Then both partners replace weight on the second part of the first beat.

Then replace it where you found it.

Then, from the Late Middle Ages onwards, cattle tended to replace sheep as the dominant animals.

Then the Industrial Revolution drew additional manpower away from hilltown farms, especially after 1850 when steam engines fueled by local wood or by coal began to replace water power.

Then some early 20th century machines used an electrically powered agitator to replace tedious hand rubbing against a washboard.

Then whenever F ( X ) would appear in a statement, you can replace it with a new symbol Y of type U and include another statement P ( X, Y ).

Then remove ' dead ' black stones, replace the white stones with black ones to complete the new generation, and repeat the process.

Then cross out the 90 ° corner angle and replace all angles non-adjacent to it by their complement to 90 ° ( i. e. replace, say, B by 90 ° − B ).

Then in Seasons 3 and 4 and the movie, his son Daniel would replace him as these episode took place in the future where Spike had grown up.

Then the attacker can replace the original content with any other content of exactly the same length, such as " 3: 30 meeting is cancelled, stay home " by encrypting it with the recovered keystream, without knowing the encryption key.

We replace all instances of j in the tables with i. Then, we fill in all possible entries of the tables, possibly leading to more deductions and coincidences.

Then, in order to help managers replace that theory / assumption, he gave " Theory Y " which takes a more modern and positive approach.

Then remove A and replace B, running the analysis again.

Then directors and producers started a search for new actors to replace him.

Then, St. Louis traded up to Cincinnati's selection to grab Jackson while the Bengals chose Chris Perry to replace the departed Corey Dillon, who was traded to the New England Patriots.

Then, just prior to the Queen's pan-country tour to celebrate her Golden Jubilee the following year, Manley ( at that point the designated minister in attendance for the sovereign's arrival in Ottawa ) again stated his preference for a " wholly Canadian " institution to replace the present monarchy after the reign of the Queen ; he was rebuked by other Cabinet members, a former prime minister, and the Leader of the Opposition, as well as a number of prominent journalists.

Then, Gheorghe Funar ( the well-known nationalist former Mayor of Cluj ) says " I say we replace the Hungarian every day!

Then, on 25 August 1907, Harris announced that Pratt would replace him as President of the Mexican Mission.

Then the cooperation was broken off and ModiLuft acquired Boeing 737-400 aircraft to replace the 737-200s from Air U K, but the future of ModiLuft was already sealed and the airline ceased operations in 1996.

Then the cooperation was broken off and ModiLuft acquired Boeing 737-400 aircraft to replace the 737-200s from Air U K, but the future of ModiLuft was already sealed and the airline ceased operations in 1996.

Then in 1319 a rumored plot was uncovered which had planned to dispose of John and replace him with their eldest son Charles.

Then, upon visiting her, he learns of Ella's sickness and that a friend will replace her once she is taken to her mother in the country.

Then, we replace the POVM elements describing the measurements in a usual method for the tomography of states by the operators.

Then x is a rational number greater than 0 and less than r < sub > 0 </ sub >.

Then by definition, torque τ = r × F.

Then the formula Cold ( r )→ High ( t ) is true for any t and therefore any t gives a correct control given r. A rigorous logical justification of fuzzy control is given in Hájek's book ( see Chapter 7 ) where fuzzy control is represented as a theory of Hájek's basic logic.

Then Q ( x ) has a zero α of multiplicity r, and in the partial fraction decomposition, r of the partial fractions will involve the powers of ( x − α ).

Then, ( ra )< sup > n </ sup > = r < sup > n </ sup > a < sup > n </ sup > is in I, so ra is in the radical.

P is a polynomial of degree n − r. Then we have the following:

For every r ≥ 0, let n ( r, f ) be the number of poles, counting multiplicity, of the meromorphic function f in the disc | z | ≤ r. Then define the Nevanlinna counting function by

Then N < sub > 1 </ sub >( r, f )

a, b, d (/ th ), e, f, g, h, i, k, l, m, n, o, p, r, s, t, and v. Then there are three special umlauted runes, that are marked by two dots above them.

for x, y in A and r, s in K. Then * is an associative operation with identity element ( 0, 1 ).

Then consider a body of mass m, moving in a circle of radius r, with an angular velocity of ω.

Then the Kronecker product A ⊗ B has r < sub > A </ sub > r < sub > B </ sub > nonzero singular values, namely

Then, the quotient of by the nullspace of its bilinear form is naturally isomorphic ( as a G-module with an invariant bilinear form ) to if r ≠ 0, and to if r

Then it is also a bounded operator from L < sup > r </ sup > to L < sup > r </ sup > for any r between p and q.

Then for any r between p and q we have that F is dense in, that Tƒ is in for any ƒ in F and that T is bounded in the norm.

Then T is also a bounded operator from to for any r between p and q.

Then, once this claim ( expressed in the previous sentence ) is proved, it will suffice to prove " φ is either refutable or satisfiable " only for φ's belonging to the class C. Note also that if φ is provably equivalent to ψ ( i. e., ( φ ≡ ψ ) is provable ), then it is indeed the case that " ψ is either refutable or satisfiable " → " φ is either refutable or satisfiable " ( the soundness theorem is needed to show this ).

Then we could have written a formula of degree k which is equivalent to φ, namely.

Then Φ ( x ) = φ.

Then γ < sub > 1 </ sub > and γ < sub > 2 </ sub > are called equivalent at 0 if the ordinary derivatives of φ ∘ γ < sub > 1 </ sub > and φ ∘ γ < sub > 2 </ sub > at 0 coincide.

In particular, let p define the coordinates of points in a reference frame M coincident with a fixed frame F. Then, when the origin of M is displaced by the translation vector d relative to the origin of F and rotated by the angle φ relative to the x-axis of F, the new coordinates in F of points in M are given by

Then the subspace of consisting of functions φ such that all functional derivatives of at φ are zero, that is:

Then its negation ¬ φ, together with the field axioms and the infinite sequence of sentences 1 + 1 ≠ 0, 1 + 1 + 1 ≠ 0, …, is not satisfiable ( because there is no field of characteristic 0 in which ¬ φ holds, and the infinite sequence of sentences ensures any model would be a field of characteristic 0 ).

Then any model of B is a field of characteristic greater than k, and ¬ φ together with B is not satisfiable.

Let U be an open set in R < sup > n </ sup > and φ: U → R < sup > n </ sup > an injective differentiable function with continuous partial derivatives, the Jacobian of which is nonzero for every x in U. Then for any real-valued, compactly supported, continuous function f, with support contained in φ ( U ),

Then φ ( U ) is measurable, and for any real-valued function f defined on φ ( U ),

Then there exists a real-valued Borel measurable function w on X such that for every Lebesgue integrable function f: Y → R, the function ( f ° φ ) w is Lebesgue integrable on X, and

Then φ < sub > 0 </ sub > and φ < sub > 1 </ sub > have inverses

Then the final formula in (*) must be true, and φ is also true.

The frame bundle F ( E ) can be given a natural topology and bundle structure determined by that of E. Let ( U < sub > i </ sub >, φ < sub > i </ sub >) be a local trivialization of E. Then for each x ∈ U < sub > i </ sub > one has a linear isomorphism φ < sub > i, x </ sub >: E < sub > x </ sub > → R < sup > k </ sup >.