calculus cTopic Vector calculus Vector calculus or vector analysis is a branch of mathematics concerned with derivative differentiation and integral integration of vector field s, primarily in 3 dimensional Euclidean space math mathbf R 3. math The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus , which includes vector calculus as well as partial derivative partial differentiation and multiple integral multiple integration . Vector calculus plays ... field s, gravitational field s and fluid flow . Vector calculus was developed from quaternion analysis ... and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, Vector Analysis . In the conventional form using cross products, vector calculus does not generalize to higher ... generalize, as Generalizations discussed below . Basic objects The basic objects in vector calculus are scalar field s scalar valued functions and vector field s vector valued functions . These are then combined ... further distinguishes pseudovector fields and pseudoscalar fields, which are identical to vector ..., the curl of a vector field is a pseudovector field, and if one reflects a vector field, the curl ..., as described below. Vector operations Algebraic operations The basic algebraic non differential operations in vector calculus are referred to as vector algebra , being defined for a vector space and then globally applied to a vector field, and consist of scalar multiplication multiplication of a scalar field and a vector field, yielding a vector field math a bold v math vector addition addition of two vector fields, yielding a vector field math bold v 1 bold v 2 math dot product multiplication of two vector fields, yielding a scalar field math bold v 1 cdot bold v 2 math cross product multiplication of two vector fields, yielding a vector field math bold v 1 times bold v 2 math There are also two triple product s scalar triple product the dot product of a vector and a cross product of two ... more details
Stochastic vector redirects here. For the concept of a random vector, see Multivariate random variable . Unreferenced date December 2009 In mathematics and statistics , a probability vector or stochastic vector is a vector space vector with non negative entries that add up to one. The positions indices of a probability vector represent the possible outcomes of a discrete random variable , and the vector gives us the probability mass function of that random variable, which is the standard way of characterizing a discrete probability distribution . Here are some examples of probability vectors math x 0 begin bmatrix 0.5 0.25 0.25 end bmatrix , x 1 begin bmatrix 0 1 0 end bmatrix , x 2 begin bmatrix 0.65 0.35 end bmatrix , x 3 begin bmatrix 0.3 0.5 0.07 0.1 0.03 end bmatrix . math Writing out the vector components of a vector math p math as math p begin bmatrix p 1 p 2 vdots p n end bmatrix math the vector components must sum to one math sum i 1 n p i 1 math One also has the requirement that each individual component must have a probability between zero and one math 0 le p i le 1 math for all ... A stochastic vector is a point on the far face of a standard orthogonal simplex . That is, a stochastic vector uniquely identifies a point on the face opposite of the orthogonal corner of the standard ... vector is math 1 n math . The shortest probability vector has the value math 1 n math as each component of the vector, and has a length of math 1 sqrt n math . The longest probability vector has the value 1 in a single component and 0 in all others, and has a length of 1. The shortest vector corresponds to maximum uncertainty, the longest to maximum certainty. No two probability vectors ... of a probability vector is equal to math sqrt n sigma 2 1 n math where math sigma 2 math is the variance of the elements of the probability vector. See also Stochastic matrix DEFAULTSORT Probability Vector Category Probability theory Category Vectors sl Verjetnostni vektor sr ... more details
notability Products date April 2010 Infobox Software name Vector Architect logo Image VectropyIcon.png center 64px Vector Architect Logo screenshot Deleted image removed Image VectropyScreenshot.png center Vector Architect Screenshot 300px caption Vector Architect Screenshot developer Owl Island Software ... Proprietary EULA website http www.vectorarchitect.com vectorarchitect.com Vector Architect is a vector graphics editor designed by Owl Island Software. Functionality Vector Architect was not a general purpose vector graphics editor , but was specifically designed to create and edit XAML vector graphics for Windows Presentation Foundation WPF and Silverlight applications. Vector Architect itself ... both its WYSIWYG front end, and underlying editing engine. In many ways, Vector Architect was similar ... is often necessary as XAML does not have exactly the same feature set as other popular vector image ... focused on XAML , Vector Architect also supported the generation of PNG images with Alpha Blend alpha .... Existing uses Vector Architect has gained a user base as an alternative to the first party XAML ... of Vector Architect have been released. ref http www.smoothcosmos.com FAQ.html Smooth Cosmos FAQ ref Availability Vector Architect no longer appears available for purchase, however http www.owlisland.com redownload downloads are available for previous customers. The first version of Vector Architect ... 2008 . Vector Architect has since been updated to version 1.5, adding a new user interface, several ... free of charge, ref http owlisland.com support.php?name VectorArchitectUpgrade Vector Architect 1.5 .... Early versions of the application were released under the name Vectropy . Vector Architect was originally ... Windows Windows XP XP , Windows Vista , Windows Server 2003 , Windows Server 2008 . Licensing Vector ... or resale. See also List of vector graphics editors Comparison of vector graphics editors References reflist External links http www.vectorarchitect.com Vector Architect product site Tutorials and guides ... more details
For a more general, but much more technical, treatment of tangent vectors, see tangent space . A tangent vector is a Vector geometry vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in R sup n sup . More generally, tangent vectors are elements of a tangent space of a differentiable manifold . Category Vectors Linear algebra stub ru sv Tangentvektor uk zh ... more details
Vector is a breakfast cereal manufacturing manufactured by Kellogg s Kellogg s Canada . It is advertised for its healthier ingredients over other cereal brands, especially in the area of sports. Kellogg s uses the term meal replacement instead of breakfast cereal for this product, but it is still classified as such. External links http www.kelloggs.ca cgi bin klog canada product.pl?family 125&template vector Kellogg Canada Inc. Products Vector Kellogg s Category Kellogg Company cereals food product stub ... more details
Cleanup rewrite date February 2010 Infobox company company name Vector Motors Corporation company logo ... unknown Vector Motors Corporation is an American automobile manufacturer originally based in Wilmington ... by Gerald Wiegert ref name Background Vector Aeromotive Corporation Corporate Backgrounder , The Vector Aeromotive Corporation, prepared by Kalmann Communications, 1990, contributed by the Vector Aeromotive ... revived as Vector Motors Corporation , and is currently developing a new supercar. Vector ... vf http drive.to vector the vectorFILES ref and teamed up with Lee Brown to create a new car called The Vector . The Vector was said to have various powerplants including a DOHC Porsche engine, and preproduction ... 20050401091020 http www.vectoraeromotiveclub.com Vector Aeromotive club through Internet Archive ref ... s planned production run never started. All that came of The Vector was an empty shell that was displayed .... The Vector was featured on the cover of Motor Trend magazine in 1972. ref name vf Wiegert renamed Vehicle Design Force to Vector Aeromotive after work began on a new project, the Vector W2 . The Vector W2 Main Vector W2 In 1978, Wiegert created another car, called the Vector W2 W2 . Like the first ... on it, even though Vector claimed the car was capable of 230 mph. ref name vac Vector W8 Main Vector W8 Image Vector W8 Twin Turbo 1992.jpg thumb right 250 1992 W8 twin turbo In 1989, Wiegert s company, now known as the Vector Aeromotive Corporation, began production of the Vector W8 W8 , an evolution ... suits against the Goodyear Tire Company trademark infringement with the Vector brand of tires and Vantage ... falinf http www.ferraris online.com Articles SCM 0004.html Vector, another fantasy flop Michael Sheehan. ref Vector delivered the car as promised. Company representatives told him that he could display it, but warned him not to drive it until the final work was completed. Wiegert and Vector Aeromotive ... were finished, and the car was resold. A total of 17 Vector W8 cars were built for public sale. ref ... more details
Orphan date December 2009 Unreferenced stub auto yes date December 2009 Reset vector is a computing term used to describe the default location a central processing unit will go to find the first instruction computer science instruction it will execute after a reset. That is to say, the reset vector is a pointer computer programming pointer or Memory address address where the CPU should always begin as soon as it is able to execute instructions. The reset vector for the 80386DX and later x86 processors is 0xFFFF0, although the value of the CS register CS register at reset is 0xF000 and the value of the program counter IP register at reset is 0xFFF0. In actuality, current x86 processors fetch from the physical address 0xFFFFFFF0. This is due to a hidden base address portion of the CS register in real mode which defaults to 0xFFFF0000 after reset. The reset vector for the 8086 processor is at address FFFF 0000 The reset vector for the 80286 processor is at address 0x00FFFFF0 just below 16Mb DEFAULTSORT Reset Vector Category Central processing unit Category Instruction processing Compu stub fr Vecteur de d marrage sv Resetvektor ... more details
Vector Burn aka Oliver Scott, is a drum and bass producer from Phoenix, Arizona , USA. With numerous releases on drum and bass labels of note in the USA and Europe, his music has been part of the burgeoning North American drum and bass scene since the turn of the millennium. Influences range from My Bloody Valentine band My Bloody Valentine to Omni Trio . He is currently signed to Metalheadz , Barcode Recordings , Human Imprint and Force Recordings, among other labels. Along with fellow Phoenix producer Castor producer Castor , he formed a politically charged drum and bass group called The Riot in 2005. External links rolldabeats artist vector burn name Vector Burn http www.myspace.com vectorburnaudio Vector Burn at MySpace http www.myspace.com theriotsound The Riot at MySpace Persondata name Burn, Vector alternative names short description date of birth place of birth date of death place of death DEFAULTSORT Burn, Vector Category American drum and bass musicians Category Living people ... more details
Image VectorField.svg right thumb 250px A portion of the vector field sin y , sin x In vector calculus , a vector field is an assignment of a vector geometry vector to each point in a subset of Euclidean space . ref name Galbis 2012 p12 A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane. Vector ... calculus extend to vector fields in a natural way. 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 ... . Vector fields can usefully be thought of as representing the velocity of a moving flow in space ..., a vector field on a domain in n dimensional Euclidean space can be represented as a vector ... of a vector field depends on the coordinate system, and there is a well defined covariance .... Vector fields are often discussed on open set open subsets of Euclidean space, but also make sense ... point a Differential geometry of curves tangent vector . More generally, vector fields are defined on differentiable ... have more complicated structure on larger scales. In this setting, a vector field gives a tangent vector at each point of the manifold that is, a Section fiber bundle section of the tangent bundle to the manifold . Vector fields are one kind of tensor field . Definition Vector fields on subsets of Euclidean space multiple image footer Two representations of the same vector field math mathbf v x .... width 140 image1 Radial vector field sparse.svg alt1 Sparse vector field representation image2 Radial vector field dense.svg alt2 Dense vector field representation. Given a subset S in R sup n sup , a vector field is represented by a vector valued function math V S to mathbf R n math in standard ... is a continuous vector field, and more generally V is a C sup k sup vector field if each component V is k times continuously differentiable . A vector field can be visualized as assigning a vector to individual ... more details
In mathematics , especially the field of group theory , the Parker vector is an integer vector that describes a permutation group in terms of the cycle structure of its elements. Definition Expand section date February 2008 The Parker vector P of a permutation group G acting on a set of size n , is the vector whose k th component for k 1, , n is given by math P k frac k G sum g in G c k g math where c sub k sub g is the number of k cycles in the cycle decomposition of g . Examples Empty section date February 2008 Applications Expand section date February 2008 The Parker vector can assist in the recognition of Galois group s. References cite book title Permutation Groups author Peter J. Cameron publisher Cambridge University Press year 1999 isbn 0521653789 url http books.google.com books?id 4bNj8K1omGAC&pg PA48&dq 22Parker Vector 22&lr &as brr 0&ei JeKoR8iKHIvsiQHfjNWqCg&sig v2x98oF0YEsxyNm8HXq0BHPDXPA cite book title Finite Geometries Proceedings of the Fourth Isle of Thorns Conference author Aart Blokhuis publisher Springer year 2001 isbn 0792369947 url http books.google.com books?id P8Ra5zHVzQUC&pg PA59&dq 22Parker Vector 22&lr &as brr 0&ei JeKoR8iKHIvsiQHfjNWqCg&sig yjCRM55fuSmS84OZ ugc9tT2kyo Expert subject mathematics date November 2008 DEFAULTSORT Parker Vector Category Permutation groups algebra stub ... more details
In mathematics and physics , the vector Laplace operator , denoted by math scriptstyle nabla 2 math , named after Pierre Simon Laplace , is a differential operator defined over a vector field . The vector Laplacian is similar to the Laplacian scalar Laplacian . Whereas the scalar Laplacian applies to scalar field and returns a scalar quantity, the vector Laplacian applies to the vector fields and returns a vector quantity. The returned vector field is equal to the vector field of the scalar Laplacian applied on the individual elements. Definition The vector Laplacian of a vector field math mathbf A math is defined as math nabla 2 mathbf A nabla nabla cdot mathbf A nabla times nabla times mathbf A math In Cartesian coordinate s, this reduces to the much simpler form This can be seen a special case of Lagrange s formula, see Vector triple product . math nabla 2 mathbf A nabla 2 A x, nabla 2 A y, nabla 2 A z math where math A x math , math A y math , and math A z math are the components of math mathbf A math . For expressions of the vector Laplacian in other coordinate systems see Nabla in cylindrical and spherical coordinates . Generalization The Laplacian of any tensor field math mathbf T math tensor includes scalar and vector is defined as the divergence of the gradient of the tensor ... mathbf T math is a vector a tensor of first rank , the gradient is a covariant derivative which results in a tensor of second rank, and the divergence of this is again a vector. The formula for the vector ... of the expression shown below for the gradient of a vector math nabla mathbf T nabla T x ..., which evaluates to a vector, of a vector by the gradient of another vector a tensor of 2nd rank ... of the usage of the vector Laplacian is the Navier Stokes equations for a Newtonian fluid Newtonian ... rho mathbf f nabla p mu left nabla 2 mathbf v right math where the term with the vector Laplacian ... VectorLaplacian.html title Vector Laplacian author MathWorld http farside.ph.utexas.edu ... more details
cylinder instead . In mathematics , a vector bundle is a topology topological construction that makes precise the idea of a family of vector space s parameterized by another space X for example X ... we associate or attach a vector space V x in such a way that these vector spaces fit together to form ... is then called a vector bundle over X . The simplest example is the case that the family of vector spaces is constant, i.e., there is a fixed vector space V such that V x V for all x in X in this case there is a copy of V for each x in X and these copies fit together to form the vector bundle X × V over X . Such vector bundles are said to be Fiber bundle Trivial ... is trivial. Vector bundles are almost always required to be locally trivial , however, which means they are examples of fiber bundle s. Also, the vector spaces are usually required to be over the real or complex numbers, in which case the vector bundle is said to be a real or complex vector bundle respectively . Complex vector bundles can be viewed as real vector bundles with additional structure. In the following, we focus on real vector bundles in the category of topological spaces . Definition and first consequences A real vector bundle consists of topological spaces X base space and E ... of a Hamel dimension finite dimensional real number real vector space on the Fiber bundle ... , and the map v mapsto x , v is an isomorphism between the vector spaces R sup k sup and sup ... of the vector bundle. The local trivialization shows that locally the map looks like the projection ... vector space and hence has a dimension k sub x sub . The local trivializations show that the Function ... of X , then k is called the rank of the vector bundle, and E is said to be a vector bundle of rank k . Often the definition of a vector bundle includes that the rank is well defined, so that k sub x sub is constant. Vector bundles of rank 1 are called line bundle s, while those of rank 2 are less commonly ... more details
For vector control of induction motors Vector control motor Image Vector Control.jpg thumb Vector control taking place in the Southern United States during the 1920s. Vector control is any method to limit or eradicate the mammal s, bird s, insect s or other arthropod s which transmit disease pathogen s. The most frequent type of vector control is mosquito control using a variety of strategies. Methods of Control Vector control focuses on utilizing preventative methods to control or eliminate vector populations. Common preventative measures are Habitat Control Removing or reducing areas where vectors can easily breed can help limit population growth. For example, stagnant water removal, destruction of old tires and cans which serve as mosquito breeding habits and good management of used water can reduce areas of excessive vector incidence. Reducing Contact Limiting exposure to insects or animals ... the awareness of vector threats. Chemical Control Insecticides , larvicides , rodenticides and repellents ... incidence of insect bites and thus infection. The use of pesticides for vector control is promoted by the World ... eng.pdf format pdf ref Biological Control The use of natural vector predators, such as bacteria bacterial toxins or botany botanical compounds, can help control vector populations. Using fish that eat ... have been shown to control vector populations and reduce infection risks. ref cite journal last ... volume 93 issue 1 pages 123 135 ref Importance of vector control For diseases where there is no effective cure, such as West Nile Virus and Dengue fever , vector control remains the only way to protect populations. However, even for vector borne diseases with effective treatments the high cost ... due to the disease. Both prevention through vector control and treatment are needed to protect ... they carried is prioritized. Vector control in many third world areas can have tremendous impacts ... reflist See also Mosquito control Vector epidemiology Vector Public health DEFAULTSORT Vector Control ... more details
In geometry , for a finite planar surface of scalar area math S math , the vector area math mathbf S math is defined as a vector whose magnitude is math S math and whose direction is perpendicular to the plane, as determined by the right hand rule on the rim moving one s right hand counterclockwise around the rim, when the palm of the hand is touching the surface, and the straight thumb indicates the direction . math mathbf S mathbf hat n S math For an orientable surface S composed of a set math S i math of flat facet areas, the vector area of the surface is given by math mathbf S sum i mathbf hat n i S i math where math mathbf hat n i math is the unit normal vector to the area math S i math . For bounded, oriented curved surfaces that are sufficiently well behaved, we can still define vector area. First, we split the surface into infinitesimal elements, each of which is effectively flat. For each infinitesimal element of area, we have an area vector, also infinitesimal. math d mathbf S mathbf hat n dS math where math mathbf hat n math is the local unit vector perpendicular to math dS math . Integrating gives the vector area for the surface. math mathbf S int d mathbf S math For a curved or faceted surface, the vector area is smaller in magnitude than the area. As an extreme example, a closed surface can possess arbitrarily large area, but its vector area is necessarily zero. ref Murray R. Spiegel, Theory and problems of vector analysis, Schaum s Outline Series, McGraw Hill, 1959, p. 25. ref Surfaces that share a boundary may have very different areas, but they must have the same vector area the vector area is entirely determined by the boundary. These are consequences of Stokes theorem . The concept of an area vector simplifies the equation for determining the flux through ... as the dot product of the field and area vector. This is much simpler than multiplying the field strength ... component of the vector area, and is given by math mathbf S z left mathbf S right cos theta math where ... more details
Infobox Software name Vector NTI logo screenshot caption developer Invitrogen latest release version 11.5.1 Windows , 7.1 OS X latest release date release date 2010 10 15 operating system Mac OS X , Microsoft Windows Windows genre Molecular biology toolkit license Proprietary website http www.invitrogen.com site us en home LINNEA Online Guides LINNEA Communities Vector NTI Community vector nti software.html Vector NTI home Vector NTI is a bioinformatics software package. The current versions are v11.5.1 for Microsoft Windows Windows PCs and v7.1 for Macs, but only supporting Mac OS X v10.3 Panther . Features create, annotate, analyse, and share DNA protein sequences perform and save BLAST searches design primer molecular biology primers for PCR , cloning , sequencing or nucleic acid hybridization hybridisation experiments plan cloning and run Gel electrophoresis gels in silico align multiple protein or DNA sequences search National Center for Biotechnology Information NCBI s Entrez , view, and save DNAs, proteins, and citations edit chromatogram data, assemble into contigs See also Bioinformatics Vector molecular biology , Vector DNA , Cloning vector , Expression vector Restriction map Computational biology List of open source bioinformatics software External links Description of software http www.invitrogen.com site us en home LINNEA Online Guides LINNEA Communities Vector NTI Community vector nti software.html Vector NTI homepage at Invitrogen.com http openwetware.org wiki VectorNTI Vector NTI at openwetware.org http bioinformatics.unc.edu software nti index.htm Vector NTI v10 only PC Tutorials http www.basic.northwestern.edu VectorNTI Documentation VectorNTI Vector NTI tutorial at NorthWestern.edu Other http register.informaxinc.com solutions vectornti molecular viewer.html description of Vector NTI Viewer Other Software http www.biology.utah.edu jorgensen wayned ape ApE A Powerful Multipurpose DNA Engineering Software, Donationware Freeware http www.clcbio.com main ... more details
In video compression , a motion vector is the key element in the motion estimation process. It is used to represent a macroblock in a picture based on the position of this macroblock or a similar one in another picture, called the reference picture. The H.264 MPEG 4 AVC standard defines motion vector as blockquote motion vector A two dimensional vector used for inter prediction that provides an offset from the coordinates in the decoded picture to the coordinates in a reference picture. ref http www.stewe.org itu recs h264.pdf Latest working draft of H.264 MPEG 4 AVC . Retrieved on 2008 February 29 02 29 . ref ref http www.hhi.fraunhofer.de fileadmin hhi downloads IP ip ic H.264 MPEG4 AVC Version8 FinalDraft.pdf Latest working drat of H.264 MPEG 4 AVC on hhi.fraunhofer.de. ref blockquote See also Video coding Motion estimation References reflist Category Vectors fr Vecteur de mouvement ... more details
Infobox automobile name Vector W8 image Image VectorW8.jpg 250px 1993 Vector W8 manufacturer Vector Motors ... Vector W2 successor Vector WX 3 class Sports car body style 2 door Coup coupe layout Rear mid ... related designer Gerald Wiegert sp us The Vector W8 was a sports car produced from 1989 to 1993. ref name ultimatecarpage.com It was manufactured by Vector Motors Vector Aeromotive , and was designed ... car 490 Vector W8 Twin Turbo.html title 1989 1993 Vector W8 Twin Turbo accessdate 2009 01 07 author ... http www.vectormotors.com company.html title Vector Motors Company accessdate 2009 01 07 publisher Vector Motors Corp. ref and David Kostka. The company claimed the newest and most advanced aerospace ... . A total of 22 automobiles produced by Vector Aeromotive over the life of the company. The car ... File Vector W8 Twin Turbo interior1.jpg thumb left Vector W8 interior. The W8 was essentially an upgrade of the same company s earlier prototype, the Vector W2 . The aluminum honeycomb semi monocoque ... in the car s assembly. Everything on the Vector was designed to last the life of the owner, assuming ... spec.html title 1992 W8 twinturbo accessdate 2009 01 07 publisher Vector Motors Corporation ref The car ... web url http www.supercars.net cars 1862.html title Vector W8 accessdate 2009 01 07 publisher Supercars.net ... Vector W8s were fitted with a removable glass roof, due to buffeting that occurred at those extreme speeds. Successor Vector intended to follow the W8 with the Vector WX 3 WX 3 and WX 3R, but series production ..., equipment, and remaining unsold cars. In 1995, following the takeover, Vector began production of their next car, the Vector M12 M12 . References Reflist External links http www.vectormotors.com Vector Motors Corporation Category Rear mid engine, rear wheel drive vehicles Category Vector Motors Category Sports cars Category 1980s automobiles Category 1990s automobiles fa it Vector W8 pl Vector W8 fi Vector W8 ... more details
Vector Training is a method of Rowing sport rowing training, developed in the 1960s as a winter training method. The first recorded usage of Vector Training was at Inverness Rowing Club in 1966, training for the Boston Rowing Marathon . Vector Training builds up endurance by maximising the amplitude of the outing, making it an ideal training technique for clubs with shorter stretches of water. Increased water resistance caused by the cross currentular path builds up the strength required for tough head of the river races. There are many danger areas involved in Vector Training. Collisions are frequent between those using the vector method and those not. Ideally, Vector Training should be carried out by all boats on the body of water, maintaining a constant distance between crews. Due to the large amount of traffic, vector training and related training methods such as spoon surfing have been banned on the River Thames http www.portoflondon.co.uk pdfs maritime rowing code printers.pdf and the Hudson River but are still widely practiced on quieter, narrower stretches of water such as the River Aire in Yorkshire and the River Nith in the Scottish Borders. References Thames Regional Rowing Council http www.portoflondon.co.uk pdfs maritime rowing code printers.pdf , New Code of Practice accessed November 28th, 2009 Category Rowing rowing stub ... more details
vectors in general Vector mathematics and physics vector In elementary mathematics , physics , and engineering , a Euclidean vector sometimes called a geometric ref harvnb Ivanov 2001 ref or spatial vector , ref harvnb Heinbockel 2001 ref or as here simply a vector is a geometric object that has ... to the parallelogram law of addition. A Euclidean vector is frequently represented by a line ... AB . math A vector is what is needed to carry the point A to the point B the Latin word vector means ... development of the word vector , see OED vector n. and cite web author Jeff Miller url http jeff560.tripod.com ... 25 . ref The magnitude of the vector is the distance between the two points and the direction refers ... generalized concept of vectors defined simply as elements of a vector space . Vectors play an important ... most of them do not represent distances except, for example, position vector position or displacement vector displacement , their magnitude and direction can be still represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector like objects that describe physical quantities and transform ... as elements of a vector space . General vectors in this sense are fixed size, ordered collections ... Euclidean concepts of length, distance and angle may not be applicable. A vector space with a definition ... of vector should be distinguished from the statistical concept of a random vector . The individual items in a random vector are individual real valued random variable s, and are often manipulated using the same sort of mathematical vector and matrix operations that apply to the other types of vectors ... is the potential correlation s among them. Overview A vector is a geometric entity characterized .... In rigorous mathematical treatments, ref harvnb Ito 1993 p 1678 ref a vector is defined ... it from vectors Vector space as defined elsewhere , this is sometimes referred to as a geometric ... more details
Image vectorwx801.jpg thumb right 250px The Vector WX8 prototype on display at the 2007 Los Angeles Auto Show The Vector WX8 is a sports car prototype released under development at Vector Motors . It was first shown officially to the public in 2007 revealing the development and the company s ambitious intentions of creating a next generation sportscar successor to their previous models. Vector claims the WX8 may achieve a top speed of convert 300 mi h km h abbr on and a zero to 60 mph time as low as 2.3 seconds for the version of the car equipped with a 10 litre turbocharged engine. This engine is described variously on the company s website as being capable of 1800 HP , 1850 HP , and over 2000 horsepower ref http www.vectormotors.com wx8 specs.html Vector Motors WX8 Specs webpage ref . It was criticized by an automotive journalist ref http blogs.motortrend.com vector wx8 shows its face at la auto show 1312.html Motor Trend Blog Vector WX8 shows its face at LA Auto Show ref and car enthusiasts Citation needed date July 2010 for its use of Toyota Supra Mark IV 1993 2002 Toyota Supra Mark IV headlamps and a front end that resembles the Chevrolet Camaro fourth generation fourth generation Chevrolet Camaro . The design of the prototype test vehicle though has continued to evolve and seen various changes since. References Reflist External links http www.vectormotors.com wx8 specs.html Vector WX 8 specs Category Vector Motors Category Rear mid engine, rear wheel drive vehicles Modern auto stub pl Vector Avtech WX 8 HPRV ru Vector WX 8 ... more details
In pattern recognition and machine learning , a feature vector is an n dimensional vector geometric vector of numerical Features pattern recognition feature s that represent some object. Many algorithm s in machine learning require a numerical representation of objects, since such representations facilitate processing and statistical analysis. When representing images, the feature values might correspond to the pixels of an image, when representing texts perhaps to term occurrence frequencies. Feature vectors are equivalent to the vectors of explanatory variable s used in statistics statistical procedures such as linear regression . Feature vectors are often combined with weights using a dot product in order to construct a linear predictor function that is used to determine a score for making a prediction. The vector space associated with these vectors is often called the feature space . In order to reduce the dimensionality of the feature space, a number of dimensionality reduction techniques can be employed. See also Feature extraction Feature selection Dimensionality reduction DEFAULTSORT Feature Vector Category Machine learning Category Data mining mathapplied stub de Merkmalsvektor ... more details
The Burgers vector , named after Dutch physicist Jan Burgers , is a Vector geometric vector , often denoted b , that represents the Magnitude vector magnitude and direction of the lattice distortion of dislocation in a Crystal structure crystal lattice . ref Callister, William D. Jr. Fundamentals of Materials Science and Engineering, John Wiley & Sons , Inc. Danvers, MA. 2005 ref Image Vector de Burgers.PNG 250px thumbnail right Burgers vectors The vector s magnitude and direction is best understood when the dislocation bearing crystal structure is first visualized without the dislocation, that is, the perfect crystal structure. In this perfect crystal structure, a rectangle whose lengths and widths ... defines the direction and magnitude of the Burgers vector. Specifically, the breadth of the opening defines the magnitude of the Burgers vector, and, when a set of fixed coordinates is introduced ... may be specified. The direction of the vector depends on the plane of dislocation, which is usually ... is the magnitude of Burgers vector and h, k, and l are the components of Burgers vector, b h k l . In most metallic materials, the magnitude of the Burgers vector for a dislocation is of a magnitude ... , the Burgers vector and dislocation line are at right angles to one another. In Dislocation ... State Physics, 7th edition, John Wiley & Sons , Inc, 1996 pp 592 593. ref The Burgers vector ... science engineering it is often useful to know the magnitude of the Burger s vector in metres. This is easily ... system is 110 the length of the Burger s vector is simply b 2 R, where R is the atomic radius. The HCP system is even simpler with the Burger s vector simply equal to the unit cell length a, I.E. b a, where a 2 R for the HCP system. Hence the Burger s vector of titanium would be 0.29 nm long. See also Frank Read Source References references External links DEFAULTSORT Burgers Vector Category ... Der Burgersvektor es Vector de Burgers it Vettore di Burgers nl Burgersvector ru tr ... more details
In mathematics , the vector flow refers to a set of closely related concepts of the flow mathematics flow determined by a vector field . These appear in a number of different contexts, including differential topology , Riemannian geometry and Lie group theory. These related concepts are explored in a spectrum of articles exponential map matrix exponential exponential function Lie group The Lie algebra associated with a Lie group infinitesimal generator Lie group integral curve vector field one parameter subgroup flow geometry geodesic flow Hamiltonian flow Ricci flow Anosov flow injectivity radius glossary Vector flow in differential topology Relevant concepts flow, infinitesimal generator, integral curve, complete vector field Let V be a smooth vector field on a smooth manifold M . There is a unique maximal flow geometry flow D M whose Lie group The Lie algebra associated to a Lie group infinitesimal generator is V . Here D R × M is the flow domain . For each p M the map D sub p sub M is the unique maximal integral curve of V starting at p . A global flow is one whose flow domain is all of R × M . Global flows define smooth actions of R on M . A vector field is vector field Complete vector fields complete if it generates a global flow. Every vector field on a compact manifold without boundary is complete. Vector flow in Riemannian geometry Relevant concepts geodesic, exponential map, injectivity radius The exponential map exp T sub p sub M &rarr M is defined as exp X 1 where I M is the unique geodesic passing through p at 0 and whose tangent vector at 0 is X . Here I is the maximal open interval of R for which the geodesic is defined. Let M be a pseudo Riemannian ... Let D sub p sub be the subset of T sub p sub M for which 1 lies in I . Vector flow in Lie group theory ... vector field on a Lie group is complete. The integral curve starting at the identity is a one parameter ... invariant vector fields on G &hArr g T sub e sub G . Let G be a Lie group and g its Lie algebra. The exponential ... more details
Vector Synthesis is a type of Synthesizer audio synthesis introduced by Sequential Circuits in the Prophet VS synthesizer during 1986. The concept was subsequently used by Yamaha manufacturer Yamaha in the SY22 TG33 and similar instruments and by Korg in the Korg Wavestation Wavestation . Image VectorSynthesisDiagram.svg right thumb Controlling the mix of four sound waves by defining a point on a vector plane using a joystick Vector synthesis provides movement in a sound by providing dynamic cross fading between usually four sound sources. The four sound sources are conceptually arranged as the extreme points of X and Y axes, and typically labelled A, B, C and D. A given mix of the four sound sources can be represented by a single point in this vector plane . Movement of the point provides sonic interest and is the power of this technique. Mixing is frequently done using a joystick, although the point can be controlled using Envelope generator envelope generators or Low frequency oscillation LFOs . Vector synthesis implementations There have been a number of different implementations of vector synthesis. These differ in what they use for the four sound sources, and what processing is done to the sound after the vector synthesis stage. The actual vector synthesis concept is identical. Prophet VS vector synthesis The Prophet VS used four digital wavetable synthesis wavetable oscillators ... to the Prophet s implementation of vector synthesis by providing two types of sound source. Each axis of the vector had both an Frequency modulation synthesis FM sound source and a sample playback source. Although it lacked any filtering, it added digital effects for processing the results of the vector ... for over a decade to feature vector synthesis. It also features an updated form of wave sequencing ... Prophet 5 and VS, is featuring vector synthesis, as well as Arturia s http www.arturia.com ..., the 2D Envelope. See also Introduction to Vector Synthesis Stanley Jungleib, Electronic Musician ... more details
Incomplete date February 2009 Vector quantization is a classical Quantization signal processing quantization ... a large set of points coordinate vectorvector s into groups having approximately the same ... other clustering algorithms. The density matching property of vector quantization is powerful ... data correction and density estimation . Vector quantization is based on the competitive learning ... for vector quantization is Pick a sample point at random Move the nearest quantization vector ... Pick a sample point at random Find the quantization vector centroid with the smallest distance sensitivity ... correlated over many samples. Applications Vector quantization is used for lossy data compression ... due to the density matching property of the algorithm . Use in data compression Vector quantization ... . It works by encoding values from a multidimensional vector space into a finite set of values from a discrete linear subspace subspace of lower dimension. A lower space vector requires less storage space, so the data is compressed. Due to the density matching property of vector quantization ... jointly rather than each sample being quantized separately. Consider a K dimensional vector math x 1,x 2,...,x k math of amplitude levels. It is compressed by choosing the nearest matching vector from ... vector math y 1,y 2,...,y n math form the vector space to which all the quantized vectors belong. Block Diagram A simple vector quantizer is shown below Image with unknown copyright status removed Image Vector quantization.JPG Only the index of the codeword in the codebook is sent instead of the quantized values. This conserves space and achieves more compression. Twin vector quantization VQF is part of the MPEG 4 standard dealing with time domain weighted interleaved vector quantization. Video codecs based on vector quantization Expand list date August 2008 Cinepak and old versions ... by the MPEG family. Audio codecs based on vector quantization Expand list date August 2008 ... more details
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