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 of Φ ( r ) is a dipole, as it is assumed here, this term is the only non-vanishing term in the multipole expansion of Φ ( r ).

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 the circumstances are faced frankly it is not reasonable to expect this to be true.

If his dancers are sometimes made to look as if they might be creatures from Mars, this is consistent with his intention of placing them in the orbit of another world, a world in which they are freed of their pedestrian identities.

If a work is divided into several large segments, a last-minute drawing of random numbers may determine the order of the segments for any particular performance.

If they avoid the use of the pungent, outlawed four-letter word it is because it is taboo ; ;

If Wilhelm Reich is the Moses who has led them out of the Egypt of sexual slavery, Dylan Thomas is the poet who offers them the Dionysian dialectic of justification for their indulgence in liquor, marijuana, sex, and jazz.

If he is the child of nothingness, if he is the predestined victim of an age of atomic wars, then he will consult only his own organic needs and go beyond good and evil.

If it is an honest feeling, then why should she not yield to it??

If he thus achieves a lyrical, dreamlike, drugged intensity, he pays the price for his indulgence by producing work -- Allen Ginsberg's `` Howl '' is a striking example of this tendency -- that is disoriented, Dionysian but without depth and without Apollonian control.

If love reflects the nature of man, as Ortega Y Gasset believes, if the person in love betrays decisively what he is by his behavior in love, then the writers of the beat generation are creating a new literary genre.

If he is good, he may not be legal ; ;

If the man on the sidewalk is surprised at this question, it has served as an exclamation.

If the existent form is to be retained new factors that reinforce it must be introduced into the situation.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

If many of the characters in contemporary novels appear to be the bloodless relations of characters in a case history it is because the novelist is often forgetful today that those things that we call character manifest themselves in surface behavior, that the ego is still the executive agency of personality, and that all we know of personality must be discerned through the ego.

If he is a traditionalist, he is an eclectic traditionalist.

If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.

If to be innocent is to be helpless, then I had been -- as are we all -- helpless at the start.

If R is commutative, then one can associate to every polynomial P in R, a polynomial function f with domain and range equal to R ( more generally one can take domain and range to be the same unital associative algebra over R ).

If is an identity element of ( i. e., S is a unital magma ) and, then is called a left inverse of and is called a right inverse of.

* If R is a unital commutative ring with an ideal m, then k = R / m is a field if and only if m is a maximal ideal.

If e < sub > 1 </ sub >, ... e < sub > d </ sub > is a basis of V, the unital zero algebra is the quotient of the polynomial ring k ..., E < sub > n </ sub > by the ideal generated by the E < sub > i </ sub > E < sub > j </ sub > for every pair ( i, j ).

If A and B are two unital algebras, then an algebra homomorphism is said to be unital if it maps the unity of A to the unity of B.

If the associative algebra A over the field K is not unital, one can adjoin an identity element as follows: take A × K as underlying K-vector space and define multiplication * by

If T is a fixed n by n matrix then the set of all polynomials in T and the identity operator forms a unital operator algebra.

If is a unital ring, we denote by the group of invertible-by-matrices with elements in.

If the algebra is not unital, it may be made so in a standard way ( see the adjoint functors page ); there is no essential difference between modules for the resulting unital ring, in which the identity acts by the identity mapping, and representations of the algebra.

If A is unital, then D ( 1 )

If is equipped with a nonsingular real symmetric bilinear form instead, the unital *- algebra generated by the elements of subject to the relations

If is unital, then ∂( 1 )