So the length of a curve γ from p to q is a functional of the curve given by

So, p and q are Euclidean vectors, starting from the origin of the space, and their tips indicate two points.

So, to prove ( 1 ), assume that m and p are surjective and q is injective.

This proves that B is the direct sum of im q and ker t. So, for all b in B, b can be uniquely identified by some a in A, k in ker t, such that b

So for k even the polynomials Z ( E, T ) have no zeros in this region, or in other words the eigenvalues of Frobenius on the stalks of E < sup > k </ sup > have absolute value at most q < sup > k ( d − 1 )/ 2 + 1 </ sup >.

So given the lengths p, q, r and s of a cyclic quadrilateral, the approximate area is while, letting, the exact area is

So the values p, q and r are also called the dimensions of the positive-definite, negative-definite and null vector subspaces of the whole vector space V that correspond to the matrix A.

So suppose p < sub > 1 </ sub >, p < sub > 2 </ sub >, p < sub > 3 </ sub > map to q < sub > 1 </ sub >, q < sub > 2 </ sub >, q < sub > 3 </ sub >; we can generate a sequence of mirrors to achieve this as follows.

So great a man could not but understand, too, that the thing that moves men to sacrifice their lives is not the error of their thought, which their opponents see and attack, but the truth which the latter do not see -- any more than they see the error which mars the truth they themselves defend.

So we see that a specialist is a man who knows more and more about less and less as he develops, as contrasted to the generalist, who knows less and less about more and more.

So in these pages the term `` technology '' is used to include any and all means which could amplify, project, or augment man's control over himself and over other men.

So it is that we relive his opening statement in the first television address with the dramatic immediacy of the present.

So far as the existing body of formal principle and procedure is concerned, categorical novelties are not to be anticipated in Jewish-Gentile relationships ; ;

Again omitting recent developments, E.T. Leeds' dictum of 1913 has stood unchallenged: `` So far as archaeology is concerned, there is not the least warrant for the second ( shore occupied by ) of these theories ''.

So far as I am concerned, the child is unmistakably father to the man, despite the obvious fact that child and father differ greatly -- sometimes for the better and sometimes for the worse.

So far as the record is concerned, the Western powers have not acquiesced and should not do so.

So, while we properly inveigh against the new poisoning, history is not likely to justify the pose of righteousness which some in the West were so quick to assume when Mr. Khrushchev made his cynical and irresponsible threat.

So don't see yourself as a heroine or fancy this little adventure is an event of major importance ''.

( Note: So far as State Police cars are concerned, only their replacement is under this division ).

So many times I have wondered why veterinarians do not wipe the table clean before each new canine patient is placed on it for examination.

So far as I can see, there is only one way out for the positivist.

So far these remarks, like most criticisms of Hardy, have tacitly assumed that his poetry is all of a piece, one solid mass of verse expressing a sensibility at a single stage of development.

So it is with Great Expectations, whether the hands be Orlick's as he strikes down Mrs. Gargery or Pip's as he steals a pie from her pantry.

So Dartmouth is moving closer to the others in the Ivy group.

So, too, is the mathematical competence of a college graduate who has majored in mathematics.

So is the time of the novel.

`` So there it is '', he said.

So what I am trying to tell you is the ' why ' -- that is my point -- and that concerns the spirit of the matter.

So you can see that Gerald G. Ramsey, director of SMU's food services, is not the ordinary type of craven, women-trodden chef.

So it is too with many other spirits which we all know: the spirit of Nazism or Communism, school spirit, the spirit of a street corner gang or a football team, the spirit of Rotary or the Ku Klux Klan.

The biblical symbol for this affirmation is expressed in the words: `` So God created man in his own image ; ;

`` So I just scooted out of his clutches.

So if all these beers was to get me in bed, man, you just spent a lot of money ''.

So Mel Chandler set out to sell him on the spirit of Garryowen, just as he himself had been sold a short time before.

So if you are made of atoms, you are just a big machine ; ;

So the audience last night was all ears and eyes just after Act 2, got a rousing opening chorus, `` Where's Charley??

So in the second case cited above, it is likely that two different versions are being conflated: one version with an embassy of three people, another with just two people.

So The Shining would be sorted as just " Shining " or " Shining, The ".

So, most constraints ended up just being described as comments.

This occurs in the context of Irenaeus ' work On the Detection and Overthrow of Knowledge Falsely So Called, ( Greek: elenchos kai anatrope tes pseudonymou gnoseos genitive case, ἔλεγχος καὶ ἀνατροπὴ τῆς ψευδωνύμου γνώσεως ) where the term " knowledge falsely so-called " ( nominative case pseudonymos gnosis ) covers various groups, not just Valentinus, and is a quotation of the apostle Paul's warning against " knowledge falsely so-called " in 1 Timothy 6: 20.

So George just told David he would not work any longer if the script was not better and he wanted the Howard script back ... he would not let his name go out over a lousy picture ... And bull-headed David said ' OK get out!

So it's a futile exercise, and it's just misleading.

So, Isaac unearthed them and began to dig for more wells all the way to Beersheba, where he made a pact with Abimelech, just like in the day of his father.

So just what is " truth " and " falsehood "?

If anything, the goal behind outing is to show just how many gay people there are among the most visible people in our society so that when someone outs the milkman or the spinster, everyone will say, ' So what?

So several new districts were founded around the city's perimeter, just outside the old fortifications.

So furious were the Byzantine officials at this harsh rejection of the wishes of their emperor and patriarch that they threatened to roast Eugene, just as they had roasted Pope Martin I. Eugene was saved from the fate of his predecessor by the advance of the Muslims, who took Rhodes in 654 and defeated Constans himself in the naval battle of Phoenix ( 655 ).

Although Orbison recorded and wrote standard structure songs before " Only the Lonely ", he claimed never to have learned how to write them: " I'm sure we had to study composition or something like that at school, and they'd say ' This is the way you do it ,' and that's the way I would have done it, so being blessed again with not knowing what was wrong or what was right, I went on my own way .... So the structure sometimes has the chorus at the end of the song, and sometimes there is no chorus, it just goes ... But that's always after the fact — as I'm writing, it all sounds natural and in sequence to me.

So, just like one can find the value of an Integral ( f = dF ) over a 1-dimensional manifolds () by considering the anti-derivative ( F ) at the 0-dimensional boundaries (), one can generalize the fundamental theorem of calculus, with a few additional caveats, to deal with the value of integrals ( dω ) over n-dimensional manifolds ( Ω ) by considering the anti-derivative ( ω ) at the ( n-1 )- dimensional boundaries ( dΩ ) of the manifold.

So when Appenzell allied with the Swiss, the town of St. Gallen followed just a few months later.

So we ’ re all talking to her, the writers and whoever, just in awe of this woman.

So these images on the Wheel of Life are just to communicate to the general audience.

So just before expiring 3 years you have decided to replace the bulb with a new one and scheduled for a maintenance.

So, in just nine years, the kingdom so hard won by Robert the Bruce had been shattered and had recovered.

So it is an acceptance that Israel has a right to exist, just as the Palestinians have a right to their homeland, and have a right to exist.

So one of the most effective strategies for regenerating biotopes is to plan a stretch of biotopes, not just a point where animals and plants come and go.