If you have neither a legal residence nor a principal place of business in any Internal Revenue district, your return should be filed with the District Director of Internal Revenue, Baltimore 2, Md..

( 2 ) If earthquakes do occur at such depths, why not deeper??

* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.

Theorem: If K < sub > 1 </ sub > and K < sub > 2 </ sub > are the complexity functions relative to description languages L < sub > 1 </ sub > and L < sub > 2 </ sub >, then there is a constant c – which depends only on the languages L < sub > 1 </ sub > and L < sub > 2 </ sub > chosen – such that

If the first allele is dominant to the second, then the fraction of the population that will show the dominant phenotype is p < sup > 2 </ sup > + 2pq, and the fraction with the recessive phenotype is q < sup > 2 </ sup >.

* If the balance factor of P is 2, then the left subtree outweighs the right subtree of the given node, and the balance factor of the left child ( L ) must be checked.

If the balance factor becomes − 2 or + 2 then the subtree is unbalanced and needs to be rotated to fix it.

If there is refraction at a collective spherical surface, or through a thin positive lens, O ' 2 will lie in front of O ' 1 so long as the angle u2 is greater than u1 ( under correction ); and conversely with a dispersive surface or lenses ( over correction ).

If the angle u1 is very small, O ' 1 is the Gaussian image ; and O ' 1 O ' 2 is termed the longitudinal aberration, and O ' 1R the lateral aberration of the pencils with aperture u2.

If the pencil with the angle u2 is that of the maximum aberration of all the pencils transmitted, then in a plane perpendicular to the axis at O ' 1 there is a circular disk of confusion of radius O ' 1R, and in a parallel plane at O ' 2 another one of radius O ' 2R2 ; between these two is situated the disk of least confusion.

If the object point O is infinitely distant, u1 and u2 are to be replaced by h1 and h2, the perpendicular heights of incidence ; the sine condition then becomes sin u ' 1 / h1 = sin u ' 2 / h2.

If the sets are short to medium length the caller will often try to run the dance until each couple has danced with every other couple both as a 1 and a 2 and returned to where they started.

" 9: 2 If the passage in Isaiah is interpreted literally, a return to the vegetarian diet of Eden seems to be a natural conclusion. Gen 1: 29-30

If a 2, 000 ( lb / ac )/ year sequestration rate was achieved on all of cropland in the United States, nearly 1. 6 billion tons of carbon dioxide would be sequestered per year, mitigating close to one quarter of the country's total fossil fuel emissions.

If there is a tie, we must consider the atoms at distance 2 from the stereocenter — as a list is made for each group of the atoms bonded to the one directly attached to the stereocenter.

If the substituents are numbered from 1 ( highest priority ) to 4 ( lowest priority ), then the sense of rotation of a curve passing through 1, 2 and 3 distinguishes the stereoisomers.

If the come-out roll is 2, 3 or 12, the bet loses ( known as " crapping out ").

If a 2, 3 or 12 is rolled, it loses.

If a 2 or 3 is rolled in the first round, it wins.

If ( x < sub > 1 </ sub >, x < sub > 2 </ sub >, x < sub > 3 </ sub >) are the Cartesian coordinates and ( u < sub > 1 </ sub >, u < sub > 2 </ sub >, u < sub > 3 </ sub >) are the orthogonal coordinates, then

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 and are invertible then is also invertible with inverse.

If G = GL < sub >*</ sub >( K ), then the set of natural numbers is a proper subset of G < sub > 0 </ sub >, since for each natural number n, there is a corresponding identity matrix of dimension n. G ( m, n ) is empty unless m = n, in which case it is the set of all nxn invertible matrices.

If the algorithm is unable to reduce A to triangular form, then A is not invertible.

If ƒ is invertible, the function g is unique ; in other words, there can be at most one function g satisfying this property.

If the domain is the real numbers, then each element in Y would correspond to two different elements in X (± x ), and therefore ƒ would not be invertible.

If the domain consists of the non-negative numbers, then the function is injective and invertible.

If ƒ is an invertible function with domain X and range Y, then

* If A is a square matrix ( i. e., m = n ), then A is invertible if and only if A has rank n ( that is, A has full rank ).

If all elements in S are invertible, S is called a loop.

If R = K is a field, then a series is invertible if and only if the constant term is non-zero, i. e., if and only if the series is not divisible by X.

If this property holds then A is an invertible matrix, if not A is a singular matrix.

If λI − T is invertible then that inverse is linear ( this follows immediately from the linearity of λI − T ), and by the bounded inverse theorem is bounded.

If an operator is not injective ( so there is some nonzero x with T ( x ) = 0 ), then it is clearly not invertible.

If the change of variables is given by an invertible matrix, not necessarily orthogonal, then the coefficients λ < sub > i </ sub > can be made to be 0, 1, and − 1.

If S is allowed to be any invertible matrix then B can be made to have only 0, 1, and − 1 on the diagonal, and the number of the entries of each type ( n < sub > 0 </ sub > for 0, n < sub >+</ sub > for 1, and n < sub >−</ sub > for − 1 ) depends only on A.

If the n eigenvalues are distinct ( that is, none is equal to any of the others ), then V is invertible, implying the decomposition.

If A is invertible, then the factorization is unique if we require that the diagonal elements of R are positive.

* If is invertible, the pseudoinverse and the inverse coincide:.

If A is a subalgebra of B, then for every invertible b in B the function which takes every a in A to b < sup >− 1 </ sup > a b is an algebra homomorphism ( in case, this is called an inner automorphism of B ).

If is a unique factorization domain with field of fractions, then by Gauss's lemma is irreducible in, whether or not it is primitive ( since constant factors are invertible in ); in this case a possible choice of prime ideal is the principal ideal generated by any irreducible element of.

An element of this ring is invertible if a ( 1 ) is invertible in R. If R is commutative, so is Ω ; if R is an integral domain, so is Ω.

If A has no 2-torsion ( in particular, if 2 is invertible ) then the grade involution can be used to distinguish the even and odd parts of A: