If the orientation of the tangent relative to some starting position is θ ( s ), then ρ ( s ) is defined by the derivative dθ / ds:

If 0 < ρ <∞, one can also define the type:

* If G is a topological group and V is a topological vector space, a continuous representation of G on V is a representation ρ such that the application defined by is continuous.

If the fluid being measured is significantly dense, hydrostatic corrections may have to be made for the height between the moving surface of the manometer working fluid and the location where the pressure measurement is desired except when measuring differential pressure of a fluid ( for example across an orifice plate or venturi ), in which case the density ρ should be corrected by subtracting the density of the fluid being measured.

If the surfaces are approximated by a finite number of planar patches, each of which is taken to have a constant radiosity B < sub > i </ sub > and reflectivity ρ < sub > i </ sub >, the above equation gives the discrete radiosity equation,

If we have a probability distribution, ρ, then ( since the phase space velocity () has zero divergence, and probability is conserved ) its convective derivative can be shown to be zero and so

:( Note: If the fluid in question is seawater, it will not have the same density ( ρ ) at every location.

If L is a real Lie algebra and ρ: L × V → V is a complex representation of it, we can construct another representation of L called its dual representation as follows.

If ρ is the charge density within some region Ω, the potential Φ must satisfy the equation

If J, P and ρ are zero, the result is:

where | x − r | is the distance between the points x and r. If there is a function ρ ( r ) representing the density of the distribution at r, so that, where dv ( r ) is the Euclidean volume element, then the gravitational potential is the volume integral

If V is a potential function coming from a continuous mass distribution ρ ( r ), then ρ can be recovered using the Laplace operator Δ using the formula:

If ρ is a real ( or pseudoreal ) representation, taking the real component is redundant, because even if the orientation of a Wilson loop is flipped, its contribution to the action remains unchanged.

If Mr. Möller's assumptions are correct, the LM-105 would have a supersonic range of ≈ 2000 m ( 2200 yd ) at a muzzle velocity of 915 m / s ( 3, 002 ft / s ) under International Standard Atmosphere sea level conditions ( air density ρ = 1. 225 kg / m < sup > 3 </ sup >).

If Mr. Möller's design assumptions are correct the LM-107 projectile with a calculated G1 BC of 1. 02 will offer a supersonic range of ≈ 2170 m ( 2373 yd ) at a muzzle velocity of 909 m / s ( 2982 ft / s ) under International Standard Atmosphere sea level conditions ( air density ρ

If G is not itself a Lie group, there must be a kernel to ρ.

If A is an algebra with the product operation, and is a representation of H on A, then ρ is said to be a representation of H on an algebra if μ is H-equivariant.

If ρ is an n-dimensional irreducible representation of G with the underlying vector space V, then we can define a G × G morphism of representations, for all g in G and x in V

If is a Lie algebra and ρ is a representation of it over the vector space V, then the dual representation is defined over the dual vector space as follows:

If is a real Lie algebra and ρ is a representation of it over the vector space V, then the conjugate representation ρ * is defined over the conjugate vector space V * as follows:

If we have an axially symmetric function f ( ρ, z )

If | B |< A, then ρ ( B )≤ ρ ( A ).

If the weight is suspended off the seabed it acts as a spring or shock absorber to dampen the sudden actions that are normally transmitted to the anchor and can cause it to dislodge and drag.

If a similar ball is charged by the same glass rod, it is found to repel the first: the charge acts to force the two balls apart.

If buried where the earth is very cold, the earth acts like a refrigerator.

If the group G acts on the set X, then we can form the action groupoid representing this group action as follows:

If the federal government assumed such powers, its acts could be declared unconstitutional by the states.

# If G is any group acting smoothly on the manifold M, then it acts on the vector fields, and the vector space of vector fields fixed by the group is closed under the Lie bracket and therefore also forms a Lie algebra.

If it lapses, the legal basis for enforcing discipline disappears, and soldiers lose their legal indemnity for acts committed under orders.

" If certain acts of violation of treaties are crimes, they are crimes whether the United States does them or whether Germany does them, and we are not prepared to lay down a rule of criminal conduct against others which we would not be willing to have invoked against us ... We must never forget that the record on which we judge these defendants is the record on which history will judge us tomorrow.

Psychological egoism has been accused of being circular: " If a person willingly performs an act, that means he derives personal enjoyment from it ; therefore, people only perform acts that give them personal enjoyment.

If a judge acts against precedent and the case is not appealed, the decision will stand.

If Bob bets $ 10 ( half the pot ), when his opponent acts, the pot will be $ 30 and it will cost $ 10 to call.

If the idea of absolute freedom and entire self-knowledge is absent from this kind of idea of God's acts in time, then God Himself is ( to express the idea anthropomorphically ) becoming something new, or discovering something new about Himself with each new moment, just as we are.

If a person occupies land for the required period of time as set out in provincial limitation acts and, during that time, no legal action is taken to evict or in trespass, the ownership in the land goes from the legal owner to the squatter.

If the center of gravity exists within the foundations, the body is stable since no net torque acts on the body.

If the drain is opened and the tumbler is kept in position over the hole, the water in the tumbler drains out leaving the glass filled with air, and this then acts as the plug.

For example, in a negative feedback loop, the transcription factor acts as its own repressor: If the transcription factor protein binds the DNA of its own gene, it will down-regulate the production of more of itself.

# Lubrication: ( for intercourse or used daily to minimize irritation ) If you have problems with yeast, or are worried you will, avoid lubricants with glycerine in them, which acts like a sugar and will only add to your problems.

If the Senate or a later emperor did not like the acts of an individual, they could have his property seized, his name erased and his statues reworked.

" If the Emperor, has no more of mercy in his heart than he reveals in his policies, then I pity Russia ; if, on the other hand, his true sentiments are really superior to his acts, then I pity the Emperor.

If water gets between the friction surfaces and the drum, it acts as a lubricant and reduces braking efficiency.

If, then he should change about, wrong the people, maim its power, and rob it of the privilege of voting, he has by his own acts deprived himself of his honourable office by not fulfilling the conditions on which he received it ; for otherwise there would be no interference with a tribune even though he should try to demolish the Capitol or set fire to the naval arsenal.

If two players have the same high upcard, the one first in clockwise rotation from the dealer acts first.

If Alice just has two pair and Ted acts strongly, Alice may think Ted has three fours and fold if she doesn't improve.

If only two terminals are used, one end and the wiper, it acts as a variable resistor or rheostat.