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

It has several strap-shaped, green leaves, 30 – 50 cm long and 2 – 3 cm broad, arranged in two rows.

This means that array a has 3 rows and 2 columns, and the array is of integer type.

The third row is the sum of the first two rows, divided by 2.

For example, a camera that makes a 2048 × 1536 pixel image typically uses a few extra rows and columns of sensor elements and is commonly said to have " 3. 2 megapixels " or " 3. 3 megapixels ", depending on whether the number reported is the " effective " or the " total " pixel count ( as opposed to the 2048 × 1536 = 3, 145, 728 finished image pixels ).

In multi-rower boats ( 2, 4, or 8 ), the lightest person typically rows in the bow seat at the front of the boat.

In ISO 646, graphic characters are contained in rows 2 through 7 of the code table.

However, two of the characters in these rows, namely the space character SP at row 2 column 0 and the delete character DEL ( also called the rubout character ) at row 7 column 15, require special mention.

( The rows correspond to the dimensions t, m, and l, and the columns to the dimensional variables T, M, L and g. For instance, the 4th column, (− 2, 0, 1 ), states that the g variable has units of.

In recreational mathematics, a magic square of order n is an arrangement of n < sup > 2 </ sup > numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant.

Two electrodes, ( 2 ) and ( 7 ), in the form of comb-shaped rows of sharp metal points, are positioned respectively near to the bottom of the lower pulley and inside the sphere, over the upper pulley.

However, every identity matrix with at least two rows and columns has an infinitude of symmetric square roots .< ref > Mitchell, Douglas W. " Using Pythagorean triples to generate square roots of I < sub > 2 </ sub >".

So, assuming all contacts are to be used, 16x16 BGA package would need minimum 4-layer PCB ( 16 / 2 ( traces can be routed to both sides ) / 2 ( 2 rows of contacts can be routed out per layer )

For example, a system with 2 < sup > 13 </ sup > = 8192 rows would require a staggered refresh rate of one row every 7. 8 µs which is 64 ms divided by 8192 rows.

For further simplification, some authors also use the convention of writing both column vectors and row vectors as rows, but separating row vector elements with commas and column vector elements with semicolons ( see alternative notation 2 in the table below ).

of one track and putting some hihat at rows 2, 6, 10, 14 etc.

is a submatrix of A formed by rows 1, 2 and columns 1, 3, 4.

2 ), in which alternating rows are numbered in opposite directions, starting from section 1 in the northeast corner and ending with section 36 in the southeast corner, as per Figure 2.

In terms of sensory structures, C. inclusum has 8 similarly sized eyes distributed in 2 parallel horizontal rows.

The three tiers in rows 2 and 3 are separated by colour filters ( intrarhabdomal filters ) that can be divided into four distinct classes, two classes in each row.

Gideon Sundbäck increased the number of fastening elements from four per inch ( about one every 6. 4 mm ) to ten or eleven ( around every 2. 5 mm ), introduced two facing rows of teeth that pulled into a single piece by the slider, and increased the opening for the teeth guided by the slider.

Proof: Notice that the nim-sum (⊕) obeys the usual associative and commutative laws of addition (+), and also satisfies an additional property, x ⊕ x = 0 ( technically speaking, the nonnegative integers under ⊕ form an Abelian group of exponent 2 ).

The prime ideals of the ring of integers are the ideals ( 0 ), ( 2 ), ( 3 ), ( 5 ), ( 7 ), ( 11 ), … The fundamental theorem of arithmetic generalizes to the Lasker – Noether theorem, which expresses every ideal in a Noetherian commutative ring as an intersection of primary ideals, which are the appropriate generalizations of prime powers.

The morphisms in E between R → S < sub > 1 </ sub > and R → S < sub > 2 </ sub > are commutative triangles of the form ( R → S < sub > 1 </ sub >, R → S < sub > 2 </ sub >, S < sub > 1 </ sub > → S < sub > 2 </ sub >) where S < sub > 1 </ sub > → S < sub > 2 </ sub > is a ring map ( which preserves the identity ).

The ring of 2 × 2 matrices is not commutative, since matrix multiplication fails to be commutative, as the following example shows:

Commutativity makes sense for a polygon of any finite number of sides ( including just 1 or 2 ), and a diagram is commutative if every polygonal subdiagram is commutative.

Reversing all the arrows in the commutative diagrams that define a Lie supergroup then shows that functions over the supergroup have the structure of a Z < sub > 2 </ sub >- graded Hopf algebra.

Formally, a Lie superalgebra is a ( nonassociative ) Z < sub > 2 </ sub >- graded algebra, or superalgebra, over a commutative ring ( typically R or C ) whose product, called the Lie superbracket or supercommutator, satisfies the two conditions ( analogs of the usual Lie algebra axioms, with grading ):

In the theory of modules over a commutative ring R, when R has Krull dimension ≥ 2, it can be useful to treat modules M and N as pseudo-isomorphic if M / N has support of codimension at least two.

For n greater than 2, multiplication of n × n rotation matrices is not commutative.

Thus a commutative superalgebra ( with 2 invertible and nonzero degree one component ) always contains nilpotent elements.

In particular, if A is commutative and x < sub > 1 </ sub > = x < sub > 2 </ sub > = … = x < sub > n </ sub >, then this formula simplifies to the familiar power rule D ( x < sup > n </ sub >) = nx < sup > n − 1 </ sup > D ( x ).

The standard unit circle, viewed as the set of complex numbers of absolute value one is a one-dimensional commutative ( and therefore solvable ) linear algebraic group over the real numbers which has a two-dimensional representation into the special orthogonal group SO ( 2 ) without an invariant ( real ) line.

A complex orientation on an associative commutative ring spectrum E is an element x in E < sup > 2 </ sup >( CP < sup >∞</ sup >) whose restriction to E < sup > 2 </ sup >( CP < sup > 1 </ sup >)

The second algebraic K-group K < sub > 2 </ sub >( R ) of a commutative ring R can be identified with the second homology group H < sub > 2 </ sub >( E ( R ), Z ) of the group E ( R ) of ( infinite ) elementary matrices with entries in R.

Unlike the coefficient of determination in a regression involving just two variables, the coefficient of multiple determination is not computationally commutative: a regression of y on x and z will in general have a different R < sup > 2 </ sup > than will a regression of z on x and y.