Then every component of the graph of F must be defined over a bounded sub-interval.

Then codenamed " Stella ," the machine was also set to utilize cartridges ; after seeing the Channel F, Atari realized they needed to release it before the market was flooded with cartridge-based machines.

Then Monroe travelled to New York to appear at a birthday celebration for John F. Kennedy at Madison Square Garden, where she famously serenaded the President.

Let the line of symmetry intersect the parabola at point Q, and denote the focus as point F and its distance from point Q as f. Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. Then ( 1 ) the distance from F to T is 2f, and ( 2 ) a tangent to the parabola at point T intersects the line of symmetry at a 45 ° angle.

Then ( Ω, F, P ) is a probability space, with sample space Ω, event space F and probability measure P.

Then by definition, torque τ = r × F.

Let X be a normed topological vector space over F, compatible with the absolute value in F. Then in X *, the topological dual space X of continuous F-valued linear functionals on X, all norm-closed balls are compact in the weak -* topology.

Then F is one-sided Lipschitz if

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 F < sub > 43 </ sub >

Then one finds a free module F < sub > 2 </ sub > and a surjective homomorphism p < sub > 2 </ sub >: F < sub > 2 </ sub > → ker ( p < sub > 1 </ sub >).

To accommodate Cibber's voice range the recitative " Then shall the eyes of the blind " and the aria " He shall feed his flock " were transposed down to F major.

Then the total number of intersection points of X and Y with coordinates in an algebraically closed field E which contains F, counted with their multiplicities, is equal to the product of the degrees of X and Y.

Then by the theorem, the equation also holds for D, E and F ′.

Pick a fixed subset L of U. Then the maps F and G, where F ( M ) is the intersection of L and M, and G ( N ) is the union of N and ( U

Then on March 26, 1916 after being there six months, Stroud was reprimanded by cafeteria guard, Andrew F. Turner, for a minor rule violation which would have annulled Stroud's visitation privilege to meet his younger brother, whom he had not seen in eight years.

* Let H be a group, and let G be the direct product H × H. Then the subgroups

Then G is a group under composition, meaning that ∀ x ∈ A ∀ g ∈ G ( = ), because G satisfies the following four conditions:

Let G be a set and let "~" denote an equivalence relation over G. Then we can form a groupoid representing this equivalence relation as follows.

Then Exxon CEO, Lawrence G. Rawl, shaped the company's response.

Let a, b, and c be elements of G. Then:

Then and become partially defined operations on G, and will in fact be defined everywhere ; so we define * to be and to be.

Then with the dawn of new technologies such as electricity, the telegraph, and new forms of powered transportation, writers including Jules Verne and H. G. Wells created a body of work that became popular across broad cross-sections of society.

Then each element in G is represented in some way by a product

⟨ H ⟩, be the group generated by H. Then the word problem in H < sup >*</ sup > is solvable: given two words h, k in the generators H of H < sup >*</ sup >, write them as words in X and compare them using the solution to the word problem in G. It is easy to think that this demonstrates a uniform solution the word problem for the class K ( say ) of finitely generated groups that can be embedded in G. If this were the case the non-existence of a universal solvable word problem group would follow easily from Boone-Rogers.

Then, in February 1905, his eldest son W. G.

Let S be a subgroup of G, and let N be a normal subgroup of G. Then:

Then, given any point x and neighbourhood G of x, there is a closed neighbourhood E of x that is a subset of G.

Then R (( G )) is the ring of formal power series on G ; because of the condition that the indexing set be well-ordered the product is well-defined, and we of course assume that two elements which differ by zero are the same.

Then you type the first component, which is also ' Y ' for the 点 stroke, then a ' G ' for the 横 stroke ， and since you now already have three strokes, you type the last stroke, which also happens to be a 捺, arriving at the keycode ' YYGY ' for the complete character.

For such a subgroup G, define Fix ( G ) to be the field consisting of all elements of L that are held fixed by all elements of G. Then the maps E Gal ( L / E ) and G Fix ( G ) form an antitone Galois connection.

Then, all but blind, he said there was nothing in Back to Methuselah --, -- `` G.B.S. ought to have known that '', -- and `` I look at my bookshelves despairingly, knowing that I can have nothing more to do with them ''.

Then you can do the finishing touches at your leisure.

Then during washing, the greasy soil rolls back at the edges so that emulsified droplets can disengage themselves from the sorbed oil mass, with the aid of mechanical action, and enter the aqueous phase.

Then every linear operator T in V can be written as the sum of a diagonalizable operator D and a nilpotent operator N which commute.

Then the enthusiasm and energy of all elements can be channeled to produce cumulative progress toward a common objective.

Then, after I'm back, another fifty so you can put some mileage on yourself and have a solid alibi somewhere while I take care of your seat cover boy ''.

Then, with the hymn writer of old, you can say:

Then our choice function can choose the least element of every set under our unusual ordering.

Then we can express the variables as the sum of the ( time averaged ) mean field () that varies in space and a small fluctuating field () that varies in space and time.

Then the momentum equation can be expressed as

Then the mass balance equation can be written as

Then the mass balance equation can be expressed as

Then one can rewrite the field in the form

Then nodules of blue earth have to be removed and an opaque crust must be cleaned off, which can be done in revolving barrels containing sand and water.

Then, in 1828, Friedrich Wöhler published a paper on the synthesis of urea, proving that organic compounds can be created artificially.

Then the bra can be computed by normal matrix multiplication.

Then the reservists have to serve up to three weeks a year and can be called up to serve two weeks during a non-military crisis.

Then we can solve for f ′.

Then it can be shown that one can write a thermodynamic version of the above calorimetric rules:

Then, according to Adkins ( 1975 ), it can be shown that one can write a further thermodynamic version of the above calorimetric rules:

Indeed, following, suppose ƒ is a complex function defined in an open set Ω ⊂ C. Then, writing for every z ∈ Ω, one can also regard Ω as an open subset of R < sup > 2 </ sup >, and ƒ as a function of two real variables x and y, which maps Ω ⊂ R < sup > 2 </ sup > to C. We consider the Cauchy – Riemann equations at z = 0 assuming ƒ ( z ) = 0, just for notational simplicity – the proof is identical in general case.

Then each point p of the line can be specified by its distance from O, taken with a + or − sign depending on which half-line contains p.

Then the Cartesian product set D < sub > 1 </ sub > D < sub > 2 </ sub > can be made into a directed set by defining ( n < sub > 1 </ sub >, n < sub > 2 </ sub >) ≤ ( m < sub > 1 </ sub >, m < sub > 2 </ sub >) if and only if n < sub > 1 </ sub > ≤ m < sub > 1 </ sub > and n < sub > 2 </ sub > ≤ m < sub > 2 </ sub >.