In mathematics , Vector multiplication refers to one of several techniques for the multiplication of two or more Euclidean vector vectors with themselves. It may concern any of the following articles Dot product &mdash Also known as the scalar product , an operation which takes two vectors and returns a scalar mathematics scalar quantity Cross product &mdash Also known as the vector product , a binary operation on two vectors that results in another Euclidean vector vector Triple product s &mdash Products involving three vectors. Multiple cross products &mdash Products involving more than three vectors. See also Scalar multiplication Matrix multiplication Category Vectors Category Multiplication Linear algebra stub eo Multipliko de vektoroj ta ... more details
Italic title Infobox Journal cover abbreviation Parasit. Vectors discipline Parasitology website http www.parasitesandvectors.com editor Chris Arme publisher BioMed Central country frequency abbreviation history 2008 present openaccess Yes license Creative Commons licenses Creative Commons Attribution 2.0 impact 2.05 impact year 2009 RSS http www.parasitesandvectors.com rss ISSN 1756 3305 eISSN LCCN 2008243698 OCLC 212423889 Parasites & Vectors is a Peer review peer reviewed Open access publishing open access medical journal published by BioMed Central . The journal publishes articles on the biology of parasite s, parasitic disease s, intermediate host s, vector epidemiology vectors and vector borne pathogen s. ref http www.parasitesandvectors.com info about About Parasites & Vectors . accessed 13 August 2010. ref Parasites & Vectors was established in 2008 as a merger of Filaria Journal and Kinetoplastid Biology . References Reflist External links Official http www.parasitesandvectors.com commons category Images from Parasites & Vectors Category BioMed Central academic journals Category Biology journals Category Publications established in 2008 Category English language journals Category Open access journals Category Parasitology journals ... more details
Q vectors are used in atmospheric dynamics to understand physical processes such as vertical motion and frontogenesis . Q vectors are not physical quantities that can be measured in the atmosphere but are derived from the quasi geostrophic equations and can be used in the previous diagnostic situations. On meteorological charts, Q vectors point toward upward motion and away from downward motion. Q vectors are an alternative to the omega equation for diagnosing vertical motion in the quasi geostrophic equations. Derivation First derived in 1978 ref cite journal last Hoskins first B. J. coauthors I. Draghici and H. C. Davies title A new look at the equation journal Quart. J. R. Met. Soc year 1978 volume 104 pages 31 38 ref , Q vector derivation can be simplified for the midlatitudes, using the midlatitude plane quasi geostrophic prediction equations ref cite book last Holton first James R. title An Introduction to Dynamic Meteorology year 2004 publisher Elsevier Academic location New York isbn 0 12 354015 1 pages 168 72 ref math frac D g u g Dt f 0 v a beta y v g 0 math x component of quasi geostrophic momentum equation math frac D g v g Dt f 0 u a beta y u g 0 math y component of quasi ... New York isbn 0 12 354015 1 pages 170 ref . Q vectors and all ageostrophic flow exist to preserve thermal wind balance. Therefore, low level Q vectors tend to point in the direction of low level ageostrophic ... 286 ref . Applications Q vectors can be determined wholly with geopotential height math Phi math and temperature on a constant pressure surface. Q vectors always point in the direction of ascending ... y 0 math , cyclones have Q vectors which point parallel to the thermal wind and anticyclones have Q vectors that point antiparallel to the thermal wind ref cite book last Holton first James R. title ... for initiation. For those situations Q vectors point toward ascending air and the tightening ... 15 March 2012 ref . In areas of convergent Q vectors, cyclonic vorticity is created, and in divergent ... more details
Vectors in three dimensional space 1978 is a book concerned with physical quantities defined in ordinary 3 space . It was written by John Stephen Roy Chisholm J.S.R.Chisholm , an English mathematical physicist , and published by Cambridge University Press . According to the author, such physical quantities are studied in Newtonian mechanics , fluid mechanics , theories of Elasticity physics elasticity and Plasticity physics plasticity , non relativistic quantum mechanics , and many parts of solid state physics . The author further states that the vector concept developed in two different ways in a wide variety of physical applications, vector notation and techniques became, by the middle of this century, almost universal on the other hand, pure mathematicians reduced vector algebra to an axiomatic system, and introduced wide generalization generalisations of the concept of a three dimensional vector space . Chisholm explains that since these two developments proceeded largely independently, there is a need to show how one can be applied to the other. ref Chisholm, J.S.R. 1978 p. vii viii ref Summary Vectors in three dimensional space has six chapters, each divided into five or more subsections. The first on Vector space linear spaces and displacement vector displacements including these sections Introduction, Scalar multiplication of vectors, Addition and subtraction of vectors, Displacements in Euclidean space, Geometrical applications. The second on dot product Scalar products and components including these sections Scalar products, Linear dependence and dimension, Components of a vector, Geometrical applications, Coordinate system s. The third on Other products of vectors . The last three chapters round out Chisholm s integration of these two largely independent developments. Notes reflist References reflist 2 Vectors in three dimensional space has been cited by the 2002 Encyclopedia Americana article on Vector Analysis John Stephen Roy Chisholm Chisholm, J.S.R. Vectors ... more details
unreferenced date September 2010 In astrodynamics or celestial dynamics orbital state vectors sometimes state vectors are cartesian coordinate system cartesian vectors of position vector position math mathbf r math and velocity math mathbf v math that together with their time epoch astronomy epoch math t , math uniquely determine the trajectory of a body in space. Image Orbital state vectors.png thumbnail left 700px Orbital position vector and orbital velocity vector and other orbit s elements br style clear both Frame of reference State vectors are defined with respect to some frame of reference , usually but not always an inertial reference frame . One of the more popular reference frames for the state vectors of bodies moving near the earth is the earth centered equatorial system defined as follows The origin is the earth s center of mass The Z axis is coincident with the earth s rotational axis, positive northward The X Y plane coincides with the earth s equatorial plane, with the X axis pointing toward the vernal equinox and the Y axis completing a right handed set. This reference frame is not truly inertial because of the slow, 26,000 year axial precession astronomy precession of the earth s axis , so the reference frames defined by the earth s orientation at a standard epoch astronomy astronomical epoch such as B1950 or J2000 are also commonly used. Many other reference frames can be used to meet various application requirements including those centered on the Sun or on other planets or moons, the one defined by the barycenter and total angular momentum of the solar system, or even by a spacecraft s own orbital plane and angular momentum. Position vector linked from ... its velocity in the same frame at the same time. Together, these two vectors and the time at which they are valid ... vectors math mathbf r math and math mathbf v math can be easily used to compute the angular momentum .... orbits Category Astrodynamics Category Celestial mechanics Category Earth orbits Category Vectors ... more details
of basis. Vectors as opposed to dual vectors are said to be contravariant . Examples of contravariant vectors include the position of an object relative to an observer, or any derivative of position ... transformation as the change of basis. Dual vectors as opposed to vectors are said to be covariant . Examples of covariant vectors generally appear when taking a gradient of a function effectively ... mathbf v v i mathbf e i , math In physics, vectors often have units of distance or distance times ... of distance times some other unit. The distinction between covariant and contravariant vectors ... that they have both covariant and contravariant components, or both vectors and dual vectors. The valence .... That is to say, the components of the vectors will transform in a certain way in passing from one ..., width, and height. Examples of contravariant vectors include displacement vector displacement , velocity ... are considered, the components of contravariant and covariant vectors behave in the same way ... of the f basis is a linear combination of the vectors X sub i sub of the f basis, so that math Y j ... of on the basis vectors X sub i sub of the f basis. Under the change of basis from f to f ... on which vectors live as tangent vector s or cotangent vector s. Given a local coordinate system ... covariant and contravariant vectors, because the bilinear form allows covectors to be identified with vectors. That is, a vector v uniquely determines a covector via math alpha w g v, w math for all vectors w . Conversely, each covector determines a unique vector v by this equation. Because of this identification of vectors with covectors, one may speak of the covariant components or contravariant ... A. clr Euclidean plane In the Euclidean plane, the dot product allows for vectors to be identified ... , respectively. Example For example, ref cite web last Bowen first Ray title Introduction to Vectors ... a basis e sub 1 sub , e sub 2 sub consisting of a pair of vectors making a 45 angle with one another ... more details
trials using retroviral vectors to treat X linked severe combined immunodeficiency X SCID represent ... vectors were raised after the 1999 death of Jesse Gelsinger while participating in a gene therapy trial. Since then, work using adenovirus vectors has focused on genetically crippled versions of the virus. Envelope protein pseudotyping of viral vectors The viral vectors described above have natural ... to transduction by a gene therapy vector. To this end, many vectors have been developed in which ... of viral vectors to one or a few host cell populations. This advance would allow for the systemic administration ... tropism have used chimeric envelope proteins bearing antibody fragments. These vectors show great promise for the development of magic bullet gene therapies. Replication Competent Vectors A replication ... vectors always contain a transfer construct . The transfer construct carries the gene to be transduced ... and neutral lipids were used for the construction of lipoplexes for synthetic vectors. However, in spite ... widely used as an alternative for gene delivery vectors, a dose dependent toxicity of cationic lipids .... ref Some of the benefits of inorganic vectors is in their storage stability, low manufacturing ... or liposomal methods alone. Other methods involve mixing other viral vectors with cationic lipids or hybridising viruses . References reflist DEFAULTSORT Vectors in Gene Therapy Category Applied genetics ... more details
Disputed date May 2009 Gene therapy using lentiviral vectors is being explored in early stage trials ... adeno associated virus rAAV vectors. Many other possible viral vectors remain options for the treatment ... using lentivirus vectors may be a way to treat a wider range of genetic disorders in the retina ... vectors. Like rAAV vectors, lentiviral vectors offer many features that make it an excellent tool for molecular biology and possible medical treatments. Like many other vectors commonly used in the laboratory, lentiviral vectors allow for efficient transfer of foreign DNA transgene to target cells, long ... Immune responses to lentiviral vectors journal Current Gene Therapy volume 7 issue 5 pages 306 15 ... vectors, lentiviral vectors do not possess any of their original DNA content, allowing as little provocation of the immune response as possible. Unlike many retroviral vectors, though, lentiviral vectors ... or not the target cells proliferate many retroviral vectors require replicating DNA to insert themselves ... vector is the parent virus that gave rise to the vector. Not all lentiviral vectors ... from between lentiviral vectors, though, and many popular lentiviral vectors have either a human immunodeficiency ... Vector Although both the lentiviral and rAAV vectors provide a high efficiency of gene transfer to cells in vivo , rAAV vectors do have some slight disadvantages that would preclude their use for certain diseases. rAAV vectors, for example, only allow genes less than 4 kb 4000 bases for insertion ... and thus does not allow the use of rAAV vectors. One such disease, Stargardt s disease OMIM 601691 ... a viral vector capable of handling such a relatively large insert. Lentiviral vectors, unlike rAAV vectors, are capable of efficiently incorporating and allowing expression of transgene fragments ... for patients suffering from Stargardt s disease see below . This is not to suggest lentiviral vectors do not efficiently transfect cells in vivo as well as rAAV vectors with transcripts less than 4 kb ... more details
Vectors is an international online Magazine journal produced by the University of Southern California s Institute for Multimedia Literacy. Launched in March 2005, the journal s current issue is its fifth, titled Difference . Through all of the issues, Vectors has featured over thirty scholarly new media projects. About the journal The journal publishes two new issues per year. Each issue features projects created by teams of fellows from a range of disciplines working together with technologists, creative directors and other scholars. Vectors mission is to publish material that can t be published in print utilizing cutting edge tools and work processes. As the journal s about page describes, blockquote This investigation at the intersection of technology and culture is not simply thematic. Rather, Vectors is realized in multimedia , melding wikt form form and wikt content content to enact a second order examination of the mediation of everyday life. Using a peer reviewed format and under the guidance of an international board, Vectors features submissions and specially commissioned works composed of moving and still images voice, music, and sound computational and interactive structures social software and much more. ref http www.vectorsjournal.org journal index.php?page Introduction Vectors Journal, Introduction ref blockquote Projects included in Vectors investigate diverse topics including evidence , Indigenous peoples indigenous communities, women s prisons , land use , war , and worker s rights. Many projects are produced by a team that includes a Vectors staff member. Other ... editorial staff ref http vectorsjournal.org journal index.php?page EditorialStaff Vectors Journal Editorial ... Director . List of issues and projects The Vectors Journal has published over thirty projects since ... www.vectorsjournal.org Vectors Journal of Culture and Technology in a Dynamic Vernacular http www.vectorsjournal.org archive Vectors Journal Issues & Projects Archive Category Online magazines ... more details
Coincident is a geometry geometric term that pertains to the relationship between two Vector geometric vectors . Vectors consist of a magnitude and a direction . Vectors can be said to be coincident when their direction is the same though the magnitude may be different that is to say, they lie one on top of the other. If two coincident vectors were to be normalized shortened or lengthened to be one unit long , the resulting vectors would be identical. The dot product of two coincident vectors is the product of their magnitudes. The cross product of two coincident vectors is a vector of all zeros. External links MathWorld urlname Coincident title Coincident geometry stub Category Euclidean geometry ... 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
State vector may refer to A Quantum state vector A state vector geographical specifies the position and velocity of an object in any location on Earth s surface Orbital state vectors are vectors of position and velocity that together with their time, uniquely determine the state of an orbiting body in astrodynamics or celestial dynamics disambiguation ... more details
Phase angle may refer to Phase angle vectors, phasors, and periodic phenomena Phase angle astronomy the angle between the incident light and reflected light disambig ... more details
to transfer foreign genetic material into another cell. The four major types of vectors are plasmid s, viral vectors , cosmid s, and Bacterial artificial chromosome artificial chromosome s. Common to all engineered vectors are an origin of replication , a multiple cloning site multicloning site , and a selectable ..., multiply, or express the insert in the target cell. Vectors called expression vector s expression constructs ... a promotor biology promoter sequence that drives expression of the transgene. Simpler vectors called transcription vectors are only capable of being transcribed but not translated they can be replicated in a target cell but not expressed, unlike expression vectors. Transcription vectors are used to amplify ... commonly used vectors are plasmid s and viral vector s. Plasmids main Plasmid vector Plasmid s are double ... cell. Plasmid vectors minimalistically consist of an origin of replication that allows for semi ... of the insert. In the case of plasmids utilized as transcription vectors, incubating bacteria with plasmids generates hundreds or thousands of copies of the vector within the bacteria in hours, and the vectors ... vectors characteristically lack crucial sequences that code for polyadenylation sequences and translation termination sequences in translated mRNAs, making protein expression from transcription vectors ..., e.g., many R and col plasmids. Viral vectors main Viral vector Viral vectors are generally genetically ... through a viral promoter. However, because viral vectors frequently are lacking infectious sequences, they require helper viruses or packaging lines for large scale transfection. Viral vectors are often ... component in all vectors the premise of a vector is to multiply the insert although expression vectors later also drive the translation of the multiplied insert . Thus, even stable expression is determined ... vectors have a variety of expression patterns constitutive consistent expression or inducible ... vectors depend on different types of promoters. Viral promoters are often used for constitutive expression ... more details
Unreferenced date November 2009 A two vector is a tensor of type 2,0 and it is the dual space dual of a two form , meaning that it is a linear functional which maps two forms to the real numbers or more generally, to scalars . The tensor product of a pair of Vector geometric vector s is a two vector. Then, any two form can be expressed as a linear combination of tensor products of pairs of vectors, especially a linear combination of tensor products of pairs of basis vectors. If f is a two vector, then math mathbf f f alpha beta , vec e alpha otimes vec e beta math where the f sup sup are the components of the two vector. Notice that both indices of the components are covariance and contravariance contravariant . This is always the case for two vectors, by definition. An example of a two vector is the inverse g sup sup of the metric tensor . The components of a two vector may be represented in a matrix like array. However, a two vector, as a tensor, should not be confused with a Matrix mathematics matrix , since a matrix is a linear function math M V rightarrow V math which Map mathematics maps vectors to vectors, whereas a two vector is a linear functional math mathbf f tilde V rightarrow V math which maps one form s to vectors. In this sense, a matrix, considered as a tensor, is a mixed tensor of type 1,1 even though of the same rank as a two vector. DEFAULTSORT Two Vector Category Tensors ... 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
Independent set may refer to Linearly independent , of a set of vectors in a vector space. Independent set of elements of a matroid. See Matroid Independent sets, bases, and circuits . Independent set graph theory , a set of vertices that share no edges. disambig ... more details
In affine geometry , a branch of mathematics , an affine frame in an affine space A consists of a choice P of origin of A along with a basis of a vector space basis of the space of vectors based at P . Category Affine geometry geometry stub ca Marc af fr Rep re affine ... more details
unreferenced date February 2012 In differential geometry in an autoparallel sub manifold parallel transport can be expressed with the sub manifold s base vectors, i.e. math nabla partial a partial b Gamma ab c partial c math . Category Differential geometry ... more details
or any other marker peptide. Expression vectors are used for molecular biology techniques such as site directed mutagenesis . Cloning vectors , which are very similar to expression vectors, involve the same ... for replication purposes. In general, DNA Vector molecular biology vectors that are used in many molecular ... vectors must have expression signals such as a strong promoter, a strong termination codon, adjustment ... years, expression vectors have been used to introduce specific genes in organism s, especially plants used in agriculture . Expression vectors have been used to introduce a vitamin A precursor, beta ... since it is produced by the modified organism. In addition expression vectors are used to extend ... ref There has been controversy over using expression vectors to modify crops due to the fact that there might ... more details
version vectors. Pairs of replicas, math a math , math b math , can be compared by inspecting their version vectors and determined to be either identical math a b math , concurrent math a parallel ... b a math , but the vectors are not identical, then the two vectors must be concurrent. Version vectors ... probabilistic guaranties. Concise Version Vectors ref Dalia Malkhi and Doug Terry. Concise Version Vectors in WinFS.Distributed Computing, Vol. 20, 2007. ref allow significant space savings when handling ... Paulo Almeida, Carlos Baquero and Victor Fonte. Version Stamps Decentralized Version Vectors. ICDCS ... version vectors and vector clocks and allows dynamic numbers of replicas processes. Bounded Version Vectors ref Jos Almeida, Paulo Almeida and Carlos Baquero. Bounded Version Vectors. DISC International ... more details
In astrodynamics , the eccentricity vector of a Kepler orbit is the vector geometric vector pointing towards the periapsis having a magnitude equal to the orbit s scalar orbital eccentricity eccentricity . The magnitude is unitless . For Kepler orbits the eccentricity vector is a constant of motion. Its main use is for almost circular orbits as perturbing non Keplarian forces on an actual orbit will cause the Osculating orbit osculating eccentricity vector to change continuously as opposed to the parameters eccentricity and argument of perigee for which eccentricity zero circular orbit corresponds to a singularity. See the article Kepler orbit Calculation The eccentricity vector math mathbf e , math can be calculated ref The Kepler Problem , By Bruno Cordani, page 22, Birkhaeuser 2003 , ISBN 3 7643 6902 7 ref math mathbf e mathbf v times mathbf h over mu mathbf r over left mathbf r right math where math mathbf v , math is orbital velocity vector , math mathbf h , math is orbital angular momentum vector , math mathbf r , math is orbital position vector , math mu , math is standard gravitational parameter . or equivalently from the orbital state vectors by math mathbf e mathbf left v right 2 mathbf r over mu mathbf r cdot mathbf v mathbf v over mu mathbf r over left mathbf r right math where math mathbf v , math is orbital state vectors Velocity vector velocity vector of the orbital state vectors , math mathbf r , math is orbital state vectors Position vector position vector of the orbital state vectors, math mu , math is standard gravitational parameter . See also Kepler orbit Orbit Eccentricity orbit Eccentricity Laplace Runge Lenz vector References Reflist 2 DEFAULTSORT Eccentricity Vector Category Astrodynamics Category Celestial mechanics Category Vectors es Vector Excentricidad it Vettore eccentricit he ru zh ... more details
Multiple issues orphan November 2006 context October 2009 Small T intron exist in some plasmid vector s used for protein expression . The function of this intron in the vectors is unknown, but it is theorized that it might be involved in splicing or translation efficiency. ref name pmid1690852 cite journal author Huang MT, Gorman CM title The simian virus 40 small t intron, present in many common expression vectors, leads to aberrant splicing. journal Mol Cell Biol volume 10 issue 4 pages 1805 10 year 1990 pmid 1690852 ref ref name pmid1654158 cite journal author Hunt AG, Mogen BD, Chu NM, Chua NH title The SV40 small t intron is accurately and efficiently spliced in tobacco cells. journal Plant Mol Biol volume 16 issue 3 pages 375 9 year 1991 pmid 1654158 ref Vectors contain such as pME18s contain it. References reflist DEFAULTSORT Small T Intron Category Gene expression Cell biology stub ... more details
Unreferenced stub auto yes date December 2009 Vector decomposition refers to decomposing a Vector geometric vector of R sup n sup into several vectors, each linearly independent in mutually distinct directions in the n dimensional space . Vector decomposition in two dimensions In two dimensions, a vector can be decomposed in many ways. In the Cartesian coordinate system , the vector is decomposed into a portion along the math hat x math or math hat i math and the math hat y math or math hat j math directions. One of the most common situations is when given a vector with magnitude and direction or given in polar coordinate system polar form , it can be converted into the Vector geometric Addition and subtraction sum of two perpendicular vectors or converted to a Cartesian coordinate . Application in physics Vector decomposition is used in physics to help adding vectors and hence solve many mechanical problems involving force , work physics work , momentum , etc. See also coordinate system Helmholtz decomposition decomposition of a vector field DEFAULTSORT Vector Decomposition Category Introductory physics Phys stub ... more details
In applied mathematics , bred vectors are perturbation theory perturbations , related to Lyapunov vector s, that capture fast growing dynamical instability instabilities of the solution of a computer simulation numerical model . They are used, for example, as initial perturbations for ensemble forecasting in numerical weather prediction . Method Bred vectors are created by adding initially random perturbations to a nonlinear model. The control unperturbed and the perturbed models are integral integrated in time, and periodically the control solution is subtracted from the perturbed solution. This difference is the bred vector. The vector is scaled to be the same size as the initial perturbation, and is then added back to the control to create the new perturbed initial condition. After a short transient period, this breeding process creates bred vectors dominated by the naturally fastest growing instabilities of the evolving control solution. References Kalnay, E. 2007 , Atmospheric Modeling, Data Assimilation and Predictability , Cambridge Cambridge University Press Glickman, T.S. 2000 Ed , Glossary of Meteorology , Second Edition, Boston, Massachusetts American Meteorological Society Category Functional analysis Category Mathematical physics mathanalysis stub ... more details
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