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

* Vector data is more compatible with relational database environments, where they can be part of a relational table as a normal column and processed using a multitude of operators.

Vector operators are defined in terms of del, and include the gradient, divergence, and curl:

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

Vector features can be made to respect spatial integrity through the application of topology rules such as ' polygons must not overlap '.

In the first novel, Initial Vector, which is set six months after Perfect Dark Zero, Joanna finds herself living in the Carrington Institute grounds and must learn to trust Daniel Carrington, as well as uncovering a conspiracy that may influence on dataDyne's new CEO election.

Professor Hector ( Player 1 ) and Professor Vector ( Player 2 ) must collect all of the bundles of dynamite in each of 40 successive levels.

Many modern cryptosystems cause some degree of expansion during the encryption process, for instance when the resulting ciphertext must include a message-unique Initialization Vector ( IV ).

Vector formats are not always appropriate in graphics work.

Vector bundles are almost always required to be locally trivial, however, which means they are examples of fiber bundles.

For instance, Vector bundles always have a zero section whether they are trivial or not and sphere bundles may admit many global sections without being trivial.

Vector gauge anomalies are always chiral anomalies.

Galvatron, however, was not yet defeated, and during his final one-on-one duel with Prime, Vector Prime appeared before Optimus once again to assure him that he would always watch over him, and bestowed upon him a gift – Rhisling, with which Optimus Prime defeated and destroyed Galvatron once and for all.

In the montage of images that fill the closing credits of the final episode, Vector Prime is seen beyond time, battling the spirit of Galvatron, a symbol that the conflict between good and evil will always go on.

Although Vector Prime may die in one incarnation, as long as time exists, these copies will exist, and Vector Prime will always be there to continue in his to watch over all of creation.

It is initially explained to Jack by Optimus as the key to the Ground Bridge power supply, but Ratchet explains to Jack in " One Shall Rise, Part 3 " that it is instead, the key to Vector Sigma, indicating that Optimus senses enough maturity in Jack to hold it in his possession and that Optimus does not plan to come back to the Autobot base after an expedition to the center of the Earth to defeat Unicron.

Vector monitors, on the other hand, can be challenging or very costly to service, and some can't be repaired at all ( they have dwindled in use since the 1980s and parts are hard to come by ).

On March 28, 1969 in San Francisco, Leo Laurence ( the editor of Vector, magazine of the United States ' largest homophile organization, the Society for Individual Rights ) called for " the Homosexual Revolution of 1969 ," exhorting gay men and lesbians to Join the Black Panthers and other left-wing groups and to " come out " en masse.

His return accelerated the search for the Omega Lock, which appeared to come to a head when the lock was apparently discovered buried in the desert ; the battle had catastrophic consequences when a Decepticon attack killed the Mini-Cons, and Vector Prime drew on his powers for the first time in ages to rewind time and save their lives.

The search box is located at the top right on every page on the standard Wikipedia skin ( Vector ), or it is usually placed in the toolbox on the left hand side of the page in other skins.

Close inspection of the image shows a small purple circle which is displaced from the Flight Path Vector slightly to the lower right.

Mon Mothma's death occurred a few weeks before the events of Vector Prime, and Admiral Ackbar died towards the end of the New Jedi Order series.

However, the emptying of the Matrix had disestablished Vector Sigma, leading the Autobots to search for its location before Optimus Prime sacrificed himself to restore the computer's balance.

However, before departing to Earth's core, Optimus entrusted the Key to Vector Sigma to Jack Darby, a means to restore his memories as well as the Matrix, as Vector Sigma contained not only the memories of Optimus, but those of any and all holders of the Matrix, which in this continuity appears to be only the original thirteen Primes and Optimus himself.

Eventually, this forced Optimus Prime to sacrifice his life by merging with Vector Sigma in order to stabilise the computer before it destroyed Cybertron from within.

Reformatted into new technorganic bodies by the Oracle-the shell program that now surrounded Vector Sigma that enabled users to commune with the afterlife dimension called the Matrix-the Maximals subsequently discovered that Cybertron had indeed been an organic world before it acquired its current metallic shell.

Vector Sigma attests that " before Cybertron was, I was.

Two novels, Perfect Dark: Initial Vector and Perfect Dark: Second Front, which were written by Greg Rucka, and a comic book, Perfect Dark: Janus ' Tears, which was written by Eric Trautmann and illustrated by Cold FuZion Studios, were released before and after the game.

Vector Direct went into voluntary liquidation just before Christmas in 2007, TV Warehouse was purchased by JML but closed in 2009.

The case, Harris v. Vector Marketing Corporation, is pending a final settlement approval for US $ 13 million before Judge Edward M. Chen.

Using the Matrix to activate Vector Sigma, Shockwave downloaded the compressed contents of the mega-computer into his network, but before he had an opportunity to view the data, he was pulled into a battle with Ultra Magnus.

His relationship with Charlie was apparently somewhat strained even before their mother's death, as Don is stunned to learn that his little brother has enough security clearance to work with both the CDC and the NSA (" Vector ").

As Vector Prime then synchronised his map of the keys ’ locations to the current arrangement of the cosmos, he was approached by the evil Megatron – unfortunately, Vector Prime ’ s nature as a Transformer who originated from an era before the division of the race into Autobots and Decepticons ( coupled with his diminished memory of the events he had seen across the multiverse due to his advanced age, as specifically noted in his Fun Publications bio ) and Megatron's own smooth charisma led to him handing the map over the Decepticon leader, realising his mistake too late.

It was destroyed before the finale by two consecutive Super Vector Punches from the Super Five Robo at the same time that Chevalier fell against Five Red.

However, recognising the benefits of vector processing IBM developed Virtual Vector Architecture for use in supercomputers coupling several scalar processors to act as a vector processor.

Vector fields are thus contrasted with scalar fields, which associate a number or scalar to every point in space, and are also contrasted with simple lists of scalar fields, which do not transform under coordinate changes.

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

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

since the divergence of the curl term is zero: ∇ • (∇ × F ) = 0 for an arbitrary field F ( see Vector calculus identities ).

Vector fields are one kind of tensor field.

* Vector magnetometers have the capability to measure the component of the magnetic field in a particular direction, relative to the spatial orientation of the device.

Vector magnetometers measure one or more components of the magnetic field electronically.

* Vector space: a module where the ring R is a division ring or field.

If we ignore the velocity field, the radial component of Poynting's Vector resulted from the Liénard – Wiechert field can be calculated to be

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.

Vector field –

* Vector field assignment of a vector to each point in a mathematical space

Vector field corresponding to " dθ ".

Vector spaces over a field are flat modules.

Vector field, a section of a vector bundle.

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

The image was created by using a pseudocolor plot of the dataset's Mach variable, a Mesh plot of the grid, and Vector plot of a slice through the Velocity field.

# REDIRECT Vector field

* Vector spaces over a given countable field.

# REDIRECT Vector field

Vector spaces ( over a field ) form an elementary triangulated category in which X = X for all X.

Prof. Kohonen has made many contributions to the field of artificial neural networks, including the Learning Vector Quantization algorithm, fundamental theories of distributed associative memory and optimal associative mappings, the learning subspace method and novel algorithms for symbol processing like redundant hash addressing.

* Vector field