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:

Because EUV operates in a vacuum and requires reflective optics, EUV lithography tools have special overlay concerns, recently studied by IMEC, along with ASML.

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

A system of preferences — which consists of market opening lists, special cooperation programs ( business rounds, preinvestment, financing, technological support ) and countervailing measures on behalf of the landlocked countries — has been granted to the countries deemed to be less developed ( Bolivia, Ecuador and Paraguay ), to favour their full participation in the integration process.

The two perspectives are related by a process of extension: wherever there is a horizon, a particular solution of General Relativity can be extended beyond it by assuming that nothing special happens there ( i. e., that it " looks like " the region within the horizon ).

The kernel does not spawn or schedule a special process to handle interrupts, but instead the handler executes in the ( often partial ) context established at the beginning of interrupt handling.

A Carnot cycle is a special kind of cyclic process affecting a body composed of material suitable for use in a heat engine.

* CNO cycle-a special stellar nuclear fusion process

" This term, which was variously used by other Chinese philosophers ( including Confucius, Mencius, Mozi, and Hanfeizi ), has special meaning within the context of Daoism, where it implies the essential, unnamable process of the universe.

Industrially this process takes place in a special cell named Down's cell.

These are discussed below, and may each be derived by means of a special case of continuous-time Markov processes known as a birth-death process.

In cryptography, encryption is the process of transforming information ( referred to as plaintext ) using an algorithm ( called a cipher ) to make it unreadable to anyone except those possessing special knowledge, usually referred to as a key.

The code table initially contains codes that are one bit longer than the symbol size in order to accommodate the two special codes clr and end and codes for strings that are added during the process.

The process continued over time, and in 1206, for example, a special commission was used to determine borders in the Munster area.

Watt started to develop the process in 1779, and made many experiments to formulate the ink, select the thin paper, to devise a method for wetting the special thin paper, and to make a press suitable for applying the correct pressure to effect the transfer.

Therefore, when a merger with a controlling stockholder was: 1 ) negotiated and approved by a special committee of independent directors ; and 2 ) conditioned on an affirmative vote of a majority of the minority stockholders, the business judgment standard of review should presumptively apply, and any plaintiff ought to have to plead particularized facts that, if true, support an inference that, despite the facially fair process, the merger was tainted because of fiduciary wrongdoing .″

The process of alpha decay is in essence a special type of spontaneous nuclear fission.

The special case of 1: 1 resonance ( between bodies with similar orbital radii ) causes large Solar System bodies to eject most other bodies sharing their orbits ; this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet.

Canada and Hungary are the depositories of the treaty in recognition of their special contribution to the Open Skies process.

The conduction of food is a complex process that is carried in the plant with the help of special cell called phloem cells.

In 1957, Hugh Everett formulated the many-worlds interpretation of quantum mechanics, which does not single out observation as a special process.

There are no serialization methods defined on the interface, but a serializable class can optionally define methods with certain special names and signatures that if defined, will be called as part of the serialization / deserialization process.

The language also allows the developer to override the serialization process more thoroughly by implementing another interface, the interface, which includes two special methods that are used to save and restore the object's state.

However, Foster stated that she was present during the setup and staging of the special effects used during the scene ; the entire process was explained and demonstrated for her, step by step.

The tendency of the growth of this process and its significance require special study.

More advanced tagging systems incorporate special markers to indicate whether or not patients have been contaminated by hazardous materials, and also tear off strips for tracking the movement of patients through the process.