If X is Cauchy distributed with median μ and scale parameter γ, then the complex variable

If is a wrapped Cauchy distribution with the parameter representing the parameters of the corresponding " unwrapped " Cauchy distribution in the variable y where, then

If the parameter is the bull's-eye of a target, and the arrows are estimates, then a relatively high variance means the arrows are dispersed, and a relatively low variance means the arrows are clustered.

If the parameter is the bull's-eye of a target, and the arrows are estimates, then a relatively high absolute value for the bias means the average position of the arrows is off-target, and a relatively low absolute bias means the average position of the arrows is on target.

* If a pure function is called with parameters that cause no side-effects, the result is constant with respect to that parameter list ( sometimes called referential transparency ), i. e. if the pure function is again called with the same parameters, the same result will be returned ( this can enable caching optimizations such as memoization ).

If no value of the rotation parameter is successful and theory is not within observational error, a modification of physical law is considered.

If parameter e is smaller than one, e is the eccentricity and a the semi-major axis of an ellipse.

If we do not alter the system, then the parameter λ is unchanged from measurement to measurement ; if, on the other hand, we modulate the system by replacing the sample with a more radioactive one, then the parameter λ would increase.

If the parameter " dopefish " is added to the executable, a sample of burping is heard and Scott's Mystical Head is seen spinning in circles on the screen.

If the transmission line is uniform along its length, then its behaviour is largely described by a single parameter called the characteristic impedance, symbol Z < sub > 0 </ sub >.

( If the object represents a static field then the parameter is ignored and may be.

( If the object represents a static method then the first parameter is ignored and may be.

Based on Ginzburg – Landau theory, the free energy of a ferroelectric material, in the absence of an electric field and applied stress may be written as a Taylor expansion in terms of the order parameter, P. If a sixth order expansion is used ( i. e. 8th order and higher terms truncated ), the free energy is given by:

If a probability distribution depends on a parameter, one may on the one hand consider — for a given value of the parameter — the probability ( density ) of the different outcomes, and on the other hand consider — for a given outcome — the probability ( density ) this outcome has occurred for different values of the parameter.

If the output is considered as undefined if a parameter is undefined then < tt > pow ( 1, qNaN )</ tt > should produce a qNaN.

If a Gaussian proposal density is used the variance parameter has to be tuned during the burn-in period.

If we use primes for derivatives with respect to parameter t, then

If the true value of the cosmological curvature parameter is larger than 10 < sup >− 3 </ sup > we will be able to distinguish between these three models even now.

If X is a zeta-distributed random variable with parameter s, then the probability that X takes the integer value k is given by the probability mass function

If this rotation parameter were real, it would be possible for a 180 ° rotation to reverse the direction of time and of z.

* If then has a Bernoulli distribution with parameter.

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 T is the total `` length '' of the process, its feed state may be denoted by a vector p(T) and the product state by p(Q).

If K is a number field, its ring of integers is the subring of algebraic integers in K, and is frequently denoted as O < sub > K </ sub >.

If X and Y are Banach spaces over the same ground field K, the set of all continuous K-linear maps T: X → Y is denoted by B ( X, Y ).

If the sets A and B are equal, this is denoted symbolically as A = B ( as usual ).

If F is clear from context then Ω < sub > F </ sub > may be denoted simply Ω, although different prefix-free universal computable functions lead to different values of Ω.

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 X is a set with an equivalence relation denoted by infix, then a groupoid " representing " this equivalence relation can be formed as follows:

If E / F is a Galois extension, then Aut ( E / F ) is called the Galois group of ( the extension ) E over F, and is usually denoted by Gal ( E / F ).

If the former, the stitch is denoted as a knit stitch or a plain stitch ; if the latter, as a purl stitch.

In arithmetic and number theory, the least common multiple ( also called the lowest common multiple or smallest common multiple ) of two integers a and b, usually denoted by LCM ( a, b ), is the smallest positive integer that is divisible by both a and b. If either a or b is 0, LCM ( a, b ) is defined to be zero.

If " this statement is false " is denoted by A and its truth value is being sought, it is necessary to find a condition that restricts the choice of possible truth values of A.

If one wishes to employ the notation for a different purpose ( such as denoting open intervals on the real number line ) the ordered pair may be denoted by the variant notation

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 n = 2k + 1, then the action of the unit vector u on the left ideal decomposes the space into a pair of isomorphic irreducible eigenspaces ( both denoted by Δ ), corresponding to the respective eigenvalues + 1 and − 1.

If an index transforms like a vector with the inverse of the basis transformation, it is called contravariant and is traditionally denoted with an upper index, while an index that transforms with the basis transformation itself is called covariant and is denoted with a lower index.

If the vector represents a directed distance or displacement from a point A to a point B ( see figure ), it can also be denoted as or < u > AB </ u >.

If a diagram F: J → C has a limit in C, denoted by lim F, there is a canonical isomorphism

In analysis the infimum or greatest lower bound of a subset S of real numbers is denoted by inf ( S ) and is defined to be the biggest real number that is smaller than or equal to every number in S. If no such number exists ( because S is not bounded below ), then we define inf ( S ) = −∞.

If M is an Hermitian positive-semidefinite matrix, one sometimes writes M ≥ 0 and if M is positive-definite one writes M > 0 .< ref > This may be confusing, as sometimes nonnegative matrices are also denoted in this way.

If a universe U is defined, then the relative complement of A in U is called the absolute complement ( or simply complement ) of A, and is denoted by A < sup > c </ sup > or sometimes A ′, also the same set often is denoted by < MATH >

If I is an index set and X < sub > I </ sub > is the set of indeterminates X < sub > i </ sub > for i ∈ I, then a monomial X < sup > α </ sup > is any finite product of elements of X < sub > I </ sub > ( repetitions allowed ); a formal power series in X < sub > I </ sub > with coefficients in a ring R is determined by any mapping from the set of monomials X < sup > α </ sup > to a corresponding coefficient c < sub > α </ sub >, and is denoted.

If n numbers are given, each number denoted by a < sub > i </ sub >, where i = 1, ..., n, the arithmetic mean is the of the a < sub > i </ sub >' s divided by n or