Then the joint distribution of X and Y is completely determined by our channel and by our choice of, the marginal distribution of messages we choose to send over the channel.

Then ƒ is invertible if there exists a function g with domain Y and range X, with the property:

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

Then, in the Brythonic epic Y Gododdin, there is a reference to Din Eidyn, " the stronghold of Eidyn ".

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.

Then, you type a 点 stroke, which is also on ' Y '.

Then define a process Y, such that each state of Y represents a time-interval of states of X.

Then Y = u ( X < sub > 1 </ sub >, X < sub > 2 </ sub >, ..., X < sub > n </ sub >) is a sufficient statistic for θ if and only if, for some function H,

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 I'll Be Tired Of You " w. E. Y. Harburg m. Arthur Schwartz

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 universally quantify over each Y immediately after the corresponding X is introduced ( that is, after X is quantified over, or at the beginning of the statement if X is free ), and guard the quantification with P ( X, Y ).

Then there is some probability distribution m on the interval and some random variable Y such that

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 Y < sub > i </ sub > can be viewed as an indicator for whether this latent variable is positive:

Then he would get to his feet, as though rising in honor of his own remarkable powers, and say almost invariably, `` Gentlemen, this is an amazing story!!

Then, Jesus indicated that God's forgiveness is unlimited.

Certainly, the meaning is clearer to one who is not familiar with Biblical teachings, in the New English Bible which reads: `` Then Jesus arrived at Jordan from Galilee, and he came to John to be baptized by him.

Then it added: `` It is not possible to determine how extensive these ill effects will be -- nor how many people will be affected ''.

Then the words fell into a pattern: `` Mollie the Mutton is scratching her nose, Scratching her nose in the rain.

Then he thought of Aaron Blaustein standing in his rich house saying: `` God is tired of taking the blame.

Then it is marked on the inside where it comes in contact with the transom, frames, keelson and all the battens.

Then it is replaced and fastened.

Then the chines are rounded off and the bottom is rough-sanded in preparation.

Then, a group of eggs is deposited in a cavity in the beebread loaf and the egg compartment is closed.

Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.

Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.

Then, too, the utmost clinical flexibility is necessary in judiciously combining carefully timed family-oriented home visits, single and group office interviews, and appropriate telephone follow-up calls, if the worker is to be genuinely accessible and if the predicted unhealthy outcome is to be actually averted in accordance with the principles of preventive intervention.

Then the editorial added prophetically: `` how far they may reach in Asia is yet undetermined, but they fall far short of our dreams of the war conferences ''.

Then she catapults into `` everything and everybody '', putting particular violence on `` everybody '', indicating to the linguist that this is a spot to flag -- that is, it is not congruent to the patient's general style of speech up to this point.

Then comes the time when the last wire is removed and Susie walks out a healthier and more attractive girl than when she first went to the orthodontist.

Then, with the new affluence, there is actually a sallying forth into the wide, wide world beyond the precincts of New York.

Then, if the middle number is activated to its greatest potential in terms of this square, through multiplying it by the highest number, 9 ( which is the square of the base number ), the result is 45 ; ;

Then it stalled, changed direction completely, became hurricane-strength and progressing west-to-east through the Caribbean Sea.

Then ρ will be the finest completely regular topology on X which is coarser than τ.

Then, completely confident in his own safety, the narrator comments on the sturdiness of the building and raps upon the wall he had built around his wife's body.

Then, carvers cut the parts with no character off the board with knives, so that the characters were cut in relief, completely different from those cut in intaglio.

Then, in 1960, Pope John XXIII issued the Code of Rubrics, completely ending the ranking of feast days by doubles etc., and replacing it by a ranking, applied not only to feast days but to all liturgical days, as I, II, III, and IV class days.

Then as a teenager, that completely changed.

Then there was the completely unexpected, late night visit by Eartha Kitt.

Then the scalars completely determine the multilinear function.

Then, " in 1988, the Public Protection Committee unanimously recommended that the California legislature completely abolish the state's UPL laws.

Then late in the first half Catchings went down with another injury ; she had completely torn her Achilles tendon.

Then in 1959 he embarked on a completely new career and by 1963, now married with two children, he was a fully qualified glacier pilot, flying to remote and inaccessible icy areas-a vocation which brought him considerable fame until he finally stopped flying in 1987 at the age of 72.

Then, the sports society proceeded to completely omit all Yugoslav Army symbols from the crest.

Then they are left outside during hot, sunny days and cold, freezing nights until they become completely dehydrated.

Then the signal beam first passes through the center for maximal amplification, but in later passes the diameter is increased to stay below the damage-threshold, to avoid amplification the outer parts of the beam, thus increasing beam quality and cutting off some amplified spontaneous emission and to completely deplete the inversion in the gain medium.

Then some troops he had out raiding returned, fell upon the forces attacking Bugha and completely routed them.

Then in 1948 the Soviet edition of the book was scrapped completely.

Then ( 1 ) is completely integrable at each point of A × B if and only if

# Captain William Bainbridge, USN, reported the surrender of HM frigate Java to USS Constitution on 29 December 1812 by the following minutes taken during the action: " At 4. 5 Having silenced the fire of the enemy completely and his colours in main Rigging being Supposed he had Struck, Then hawl'd about the Courses to shoot ahead to repair our rigging, which was extremely cut, leaving the enemy a complete wreck, soon after discovered that The enemies flag was still flying hove too to repair Some of our damages.

Then it was completely destroyed when the asteroid exploded, right after Hulk, Angel, and Iceman managed to escape.

Then in April 1657, Blake completely destroyed another Spanish merchant convoy — the West Indian Fleet — that had stopped at Santa Cruz harbour on its return voyage.

Then she gave me a completely unrealistic eating plan which involved very little meat or fish and lots of food that disagreed with my system like avocado — which makes me sick — and cucumber.

Then each sentence of the draft SPM, displayed on a giant screen, was discussed at length by the delegates and often ended up completely rewritten.

Then they began to move, and once in retreat they fled for dear life … discipline was completely forgotten ".