Then, by squeezing her foot three times, he came up -- presto -- with a different diagnosis with each squeeze.

Then, starting with the first player, each player draws six tiles.

Then X is reflexive if and only if each X < sub > j </ sub > is reflexive.

Then the required information is collected from a simple random sample of the elements within each selected group.

Then after-depolarization this effect leads initially to bigeminy: regular ectopic beats following each ventricular contraction.

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 all elements of X equivalent to each other are also elements of the same equivalence class.

" Then in Col 3: 16, Paul's goal is that the Colossians themselves to in some manner continue in this ministry and admonish and test each other, ' one another ' as Paul did for them.

Then, using back-substitution, each unknown can be solved for.

Then one need only check the records in each bucket T against those in buckets T where k ranges between − m and m.

For instance, suppose that each input is an integer z in the range 0 to N − 1, and the output must be an integer h in the range 0 to n − 1, where N is much larger than n. Then the hash function could be h

Then the analyst would have SMEs rate those examples on a Likert scale and compute inter-rater agreement statistics to judge the adequacy of each item.

Then, on paper, they bought $ 200 worth of each, for a total bet of $ 1, 000, using the prices on September 29, 1980, as an index.

We wish to maximize total value subject to the constraint that total weight is less than or equal to W. Then for each w ≤ W, define m to be the maximum value that can be attained with total weight less than or equal to w. m then is the solution to the problem.

Then, choice of law clauses may specify which laws the court or tribunal should apply to each aspect of the dispute.

Then, perhaps with some comic friction or awkwardness, they declare their love for each other and the film ends happily.

Then the composite was rewound and the negative of the second action was copied onto the right side of each frame.

Then simple random sampling or systematic sampling is applied within each stratum.

" Then he pointed to each person around him: " And so are you, and you, and you.

Then we have a universal morphism for each object in C and D:

Then they take their places, one on each side of the Hazzan, and the three recite ( in Hebrew ):

For f ∈ R, define D < sub > f </ sub > to be the set of ideals of R not containing f. Then each D < sub > f </ sub > is an open subset of Spec ( R ), and is a basis for the Zariski topology.

Then to perform, two's complement theory says to invert each bit with a NOT gate then add one.

Then move all spars as far away from each other as possible.

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

Then is a group whose identity element is The group inverse of an arbitrary group element is the function inverse

Then an element e of S is called a left identity if e * a = a for all a in S, and a right identity if a * e = a for all a in S. If e is both a left identity and a right identity, then it is called a two-sided identity, or simply an identity.

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

Then, after the pump energy stored in the laser medium has approached the maximum possible level, the introduced loss mechanism ( often an electro-or acousto-optical element ) is rapidly removed ( or that occurs by itself in a passive device ), allowing lasing to begin which rapidly obtains the stored energy in the gain medium.

For f a real polynomial in x, and for any a in such an algebra define f ( a ) to be the element of the algebra resulting from the obvious substitution of a into f. Then for any two such polynomials f and g, we have that ( fg ) ( a )

Then, for any non-zero element x of M, the cyclic submodule xR must equal M. Fix such an x.

Then, in 1846, the element ilmenium was claimed to have been discovered, but later was determined to be impure niobium.

Then in 1908, the Japanese chemist Masataka Ogawa found evidence in the mineral thorianite, which he thought indicated the presence of element 43.

Suppose a partially ordered set P has the property that every chain ( i. e. totally ordered subset ) has an upper bound in P. Then the set P contains at least one maximal element.

Suppose a non-empty partially ordered set P has the property that every non-empty chain has an upper bound in P. Then the set P contains at least one maximal element.

Then p + q = ( p < sub > 1 </ sub >+ q < sub > 1 </ sub >, p < sub > 2 </ sub >+ q < sub > 2 </ sub >); since p < sub > 1 </ sub > = p < sub > 2 </ sub > and q < sub > 1 </ sub > = q < sub > 2 </ sub >, then p < sub > 1 </ sub > + q < sub > 1 </ sub > = p < sub > 2 </ sub > + q < sub > 2 </ sub >, so p + q is an element of W.

# Let p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >) be an element of W, that is, a point in the plane such that p < sub > 1 </ sub > = p < sub > 2 </ sub >, and let c be a scalar in R. Then cp = ( cp < sub > 1 </ sub >, cp < sub > 2 </ sub >); since p < sub > 1 </ sub > = p < sub > 2 </ sub >, then cp < sub > 1 </ sub > = cp < sub > 2 </ sub >, so cp is an element of W.

Then for each x in I, there is a base element B < sub > 3 </ sub > containing x and contained in I.

Then, for example, (−∞, 1 ) and ( 0, ∞) would be in the topology generated by S, being unions of a single base element, and so their intersection ( 0, 1 ) would be as well.

Then if we intersect each element of B with Y, the resulting collection of sets is a base for the subspace Y.

" Then with her right hand she would sprinkle water at the head of the child and say, " Behold this element without whose assistance no mortal being can survive.

Then the union ( written as +) and the concatenation ( written as ·) of two elements of A again belong to A, and so does the Kleene star operation applied to any element of A.

Let B be a complex Banach algebra containing a unit e. Then we define the spectrum σ ( x ) ( or more explicitly σ < sub > B </ sub >( x )) of an element x of B to be the set of those complex numbers λ for which λe − x is not invertible in B.

Then the film was rewound, and everything except the foreground element matted out so that the foreground element would now photograph in the previously blacked out area.

Then the element c = ba is nilpotent ( if non-zero ) as c < sup > 2 </ sup > = ( ba )< sup > 2 </ sup > = b ( ab ) a = 0.