# Vector fields on any smooth manifold M can be thought of as derivations X of the ring of smooth functions on the manifold, and therefore form a Lie algebra under the Lie bracket = XY − YX, because the Lie bracket of any two derivations is a derivation.

Vector calculus ( or vector analysis ) is a branch of mathematics concerned with differentiation and integration of vector fields, primarily in 3 dimensional Euclidean space 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 differentiation and multiple integration.

Vector calculus studies various differential operators defined on scalar or vector fields, which are typically expressed in terms of the del operator ().

Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point.

Vector fields can usefully be thought of as representing the velocity of a moving flow in space, and this physical intuition leads to notions such as the divergence ( which represents the rate of change of volume of a flow ) and curl ( which represents the rotation of a flow ).

Vector fields are often discussed on open subsets of Euclidean space, but also make sense on other subsets such as surfaces, where they associate an arrow tangent to the surface at each point ( a tangent vector ).

Vector fields are one kind of tensor field.

Vector fields can be constructed out of scalar fields using the gradient operator ( denoted by the del: ∇).

* Vector fields, which associate a vector to every point in space.

Magnetic fields add as vectors. Vector sum of the magnetic field vectors of the stator coils produces a single rotating vector of resulting rotating magnetic field.

Examples of potential and gradient fields in physicsScalar fields ( scalar potentials ) (< span style =" color: yellow "> yellow </ span >): V < sub > G </ sub >-gravitational potential ; W < sub > pot </ sub >-potential energy ; V < sub > C </ sub >-Coulomb potential ; Vector fields ( gradient fields ) (< span style =" color: cyan "> cyan </ span >): a < sub > G </ sub >-gravitational acceleration ; F-force ; E-electric field strength

* Vector fields on spheres

It is known as TeVeS for Tensor / Vector / Scalar and it introduces three different fields in space time to replace the one gravitational field.

Vector fields can have several special points: a stable point, called a sink, that attracts in all directions ( forcing the concentrations to be at a certain value ), an unstable point, either a source or a saddle point which repels ( forcing the concentrations to change away from a certain value ), and a limit cycle, a closed trajectory towards which several trajectories spiral towards ( making the concentrations oscillate ).

Vector gauge theories with massless Dirac fermion fields exhibit chiral symmetry, i. e., rotating the left-handed and the right-handed components independently makes no difference to the theory.

Vector fields that satisfy the conformal Killing equation are exactly those vector fields whose flow preserves the conformal structure of the manifold.

Vector fields can be specified as first order linear partial differential operators, such as

The most widely used learning algorithms are Support Vector Machines, linear regression, logistic regression, naive Bayes, linear discriminant analysis, decision trees, k-nearest neighbor algorithm, and Neural Networks ( Multilayer perceptron ).

Examples of software packages that handle plasmid maps are pDraw32, Geneious, Lasergene, GeneConstructionKit, ApE, Clone Manager, and Vector NTI.

Vector graphics is the use of geometrical primitives such as points, lines, curves, and shapes or polygon ( s ), which are all based on mathematical expressions, to represent images in computer graphics.

Vector formats are not always appropriate in graphics work.

Vector graphics systems were only retired from U. S. en route air traffic control in 1999, and are likely still in use in military and specialised systems.

Vector graphics are ideal for simple or composite drawings that need to be device-independent, or do not need to achieve photo-realism.

What share had it in generating the Vector Analysis and the mathematics by which investigations in physical science are now conducted?

The routing protocols in use today are based on one of two algorithms: Distance Vector or Link State.

Vector graphics editors are often contrasted with raster graphics editors, yet their capabilities complement each other.

Vector images are created mathematically ( using formulas, as in geometry ).

Vector editors are often contrasted with bitmap editors, and their capabilities complement each other.

Vector editors are often better for page layout, typography, logos, sharp-edged artistic illustrations ( e. g. cartoons, clip art, complex geometric patterns ), technical illustrations, diagramming and flowcharting.

Vector editors are closely related to desktop publishing software such as Adobe InDesign or Scribus, which also usually include some vector drawing tools ( usually less powerful than those in standalone vector editors ).

By default, only total delay and minimum bandwidth are considered when EIGRP is started on a router, but an administrator can enable or disable all the K values as needed to consider the other Vector metrics.

Common examples include VIS, MMX, SSE, AltiVec and AVE. Vector processing techniques are also found in video game console hardware and graphics accelerators.

Vector processing techniques have since been added to almost all modern CPU designs, although they are typically referred to as SIMD.

Vector magnetometers are subject to temperature drift and the dimensional instability of the ferrite cores.

Distance Vector means that Routers are advertised as vector of distance and Direction.

Vector shapes are supported using a separate vector layer, and can be used to

* In The Transformers episode " The Key to Vector Sigma ", Optimus Prime assists in the creation of the Aerialbots who, in the later episode " War Dawn ", are sent back through time, thus activating their vital role, and ensuring Optimus Prime's existence into the future.

Vector spaces are a central theme in modern mathematics ; thus, linear algebra is widely used in both abstract algebra and functional analysis.

Vector Sigma, the Allspark, chooses which Autobot is to be granted the Matrix and thus the position of commander-in-chief.

In the 2008 case Vector Marketing Corporation v. New Hampshire Department of Revenue Administration, the Supreme Court of New Hampshire ruled that Vector employees are independent contractors and Vector is thus exempt from the state business profit tax.

Vector relationships for uniform circular motion ; vector Ω representing the rotation is normal to the plane of the orbit with polarity determined by the right-hand rule and magnitude dθ / dt.

Christian alternative music has its roots in the early 1980s, as the earliest efforts at Christian punk and new wave were recorded by artists like Andy McCarroll and Moral Support, Undercover, The 77s, Adam Again, Quickflight, Daniel Amos, Youth Choir ( later renamed The Choir ), Lifesavers Underground, Michael Knott, The Altar Boys, Breakfast with Amy, Steve Taylor, 4-4-1, David Edwards and Vector.

* 1987 – History's worst peacetime sea disaster, when the passenger ferry Doña Paz sinks after colliding with the oil tanker Vector 1 in the Tablas Strait in the Philippines, killing an estimated 4, 000 people ( 1, 749 official ).

If each of the features makes an independent contribution to the output, then algorithms based on linear functions ( e. g., linear regression, logistic regression, Support Vector Machines, naive Bayes ) and distance functions ( e. g., nearest neighbor methods, support vector machines with Gaussian kernels ) generally perform well.

Vector analysis related the fluid flow with turbine shape and rotation.

Vector graphics can be created in hardcopy form using a pen plotter, a special type of printer that uses a series of ballpoint and / or felt-tip pens on a servo-driven mount that moves horizontally across the paper, with the plotter moving the paper back and forth through its paper path for vertical movement.

* December 20 – In history's worst peacetime sea disaster, the passenger ferry MV Doña Paz sinks after colliding with the oil tanker Vector 1 in the Tablas Strait in the Philippines, killing an estimated 4, 000 people ( 1, 749 official ).

Vector processors use this technique with one additional " trick ".

In Vector Prime, Calrissian asks Solo and Chewie to help him with a business transaction on the planet of Sernpidal.

Vector processor ( SIMD ) cores can be combined with VLIW architecture as the Fujitsu FR-V, further increasing throughput and speed.

Vector data encoding requires less memory and less data storage, in situations where the shapes may need to be resized, as with font typefaces.

Parker Vector stainless steel with proprietary Quink cartridges containing 1. 4 ml ink

* Campbell, Colin ; and Ying, Yiming ; Learning with Support Vector Machines, 2011, Morgan and Claypool.

Smith has recorded and toured with dozens of other artists over the years, including Jimmy Abegg, Michael W. Smith, Margaret Becker, Vector, dc Talk, Rick Elias, Mitch McVicker, Riki Michele, Cindy Morgan, Sixpence None the Richer, Engelbert Humperdinck, Charlie Peacock, Romeo Void, and Steve Scott.

In the 1980s, he formed the pop-rock band Vector with Steve Griffith.

The CEVA-XC DSP family targets Software-defined Radio ( SDR ) modem designs and leverages a unique combination of VLIW and Vector architectures with 32 16-bit MACs.

** The implicit Initialization Vector ( IV ) was replaced with an explicit IV.

The Roof rat ( rattus rattus ) is a Host ( biology ) | reservoir host of bubonic plague with the oriental rat flea s that infest them being a prime Vector ( epidemiology ) | vector of the disease.

* Renaissance Vector — A primarily urban world, with major centres named after giants of the Italian Renaissance.

On June 20, 2012, Vector Capital won a competitive bid for a minority stake in Technicolor, beating JP Morgan with a surprise, last-minute bid.