Then there are a pair of old biddies played by Grace Carney and Sibly Bowan who may be right off the shelf of stock Irish characters, but they put such a combination of good will and malevolence into their parts that they're quite entertaining.

Then the equivalence class of the pair can be identified with the rational number, and this equivalence relation and its equivalence classes can be used to give a formal definition of the set of rational numbers.

Then, in 1915, William Henry Bragg and William Lawrence Bragg, a British father-son pair, shared this Nobel Prize for their discoveries in the reverse problem-determining the structure of crystals using X-rays.

Then the pair (( A < sub > i </ sub >)< sub > i ∈ I </ sub >, ( f < sub > ij </ sub >)< sub > i ≤ j ∈ I </ sub >) is called an inverse system of groups and morphisms over I, and the morphisms f < sub > ij </ sub > are called the transition morphisms of the system.

Then, the electrons to be placed in the molecular orbitals are slotted in one by one, keeping in mind the Pauli exclusion principle and Hund's rule of maximum multiplicity ( only 2 electrons, having opposite spins, per orbital ; place as many unpaired electrons on one energy level as possible before starting to pair them ).

Then the characteristic ( or defining ) property of the ordered pair is:

Then the pair ( x < sub > 1 </ sub >, y < sub > 1 </ sub >) solving Pell's equation and minimizing x satisfies x < sub > 1 </ sub >

Then, the single-sideband complex signal centered at zero is upconverted to a real signal, by another pair of quadrature mixers, to the desired center frequency.

Then ( X × Y, ( π < sub > 1 </ sub >, π < sub > 2 </ sub >)) is a terminal morphism from Δ to the object ( X, Y ) of D × D. This is just a restatement of the above since the pair ( f, g ) represents an ( arbitrary ) morphism from Δ ( Z ) to ( X, Y ).

Then one way of representing the truth condition of " Nixon is alive " is as the ordered pair < Nixon,

Then while standing in front of a full-length mirror, he committed suicide by stabbing himself with a pair of sewing scissors seven times ( supposedly while surrounded by newspaper clippings of his career ), resulting in lurid press coverage.

Then Maelgwn challenged the pair to a horse race.

Then, from 2001 through 2004, Fordland teams won 63 games while losing only 20, winning a pair of Summit Conference championships and a Class 2 district championship in 2003.

Then the dead person's heart was weighed on a pair of scales, against the goddess Ma ' at, who embodied truth and justice.

Then apply the following 4 rules, in order, to each pair of letters in the plaintext:

Then with 3: 45 left in the half, Tampa Bay drove 77 yards, assisted by a pair of catches by Alstott for 28 total yards.

Then the pair is called a direct system over.

Then S carries a pair of coordinate patches: one covering a neighborhood of the north pole, and the other of the south pole.

A pair of official live albums, All Night Wrong and Then !, were released in 2002 and 2003, respectively, along with a double compilation album, The Best of Allan Holdsworth: Against the Clock, in 2005.

Then, when asked about how the pair of them had managed to get home a day before the rescue ship carrying the survivors was due, their story begins to unravel ; they say they jumped ship and " ship-hiked " their way home.

Then one seeks vectors maximizing the same correlation subject to the constraint that they are to be uncorrelated with the first pair of canonical variables ; this gives the second pair of canonical variables.

Then, he creates " survey codes " for each pair of the rulers, which contain a number which describes degree of the match of each considered property of two rulers.

Then a new pair of basis points is selected, and the process is repeated.

Then the statistician must analyze the properties of and, which are viewed as random vectors since a randomly different selection of n cases to observe would have resulted in different values for them.

Let vectors and let denote the matrix with elements of a and b. Then the area of the parallelogram generated by a and b is equal to.

Let vectors and let Then the area of the parallelogram generated by a and b is equal to.

Then express the seed ( the initial conditions of the LRS ) as a linear combination of the eigenbasis vectors:

Then the dual basis vectors are given as follows:

Then the contravariant coordinates of any vector v can be obtained by the dot product of v with the contravariant basis vectors:

Then can be broken down to its column vectors as follows:

Then applying the Gram – Schmidt process to the three vectors ( A < sub > 2 </ sub >− A < sub > 1 </ sub >, A < sub > 3 </ sub >− A < sub > 1 </ sub >, V ) produces an orthonormal basis of space, the third vector of which will be normal to plane A.

Then labeling the basis elements of V by 0, 1, 2, ..., 22, ∞, W can be defined as the span of the words S < sub > t </ sub > together with the word consisting of all basis vectors.

Then this inner product between f and g can be roughly understood as the dot product between approximating vectors and, in the limit as the number of sampling points goes to infinity.

Then the inner product of two tangent vectors is

Then from the known formulae you can calculate the basis vectors of the reciprocal lattice.

Then the locus of points at the end of such vectors is called the radial of the curve.

Then for every there is a unique linear combination of the basis vectors that equals v:

: Then the kernel of s is the one-dimensional subspace consisting of all vectors ( x < sub > 1 </ sub >, 0, 0, ...).

Then their respective planes are perpendicular to vectors a and b, and the direction of L must be perpendicular to both.

Then the general expression of a structural form is, where f is a function, possibly from vectors to vectors in the case of a multiple-equation model.

# A " Min-max " Collatz – Wielandt formula takes a form similar to the one above: for all strictly positive vectors x, let g ( x ) be the maximum value of < sub > i </ sub > / x < sub > i </ sub > taken over i. Then g is a real valued function whose minimum is the Perron – Frobenius eigenvalue.

Fix a point p ∈ M, and an orthonormal basis X < sub > 1 </ sub >, X < sub > 2 </ sub > of tangent vectors at p. Then the principal curvatures are the eigenvalues of the symmetric matrix

) Then a linear transformation for such vectors can be defined by a square matrix with one row and one column for each element of the vector.

Then, any two-form can be expressed as a linear combination of tensor products of pairs of vectors, especially a linear combination of tensor products of pairs of basis vectors.