This enables a convenient choice of a coordinate system to be made, called comoving coordinates.

By a proper choice of coordinate system, the ellipse can be described by the canonical implicit equation

However, the unified nature of spacetime and the freedom of coordinate choice it allows imply that to express the temporal coordinate in one coordinate system requires both temporal and spatial coordinates in another coordinate system.

This choice is arbitrary, and is part of the coordinate system's definition.

Because they express a relationship between vectors, tensors themselves must be independent of a particular choice of coordinate system.

The choice of a coordinate system doesn't affect the properties of a vector or its behaviour under transformations.

Each coordinate system is named for its choice of fundamental plane.

Once a time coordinate is defined, the three-dimensional space corresponding to a particular time is generally a curved Riemannian manifold ; but since the time coordinate choice is largely arbitrary, it is the underlying space-time curvature that is physically significant.

The values of the coordinate vectors of points vary with the choice of coordinate frame, however the relative position vector between a pair of points has the same length no matter what coordinate frame is used and is said to be frame invariant.

In this article the term observational frame of reference is used when emphasis is upon the state of motion rather than upon the coordinate choice or the character of the observations or observational apparatus.

* A coordinate system is a mathematical concept, amounting to a choice of language used to describe observations .< ref name

Comoving coordinates are an example of such a natural coordinate choice.

This is a particularly unfortunate choice as it leads to confusion with the notion of a complex structure, which often has the same coordinate expression as Ω but represents a very different structure.

This list of numbers depends on the choice of coordinate system.

The choice of basis f on the vector space V defines uniquely a set of coordinate functions on V, by means of

In particular, if v = e < sub > j </ sub > is the jth coordinate vector then ∂< sub > v </ sub > f is the partial derivative of f with respect to the jth coordinate function, i. e., ∂ f / ∂ x < sup > j </ sup >, where x < sup > 1 </ sup >, x < sup > 2 </ sup >, ... x < sup > n </ sup > are the coordinate functions on U. By their very definition, partial derivatives depend upon the choice of coordinates: if new coordinates y < sup > 1 </ sup >, y < sup > 2 </ sup >, ... y < sup > n </ sup > are introduced, then

In a media interview, Nhu said that if the Buddhist crisis was not resolved, he would stage a coup, quickly demolish the Xá Lợi pagoda, where the Buddhists were massing to coordinate their activities, and head a new anti-Buddhist government.

Even on many international issues beyond western Europe, Spain prefers to coordinate its efforts with its EU partners through the European political cooperation mechanisms.

Ground rules in relationships allow partners to coordinate their behaviors so they achieve shared goals with fewer conflicts.

In a JavaSpace, all communication partners ( peers ) communicate and coordinate by sharing state.

The organization seeks to bring together community partners to coordinate social, health and community services advocate for change in government policies and systems, and generally work for greater community involvement and community-based decision making.

The council also serves to coordinate social and cultural policies of the participating countries and has promoted increased cooperation in many fields.

After Domengeaux's death in 1988, CODOFIL continued to coordinate French education in Louisiana's public schools, and to serve as a cultural watchdog group.

* OKIE ( Oklahoma Israel Exchange ) is an independent non-profit organization established to coordinate economic and cultural activities between the state of Oklahoma and the state of Israel.

The Australian Centre for Egyptology ( ACE ) is an umbrella organisation established in 1989 by Macquarie University, Sydney, Australia, in order both to coordinate Australian excavation efforts in Egypt with the Egyptian Supreme Council of Antiquities ( SCA ), and to promote Egyptology within the Australian cultural landscape.

While the organization retained its staunch supporters in the Narkompros apparatus seeking to coordinate activities, it also contained no small number of activists like Alexander Bogdanov who tried to promote the organization as an independent cultural institution with a homogeneous working class constituency.

The EIRP is used to estimate the service area of the transmitter, and to coordinate transmitters on the same frequency so that their coverage areas do not overlap.

" Follow-up " groups often coordinate telescopes around the world to provide intensive coverage of select events.

Kaplan was appointed Senior Vice President after he was brought back to ABC News to coordinate the network ’ s control room production and news coverage of America ’ s War with Iraq.

This was confirmed in a 1975 study commissioned by CCG and led to the Canadian Marine Rescue Auxiliary or CMRA being formed in late 1978 as a non-profit organization in an effort to enhance search and rescue coverage and capability, and to better coordinate volunteer efforts.

His application of reference lines, a diameter and a tangent is essentially no different than our modern use of a coordinate frame, where the distances measured along the diameter from the point of tangency are the abscissas, and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates.

While their coordinate distance ( comoving distance ) remains constant, the physical distance between two such comoving points expands proportionally with the scale factor of the Universe.

where are the direction cosines between the material and spatial coordinate systems with unit vectors and, respectively.

The two integers a and b are coprime if and only if the point with coordinates ( a, b ) in a Cartesian coordinate system is " visible " from the origin ( 0, 0 ), in the sense that there is no point with integer coordinates between the origin and ( a, b ).

Coordination refers to the " coordinate covalent bonds " ( dipolar bonds ) between the ligands and the central atom.

The coordinate transformation between these two systems is described to good approximation by ( apparent ) sidereal time, which takes into account variations in the Earth's axial rotation ( length-of-day variations ).

This may involve transformations between or among astronomical and terrestrial coordinate systems.

Consistent with the symmetry of the hyperbola, if the transverse axis is aligned with the x-axis of a Cartesian coordinate system, the slopes of the asymptotes are equal in magnitude but opposite in sign, ±, where b = a × tan ( θ ) and where θ is the angle between the transverse axis and either asymptote.

: The point-slope form expresses the fact that the difference in the y coordinate between two points on a line ( that is, y − y < sub > 1 </ sub >) is proportional to the difference in the x coordinate ( that is, x − x < sub > 1 </ sub >).

A symmetric presentation between the forward Lorentz Transformation and the inverse Lorentz Transformation can be achieved if coordinate systems are in symmetric configuration.

In the equatorial coordinate system, the right ascension coordinates of these borders lie between and, while the declination coordinates are between − 27. 45 ° and − 45. 09 °.

The Central Security Service is a co-located agency created to coordinate intelligence activities and co-operation between NSA and other U. S. military cryptanalysis agencies.

The nervous system is an organ system containing a network of specialized cells called neurons that coordinate the actions of an animal and transmit signals between different parts of its body.

In the equatorial coordinate system, the right ascension coordinates of these borders lie between and, while the declination coordinates are between-24. 83 ° and-36. 46 °.

In rebuilding a war torn nation's infrastructure, for example, a private firm would, in order to provide security, either have to hire security, which would be both necessarily limited and complicate their functions, or coordinate with government, which, due to a lack of command structure shared between firm and government, might be difficult.

In Method of Fluxions ( written 1671, published 1736 ), Sir Isaac Newton examined the transformations between polar coordinates, which he referred to as the " Seventh Manner ; For Spirals ", and nine other coordinate systems.

The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.

In the equatorial coordinate system, the right ascension coordinates of these borders lie between and, while the declination coordinates are between – 56. 31 ° and-75. 35 °.

In the equatorial coordinate system, the right ascension coordinates of these borders lie between and, while the declination coordinates are between-60. 26 ° and-70. 51 °.

In the equatorial coordinate system, the right ascension coordinates of these borders lie between and, while the declination coordinates are between − 45. 09 ° and − 56. 98 °.