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Derivatives (finance)
The derivative of a function is the rate of change of the function's output relative to its input value. Derivative may also refer to: In mathematics and economics * Brzozowski derivative in the theory of formal languages *Covariant derivative, a way of specifying a derivative along tangent vectors of a manifold with a connection. * Exterior derivative, an extension of the concept of the differential of a function to differential forms of higher degree. *Formal derivative, an operation on elements of a polynomial ring which mimics the form of the derivative from calculus * Fréchet derivative, a derivative defined on normed spaces. * Gateaux derivative, a generalization of the concept of directional derivative in differential calculus. * Lie derivative, the change of a tensor field (including scalar functions, vector fields and one-forms), along the flow defined by another vector field. * Radon–Nikodym derivative in measure theory * Derivative (set theory), a concept app ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative
In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation. There are multiple different notations for differentiation. '' Leibniz notation'', named after Gottfried Wilhelm Leibniz, is represented as the ratio of two differentials, whereas ''prime notation'' is written by adding a prime mark. Higher order notations represent repeated differentiation, and they are usually denoted in Leib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Field
In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space \mathbb^n. A vector field on a plane can be visualized as a collection of arrows with given magnitudes and directions, each attached to a point on the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout three dimensional space, such as the wind, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from one point to another point. The elements of differential and integral calculus extend naturally to vector fields. When a vector field represents force, the line integral of a vector field represents the work done by a force moving along a path, and under this interpretation conservation of energy is exhibited as a special case of the fundamental theorem of calculus. Vector fields can usefully be thought of as representing the velocit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative (film)
''Derivative'' () is a 2005 Turkish drama film, written, produced and directed by Ulaş İnaç based on a short story by Miguel de Cervantes Miguel de Cervantes Saavedra ( ; ; 29 September 1547 (assumed) – 22 April 1616 Old Style and New Style dates, NS) was a Spanish writer widely regarded as the greatest writer in the Spanish language and one of the world's pre-eminent novelist ..., about the complicated relationships between three people who confess their thoughts each evening to the camera for a movie project. The film, which went on nationwide general release across Turkey on , won the Golden Orange for Best Film at the 42nd Antalya "Golden Orange" International Film Festival. Plot Nazım (Güçlü Yalçıner) is a successful young Istanbul writer who is about to marry Süreyya (Gülçin Santırcıoğlu). Süreyya is not sure about Nazım's love and so she asks her best friend Burcu (Beste Bereket) to seduce him in order to test his fidelity. Reluctantly Burcu compl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fork (software Development)
In software development, a fork is a codebase that is created by duplicating an existing codebase and, generally, is subsequently modified independently of the original. Software built from a fork initially has identical behavior as software built from the original code, but as the source code is increasingly modified, the resulting software tends to have increasingly different behavior compared to the original. A fork is a form of branching, but generally involves storing the forked files separately from the original; not in the repository. Reasons for forking a codebase include user preference, stagnated or discontinued development of the original software or a schism in the developer community. Forking proprietary software (such as Unix) is prohibited by copyright law without explicit permission, but free and open-source software, by definition, may be forked without permission. Etymology The word ''fork'' has been used to mean "to divide in branches, go separate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative Work
In copyright law, a derivative work is an expressive creation that includes major copyrightable elements of a first, previously created original work (the underlying work). The derivative work becomes a second, separate work independent from the first. The transformation, modification or adaptation of the work must be substantial and bear its author's personality sufficiently to be original and thus protected by copyright. Translations, cinematic adaptations and musical arrangements are common types of derivative works. Most countries' legal systems seek to protect both original and derivative works. They grant authors the right to impede or otherwise control their integrity and the author's commercial interests. Derivative works and their authors benefit in turn from the full protection of copyright without prejudicing the rights of the original work's author. Definition Berne The Berne Convention for the Protection of Literary and Artistic Works, an international copy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aeroderivative Gas Turbine
A gas turbine or gas turbine engine is a type of continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas generator or core) and are, in the direction of flow: * a rotating gas compressor * a combustor * a compressor-driving turbine. Additional components have to be added to the gas generator to suit its application. Common to all is an air inlet but with different configurations to suit the requirements of marine use, land use or flight at speeds varying from stationary to supersonic. A propelling nozzle is added to produce thrust for flight. An extra turbine is added to drive a propeller (turboprop) or ducted fan (turbofan) to reduce fuel consumption (by increasing propulsive efficiency) at subsonic flight speeds. An extra turbine is also required to drive a helicopter rotor or land-vehicle transmission (turboshaft), marine propeller or electrical generator (power turbine). Greater thrust-to-w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative (linguistics)
Morphological derivation, in linguistics, is the process of forming a new word from an existing word, often by adding a prefix or suffix, such as For example, ''unhappy'' and ''happiness'' derive from the root word ''happy.'' It is differentiated from inflection, which is the modification of a word to form different grammatical categories without changing its core meaning: ''determines'', ''determining'', and ''determined'' are from the root ''determine''. Derivational patterns Derivational morphology often involves the addition of a derivational suffix or other affix. Such an affix usually applies to words of one lexical category (part of speech) and changes them into words of another such category. For example, one effect of the English derivational suffix ''-ly'' is to change an adjective into an adverb (''slow'' → ''slowly''). Here are examples of English derivational patterns and their suffixes: * adjective-to-noun: ''-ness'' (''slow'' → ''slowness'') * adjective- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative (chemistry)
In chemistry, a derivative is a compound that is derived from a similar compound by a chemical reaction. In the past, derivative also meant a compound that ''can be imagined to'' arise from another compound, if one atom or group of atoms is replaced with another atom or group of atoms, but modern chemical language now uses the term structural analog for this meaning, thus eliminating ambiguity. The term "structural analogue" is common in organic chemistry. In biochemistry, the word is used for compounds that at least theoretically can be formed from the precursor compound. Chemical derivatives may be used to facilitate analysis. For example, melting point (MP) analysis can assist in identification of many organic compounds. A crystalline derivative may be prepared, such as a semicarbazone or 2,4-dinitrophenylhydrazone (derived from aldehydes or ketones), as a simple way of verifying the identity of the original compound, assuming that a table of derivative MP values is avai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative Suit
A shareholder derivative suit is a lawsuit brought by a shareholder on behalf of a corporation against a third party. Often, the third party is an insider of the corporation, such as an executive officer or director. Shareholder derivative suits are unique because under traditional corporation, corporate law, management is responsible for bringing and defending the corporation against suit. Shareholder derivative suits permit a shareholder to initiate a suit when management has failed to do so. To enable a diversity of management approaches to risks and reinforce the most common forms of corporate rules with a high degree of permissible management power, many jurisdictions have implemented minimum thresholds and grounds (procedural and substantive) to such suits. Purpose and difficulties Under traditional corporate business law, shareholders are the owners of a corporation. However, they are not empowered to control the day-to-day operations of the corporation. Instead, shareholders ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative (finance)
In finance, a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has the following four elements: # an item (the "underlier") that can or must be bought or sold, # a future act which must occur (such as a sale or purchase of the underlier), # a price at which the future transaction must take place, and # a future date by which the act (such as a purchase or sale) must take place. A derivative's value depends on the performance of the underlier, which can be a commodity (for example, corn or oil), a financial instrument (e.g. a stock or a bond), price index, a price index, a currency, or an interest rate. Derivatives can be used to insure against price movements (Hedge (finance)#Etymology, hedging), increase exposure to price movements for speculation, or get access to otherwise hard-to-trade assets or markets. Most derivatives are price guarantees. But some are based on an event or p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative (graph Theory)
In the mathematical discipline of graph theory, the line graph of an undirected graph is another graph that represents the adjacencies between edges of . is constructed in the following way: for each edge in , make a vertex in ; for every two edges in that have a vertex in common, make an edge between their corresponding vertices in . The name ''line graph'' comes from a paper by although both and used the construction before this. Other terms used for the line graph include the covering graph, the derivative, the edge-to-vertex dual, the conjugate, the representative graph, and the θ-obrazom, as well as the edge graph, the interchange graph, the adjoint graph, and the derived graph., p. 71. proved that with one exceptional case the structure of a connected graph can be recovered completely from its line graph. Many other properties of line graphs follow by translating the properties of the underlying graph from vertices into edges, and by Whitney's theorem the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derivative (set Theory)
In axiomatic set theory, a function is called normal (or a normal function) if it is continuous (with respect to the order topology) and strictly monotonically increasing. This is equivalent to the following two conditions: # For every limit ordinal (i.e. is neither zero nor a successor), it is the case that . # For all ordinals , it is the case that . Examples A simple normal function is given by (see ordinal arithmetic). But is ''not'' normal because it is not continuous at any limit ordinal (for example, f(\omega) = \omega+1 \ne \omega = \sup \). If is a fixed ordinal, then the functions , (for ), and (for ) are all normal. More important examples of normal functions are given by the aleph numbers f(\alpha) = \aleph_\alpha, which connect ordinal and cardinal numbers, and by the beth numbers f(\alpha) = \beth_\alpha. Properties If is normal, then for any ordinal , :. Proof: If not, choose minimal such that . Since is strictly monotonically increasing, , contra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
