Then one must extract the principles, analogies and statements by various courts of what they consider important to determine how the next court is likely to rule on the facts of the present case.

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 consider a vector tangent to:

Then he made a serious gaffe by announcing to an audience of New York City's Jewish community that, if nominated, he would consider Reverend Jesse Jackson as a Vice Presidential candidate.

Then we may consider two concepts: Empty and Full.

Then consider two scenarios:

: Then consider the God's rivals, hear what Claudius

Then consider the island only has one street ( Indian Creek Island Drive ) with only 32 waterfront homes spread out over 38 waterfront lots, all with estimated values ranging from $ 7 to $ 30 million ( current listings range from $ 15 to over $ 50 million on this brokerage site ).

Then again, in biology we often need to consider motherhood over an arbitrary number of generations: the relation " is a matrilinear ancestor of ".

We can consider this an exchange ( Margrabe ) option by considering the first asset to be and the second asset to be the riskless bond paying off $ 1 at time T. Then the call option is exercised at time T when the first asset is worth more than K riskless bonds.

Then, if a and b are two periods of f such that < sup > a </ sup >⁄< sub > b </ sub > is not real, consider the parallelogram P whose vertices are 0, a, b and a + b. Then the image of f is equal to f ( P ).

Then it will be in a position to consider how to distribute assets between asset types ( i. e. asset allocation ); the institution can also calculate the scenario-weighted expected return ( which figure will indicate the overall attractiveness of the financial environment ).

Then sheaf cohomology enables us to consider a similar extension problem while " continuously varying " the Abelian group.

One visitor refused to remove his " even if the King were present " but Lambert replied that " Then by G ——, Sir, you must instantly quit this room, as I do not consider it a mark of respect due to myself, but to the ladies and gentlemen who honor me with their company.

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

Then the Falcons crew and Harrar make it to the dhuryam and they try to coerce Master Shaper Qelah Kwaad into convincing the brain to cease its destructive activities before they consider killing it.

Then as a being Man divides into two distinct groups: those who recognize their cosmic condition, seek divine guidance ( by ' reading ' God's word ), and bow to God's will ( symbolized by ' prostration '); and those who even in the face of these apparent wonders of Man's condition, consider the Human to be an ' independent ' entity, answerable to no transcendent authority, and even more contentiously, take it upon themselves to prevent the first class of man from following God's Word and submitting to Him.

* Then Portsmouth first-team coach Kevin Bond, who was first team coach of Newcastle United at the time of airing, is secretly recorded admitting he would consider discussing receiving payments from a proposed new agency involving agent Peter Harrison.

Then, in 2002, just prior to the Queen's pan-country tour to celebrate the Golden Jubilee, Manley ( at that point the designated minister in attendance for the sovereign's arrival in Ottawa ) stated: " I continue to think that for Canada after Queen Elizabeth, it should be time to consider a different institution for us, and personally I would prefer a wholly Canadian institution.

Then, it is natural to consider the problem of finding eigenvalues and eigenvectors ( which are now referred to as eigenbivectors ) such that

Then consider a propagating radio wave normal to that plane.

Then one may consider the set of pseudoholomorphic curves

Then in August 2003 he was accused of biting and then eye-gouging Wallabies hooker Brendan Cannon, and although there was insufficient video evidence to consider the biting charge, and he was found not guilty of gouging, he was still suspended for eight weeks for " attacking the face ".

Then the various officers of the college might take up the case.

Then it was that District Attorney Welch entered the case.

Then, when the case went to the jury, the judge excused one of the jurors, saying the juror had told him he had been accosted by masked men at his motel the night before the trial opened.

Then, when Macbeth approaches, Banquo, having had dreams about Macbeth's deeds, takes back his sword as a precaution in this case.

Then Fick's first law ( one-dimensional case ) can be written as:

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 the case is settled by three judges and four lay-judges.

#* Proof: Then so Thus However, is prime, so or In the former case, hence ( which is a contradiction, as neither 1 nor 0 is prime ) or In the latter case, or If however, which is not prime.

Then the first case of Fermat's Last Theorem holds true for p.

⟨ 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 the question being whether legislative interference was required I was at length induced to look at a remedy of an extraordinary character as the only one I thought applicable to the case ... it was a great innovation ".

Then she shows him a long, narrow case, which she tells him holds her only sacred treasure, but she cannot open it, because there are too many people around.

The incident, like others in Matthew, is described as the fulfillment of a passage in the Old Testament read as prophecy, in this case a reading of Jeremiah: " Then was fulfilled that which was spoken through Jeremiah the prophet, saying, A voice was heard in Ramah, Weeping and great mourning, Rachel weeping for her children.

Then he threw the lid of the case to a placed called Guneshwara ( now Gunavanthe ) and Dhareshwara, 10 – 12 miles away.

In this case we can write the eigenvalues as Then it can be shown that can be rewritten as

Then gcd ( a < sup > e </ sup > − 1, n ) is likely to produce a factor of n. However, the algorithm fails when p-1 has large prime factors, as is the case for numbers containing strong primes, for example.

Then a C-valued presheaf on X is the same as a contravariant functor from O ( X ) to C. This definition can be generalized to the case when the source category is not of the form O ( X ) for any X ; see presheaf ( category theory ).

Then though Gettier's cases stipulate that Smith has a certain belief and that his belief is true, it seems that in order to propose ( 1 ), one must argue that Gettier, ( or, that is, the writer responsible for the particular form of words on this present occasion known as case ( 1 ), and who makes assertion's about Smith's " putative " beliefs ), goes wrong because he has the wrong notion of justification.

Then for an equation to have a solution, we must have ( one constraint ), and in that case the solution space is or equivalently stated, ( one degree of freedom ).

" Then the band " changed the letter so that we wouldn't find a band with the same name again like it was the case with Crystaline Darkness.

Then this can be seen by a direct computation for n any integer, and the general case reduces to this case without much difficulty.