Angular momentum in terms of scalar and vector components.

In physics, basis vectors allow any vector to be represented geometrically using angles and lengths, in different directions, i. e. in terms of the spatial orientations.

The curl of a vector field F, denoted by curl F or ∇ × F, at a point is defined in terms of its projection onto various lines through the point.

The direction and magnitude of such distortion is expressed in terms of a Burgers vector ( b ).

In vector calculus, divergence is a vector operator that measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar.

In physical terms, the divergence of a three dimensional vector field is the extent to which the vector field flow behaves like a source or a sink at a given point.

( Note that we are imagining the vector field to be like the velocity vector field of a fluid ( in motion ) when we use the terms flow, sink and so on.

The source-free part, B, can be similarly written: one only has to replace the scalar potential Φ ( r ) by a vector potential A ( r ) and the terms −∇ Φ by +∇× A, and finally the source-density

The transform is sometimes denoted by the symbol, as in or or < ref group =" note "> As a linear transformation on a finite-dimensional vector space, the DFT expression can also be written in terms of a DFT matrix ; when scaled appropriately it becomes a unitary matrix and the X < sub > k </ sub > can thus be viewed as coefficients of x in an orthonormal basis .</ ref >

In the following discussion the terms " sequence " and " vector " will be considered interchangeable.

As the electric field is defined in terms of force, and force is a vector, so it follows that an electric field is also a vector, having both magnitude and direction.

In technical terms, they are vector gauge bosons that mediate strong interactions of quarks in quantum chromodynamics ( QCD ).

In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces ; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.

The blue and orange vectors are the elements of the basis ; the green vector can be given in terms of the basis vectors, and so is linearly dependent upon them.

In terms of vector spaces, an operator is a mapping from one vector space or module to another.

Oliver Heaviside FRS ( ( 18 May 1850 – 3 February 1925 ) was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations ( later found to be equivalent to Laplace transforms ), reformulated Maxwell's field equations in terms of electric and magnetic forces and energy flux, and independently co-formulated vector analysis.

The components of a vector can respond in two distinct ways to a change of basis ( see covariance and contravariance of vectors ), where the new basis vectors are expressed in terms of the old basis vectors as,

In terms of these, any vector a in can be expressed in the form:

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

What we have left as reasonably comparable are four classes: ( 1 ) body parts and products, which with a proportionally nearly even representation ( 51 terms out of 253, 25 out of 100 ) come out with nearly even ratios ; ;

1 ) Every age rewrites the events of its history in terms of what should have been, creating legends about itself that rationalize contemporary beliefs and excuse contemporary actions.

Exports from producing countries in terms of equivalent oil were a little more than 1 million tons, about half of which was palm kernels or oil from them and about half was palm oil.

The practical definition may lead to confusion with the definition of a coulomb ( i. e., 1 amp-second ), but in practical terms this means that measures of a constant current ( e. g., the nominal flow of charge per second through a simple circuit ) will be defined in amperes ( e. g., " a 20 mA circuit ") and the flow of charge through a circuit over a period of time will be defined in coulombs ( e. g., " a variable-current circuit that flows a total of 10 coulombs over 5 seconds ").

He reprised resolutions for constitutional amendments to provide for 1 ) the direct election of the president, rather than by the electoral college, 2 ) the direct election of U. S. Senators, rather than by state legislatures and 3 ) the limiting of judges ' terms to twelve years.

The terms of the Artistic License 1. 0 were at issue in a 2007 federal district court decision in the US which was criticized by some for suggesting that FOSS-like licenses could only be enforced through contract law rather than through copyright law, in contexts where contract damages would be difficult to establish.

When Alaska Natives enrolled in their regional corporations under the terms of the Alaska Native Claims Settlement Act of 1971 ( ANCSA ), the Aleut Corporation attracted only about 2, 000 enrolees who could prove a blood quantum of 1 / 4 or more Alaska Native ( including Aleut ).

The Boltzmann distribution is often expressed in terms of β = 1 / kT where β is referred to as thermodynamic beta.

Under the terms of the Bank of England Act 1998 ( which came into force on 1 June 1998 ), the bank's Monetary Policy Committee was given sole responsibility for setting interest rates to meet the Government's stated Retail Prices Index ( RPI ) inflation target of 2. 5 %.

( The Taylor series indicates that − J < sub > 1 </ sub >( x ) is the derivative of J < sub > 0 </ sub >( x ), much like − sin x is the derivative of cos x ; more generally, the derivative of J < sub > n </ sub >( x ) can be expressed in terms of J < sub > n ± 1 </ sub >( x ) by the identities below.

In 1927, the International Conference on Weights and Measures redefined the meter in terms of a red cadmium spectral line ( 1 m = 1, 553, 164. 13 wavelengths ).

For instance, the odd-numbered terms of the sequence get arbitrarily close to 0, while the even-numbered ones get arbitrarily close to 1.

Carl Philipp Gottfried von Clausewitz (; July 1, 1780 – November 16, 1831 ) was a Prussian soldier and military theorist who stressed the moral ( in modern terms, " psychological ") and political aspects of war.

Gauss's presumed method was to realize that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050.

If at most one of the two terms in ( 2 ) is infinite, then ( 1 ) is the same as ( 2 ).

If F ( r ) represents gravity, it is a negative term proportional to 1 / r < sup > 2 </ sup >, so the net acceleration in r in the rotating frame depends on a difference of reciprocal square and reciprocal cube terms, which are in balance in a circular orbit but otherwise typically not.

Consequently, the traditional usage of the terms is based on the orbit ’ s semi-major axis, and includes objects situated between the 2: 3 and 1: 2 resonances, that is between 39. 4 and 47. 8 AU ( with exclusion of these resonances and the minor ones in-between ).

But while Eisenhower argued with Roosevelt and Churchill, who both insisted on unconditional terms of surrender in exchange for helping the Italians, the Germans pursued an aggressive buildup of forces in the country – making the job more difficult, by adding 19 divisions and initially outnumbering the Allied forces 2 to 1, Nevertheless, the invasion of Italy was highly successful.

The dipole term is the dominant one at large distances: Its field falls off in proportion to 1 / r < sup > 3 </ sup >, as compared to 1 / r < sup > 4 </ sup > for the next ( quadrupole ) term and higher powers of 1 / r for higher terms, or 1 / r < sup > 2 </ sup > for the monopole term.

Equivalently, the determinant can be expressed as a sum of products of entries of the matrix where each product has n terms and the coefficient of each product is − 1 or 1 or 0 according to a given rule: it is a polynomial expression of the matrix entries.

For example, it was acceptable for a loan of 1000 gold dinars to be paid back as 1050 dinars of equal aggregate weight ( i. e., the value in terms of weight had to be same because all makes of coins did not carry exactly similar weight )...

' In geometric terms, the eternal triangle can be represented as comprising three points-a jealous mate ( A ) in a relationship with an unfaithful partner ( B ) who has a lover ( C )... A feels abandoned, B is between two mates, and C is a catalyst for crisis in the union A-B '.