|
Hessian
A Hessian is an inhabitant of the German state of Hesse. Hessian may also refer to: Named from the toponym *Hessian (soldier), eighteenth-century German regiments in service with the British Empire **Hessian (boot), a style of boot **Hessian fabric, coarse woven material **Hessian fly or barley midge, a species of fly (thought to be introduced by Hessian soldiers) *Hessian dialects, West Central German group of dialects *Hessian crucible, a type of ceramic crucible *Hessian Cup, a regional cup competition in German football Named for Otto Hesse *Hessian matrix, in mathematics, is a matrix of second partial derivatives ** Hessian affine region detector, a feature detector used in the fields of computer vision and image analysis **Hessian automatic differentiation ** Hessian equations, partial differential equations (PDEs) based on the Hessian matrix *Hessian pair or Hessian duad in mathematics *Hessian form of an elliptic curve *Hessian group * Hessian polyhedron * Glossary of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian (soldier)
Hessians ( or ) were German soldiers who served as auxiliaries to the British Army during the American Revolutionary War. The term is an American synecdoche for all Germans who fought on the British side, since 65% came from the German states of Hesse-Kassel and Hesse-Hanau. Known for their discipline and martial prowess, around 30,000 Germans fought for the British during the war, comprising a quarter of British land forces. While regarded, both contemporaneously and historiographically, as mercenaries, Hessians were legally distinguished as auxiliaries: whereas mercenaries served a foreign government of their own accord, auxiliaries were soldiers hired out to a foreign party by their own government, to which they remained in service. Auxiliaries were a major source of income for many small and relatively poor German states, typically serving in wars in which their governments were neutral. Like most auxiliaries of this period, Hessians served with foreign armies as entire uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian Matrix
In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and later named after him. Hesse originally used the term "functional determinants". Definitions and properties Suppose f : \R^n \to \R is a function taking as input a vector \mathbf \in \R^n and outputting a scalar f(\mathbf) \in \R. If all second-order partial derivatives of f exist, then the Hessian matrix \mathbf of f is a square n \times n matrix, usually defined and arranged as follows: \mathbf H_f= \begin \dfrac & \dfrac & \cdots & \dfrac \\ .2ex \dfrac & \dfrac & \cdots & \dfrac \\ .2ex \vdots & \vdots & \ddots & \vdots \\ .2ex \dfrac & \dfrac & \cdots & \dfrac \end, or, by stating an equation for the coefficients using indices i and j, (\mathbf H_f)_ = \fra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hesse
Hesse (, , ) or Hessia (, ; german: Hessen ), officially the State of Hessen (german: links=no, Land Hessen), is a States of Germany, state in Germany. Its capital city is Wiesbaden, and the largest urban area is Frankfurt. Two other major historic cities are Darmstadt and Kassel. With an area of 21,114.73 square kilometers and a population of just over six million, it ranks seventh and fifth, respectively, among the sixteen German states. Frankfurt Rhine-Main, Germany's second-largest metropolitan area (after Rhine-Ruhr), is mainly located in Hesse. As a cultural region, Hesse also includes the area known as Rhenish Hesse (Rheinhessen) in the neighbouring state of Rhineland-Palatinate. Name The German name '':wikt:Hessen#German, Hessen'', like the names of other German regions (''Schwaben'' "Swabia", ''Franken'' "Franconia", ''Bayern'' "Bavaria", ''Sachsen'' "Saxony"), derives from the dative plural form of the name of the inhabitants or German tribes, eponymous tribe, the Hes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian Dialects
Hessian (german: Hessisch) is a West Central German group of dialects of the German language in the central German state of Hesse. The dialect most similar to Hessian is Palatinate German (german: Pfälzisch, links=no) of the Rhine Franconian sub-family. However, the Hessian dialects have some features which set them somewhat apart from other West-Central German dialects. Dialects Hessian can be divided into four main dialects: * North Hessian (, around the city of Kassel), * Central Hessian (, including the Marburg and Gießen areas), * East Hessian (, around Fulda), * South Hessian (, around Darmstadt). To understand this division, one must consider the history of Hesse and the fact that this state is the result of an administrative reform. ''s'' regularly occurred in the pronouns and , unlike in Central Franconian to the west, which has and . *West Germanic initial ''p'' and medial/final ''pp'' have remained plosives ( 'pound', 'apple'), contrasting to the east with Ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian Affine Region Detector
The Hessian affine region detector is a feature detector used in the fields of computer vision Computer vision is an interdisciplinary scientific field that deals with how computers can gain high-level understanding from digital images or videos. From the perspective of engineering, it seeks to understand and automate tasks that the hum ... and image analysis. Like other feature detectors, the Hessian affine detector is typically used as a preprocessing step to algorithms that rely on identifiable, characteristic Interest point detection, interest points. The Hessian affine detector is part of the subclass of feature detectors known as ''affine-invariant'' detectors: Harris affine region detector, Hessian affine regions, maximally stable extremal regions, Kadir–Brady saliency detector, edge-based regions (EBR) and intensity-extrema-based (IBR) regions. Algorithm description The Hessian affine detector algorithm is almost identical to the Harris affine region detector. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian Automatic Differentiation
In applied mathematics, Hessian automatic differentiation are techniques based on automatic differentiation (AD) that calculate the second derivative of an n-dimensional function, known as the Hessian matrix In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field. It describes the local curvature of a function of many variables. The Hessian matrix was developed .... When examining a function in a neighborhood of a point, one can discard many complicated global aspects of the function and accurately approximate it with simpler functions. The quadratic approximation is the best-fitting quadratic in the neighborhood of a point, and is frequently used in engineering and science. To calculate the quadratic approximation, one must first calculate its gradient and Hessian matrix. Let f: \mathbb^n \rightarrow \mathbb , for each x \in \mathbb^n the Hessian matrix H(x) \in \mathbb^ is the seco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian Fabric
Hessian (, ), burlap in the United States and Canada, or crocus in Jamaica and the wider Caribbean, is a woven fabric usually made from skin of the jute plant or sisal fibres, which may be combined with other vegetable fibres to make rope, nets, and similar products. Gunny is similar in texture and construction. Hessian, a dense woven fabric, has historically been produced as a coarse fabric, but more recently it is being used in a refined state known simply as jute as an eco-friendly material for bags, rugs and other products. The name "hessian" is attributed to the historic use of the fabric as part of the uniform of soldiers from the former Landgraviate of Hesse and its successors, including the current German state of Hesse, who were called " Hessians". Hessian cloth is available in different types of construction, form, size and color. The origin of the word ''burlap'' is unknown, though its earliest known appearance is in the late 17th century, and its etymology is specu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian (Web Service Protocol)
Hessian is a binary Web service protocol that makes Web services usable without requiring a large framework, and without learning a new set of protocols . Because it is a binary protocol, it is well-suited to sending binary data without any need to extend the protocol with attachments. Hessian was developed by Caucho Technology, Inc. The company has released Java, Python and ActionScript for Adobe Flash implementations of Hessian under an open source license (the Apache license). Third-party implementations in several other languages (C++, C#, JavaScript, Perl, PHP, Ruby, Objective-C, D, and Erlang) are also available as open-source. Adaptations Although Hessian is primarily intended for Web services, it can be adapted for TCP traffic by using the ''HessianInput'' and ''HessianOutput'' classes in Caucho's Java implementation. Implementations Cotton( Erlang) HessDroid( Android) Hessian (on Rubyforge)(Ruby) Hessian.js(JavaScript) Hessian4J(Java) HessianC#( C#) HessianCPP( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian Polyhedron
In geometry, the Hessian polyhedron is a regular complex polyhedron 333, , in \mathbb^3. It has 27 vertices, 72 3 edges, and 27 33 faces. It is self-dual. Coxeter named it after Ludwig Otto Hesse for sharing the ''Hessian configuration'' \left begin 9&4\\3&12 \end\right /math> or (94123), 9 points lying by threes on twelve lines, with four lines through each point. Its complex reflection group is 3 sub>3 sub>3 or , order 648, also called a Hessian group. It has 27 copies of , order 24, at each vertex. It has 24 order-3 reflections. Its Coxeter number is 12, with degrees of the fundamental invariants 3, 6, and 12, which can be seen in projective symmetry of the polytopes. The Witting polytope, 3333, contains the Hessian polyhedron as cells and vertex figures. It has a real representation as the ''221'' polytope, , in 6-dimensional space, sharing the same 27 vertices. The 216 edges in ''221'' can be seen as the 72 3 edges represented as 3 simple edges. Coordinates Its 27 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian Equation
In mathematics, ''k''-Hessian equations (or Hessian equations for short) are partial differential equations (PDEs) based on the Hessian matrix. More specifically, a Hessian equation is the ''k''-trace, or the ''k''th elementary symmetric polynomial of eigenvalues of the Hessian matrix. When ''k'' ≥ 2, the ''k''-Hessian equation is a fully nonlinear partial differential equation. It can be written as _k f, where 1\leqslant k \leqslant n, _k \sigma_k(\lambda(^2u)), and \lambda(^2u)=(\lambda_1,\cdots,\lambda_n), are the eigenvalues of the ''Hessian matrix'' ^2u= partial_i \partial_ju and \sigma_k(\lambda)=\sum_\lambda_\cdots\lambda_, is a k th elementary symmetric polynomial. Much like differential equations often study the actions of differential operators (e.g. elliptic operators and elliptic equations), Hessian equations can be understood as simply eigenvalue equations acted upon by the Hessian differential operator. Special cases include the Monge–Ampère equation. and Po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hessian Form Of An Elliptic Curve
In geometry, the Hessian curve is a plane curve similar to folium of Descartes. It is named after the German mathematician Otto Hesse. This curve was suggested for application in elliptic curve cryptography, because arithmetic in this curve representation is faster and needs less memory than arithmetic in standard Weierstrass form.Cauchy-Desbove's Formulae: ''Hessian-elliptic Curves and Side-Channel Attacks'', Marc Joye and Jean-Jacques Quisquarter Definition Let K be a field and consider an elliptic curve E in the following special case of Weierstrass form over K : Y^2+a_1 XY+a_3 Y=X^3 where the curve has discriminant \Delta = \left(a_3^3 \left(a_1^3 - 27a_3\right)\right) = a_3^3 \delta. Then the point P=(0,0) has order 3. To prove that P=(0,0) has order 3, note that the tangent to E at P is the line Y=0 which intersects E with multiplicity 3 at P. Conversely, given a point P of order 3 on an elliptic curve E both defined over a field K one can put the curve into Weier ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glossary Of Classical Algebraic Geometry
The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David Hilbert and the Italian school of algebraic geometry in the beginning of the century, and later formalized by André Weil, Jean-Pierre Serre and Alexander Grothendieck. Much of the classical terminology, mainly based on case study, was simply abandoned, with the result that books and papers written before this time can be hard to read. This article lists some of this classical terminology, and describes some of the changes in conventions. translates many of the classical terms in algebraic geometry into scheme-theoretic terminology. Other books defining some of the classical terminology include , , , , , . Conventions The change in terminology from around 1948 to 1960 is not the only difficulty in understanding classical algebraic geometry. There was also a lot of background knowledge and assumptions, much of which has now ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
