) Then X < sub > i </ sub > is the value ( or realization ) produced by a given run of the process at time i. Suppose that the process is further known to have defined values for mean μ < sub > i </ sub > and variance σ < sub > i </ sub >< sup > 2 </ sup > for all times i. Then the definition of the autocorrelation between times s and t is

: Then the estimated value of the weight θ < sub > 1 </ sub > is

Then b < sub > 0 </ sub > is the value of p ( x < sub > 0 </ sub >).

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 for a specific value x of X, the function L ( θ | x )

Then the probability of a measurement returning the value λ < sub > i </ sub > can be calculated by integrating the spectral measure

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, to construct the elements of following rows, add the number above and to the left with the number above and to the right to find the new value.

Then, the problem of computing the function value can be rephrased as " zeroing-in " on the corresponding matrix entry.

Then, any single value has an uncertainty equal to the standard deviation.

Then, if opening or cold calling, the player may exchange a large chip for its full equivalent value out of the pot before placing his bet, or if overcalling may place the chip ( announcing that he is calling or raising a lesser amount ) and remove the change from his own bet for the round.

Let be the mean of the values in associated with class c, and let be the variance of the values in associated with class c. Then, the probability of some value given a class,, can be computed by plugging into the equation for a Normal distribution parameterized by and.

Then the area of the parallelogram with vertices at a, b and c is equivalent to the absolute value of the determinant of a matrix built using a, b and c as rows with the last column padded using ones as follows:

Abstractly, we can say that D is a linear transformation from some vector space V to another one, W. We know that D ( c ) = 0 for any constant function c. We can by general theory ( mean value theorem ) identify the subspace C of V, consisting of all constant functions as the whole kernel of D. Then by linear algebra we can establish that D < sup >− 1 </ sup > is a well-defined linear transformation that is bijective on Im D and takes values in V / C.

Then one would find the actual velocity fluctuating about a mean value:

Then, ten tricks are played, allowing players to take trick points: each card has a face value ( except in Null games ) and is worth that amount in points for the player winning the trick.

Then, the value of m can be written in three ways:

Then the starting value after pressing " CLEAR " has to be 1.

* Then, the BPI process owners should determine what outcomes would add value to the organization's objectives and how best to align its processes to achieve those outcomes ( TO-BE ).

Then, if the value of an option at time t is f ( t, S < sub > t </ sub >), Itō's lemma gives

Then apply the differential correction for the new full moon cycle phase: use the value of 18 under entry 1 in the second, cyclic table above.

Then at any time t you can unwind your obligation for the forward contract by shorting another forward with the same delivery date to get the difference in forward prices, but discounted to present value:.

Then the curved scale used for the expected value is selected based on the range.

Then, for, the river forms part of the national border line between Spain and Portugal, in a region of narrow canyons, making it a historical barrier for invasions and a cultural / linguistic divide.

Then, the same strategy was tried by co-opting Acción Nacionalista Vasca a historical, yet basically inactive Basque party.

Then, after a performance where Kean went out of his way to botch the opening night of " Switzerland " by historical novelist Jane Porter in February 1819, for whom Kean had had a personal dislike, Bucke pulled the play out of contempt for Kean's conduct .. After much cajoling to still perform the play by the theatre staff, Mr. Bucke then later had it republished with a preface concerning the incident, including excerpts from correspondences between the involved parties, which was later challenged in two books, The Assailant Assailed and A Defense of Edmund Kean, Esq.

Then came the historical moment, Jugović conducted the ball along the diagonal and double-passed with Pančev.

Then, for a disk drive connected via Parallel ATA, each of them must be converted to logical ( means fake ) cylinder-head-sector address due to the interface historical shortcomings.

Then later writers might have mistaken it for a historical account.

Then, on or around June 1, 1838 Parrant completed building a small shack that, according to a historical publication by Albert A. Jones, dated 1892, became “ the first habitation, and the first business house of Saint Paul .” Thus Pierre “ Pig ’ s Eye ” Parrant became the first inhabitant of the future city of Saint Paul.

Then, in an empirical part of legal science, this framework would be applied to empirical ( sociological, historical and so on ) material so as to understand that material as ' law '.

How Should We Then Live: The Rise and Decline of Western Thought and Culture is a major Christian cultural and historical documentary film series and book.

Then another period of not brilliant results followed, before they could celebrate their fifth title in 1993-1994 after having defeated Milan 23-14 in the historical final in Padua.

" Then a wave of " nothingness " is seen moving from the end of time to its beginning, erasing entire historical ages in the process ( an effect similar to the anti-matter wave that destroyed many universes in Crisis on Infinite Earths ).

Then the Doctor sets the medical transport to explode, thus destroying the technology and matching the historical records of an explosion at the site.

On public television, these are replaced by segments that include " The Liberty News Network " ( a newscast delivered by Cronkite summarizing the events of the episode, with each including his signature sign off " that's the way it is "), " Mystery Guest " ( a guessing game where the kids guess a historical figure, who often is a character in the episode ), " Now and Then " ( a segment comparing life in the Revolutionary Era and today ), and " Continental Cartoons " ( a rebus word guessing game ).

Then came the political drama The Warriors and Those Who Wait ( 1864 ) and the dramatic dilogy Old Birds ( 1864 ), and Birds of the Latest Gathering ( 1865 ), followed by the tragedy Men Above the Law, as well as two historical plays, full of melodramatic turns and naturalistic elements, Lieutenant Gladkov and Miloslavskys and Naryshkins ( both 1867 ).

Then came an even more shocking confession: according to the CIA document, al-Faruq said two senior al-Qaeda officials, Abu Zubaydah and Ibn al-Shaykh al-Libi, had ordered him to ' plan large-scale attacks against U. S. interests in Indonesia, Malaysia, ( the ) Philippines, Singapore, Thailand, Taiwan, Vietnam and Cambodia.

Then she flings herself into his embrace and with her confession of love and loyalty, he transforms into the handsome man, the spell lifted by her fidelity and affection.

Then, the public confession of King Reccared was read aloud by a notary.

The Guru responded, " Then you should also give them ointment to heal their wounds.

Then, should Octavian's ships approach Antony's, the sea would push them into the shore.

* " Then opened he their understanding, that they might understand the scriptures, And said unto them, Thus it is written, and thus it behooved Christ to suffer, and to rise from the dead the third day: And that repentance and remission of sins should be preached in his name among all nations, beginning at Jerusalem.

Then, the balance sheet of the buyer will be modified and the decision maker should take into account the effects on the reported financial results.

Then Ross comes and Duncan decides that Macbeth should take the title of Thane of Cawdor.

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

Then on the orders of the papal Chartularius, Gratiosus, Constantine was removed from his monastic cell, blinded, and left on the streets of Rome with specific instructions that no-one should aid him.

Then, after putting the matter to God in prayer, he determined that the first person to enter his room the next morning should be the next Emperor, and that person was Justin, the chief of his guards.

Then the binary collision approximation is no longer valid, but rather the collisional process should be understood as a many-body process.

Then the shape of the organisation should follow to allow this to happen.

Then I read David Copperfield and realized I could never write at that level, and therefore I should find something else to do.

) Then it explains the situation and ends with " Your mission Dan / Jim, should you decide to accept it " or words to that effect, with a brief explanation of the mission.

Then they should take a careful patient history and seek medical records, to look for early deprivation, childhood abuse, or mental illness.

" Then all repeat: " Lord, I am not worthy that you should enter under my roof, but only say the word and my soul shall be healed.

Then you should be able to deduce what factors match the occurrence of the phenomenon in one list and don't occur in the other list, and also what factors change in accordance with the way the data had been ranked.

In the Book of Acts, Paul and other men performed ablution before entering the Temple in Jerusalem: " Then Paul took the men, and the next day purifying himself with them entered into the temple, to signify the accomplishment of the days of purification, until that an offering should be offered for every one of them.

Ibn Arabi suggested: " The Sufi should shut his door against the world for forty days and occupy himself with remembrance of Allah, that is to keep repeating, " Allah, Allah ..." Then, " Almighty God will spread before him the degrees of the kingdom as a test.

Then, complaining to Persephone that this was a sign of his wife's disrespect for him, King Sisyphus persuaded her to allow him to return to the upper world and scold his wife for not burying his body and giving it a proper funeral ( as a loving wife should ).

Then I told the rest to go on board at once, lest any of them should taste of the lotus and leave off wanting to get home, so they took their places and smote the grey sea with their oars.

Then Útgarda-Loki said that she should grapple with Ása-Thor.

Then Útgarda-Loki went up and bade them cease the wrestling, saying that Thor should not need to challenge more men of his body-guard to wrestling.

Then Thor snatched up a great stone out of the river and cast it at her, saying these words: ' At its source should a river be stemmed.

Then Spider Man said that the ball of thread should be called "," meaning " rolling with the beautiful goods.

Then he should stand up, take the bragafull, make solemn vows to be afterwards fulfilled, and thereupon empty the beaker.

Then he should ascend the high seat which his father had occupied ; and thus he came to the full heritage after his father.