose as: ...
ISO/IEC 8859-15ISO/IEC 8859-15:1999, Information technology — 8-bit single-byte coded graphic character sets — Part 15: Latin alphabet No. 9, is part of the ISO/IEC 8859 series of ASCII-based standard character encodings, first edition published in 1999. It is informally referred to as Latin-9 (and for a while Latin-0). It is similar to ISO 8859-1, and thus also intended for “Western European” languages, but replaces some less common symbols with the euro sign and some letters that were deemed necessary: This encoding is by far most used, close to half the use, by German, though this is the least used encoding for German.
Unicode blockA Unicode block is one of several contiguous ranges of numeric character codes (code points) of the Unicode character set that are defined by the Unicode Consortium for administrative and documentation purposes. Typically, proposals such as the addition of new glyphs are discussed and evaluated by considering the relevant block or blocks as a whole. Each block is generally, but not always, meant to supply glyphs used by one or more specific languages, or in some general application area such as mathematics, surveying, decorative typesetting, social forums, etc.
Representation theory of finite groupsThe representation theory of groups is a part of mathematics which examines how groups act on given structures. Here the focus is in particular on operations of groups on vector spaces. Nevertheless, groups acting on other groups or on sets are also considered. For more details, please refer to the section on permutation representations. Other than a few marked exceptions, only finite groups will be considered in this article. We will also restrict ourselves to vector spaces over fields of characteristic zero.
Character (mathematics)In mathematics, a character is (most commonly) a special kind of function from a group to a field (such as the complex numbers). There are at least two distinct, but overlapping meanings. Other uses of the word "character" are almost always qualified. multiplicative character A multiplicative character (or linear character, or simply character) on a group G is a group homomorphism from G to the multiplicative group of a field , usually the field of complex numbers.
Standard errorThe standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation. If the statistic is the sample mean, it is called the standard error of the mean (SEM). The sampling distribution of a mean is generated by repeated sampling from the same population and recording of the sample means obtained. This forms a distribution of different means, and this distribution has its own mean and variance.
Standard deviationIn statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter s, for the sample standard deviation.
BitThe bit is the most basic unit of information in computing and digital communications. The name is a portmanteau of binary digit. The bit represents a logical state with one of two possible values. These values are most commonly represented as either "" or "", but other representations such as true/false, yes/no, on/off, or +/− are also widely used. The relation between these values and the physical states of the underlying storage or device is a matter of convention, and different assignments may be used even within the same device or program.
Variable (mathematics)In mathematics, a variable (from Latin variabilis, "changeable") is a symbol that represents a mathematical object. A variable may represent a number, a vector, a matrix, a function, the argument of a function, a set, or an element of a set. Algebraic computations with variables as if they were explicit numbers solve a range of problems in a single computation. For example, the quadratic formula solves any quadratic equation by substituting the numeric values of the coefficients of that equation for the variables that represent them in the quadratic formula.
Bit numberingIn computing, bit numbering is the convention used to identify the bit positions in a binary number. In computing, the least significant bit (LSb) is the bit position in a binary integer representing the binary 1s place of the integer. Similarly, the most significant bit (MSb) represents the highest-order place of the binary integer. The LSb is sometimes referred to as the low-order bit or right-most bit, due to the convention in positional notation of writing less significant digits further to the right.
Random variableA random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. The term 'random variable' can be misleading as it is not actually random nor a variable, but rather it is a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads and tails ) in a sample space (e.g., the set ) to a measurable space (e.g., in which 1 corresponding to and −1 corresponding to ), often to the real numbers.
