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Page "lore" ¶ 64
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If and fourth
If you were required to file a declaration of estimated tax for the calendar year 1961, it is not necessary to pay the fourth installment otherwise due on January 15, 1962, if you file your income tax return Form 1040, and pay your tax in full for the calendar year 1961 by January 31, 1962.
If your side has two aces and a void, then you are not at risk of losing the first two tricks, so long as ( a ) your void is useful ( i. e., does not duplicate the function of an ace that your side holds ) and ( b ) you are not vulnerable to the loss of the first two tricks in the fourth suit ( because, for instance, one of the partnership hands holds a singleton in that suit or the protected king, giving your side second round control ).
If there are four alternative symbols ( corresponding to a musical instrument that can generate four different tones, one at a time ), the first symbol may represent the bit sequence 00, the second 01, the third 10 and the fourth 11.
If their estimates are correct, 6. 1 percent of North Korea's total population was in the military, numerically the world's fifth largest military force, in the late 1980s ( fourth largest as of 2006 ).
If reflections of a pentomino are considered distinct, as they are with one-sided pentominoes, then the first and fourth categories above double in size, resulting in an extra 6 pentominoes for a total of 18.
If there are cranial nerve abnormalities, these may be noticed on eye examination in the form of a squint ( third, fourth, or sixth nerve palsy ) or as facial nerve palsy.
If a player finishes in fifth to eighth position they are " ranked out " and the race must be replayed – at the cost of one of a limited number of lives – until a placing of fourth or above is achieved.
In response he devised his own anti-razor: " If three things are not enough to verify an affirmative proposition about things, a fourth must be added, and so on.
If there is a previous NASCAR Champion without a spot, he will get one of those four spots, otherwise, the fourth fastest car is added to the field.
he described as " Murphy's law or the fourth law of thermodynamics " which states: " If anything can go wrong, it will.
If we take four quantities: a, b, c, and d, then the first and second have a ratio ; similarly the third and fourth have a ratio.
If any additional teeth form, for example, fourth and fifth molars, which are rare, they are referred to as supernumerary teeth ( hyperdontia ).
Putting any of the four vertices in the role of O yields four such identities, but in a sense at most three of them are independent: If the " clockwise " sides of three of them are multiplied and the product is inferred to be equal to the product of the " counterclockwise " sides of the same three identities, and then common factors are cancelled from both sides, the result is the fourth identity.
If this is true, the text is important because Perpetua is one of the first Christian female writers before the fourth century whose works have survived.
If he is surrounded on three sides, he may escape by the fourth.
* If the king is on a square adjoining the konakis and is surrounded on three sides by his enemies and the fourth by the konakis, he is captured.
If Slayton had flown MA-7, his spacecraft would have been named Delta 7, as this would have been the fourth manned flight and Delta ( Δ ) is the fourth letter in the Greek alphabet.
* If an additional third, fourth, or fifth version of the product is envisaged down the line, this approach is far stronger, because the ready-made code libraries dramatically shorten the development life cycle for any additional products after the second.
If we go up a fifth from the lowest note in the octave and then up a fourth from there, we will reach the upper note of the octave.
If the winners of the Welsh Cup have already qualified for Europe via their league placing ( e. g. finishing first and winning the Cup ) the fourth placed team inherits the Europa spot.
It follows two other solo albums, Little Songs ( 1998 ) and Morning Orbit ( 2001 ), and precedes a fourth solo album, If God Had Curves ( 2005 ).
* If there is a third round it will always finish the game, a fourth round is practically never played although it is technically possible ( most life long players have never seen it ).
If reflections of a hexomino are considered distinct, as they are with one-sided hexominoes, then the first and fourth categories above would each double in size, resulting in an extra 25 hexominoes for a total of 60.

If and dimension
If V is finite-dimensional, then V * has the same dimension as V. Given a basis
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 a spatial extra dimension is of radius R, the invariant mass of such standing waves would be M < sub > n </ sub > = nh / Rc with n an integer, h being Planck's constant and c the speed of light.
If the input feature vectors have very high dimension, the learning problem can be difficult even if the true function only depends on a small number of those features.
If this happens in an even dimension, the Majorana spinor representation will sometimes decompose into two Majorana – Weyl spinor representations.
If this surface is folded along a third dimension, it allows one to picture a wormhole " bridge ".
If the dimension of V is n and
( If utility U = f ( x, y ), U, in the third dimension, does not have a local maximum for any x and y values.
If the supposed rock was out of space-time dimension, then the question would not make sense, because it would be impossible to move an object from one location in space to another if there is no space to begin with, meaning the faulting is with the logic of the question and not God's capabilities.
If the Noetherianity hypothesis is dropped, then R can have dimension anywhere between d + 1 and 2d + 1.
If R is a commutative ring, and M is an R-module, we define the Krull dimension of M to be the Krull dimension of the quotient of R making M a faithful module.
If V has finite dimension n, then GL ( V ) and GL ( n, F ) are isomorphic.
If we take the modules to be over a field, then the dimension of the n-th homology of X turns out to be the number of " holes " in X at dimension n.
If the polytope lies in n-dimensions, a face in the ( n − 1 )- dimension is called a facet.
If the primary key of the source data is required for reporting, the dimension already contains that piece of information for each row.
If A is torsion-free then it embeds into a vector space over the rational numbers of dimension rank A.
If there exist one or more eigenvalues, then if the corresponding b < sub > i </ sub > ≠ 0, it is a paraboloid ( either elliptic or hyperbolic ); if the corresponding, the dimension i degenerates and does not get into play, and the geometric meaning will be determined by other eigenvalues and other components of b. When it is a paraboloid, whether it is elliptic or hyperbolic is determined by whether all other non-zero eigenvalues are of the same sign: if they are, then it is elliptic ; otherwise, it is hyperbolic.
An extension of the tensor field idea incorporates an extra line bundle L on M. If W is the tensor product bundle of V with L, then W is a bundle of vector spaces of just the same dimension as V. This allows one to define the concept of tensor density, a ' twisted ' type of tensor field.
If the graph has n vertices and m edges then the dimension is m − n + 1.
If R is a field, the cycle space is a vector space over R with dimension m-n + c, where c is the number of connected components of G. If R is any commutative ring, the cycle space is a free R-module with rank m-n + c.
If the source has a maximum overall dimension or aperture width ( D ) that is large compared to the wavelength λ, the far-field region is commonly taken to exist at distances from the source, greater than Fresnel parameter S = D < sup > 2 </ sup >/( 4λ ), S > 1.

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