Lemniscate elliptic functionsIn mathematics, the lemniscate elliptic functions are elliptic functions related to the arc length of the lemniscate of Bernoulli. They were first studied by Giulio Fagnano in 1718 and later by Leonhard Euler and Carl Friedrich Gauss, among others. The lemniscate sine and lemniscate cosine functions, usually written with the symbols sl and cl (sometimes the symbols sinlem and coslem or sin lemn and cos lemn are used instead), are analogous to the trigonometric functions sine and cosine.
Chinese dictionaryChinese dictionaries date back over two millennia to the Han dynasty, which is a significantly longer lexicographical history than any other language. There are hundreds of dictionaries for the Chinese language, and this article discusses some of the most important. The general term císhū (辭書, "lexicographic books") semantically encompasses "dictionary; lexicon; encyclopedia; glossary". The Chinese language has two words for dictionary: zidian (character/logograph dictionary) for written forms, that is, Chinese characters, and cidian (word/phrase dictionary), for spoken forms.
Data compressionIn information theory, data compression, source coding, or bit-rate reduction is the process of encoding information using fewer bits than the original representation. Any particular compression is either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by removing unnecessary or less important information.
Persistent data structureIn computing, a persistent data structure or not ephemeral data structure is a data structure that always preserves the previous version of itself when it is modified. Such data structures are effectively immutable, as their operations do not (visibly) update the structure in-place, but instead always yield a new updated structure. The term was introduced in Driscoll, Sarnak, Sleator, and Tarjans' 1986 article. A data structure is partially persistent if all versions can be accessed but only the newest version can be modified.
Tree structureA tree structure, tree diagram, or tree model is a way of representing the hierarchical nature of a structure in a graphical form. It is named a "tree structure" because the classic representation resembles a tree, although the chart is generally upside down compared to a biological tree, with the "stem" at the top and the "leaves" at the bottom. A tree structure is conceptual, and appears in several forms. For a discussion of tree structures in specific fields, see Tree (data structure) for computer science; insofar as it relates to graph theory, see tree (graph theory) or tree (set theory).
Theta functionIn mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces, quadratic forms, and solitons. As Grassmann algebras, they appear in quantum field theory. The most common form of theta function is that occurring in the theory of elliptic functions. With respect to one of the complex variables (conventionally called z), a theta function has a property expressing its behavior with respect to the addition of a period of the associated elliptic functions, making it a quasiperiodic function.
Tree (data structure)In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the root node, which has no parent (i.e., the root node as the top-most node in the tree hierarchy). These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal.
Compression artifactA compression artifact (or artefact) is a noticeable distortion of media (including , audio, and video) caused by the application of lossy compression. Lossy data compression involves discarding some of the media's data so that it becomes small enough to be stored within the desired or transmitted (streamed) within the available bandwidth (known as the data rate or bit rate). If the compressor cannot store enough data in the compressed version, the result is a loss of quality, or introduction of artifacts.
Lossless compressionLossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits statistical redundancy. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though usually with greatly improved compression rates (and therefore reduced media sizes).
Lossy compressionIn information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size for storing, handling, and transmitting content. The different versions of the photo of the cat on this page show how higher degrees of approximation create coarser images as more details are removed. This is opposed to lossless data compression (reversible data compression) which does not degrade the data.
