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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 conservation of energy is exhibited as a special case of the fundamental theorem of calculus.
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When and vector
When it was decided that Asteroids would be a vector game as well, Delman modified a Lunar Lander circuit board for Ed Logg.
* In linear algebra, an endomorphism of a vector space V is a linear operator V → V. An automorphism is an invertible linear operator on V. When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL ( V ).
When the angular velocity of this co-rotating frame is not constant, that is, for non-circular orbits, other fictitious forces — the Coriolis force and the Euler force — will arise, but can be ignored since they will cancel each other, yielding a net zero acceleration transverse to the moving radial vector, as required by the starting assumption that the vector co-rotates with the planet.
When applied to vector spaces of functions ( which typically are infinite-dimensional ), dual spaces are employed for defining and studying concepts like measures, distributions, and Hilbert spaces.
When defined for a topological vector space there is a subspace of this dual space, corresponding to continuous linear functionals, which constitutes a continuous dual space.
When the evolution map Φ < sup > t </ sup > ( or the vector field it is derived from ) depends on a parameter μ, the structure of the phase space will also depend on this parameter.
When light crosses an optical element the resulting polarization of the emerging light is found by taking the product of the Jones matrix of the optical element and the Jones vector of the incident light.
When making a gun-like configuration, with the middle finger crossing under the index finger, the fingers represent the velocity vector, magnetic field vector, and force vector, respectively.
When only the magnitude and direction of the vector matter, then the particular initial point is of no importance, and the vector is called a free vector.
When the length of vectors is defined, it is possible to also define a dot product — a scalar-valued product of two vectors — which gives a convenient algebraic characterization of both length ( the square root of the dot product of a vector by itself ) and angle ( a function of the dot product between any two vectors ).
When the coordinates are transformed, for example by rotation or stretching, then the components of the vector also transform.
When considered a vector, weight is often denoted by a bold letter W.
When the system S is prepared in a pure state, it is associated with a vector in H. Measurable quantities are associated with Hermitian operators acting on H: these are referred to as observables.
When new SIMD architectures need to be distinguished from older ones, the newer architectures are then considered " short-vector " architectures, as earlier SIMD and vector supercomputers had vector lengths from 64 to 64, 000.
When applied to a tangent vector X to the surface, the shape operator is the tangential component of the rate of change of the normal vector when moved along a curve on the surface tangent to X.
When and field
When some question arises in the medical field concerning cancer, for instance, we do not turn to free and open discussion as in a political campaign.
When this occurs, I make the change on the sketch or on the final watercolor -- if I have been working on a full sheet in the field.
When the ballplayers started to carry the catcher off the field he said: `` That ought to teach the sonofabitch ''.
When a beam of silver atoms was passed through a specially shaped magnetic field, the beam was split based on the direction of an atom's angular momentum, or spin.
When it finally sank in, the crowd swarmed onto the field, cheering loudly and chairing Boyle and Spofforth to the pavilion.
When the Viking raids resumed in 892, Alfred was better prepared to confront them with a standing, mobile field army, a network of garrisons, and a small fleet of ships navigating the rivers and estuaries.
When the Vikings returned in force in 892 they found a kingdom defended by a standing, mobile field army and a network of garrisoned fortresses that commanded its navigable rivers and Roman roads.
When questioned on why she followed Thomas to the second job after he had already allegedly harassed her, she said she had wanted to work in the civil rights field, she had no alternative job, " and at that time, it appeared that the sexual overtures ... had ended.
When artificial intelligence came into existence in the 1960s, the field of computational linguistics became that sub-division of artificial intelligence dealing with human-level comprehension and production of natural languages.
When a metal wire is connected across the two terminals of a DC voltage source such as a battery, the source places an electric field across the conductor.
When this field is instead studied using the QED vacuum of quantum electrodynamics, it is seen that the plates do affect the virtual photons which constitute the field, and generate a net force — either an attraction or a repulsion depending on the specific arrangement of the two plates.
When placed in an electric or magnetic field, equal but opposite forces arise on each side of the dipole creating a torque τ:
When the current changes, the magnetic field does too, inducing a voltage between the ends of the conductor.
When a field travels across to different media, the properties of the field change according to the various boundary conditions.
Using the principle of equivalence, Einstein concluded that the same thing holds in any gravitational field, that the rate of clocks R at different heights was altered according to the gravitational field g. When g is slowly varying, it gives the fractional rate of change of the ticking rate.
When the ball is played on the right side of the field, the defensive players on the right side move upfield.
When the flow is everywhere irrotational and inviscid, Bernoulli's equation can be used throughout the flow field.
When calculating scattering cross sections in particle physics, the interaction between particles can be described by starting from a free field which describes the incoming and outgoing particles, and including an interaction Hamiltonian to describe how the particles deflect one another.
When these tiny magnetic dipoles are aligned in the same direction, their individual magnetic fields add together to create a measurable macroscopic field.
When the temperature rises beyond a certain point, called the Curie temperature, there is a second-order phase transition and the system can no longer maintain a spontaneous magnetization, although it still responds paramagnetically to an external field.
When they first met, he was standing on his head in a field.
When and represents
When a word represents a larger construction of which it is the only expressed part, it normally has more stress than it would have in fully expressed construction.
When go represents itself and a complement ( being equivalent, say, to go to Martinique ) in which boat did Jack go on??
Bruce Hindmarsh suggests that the secular popularity of " Amazing Grace " is due to the absence of any mention of God in the lyrics until the fourth verse ( by Excell's version, the fourth verse begins " When we've been there ten thousand years "), and that the song represents the ability of humanity to transform itself instead of a transformation taking place at the hands of God.
When particles in a beam are thrown against a foil made of a certain substance, the cross section is a hypothetical area measure around the target particles of the substance ( usually its atoms ) that represents a surface.
When used to represent carried traffic, a value ( which can be a non-integer such as 43. 5 ) followed by “ erlangs ” represents the average number of concurrent calls carried by the circuits ( or other service-providing elements ), where that average is calculated over some reasonable period of time.
When used to describe offered traffic, a value followed by “ erlangs ” represents the average number of concurrent calls that would have been carried if there were an unlimited number of circuits ( that is, if the call-attempts that were made when all circuits were in use had not been rejected ).
When it is shown with a royal crown it represents the County Administrative Board.
When compared with previous generations, Generation X represents a more heterogeneous generation, exhibiting great variety of diversity in such aspects as race, class, religion, ethnicity, and sexual orientation.
" When the narrator is separated from Ruth, with whom he has fallen in love, he is free to explore other sexual ( and religious ) possibilities before deciding at the end of the poem to participate in the ritualistic order marriage represents.
When playing for money, each point generally represents a common money unit.
When associated with Carolyn, the rose represents a " façade for suburban success ".
When the independent variable x represents time ( with SI unit of seconds ), the transform variable ξ represents frequency ( in hertz ).
In the 1983 " Liber Hymnarius " from Solesmes, it is stated that, " When an ordinary syllable is set to one note, this represents the fundamental rhythmic value used in Gregorian chant ( i. e. valor syllabicus medius ).
When the velocity is zero, the energy expressed above is not zero, and represents the rest energy:
When he introduced the notion of secondary average, it was as a vehicle for the then-counterintuitive concept that batting average represents only a fraction of a player's offensive contribution.
When the uncertainty represents the standard error of the measurement, then about 68. 2 % of the time, the true value of the measured quantity falls within the stated uncertainty range.
When it is shown with a royal crown it represents the County Administrative Board.
When it is shown with a royal crown it represents the County Administrative Board.
When the concept of financial capital maintenance is defined in terms of constant purchasing power units, profit represents the increase in invested purchasing power over the period.
When it is shown with a royal crown it represents the County Administrative Board.
When it is shown with a royal crown it represents the County Administrative Board.
When the arms is shown with a royal crown it represents the County Administrative Board, which is the regional presence of ( royal ) government authority.
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