Some theorems related to compactness ( see the glossary of topology for the definitions ):

Some definitions also add that for any production rule of the form u → v of a context-sensitive grammar, it shall be true that | u |≤| v |.

Some definitions focus on the question of the probability of encountering a given condition of a system once characteristics of the system are specified.

Some definitions:

Some definitions of epilepsy require that seizures be recurrent and unprovoked, but others require only a single seizure combined with brain alterations which increase the chance of future seizures.

Some definitions of Mersenne numbers require that the exponent p be prime, since the associated number must be composite if p is composite.

Some scientific materialists have been criticized, for example by Noam Chomsky, for failing to provide clear definitions for what constitutes matter, leaving the term ' materialism ' without any definite meaning.

Some definitions of management are:

Some authors use the term " grammatical gender " as a synonym of " noun class ", but others use different definitions for each ( see below ).

") Some critics have argued for more or fewer dimensions while others have proposed entirely different theories ( often assuming different definitions of " personality ").

Some definitions would have it that any assumption that a person's behavior would be influenced by their racial categorization is racist, regardless of whether the action is intentionally harmful or pejorative.

Some definitions of racism also include discriminatory behaviors and beliefs based on cultural, national, ethnic, caste, or religious stereotypes.

Some definitions simply refer to all forms of socialism that follow an electoral, reformist or evolutionary path to socialism, rather than a revolutionary one.

Some definitions now include acts of unlawful violence and war.

Some theorems are " trivial ," in the sense that they follow from definitions, axioms, and other theorems in obvious ways and do not contain any surprising insights.

Some definitions suggest xenophobia as arising from irrationality or unreason.

Some authors use more general definitions of " positive definite " that include some non-symmetric real matrices, or non-Hermitian complex ones.

Some common definitions include:

Some definitions simply refer to all forms of socialism that follow an electoral, reformist or evolutionary path to socialism, rather than a revolutionary one.

Some definitions of famines are:

Some definitions also set a minimum level for population density ( at least 2, 000 persons / square km ).

Some modern magicians, such as Aleister Crowley and those who follow the traditions of the Hermetic Order of the Golden Dawn and Ordo Templi Orientis, describe magic in rational terms, using definitions, postulates and theorems.

( Some definitions do not consider the second form of rule to be permitted, in which case a context-free grammar that can generate the empty word cannot be so transformed.

Some also create new terms without substantially changing the definitions of uncertainty or risk.

Some contracts specify a scale of royalties payable ( for example, where royalties start at 10 % for the first 10, 000 sales, but then increase to a higher percentage rate at higher sale thresholds ).

Some political scientists define a civil war as having more than 1000 casualties, while others further specify that at least 100 must come from each side.

Some signals carry encryption and specify use conditions ( such as " may not be recorded " or " may not be viewed on displays larger than 1 m in diagonal measure ") backed up with the force of law under the WIPO Copyright Treaty and national legislation implementing it, such as the U. S. Digital Millennium Copyright Act.

Some newsreader programs also allow the user to specify a time period to keep an author in the kill file.

Some of the main changes were clauses enabling volunteer's to be included under such terms and conditions as the Governor may specify.

Some phonologists prefer not to specify a unique phoneme in such cases, since to do so would mean providing redundant or even arbitrary information – instead they use the technique of underspecification.

Some of these RFCs would not be published at all today ; an early RFC was often just that: a simple request for comments, not intended to specify a protocol, administrative procedure, or anything else for which the RFC series is used today.

Some composers actually specify that choirs should be separated, such as in Benjamin Britten's War Requiem.

" Some authors specify two types of prior knowledge necessary for successful comprehension.

Some recipes explicitly specify or permit all-purpose flour, notably where a firmer or denser cake texture is desired.

Some of these words specify the citizen's origin ( place of birth or manufacture ), some an occupation, and some may denote specific philosophical or political alignments ( chosen later in life by the citizen themselves ), or make other similarly personal statements.

Some of the most important examples are also fields F. To have a topological field we should also specify that inversion is continuous, when restricted to F

Some compilers in this category provide special constructs or extensions to allow programmers to directly specify operations to be performed in parallel ( e. g., DO FOR ALL statements in the version of FORTRAN used on the ILLIAC IV, which was a SIMD multiprocessing supercomputer ).

Some states specify a greater frequency of fire drills at the beginning of the school year:

Some encoders also allow the user to specify a maximum allowed bitrate or maximum quality value.

Some systems specify the default path in a configuration file ; others hard-code it into the dynamic loader.

Some executable file formats can specify additional directories in which to search for libraries for a particular program.

Some accounts specify that one of the commonest red bricks was necessary for ordinary membership, a rarer white brick for higher-level membership, and one of the rarest blue bricks for chairmanship.

Some analog tape manufacturers specify frequency responses up to 20 kHz, but these measurements may have been made at lower signal levels.

Some manufacturers specify 2 %, others 3 %, but other values are also possible.

Some engine manufacturers specify which SAE viscosity grade of oil should be used, but different viscosity motor oil may perform better based on the operating environment.

Some report sound pressure measurements, but those that do often do not specify how sound pressure measurements were taken.

Some variations of the term genre works specify the medium or type of visual work, as in genre painting, genre prints, genre photographs, and so on.

Some building codes also specify a minimum riser height, often.