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∂
The character ∂ (Unicode: U+2202) is a stylized cursive '' d'' mainly used as a mathematical symbol, usually to denote a partial derivative such as / (read as "the partial derivative of ''z'' with respect to ''x''"). It is also used for boundary of a set, the boundary operator in a chain complex, and the conjugate of the Dolbeault operator on smooth differential forms over a complex manifold. It should be distinguished from other similar-looking symbols such as lowercase Greek letter delta (δ) or the lowercase Latin letter eth (ð). History The symbol was introduced originally in 1770 by Nicolas de Condorcet, who used it for a partial differential, and adopted for the partial derivative by Adrien-Marie Legendre in 1786. It represents a specialized cursive type of the letter ''d'', just as the integral sign originates as a specialized type of a long s (first used in print by Leibniz in 1686). Use of the symbol was discontinued by Legendre, but it was taken up again by Ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Mathematical Symbols
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula or a mathematical expression. More formally, a ''mathematical symbol'' is any grapheme used in mathematical formulas and expressions. As formulas and expressions are entirely constituted with symbols of various types, many symbols are needed for expressing all mathematics. The most basic symbols are the decimal digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), and the letters of the Latin alphabet. The decimal digits are used for representing numbers through the Hindu–Arabic numeral system. Historically, upper-case letters were used for representing points in geometry, and lower-case letters were used for variables and constants. Letters are used for representing many other types of mathematical object. As the number of these types has increased, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partial Derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry. The partial derivative of a function f(x, y, \dots) with respect to the variable x is variously denoted by It can be thought of as the rate of change of the function in the x-direction. Sometimes, for the partial derivative of z with respect to x is denoted as \tfrac. Since a partial derivative generally has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in: f'_x(x, y, \ldots), \frac (x, y, \ldots). The symbol used to denote partial derivatives is ∂. One of the first known uses of this symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Gustav Jacob Jacobi
Carl Gustav Jacob Jacobi (; ; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions to elliptic functions, dynamics, differential equations, determinants and number theory. Biography Jacobi was born of Ashkenazi Jewish parentage in Potsdam on 10 December 1804. He was the second of four children of a banker, Simon Jacobi. His elder brother, Moritz, would also become known later as an engineer and physicist. He was initially home schooled by his uncle Lehman, who instructed him in the classical languages and elements of mathematics. In 1816, the twelve-year-old Jacobi went to the Potsdam Gymnasium, where students were taught all the standard subjects: classical languages, history, philology, mathematics, sciences, etc. As a result of the good education he had received from his uncle, as well as his own remarkable abilities, after less than half a year Jacobi was moved to the senior year despite his young age. However, as the Unive ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HTML Entities
In SGML, HTML and XML documents, the logical constructs known as ''character data'' and ''attribute values'' consist of sequences of characters, in which each character can manifest directly (representing itself), or can be represented by a series of characters called a ''character reference'', of which there are two types: a ''numeric character reference'' and a ''character entity reference''. This article lists the character entity references that are valid in HTML and XML documents. A character entity reference refers to the content of a named entity. An entity declaration is created in XML, SGML and HTML documents (before HTML5) by using the syntax in a document type definition (DTD). Character reference overview In HTML and XML, a ''numeric character reference'' refers to a character by its Universal Coded Character Set/Unicode ''code point'', and uses the format: &#x''hhhh''; or &#''nnnn''; where the x must be lowercase in XML documents, ''hhhh'' is the code po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chain Complex
In mathematics, a chain complex is an algebraic structure that consists of a sequence of abelian groups (or modules) and a sequence of homomorphisms between consecutive groups such that the image of each homomorphism is contained in the kernel of the next. Associated to a chain complex is its homology, which is (loosely speaking) a measure of the failure of a chain complex to be exact. A cochain complex is similar to a chain complex, except that its homomorphisms are in the opposite direction. The homology of a cochain complex is called its cohomology. In algebraic topology, the singular chain complex of a topological space X is constructed using continuous maps from a simplex to X, and the homomorphisms of the chain complex capture how these maps restrict to the boundary of the simplex. The homology of this chain complex is called the singular homology of X, and is a commonly used invariant of a topological space. Chain complexes are studied in homological algebra, but a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adrien-Marie Legendre
Adrien-Marie Legendre (; ; 18 September 1752 – 9 January 1833) was a French people, French mathematician who made numerous contributions to mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him. He is also known for his contributions to the Least squares, method of least squares, and was the first to officially publish on it, though Carl Friedrich Gauss had discovered it before him. Life Adrien-Marie Legendre was born in Paris on 18 September 1752 to a wealthy family. He received his education at the Collège Mazarin in Paris, and defended his thesis in physics and mathematics in 1770. He taught at the École Militaire in Paris from 1775 to 1780 and at the École Normale Supérieure, École Normale from 1795. At the same time, he was associated with the Bureau des Longitudes. In 1782, the Prussian Academy of Sciences, Berlin Academy awarded Legendre a prize for his treatise on projectiles in resistant m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Modern
Computer Modern is the original family of typefaces used by the typesetting program TeX. It was created by Donald Knuth with his Metafont program, and was most recently updated in 1992. Computer Modern and its variants remain very widely used in scientific publishing, especially in disciplines that make frequent use of mathematical notation. Design Computer Modern is a "Didone (typography), Didone", or modern serif font, a genre that emerged in the late 18th century as a contrast to the more organic designs that preceded them. Didone fonts have high contrast between thick and thin elements, and their axis of "stress" or thickening is perfectly vertical. Computer Modern was specifically based on the 10 point size of the American Monotype Corporation, Lanston Monotype Company's Modern Extended 8A, part of a family Monotype originally released in 1896. This was one of many modern faces issued by typefounders and Monotype around this period, and the standard style for body text print ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differentiable Programming
Differentiable programming is a programming paradigm in which a numeric computer program can be differentiated throughout via automatic differentiation. This allows for gradient-based optimization of parameters in the program, often via gradient descent, as well as other learning approaches that are based on higher-order derivative information. Differentiable programming has found use in a wide variety of areas, particularly scientific computing and machine learning. One of the early proposals to adopt such a framework in a systematic fashion to improve upon learning algorithms was made by the Advanced Concepts Team at the European Space Agency in early 2016. Approaches Most differentiable programming frameworks work by constructing a graph containing the control flow and data structures in the program. Attempts generally fall into two groups: * Static, compiled graph-based approaches such as TensorFlow,TensorFlow 1 uses the static graph approach, whereas TensorFlow 2 uses the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
D'Alembert Operator
In special relativity, electromagnetism and wave theory, the d'Alembert operator (denoted by a box: \Box), also called the d'Alembertian, wave operator, box operator or sometimes quabla operator (''cf''. nabla symbol) is the Laplace operator of Minkowski space. The operator is named after French mathematician and physicist Jean le Rond d'Alembert. In Minkowski space, in standard coordinates , it has the form : \begin \Box & = \partial^\mu \partial_\mu = \eta^ \partial_\nu \partial_\mu = \frac \frac - \frac - \frac - \frac \\ & = \frac - \nabla^2 = \frac - \Delta ~~. \end Here \nabla^2 := \Delta is the 3-dimensional Laplacian and is the inverse Minkowski metric with :\eta_ = 1, \eta_ = \eta_ = \eta_ = -1, \eta_ = 0 for \mu \neq \nu. Note that the and summation indices range from 0 to 3: see Einstein notation. (Some authors alternatively use the negative metric signature of , with \eta_ = -1,\; \eta_ = \eta_ = \eta_ = 1.) Lorentz transformations leave the Mi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cut (graph Theory)
In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one endpoint in each subset of the partition. These edges are said to cross the cut. In a connected graph, each cut-set determines a unique cut, and in some cases cuts are identified with their cut-sets rather than with their vertex partitions. In a flow network, an s–t cut is a cut that requires the ''source'' and the ''sink'' to be in different subsets, and its ''cut-set'' only consists of edges going from the source's side to the sink's side. The ''capacity'' of an s–t cut is defined as the sum of the capacity of each edge in the ''cut-set''. Definition A cut is a partition of of a graph into two subsets and . The cut-set of a cut is the set of edges that have one endpoint in and the other endpoint in . If and are specified vertices of the graph , then an – cut is a cut in which belongs to the set and belongs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') which are connected by ''Glossary of graph theory terms#edge, edges'' (also called ''arcs'', ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a Set (mathematics), set of vertices (also called nodes or points); * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
