In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

If Af is the null space of Af, then Theorem 12 says that Af.

The fact that ( 5 ) implies ( 4 ) requires us to assume that G is σ-compact ( and locally compact ) ( Bekka et al., Theorem 2. 12. 4 ).

A well documented classical application of the " Second Theorem " as illustrated in the diagram is the determination of chord BC subtending 12 degrees of arc.

A generalized form of Zariski Main Theorem is the following :< ref > EGA IV < sub > 3 </ sub >, Théorème 8. 12. 6 .</ ref > Suppose Y is quasi-compact and quasi-separated.

** Theorem 12: The level of communication intimacy and information seeking are inversely related.

The reader will find it helpful to think of the special case when the primes are of degree 1, and even more particularly, to think of the proof of Theorem 10, a special case of this theorem.

Since Af are distinct prime polynomials, the polynomials Af are relatively prime ( Theorem 8, Chapter 4 ).

By Theorem 10, D is a diagonalizable operator which we shall call the diagonalizable part of T.

Theorem 13.

Theorem: K is not a computable function.

He is most famous for proving Fermat's Last Theorem.

Wiles discovered Fermat's Last Theorem on his way home from school when he was 10 years old.

* Lawrence C. Paulson of the University of Cambridge, work on higher-order logic system, co-developer of the Isabelle Theorem Prover

* Theorem If X is a normed space, then X ′ is a Banach space.

* Theorem Let X be a normed space.

* Theorem Every reflexive normed space is a Banach space.

many small primes p, and then reconstructing B < sub > n </ sub > via the Chinese Remainder Theorem.

George Boolos ( 1989 ) built on a formalized version of Berry's paradox to prove Gödel's Incompleteness Theorem in a new and much simpler way.

* Weisstein, Eric W. " Second Fundamental Theorem of Calculus.

: Theorem XXX: " The following classes of partial functions are coextensive, i. e. have the same members: ( a ) the partial recursive functions, ( b ) the computable functions.

: Turing's thesis: " Turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i. e. by one of his machines, is equivalent to Church's thesis by Theorem XXX.

Though it centers around the brilliant and enigmatic figure of Charles 12,, the true hero is not finally the king himself.

The career of Charles 12, is obviously very similar to that of Napoleon.

Of Gustavus Adolphus and Charles 12, it is unnecessary to speak.

Land was near, and on June 12, one hundred and fourteen days after leaving America, they actually saw, twenty miles away, the coast of Orissa.

The wartime protocol of September 12, 1944, designated a special `` Greater Berlin '' area, comprising the entire city, to be under joint occupation.

Much happened in this field during the past 12 months.

The Free Democrats ( 12 per cent of the vote ) believe a nuclear war can be avoided by negotiating with the Soviet Union, and more dealings with the Communist bloc.

Each year another grade is added to the process, until finally all 12 grades are integrated.

If it is not enough that all of our internationalist One Worlders are advocating that we join this market, I refer you to an article in the New York Times' magazine section ( Nov. 12, 1961 ), by Mr. Eric Johnston, entitled `` We Must Join The Common Market ''.

Middletown bases its claim on the general provision of the law that `` all rateable property, both tangible and intangible, shall be taxed to the owner thereof in the town in which such owner shall have had his actual place of abode for the larger portion of the twelve ( 12 ) months next preceding the first day of April in each year ''.

The Armed Forces Epidemiological Board agreed to submit each month a report for one of its 12 commissions, so that each commission will report once a year on some phase of its work calculated to be of particular interest and value to medical officers of the Armed Forces.

) 12.

The shelter illustrated in figure 12 is based on such a room built in a new home in the Washington, D.C. area in the Spring of 1959.

12.

( See Chapter 12.

It must have been with some pleasure and relief that on September 12, 1848, Joseph Brown made the momentous entry in his job book, in his characteristically cryptic style, `` Lucian Sharpe came to work for me this day as an apprentice ''.

Now when Henri was just 12 he was only 4' 10'' '' tall and weighed an astounding 72 pounds, and his greatest desire was to pack on some weight.

If, for some reason such as economy, we are not going to develop aircraft nuclear propulsion with a sense of national urgency, then we should turn our effort to developing jet engines with a thrust-to-weight ratio of 12 or 15 to one.

Now lay 12 pieces of Af cut 5-3/4'' '' long side by side but separated by 12 pieces of the same material 1/2'' '' sq..

Now place 12 pieces 1/2'' '' sq. on this edge as we did before and space them with the 5-3/4'' '' long `` tappets '', as they are called.

Put the 12 tappets and some Af locking bar spacers in the frame to help align all the components before you tighten the screws.

This would be reduced by multiplying 8 times 6 and then dividing the product by 12.

The Colt line now includes a new scattergun, the Standard or Custom Pump Model ( about $90 and $150, respectively ) in 12, 16 and 20.

The Flite-King Trophy ( beginning at just over $85 ) is a pump gun in 12 or 16.