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.

For many years, Austria had a special form of the language for official government documents.

There are no regional variations, because this special written form has mainly been used by a government that has now for centuries been based in Vienna.

Because the original designer had left the company another employee completely redesigned most of the system, ( adding a display snow remover circuit, true 80 / 64 column text mode support, ( with different size letters for TRS-80 and CP / M mode, so that in TRS-80 mode the full screen was also used, not just a 64x16 portion of the 80x25 screen ) with an improved font set ( adding " gray scale " version of the TRS-80 mozaik graphics and many special PETSCII like characters ), and a more flexible and reliable floppy disk controller and keyboard interface plus many other small improvements ), also an enclosure was developed for the main computer system, ( in the form of a 19-inch rack for the Eurocards ) and for two floppy disk drives and the power supply.

When amino acids combine, they form a special bond called a peptide bond through dehydration synthesis, and become a polypeptide, or protein.

As a vine, bean plants need external support, which may be provided in the form of special " bean cages " or poles.

There are several special cases of the Boolean satisfiability problem in which the formula are required to be conjunctions of clauses ( i. e. formulae in conjunctive normal form ).

Double-walled carbon nanotubes ( DWNT ) form a special class of nanotubes because their morphology and properties are similar to those of SWNT but their resistance to chemicals is significantly improved.

Drag is a special form of performance art based on the act of cross-dressing.

The factored number was of a special form ; the special number field sieve cannot be used on RSA keys.

A special case of the acid-base reaction is the neutralization where an acid and a base, taken at exactly same amounts, form a neutral salt.

The order instructed agencies everywhere to unite the Military control and the military sections of Chekas and to form special sections of frontlines, armies, military districts, and guberniyas.

When ITV did return, its first evening schedule included a special " catch-up " edition of Coronation Street, in which storylines which would have taken place during the strike were explained away in the form of a narrative chat between Len Fairclough and Bet Lynch.

Such intractable disputes form a special area in dispute resolution studies.

Under US law and the laws of most other developed countries, derivatives have special legal exemptions that make them a particularly attractive legal form to extend credit.

In Thespiai ( Boeotia ), a special letter form consisting of a vertical stem with a single rightward-pointing horizontal bar ( x12px ) was used for what was probably a raised variant of in pre-vocalic environments.

To the futurists, cinema was an ideal art form, being a fresh medium, and able to be manipulated by speed, special effects and editing.

This is a special form of cast and mold formation.

Unihockey is derived from " universal hockey " since it is meant to be a special and simplified hockey form.

He experimented with lighting, camera techniques and special effects in order to achieve true integration of dance with film, and was one of the first to use split screens, double images, live action with animation and is credited as the person who made the ballet form commercially acceptable to film audiences.

Gödel's original proof of the theorem proceeded by reducing the problem to a special case for formulas in a certain syntactic form, and then handling this form with an ad hoc argument.

* Love is total — that very special form of personal friendship in which husband and wife generously share everything, allowing no unreasonable exceptions and not thinking solely of their own convenience.

According to the first postulate of special relativity, all physical laws take their simplest form in an inertial frame, and there exist multiple inertial frames interrelated by uniform translation:

`` Now that Bruno Walter is virtually in retirement and my dear friend Dimitri Mitropoulos is no longer with us, I am probably the only one -- with the possible exception of Leonard Bernstein -- who has this special affinity for and champions the works of Bruckner and Mahler ''.

Accordingly, they took special pains to preserve their papers as essential sources for posterity.

In light of all this, one would require special reasons for saying that the paths of the heavenly bodies were other than circular.

The strongest appeal of the Copernican formulation consisted in just this: ideally, the justification for dealing with special problems in particular ways is completely set out in the basic ' rules ' of the theory.

Two facets of this aspect of the literary process have special significance for our time.

There is a second feature of the influences of literature, good literature, on emotional life which may have some special value for our time.

In Europe, Premier Clemenceau, showing his animal proclivities as the `` Tiger of France '', asked Pershing by letter for the creation of special houses where the sexual desires of American men could be satisfied.

To do this successfully required great skill and a special talent for both solemn and ribald raillery, a talent not bestowed on many persons, but one with which Milton was marked as being endowed and in which, at least in this performance, he obviously reveled.

But I've got news for Krim: he's not typical, he's pretty special.

-- Rep. Frelinghuysen, R-5th Dist., had a special reason for attending the reception at the Korean Embassy for Gen. Chung Hee Park, the new leader of South Korea.

According to the official interpretation of the Charter, a member cannot be penalized by not having the right to vote in the General Assembly for nonpayment of financial obligations to the `` special '' United Nations' budgets, and of course cannot be expelled from the Organization ( which you suggested in your editorial ), due to the fact that there is no provision in the Charter for expulsion.

A special grandstand, protected by awnings from the midsummer sun of Illinois, should be erected for occupancy by honored guests, who should include the ambassadors of all those new African nations as yet not quite convinced that the United States is thoroughly civilized.

The phone had been disconnected but telegrams came for him and notes by special messenger.

In addition to the regular schedule, advertisements were run for maximum impact in special editions of the New York Times, Boston Herald, American Banker, Electronic News and, for local promotion, the Providence Sunday Journal.

During fiscal years 1959 and 1960, there were 139 military and civilian students who came to the Institute for varying periods of special instruction.

Two special issues were published, one for November 1959 on Space Medicine, the other the Tenth Anniversary issue for January 1960.

a special fund created for that purpose pursuant to subsection ( A ) of this section any amounts hereafter paid, in United States dollars, by a foreign government which has entered into a claims settlement agreement with the Government of the United States as described in subsection ( A ) of Section 4 of this Title.

The Peace Corps can either begin in very low gear, with only preparatory work undertaken between now and when Congress finally appropriates special funds for it -- or it can be launched now and in earnest by executive action, with sufficient funds and made available from existing Mutual Security appropriations to permit a number of substantial projects to start this summer.

During these early years the repair of watches and clocks and the building of special clocks for church steeples formed an important part of the young man's occupation.

Our plan is to keep abreast of these advances, and select for development those fields which seem most promising for our special capabilities.