The following is a well-known result characterizing the minimal separators:

Furthermore, proved that the predecessor relation gives rise to a complete lattice when restricted to the set of minimal ( a, b )- separators in G.

The characteristic polynomial for A is Af and this is plainly also the minimal polynomial for A ( or for T ).

In states where a quantum mechanical particle is bound, it must be localized as a wave packet, and the existence of the packet and its minimum size implies a spread and minimal value in particle wavelength, and thus also momentum and energy.

They also responded to the promise of a " minimal dwelling " written into the new Weimar Constitution.

Concrete also provides the best resistance of any building material to high winds, hurricanes, tornadoes due to its lateral stiffness that results in minimal horizontal movement.

Such projects also promote standardising metadata by projects such as SDMX so that best use can be made of the minimal data available.

Type of data structure selected for a certain task typically also takes into consideration the type of storage it resides in ( e. g., speed of access, minimal size of storage chunk accessed, etc .).

Type of data structure selected for a certain task typically also takes into consideration the type of storage it resides in ( e. g., speed of access, minimal size of storage chunk accessed, etc .).

Munch also began to favor a shallow pictorial space and a minimal backdrop for his frontal figures.

Such a ladder can also be designed to have minimal sensitivity to component variation a property hard to evaluate without computer tools.

However, mostly since 2000, due to the always increasing expenditures, several teams, including works teams from car makers and those teams with minimal support from the automotive industry, have become bankrupt or been bought out by companies wanting to establish a team within the sport ; these buyouts are also influenced by Formula One limiting the number of participant teams.

Heawood noticed Kempe's mistake and also observed that if one was satisfied with proving only five colors are needed, one could run through the above argument ( changing only that the minimal counterexample requires 6 colors ) and use Kempe chains in the degree 5 situation to prove the five color theorem.

Some minimal effect on thyroid hormone production however also comes with Propranolol-which has two roles in the treatment of hyperthyroidism, determined by the different isomers of propranolol.

Besides providing single-step lookup, a minimal perfect hash function also yields a compact hash table, without any vacant slots.

The Navy also emerged from the fleet action of the Battle of Jutland having destroyed more ships than it lost, although the strategic value of both of these encounters was minimal.

Gamma rays, however, are not absorbed or attenuated by atmospheric gases, and can also escape from deep within the sample with minimal absorption.

There may also be " near minimal pairs " or other data which show that speakers of the language perceive two sounds as significantly different even if no exact minimal pairs exist in the lexicon.

From the theory, Kelly derived a psychotherapy approach and also a technique called The Repertory Grid Interview that helped his patients to uncover their own " constructs " ( defined later ) with minimal intervention or interpretation by the therapist.

Rutherford scattering is also sometimes referred to as Coulomb scattering because it relies only upon static electric ( Coulomb ) forces, and the minimal distance between particles is set only by this potential.

The impact of the Statute on authors was also minimal.

If I is a right ideal of R, then I is simple as a right module if and only if I is a minimal non-zero right ideal: If M is a non-zero proper submodule of I, then it is also a right ideal, so I is not minimal.

Japanese also prominently features geminate consonants, such as in the minimal pair 来た kita ' came ' and 切った kitta ' cut '.

Freud's theories imply that humans lack free will, but also that genetic influences on human personality are minimal.

This is also representative of one kind of broken consort, albeit with minimal instrumentation.

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 since it is nilpotent, the minimal polynomial for this operator is of the form Af for some Af ; ;

For given nonzero integers a and b there is a nonzero integer of minimal absolute value among all those of the form ax + by with x and y integers ; one can assume d > 0 by changing the signs of both s and t if necessary.

A transition from one state of minimal free energy requires some form of activation energy to penetrate the barrier ( compare activation energy and Arrhenius equation for the chemical case ).

MWI is distinguished by two qualities: it assumes realism, which it assigns to the wavefunction, and it has the minimal formal structure possible, rejecting any hidden variables, quantum potential, any form of a collapse postulate ( i. e., Copenhagenism ) or mental postulates ( such as the many-minds interpretation makes ).

In Shaka's day, warriors often wore elaborate plumes and cow tail regalia in battle, but by the Anglo-Zulu War of 1879, many warriors wore only a loin cloth and a minimal form of headdress.

Its chief focus is the sound changes that take place in morphemes ( minimal meaningful units ) when they combine to form words.

For Bloomfield, the morpheme was the minimal form with meaning, but it was not meaning itself.

It has superior electrical properties as an insulator and as a dielectric, and can support an electrostatic field while dissipating minimal energy in the form of heat ; it can be split very thin ( 0. 025 to 0. 125 millimeters or thinner ) while maintaining its electrical properties, has a high dielectric breakdown, is thermally stable to 500 ° C, and is resistant to corona discharge.

The attack took the form of a SYN flood which caused only minimal damage.

On introducing the external electromagnetic 4-vector potential into the Dirac equation in a similar way, known as minimal coupling, it takes the form ( in natural units )

The added cost of adding a question to the registration form is minimal.

Pan frying is a form of frying characterized by the use of minimal cooking oil or fat ( compared to shallow frying or deep frying ); typically using just enough oil to lubricate the pan ( although, in the case of a greasy food such as bacon, no oil or fats may be needed ).

Since virtually all video game consoles and arcade cabinets designed and built after 1980 were true digital machines ( unlike the analog Pong clones and derivatives ), some of them carried a minimal form of BIOS or built-in game, such as the ColecoVision, the Sega Master System and the SNK Neo Geo.

Some patients have a mild form with minimal motor disability and good mental development, while others may have severe motor disability and moderate mental retardation.

If a wound becomes covered with epithelial tissue within two weeks, minimal collagen will be deposited and no scar will form.

The new constitution specified a form of government that still was authoritarian in character, with the emperor holding the ultimate power and only minimal concessions made to popular rights and parliamentary mechanisms.

The second official language is introduced with a minimal amount of allocated time provided each week in the form of just one single subject.

The basis for his claim is that the study of simple programs is the minimal possible form of science, which is equally grounded in both abstraction and empirical experimentation.

the matrices satisfy various polynomials such as their minimal polynomials, which form a proper ideal ( because they are not all zero, in which case the result is trivial ); one might call this the characteristic ideal, by analogy with the characteristic polynomial.

As is common in the development of pidgins and trade languages, the interaction of fishermen and traders with no common language necessitated the creation of some minimal form of communication.

The vote may be on a proposed statute, constitutional amendment, charter amendment or ordinance, or, in its minimal form, to simply oblige the executive or legislative bodies to consider the subject by submitting it to the order of the day.

Often, within countries such as the US, the UK ( and, in all likelihood, China ) there are standardised qualifications, examinations and workbooks that form the concrete teaching materials needed for secondary-school and pre-university courses ( for example, within the UK, all students are required to sit or take Scottish Highers / Advanced Highers, A-levels or their equivalent in order to ensure that a certain minimal level of mathematical competence in a wide variety of topics has been obtained ).

This algorithm is a form of topological sort, and is the guts of the algorithm that controls a minimal spanning switch.

The albums are also distinguished by lean, blues-flavored songs with minimal lyrics, though these lyrics can run from brutal to humorously baffling (" Please don't push any buttons on this machine / On what machine ?/ Wet paint / Get out " form the entirety of " Bludgeon ," for instance ).