However, it is important to understand the precise technical definition of these terms.

Aerodynamicists disagree over the precise definition of hypersonic flow ; minimum Mach numbers for hypersonic flow range from 3 to 12.

A precise definition for the word has proved elusive.

Before giving a mathematically precise definition, we give a brief example.

Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.

) In reliance on this assumption, modern statutes often leave a number of terms and fine distinctions unstated — for example, a statute might be very brief, leaving the precise definition of terms unstated, under the assumption that these fine distinctions will be inherited from pre-existing common law.

::" We have no idea how consciousness emerges from the physical activity of the brain and we do not know whether consciousness can emerge from non-biological systems, such as computers ... At this point the reader will expect to find a careful and precise definition of consciousness.

There is continual argument over the precise definition of each of these periods, and one historian might group them differently, or choose different names or descriptions.

Rosser 1939 addresses the notion of " effective computability " as follows: " Clearly the existence of CC and RC ( Church's and Rosser's proofs ) presupposes a precise definition of " effective ".

:" Since a precise mathematical definition of the term effectively calculable ( effectively decidable ) has been wanting, we can take this thesis ... as a definition of it ..."

There is no precise definition for the term " Chicagoland ," but it generally means the city and its suburbs combined together.

It is necessary to have a precise definition of residence to decide whether visitors to a country should be included in the population count.

The most common approach to turn this intuitive idea into a precise definition uses limits, but there are other methods, such as non-standard analysis.

( To be precise: for the definition of the dipole moment one should always consider the " dipole limit ", where e. g. the distance of the generating charges should converge to 0, while simultaneously the charge strength should diverge to infinity in such a way that the product remains a positive constant.

" It also notes that "... no definition adequately specifies precise boundaries for the concept of ' mental disorder '... different situations call for different definitions ".

There is no scientifically precise definition of genius, and the question of whether the notion itself has any real meaning has long been a subject of debate.

While a precise definition varies among genocide scholars, a legal definition is found in the 1948 United Nations Convention on the Prevention and Punishment of the Crime of Genocide ( CPPCG ).

The precise level of glucose considered low enough to define hypoglycemia is dependent on ( 1 ) the measurement method, ( 2 ) the age of the person, ( 3 ) presence or absence of effects, and ( 4 ) the purpose of the definition.

For instance, the precise definition for a homomorphism f to be iso is not only that it is bijective, and thus has an inverse f < sup >- 1 </ sup >, but also that this inverse is a homomorphism, too.

Today, law enforcement agencies, popular media, the United Nations, other nations and even some medical practitioners can be observed applying the term very broadly and often pejoratively in reference to a wide range of illicit substances, regardless of the more precise definition existing in medical contexts.

Latency is a measure of time delay experienced in a system, the precise definition of which depends on the system and the time being measured.

The first modern and more precise definition of a vector space was introduced by Peano in 1888 ; by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged.

However, firing a pistol effectively at any significant range requires good training, since the absence of a buttstock makes precise ranged aim difficult.

The traditional spirit level produces these practically most useful heights above sea level directly ; the more economical use of GPS instruments for height determination requires precise knowledge of the figure of the geoid, as GPS only gives heights above the GRS80 reference ellipsoid.

* Although the mean speed of the electron in hydrogen is only 1 / 137th of the speed of light, many modern experiments are sufficiently precise that a complete theoretical explanation requires a fully relativistic treatment of the problem.

Puppetry allows for improvisation and offers controls familiar to gamers, but requires more personnel than the other methods and is less precise than scripted recordings.

To generate truly random numbers requires precise, accurate, and repeatable system measurements of absolutely non-deterministic processes.

Synchronized swimming demands advanced water skills, and requires great strength, endurance, flexibility, grace, artistry and precise timing, as well as exceptional breath control when upside down underwater.

Although Article VI requires that the Vice-President take an oath or affirmation of allegiance to the US Constitution, unlike the President, the United States Constitution does not specify the precise wording of the oath of office for the Vice President.

To function properly, the body requires between one and seven liters of water per day to avoid dehydration ; the precise amount depends on the level of activity, temperature, humidity, and other factors.

The term " liturgy " can also be used as a precise term that distinguishes between those religious groups who believe their ritual requires the " people " to do the " work " of responding to the priest, and those who do not ( hence leitourgia = work of the people ).

Grade 5: Whitewater, large waves, large volume, possibility of large rocks and hazards, possibility of a large drop, requires precise maneuvering.

Each base site requires precise timing and location information to synchronize data across the network.

However, low duty cycle operation with long beacon intervals requires precise timing, which can conflict with the need for low product cost.

One disadvantage of this approach is that it requires re-calibration because the precise non-linear voltage needed to correct non-linear movement will change as the piezo ages ( see below ).

Soldering of BGA devices requires precise control and is usually done by automated processes.

Achieving a glider's best L / D in practice requires precise control of airspeed and smooth and restrained operation of the controls to reduce drag from deflected control surfaces.

To make precise the statement that there is no canonical isomorphism between finite abelian groups and their dual groups ( in general ) requires thinking about dualizing not only on groups, but also on maps between the groups, in order to treat dualization as a functor and prove the identity functor and the dualization functor are not naturally equivalent.

This technique requires extremely precise guidance and control, in addition to a large infrastructure, and is thus not yet a viable option-although it may be in the future.

However, parrying requires precise timing.

This results in the photorealist style being tight and precise, often with an emphasis on imagery that requires a high level of technical prowess and virtuosity to simulate, such as reflections in specular surfaces and the geometric rigor of man-made environs.

The increasing prevalence of vessels of the maximum size is a problem for the canal as a Panamax ship is a tight fit that requires precise control of the vessel in the locks, possibly resulting in longer lock time, and requiring that these ships transit in daylight.

An effective one timer requires precise timing on the part of both players involved, especially the shooter.

This is a rather precise method but requires some previous training.

Felsite is a field term for a light colored rock that typically requires petrographic examination or chemical analysis for more precise definition.

The precise reason for the difference at dimension 5 is because the Whitney embedding theorem, the key technical trick which underlies surgery theory, requires 2 + 1 dimensions.