If a source emits a known luminous intensity I < sub > v </ sub > ( in candelas ) in a well-defined cone, the total luminous flux Φ < sub > v </ sub > in lumens is given by

If the source emits light uniformly in all directions, the flux can be found by multiplying the intensity by 4π: a uniform 1 candela source emits 12. 6 lumens.

If the combustion takes place using air as the oxygen source, the nitrogen can be added to the equation, as and although it does not react, to show the composition of the flue gas:

If the glass is cooled quickly in the absence of a strong light source by putting ice on the glass or placing it in the freezer with the door almost closed, it turns backwards ( i. e. the silver sides trail ).

If the divergence is nonzero at some point then there must be a source or sink at that position.

If the source is located at an arbitrary source point, denoted by the vector and the field point is located at the point, then we may represent the scalar Green's function ( for arbitrary source location ) as:

If waves are emitted from an extended source, this can lead to incoherence in the transversal direction.

If the observer is at a lower gravitational potential than the source, a gravitational blueshift can be observed instead.

If the depletion region expands to completely close the channel, the resistance of the channel from source to drain becomes large, and the FET is effectively turned off like a switch.

If drain-to-source voltage is increased, this creates a significant asymmetrical change in the shape of the channel due to a gradient of voltage potential from source to drain.

If drain-to-source voltage is increased further, the pinch-off point of the channel begins to move away from the drain towards the source.

If a laser is swept across a distant object, the spot of laser light can easily be made to move across the object at a speed greater than c. Similarly, a shadow projected onto a distant object can be made to move across the object faster than c. In neither case does the light travel from the source to the object faster than c, nor does any information travel faster than light.

If f is an element of G ( x, y ) then x is called the source of f, written s ( f ), and y the target of f ( written t ( f )).

If the DNA is to be used after separation on the agarose gel, it is best to avoid exposure to UV light by using a blue light excitation source such as the XcitaBlue UV to blue light conversion screen from Bio-Rad or Dark Reader from Clare Chemicals.

If the political situation stabilizes, high crime levels wane, and new investment increases, tourism could take its place next to export-oriented manufacturing ( the assembly sector ) as a potential source of foreign exchange.

If an inductor is connected to a direct current source with value I via a resistance R, and then the current source is short-circuited, the differential relationship above shows that the current through the inductor will discharge with an exponential decay:

If the resulting TTL is 0, the packet is discarded and an ICMP Time To Live exceeded in transit message is sent to the datagram's source address.

If this process is the source of our feelings about justice, that ought to undermine our confidence in them.

If one considers a small fluorescent light source ( essentially a bright spot ), light coming from this spot spreads out the further out of focus one is.

If a clot is large enough to block one or both femoral arteries, there may be hind leg paralysis because the major source of blood flow to the hind leg is blocked.

If Φ is a unital positive map, then for every normal element a in its domain, we have Φ ( a * a ) ≥ Φ ( a *) Φ ( a ) and Φ ( a * a ) ≥ Φ ( a ) Φ ( a *).

If one is given an object L of C together with a natural isomorphism Φ: Hom (–, L ) → Cone (–, F ), the object L will be a limit of F with the limiting cone given by Φ < sub > L </ sub >( id < sub > L </ sub >).

If S is a commutative associative algebra over R, if I is an ideal of S such that the I-adic topology on S is complete, and if x is an element of I, then there is a unique Φ: R < nowiki ></ nowiki > X < nowiki ></ nowiki > → S with the following properties:

If S is a commutative associative algebra over R, if I is an ideal of S such that the I-adic topology on S is complete, and if x < sub > 1 </ sub >, ..., x < sub > r </ sub > are elements of I, then there is a unique Φ: R < nowiki ></ nowiki > X < sub > 1 </ sub >, ..., X < sub > n </ sub >< nowiki ></ nowiki > → S with the following properties:

If the system attenuates it by a factor x and phase shifts it by − Φ the signal out of the system will be ( A / x ) sin ( ωt − Φ ).

If Φ is a complete set, i. e., an orthonormal basis of the space of all square-integrable functions on b, as opposed to a smaller orthonormal set,

If Φ is a complete set,

# ( Integrality condition ) If α and β are roots in Φ, then the projection of β onto the line through α is a half-integral multiple of α.

If T is a statistic that is approximately normally distributed under the null hypothesis, the next step in performing a Z-test is to estimate the expected value θ of T under the null hypothesis, and then obtain an estimate s of the standard deviation of T. We then calculate the standard score Z = ( T − θ ) / s, from which one-tailed and two-tailed p-values can be calculated as Φ (−| Z |) and 2Φ (−| Z |), respectively, where Φ is the standard normal cumulative distribution function.

) If a variable is not live, the result of the Φ function cannot be used and the assignment by the Φ function is dead.

If the original variable name isn't live at the Φ function insertion point, the Φ function isn't inserted.

If we define r < sub > i </ sub > as the displacement of particle i from the center of mass, and v < sub > i </ sub > as the velocity of particle i with respect to the center of mass, then we have

If the exponent r is even, then the inequality is valid for all real numbers x.

If the relative priorities of these substituents need to be established, R takes priority over S. When this happens, the descriptor of the stereocenter is a lowercase letter ( r or s ) instead of the uppercase letter normally used.

If u ( t ) is the control signal sent to the system, y ( t ) is the measured output and r ( t ) is the desired output, and tracking error, a PID controller has the general form

If the weight of the roadway per unit length is w and the weight of the cable and the wire supporting the bridge is negligible in comparison, then the weight on the cable from c to r is wx where x is the horizontal distance between c to r. Proceeding as before gives the differential equation

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.

If it is generally by temporary uninhabitability, for example a nuclear winter, then n < sub > r </ sub > may be relatively high.

*( EF1 ) If a and b are in R and b is nonzero, then there are q and r in R such that and either r = 0 or.

If r represents an arbitrary element of R, f can be viewed as a right R-homomorphism so that, or f can also be viewed as a left R module homomorphism, where.

Thus the set of all polynomials with coefficients in the ring R forms itself a ring, the ring of polynomials over R, which is denoted by R. The map from R to R sending r to rX < sup > 0 </ sup > is an injective homomorphism of rings, by which R is viewed as a subring of R. If R is commutative, then R is an algebra over R.

If R is an integral domain and f and g are polynomials in R, it is said that f divides g or f is a divisor of g if there exists a polynomial q in R such that f q = g. One can show that every zero gives rise to a linear divisor, or more formally, if f is a polynomial in R and r is an element of R such that f ( r ) = 0, then the polynomial ( X − r ) divides f. The converse is also true.

If F is a field and f and g are polynomials in F with g ≠ 0, then there exist unique polynomials q and r in F with

If a root r < sub > 1 </ sub >

If an object moves with angular velocity ω around a circle of radius r centered at the origin of the x-y plane, then its motion along each coordinate is simple harmonic motion with amplitude r and angular frequency ω.

Consider now the acceleration due to the sphere of mass M experienced by a particle in the vicinity of the body of mass m. With R as the distance from the center of M to the center of m, let ∆ r be the ( relatively small ) distance of the particle from the center of the body of mass m. For simplicity, distances are first considered only in the direction pointing towards or away from the sphere of mass M. If the body of mass m is itself a sphere of radius ∆ r, then the new particle considered may be located on its surface, at a distance ( R ± ∆ r ) from the centre of the sphere of mass M, and ∆ r may be taken as positive where the particle's distance from M is greater than R. Leaving aside whatever gravitational acceleration may be experienced by the particle towards m on account of ms own mass, we have the acceleration on the particle due to gravitational force towards M as: