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.

The precise definition requires that the dimension " d " so defined is a critical boundary between growth rates that are insufficient to cover the space, and growth rates that are overabundant.

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.

* We need higher world class standards for the 21st century ( though no state has yet found a precise definition of the term " world-class standards ").

The advantages of the Alexandroff compactification lie in its simple, often geometrically meaningful structure and the fact that it is in a precise sense minimal among all compactifications ; the disadvantage lies in the fact that it only gives a Hausdorff compactification on the class of locally compact, noncompact Hausdorff spaces, unlike the Stone – Čech compactification which exists for any Tychonoff space, a much larger class of spaces.

Having the same shape is an equivalence relation, and accordingly a precise mathematical definition of the notion of shape can be given as being an equivalence class of subsets of a Euclidean space having the same shape.

Unlike more experiential approaches where students are encouraged to independently " find their way " to the asanas by imitating the teacher, an Iyengar Yoga class is highly verbal and precise, with misalignments and errors actively corrected.

To be precise, a " backend " is a class of storage interface, and a " database " is an instance of a

A former lecturer remembers the importance of being particularly precise if addressing a class that included Josephson ; if a mistake was made, Josephson would not be afraid to politely point it out after the lecture.

The standard of training is officially specified in the Commercial Diver Training Standards for each class of diver, but the precise definitions for many of the specified items is unclear.

The Cohen-Lenstra heuristics are a set of more precise conjectures about the structure of class groups of quadratic fields.

Whiteness has so many different definitions that the word is “ nothing less than a moving target .” Arnsen moreover notes that whiteness studies scholars are entirely on the far left of the political spectrum, and suggests that their apparent vitriol towards white Americans is due in part to white workers not fulfilling the predictions of Marxist theory that the proletariat would overcome racial, national and class distinctions to unite and overthrow capitalism ; he cites as an example Roediger ’ s afterword to the seminal < I > Wages of Whiteness </ i > which asserts that the book was written as a reaction to “ the appalling extent to which white male workers voted for Reaganism in the 1980s .” Arnsen also argues that in the absence of supporting evidence, whiteness studies often relies on amateurish Freudian speculation about the motives of white people: “ The psychoanalysis of whiteness here differs from the ' talking cure ' of Freudianism partly in its neglect of the speech of those under study .” Without more accurate scholarship, Arnsen writes that “ it is time to retire whiteness for more precise historical categories and analytical tools .”

The precise wording of Xenophon's description suggests the possibility that the kopis was regarded as a specific variant within a more general class, with the term makhaira denoting any single-edged cutting sword.

Both Stensioellida and Pseudopetalichthyida are considered to be basal or primitive groups within Placodermi, though, their precise placement within the class remains unsure.

In the idelic formulation of class field theory, one obtains a precise one-to-one correspondence between abelian extensions and appropriate groups of ideles, where equivalent generalized ideal class groups in the ideal-theoretic language correspond to the same group of ideles.

The precise axioms for this distinguished class do not matter for the construction of the Grothendieck group.

Still, that Java Card uses a precise subset of the Java language speeds up the learning curve, and enables using a Java environment to develop and debug a Java Card program ( caveat: even if debugging occurs with Java bytecode, make sure that the class file fits the limitation of Java Card language by converting it to Java Card bytecode ; and test in a real Java Card smart card early on to get an idea of the performance ); further, one can run and debug both the Java Card code for the application to be embedded in a smart card, and a Java application that will be in the host using the smart card, all working jointly in the same environment.

To be precise, the Kirby-Siebenmann class is the obstruction to placing a PL-structure on M x R and in dimensions n > 4 this ensures that M has a PL-structure.

According to the second edition Player's Handbook, the bard class is a more generalized character than the more precise historical term, which applied only to certain groups of Celtic poets who sang the history of their tribes in long, recitative poems.

They arise in situations in which one believes that what happens depends not only on the external world, but also on the precise pattern of behavior of the individual or group.

Wedge-shaped polycrystals were identified by transmission electron microscopy to grow out of the amorphous phase only after the latter has exceeded a certain thickness, the precise value of which depends on deposition temperature, background pressure and various other process parameters.

The point of saturation depends on many variables such as ambient temperature and the precise chemical nature of the solvent and solute.

( The precise resolution of a raster graphic necessary for high-quality results depends on the viewing distance ; e. g., a billboard may still appear to be of high quality even at low resolution if the viewing distance is large enough.

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.

In fact, the modern explanation of the uncertainty principle, extending the Copenhagen interpretation first put forward by Bohr and Heisenberg, depends even more centrally on the wave nature of a particle: Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions ; likewise, just as it is nonsensical to discuss the wavelength of a " pulse " wave traveling down a string, particles do not have perfectly precise momenta ( which corresponds to the inverse of wavelength ).

Above and below the ends of the more or less rectangular ribbon, there is less audible output due to phase cancellation, but the precise amount of directivity depends on ribbon length.

When all of the details are worked out one ends up with an expression that again takes the form of an Arrhenius exponential multiplied by a slowly varying function of T. The precise form of the temperature dependence depends upon the reaction, and can be calculated using formulas from statistical mechanics involving the partition functions of the reactants and of the activated complex.

The precise meaning of " structure-preserving " depends on the kind of mathematical structure of which X and Y are instances.

The precise usage depends on the rank of the peerage and on certain other general considerations.

The precise period depends on the energy of the photons, which determines their color.

The theorem crucially depends upon the precise definitions of compactness and of the product topology ; in fact, Tychonoff's 1935 paper defines the product topology for the first time.

Various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context.

The precise limit is unknown, as it depends on the equations of state of nuclear matter, for which a highly accurate model is not yet available.

The precise nature of the effects depends on the nature of the wave: an atmospheric wave, for instance, may dissipate close to the surface due to friction with the land mass, and at higher levels due to radiative cooling.

The use of silicon and other semiconductors in electronics depends on precise control of impurities.

Furthermore, individual performers treat pitches quite differently, and the precise intonation of a given note depends on melodic context.

The precise semantics of subtyping crucially depends on the particulars of what " safely used in a context where " means in a given programming language.

The precise definition of stability depends on the context, but it is derived from the accuracy of the algorithm.

The terms sardine and pilchard are not precise, and what is meant depends on the region.

The design emphasis for industrial users depends on the precise application and extends from the bottom end which is cost critical, to the most severe environments where the SCBA is one part of an integrated protective environment which includes gas tight suits for whole body protection and ease of decontamination.