These notions ( packing dimension, Hausdorff dimension, Minkowski – Bouligand dimension ) all give the same value for many shapes, but there are well documented exceptions.

These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively ( see English numerals ).

These notions refer more to the kind of polynomials one is generally working with than to individual polynomials ; for instance when working with univariate polynomials one does not exclude constant polynomials ( which may result, for instance, from the subtraction of non-constant polynomials ), although strictly speaking constant polynomials do not contain any variables at all.

These notions later took shape in the theory of wahdat ul-wujud ( the Unity of All Things ).

These notions would be enough to explain the origin and the nature of laws that we call revolutionary ...

These notions sharply contrasted with the previously held Platonic notions of the human mind as an entity that preexisted somewhere in the heavens, before being sent down to join a body here on Earth ( see Plato's Phaedo and Apology, as well as others ).

These notions are today denoted by potentially infinite and actually infinite, respectively.

These fabulous notions have stemmed from popular imagination regarding the ninja's mysterious status, as well as romantic ideas found in later Japanese art of the Edo period.

These notions were what prompted him to investigate the peasant uprisings in Hunan while the rest of the China's communists were in the cities and focused on the orthodox Marxist proletariat.

These notions are of course imprecise, but at least explain why the nilradical of a commutative ring is contained in the ring's Jacobson radical.

These notions were alien to Paris at that time, and as a result, his first recognition came not from other painters but from poets such as Blaise Cendrars and Guillaume Apollinaire.

These and other examples have led skeptics to believe that many of these terms are derived from notions that would have been contemporary in Dee and Kelley's time.

These rules rely on common sense to make notions such as " connected group " and " surround " precise.

These poets would often share themes that parallel Schopenhauer's aesthetics and notions of will, fatality and unconscious forces, and used themes of sex ( such as prostitutes ), the city, irrational phenomena ( delirium, dreams, narcotics, alcohol ), and sometimes a vaguely medieval setting.

These concepts do not generalize numbers but combine notions of functions and sets which are not yet formalized, breaking away from familiar mathematical objects.

These notions generalize the algebraic numbers and the transcendental numbers ( where the field extension is C / Q, C being the field of complex numbers and Q being the field of rational numbers ).

These two notions are generalized in different directions.

These new art forms pushed the limits of traditional notions of " art " and corresponded to the similar rapid changes that were taking place in human society, technology, and thought.

These notions have been drawn upon by Thomas Kuhn.

These two notions being granted, it can be said that statements of " ought " are measured by their prescriptive truth, just as statements of " is " are measured by their descriptive truth ; and the descriptive truth of an " is " judgment is defined by its correspondence to reality ( actual or in the mind ), while the prescriptive truth of an " ought " judgment is defined according to a more limited scope — its correspondence to right desire ( conceivable in the mind and able to be found in the rational appetite, but not in the more " actual " reality of things independent of the mind or rational appetite )

These characteristics correspond to Western notions of the religious life as practiced in monastic settings.

Among the sramanic traditions, Brahmacharya is the term used for the practice of self-imposed celibacy that is generally considered an essential prerequisite for spiritual practice. These characteristics correspond to Western notions of the religious life as practised in monastic settings but in the Brahma Kumaris and Prajapita Brahma Kumaris religion, it is practised by married couples and householders too, as a way of formalizing sexual behavior into a conscious, co-creative practice rather than merely an unconscious habit.

These characters are also contrasted to Jonah's passivity.

These expenses were called ultrotributa, and hence we frequently find vectigalia and ultrotributa contrasted with one another.

These faces are often contrasted with that of a warrior.

These expressly working-class bands contrasted with others in the second wave that presaged the post-punk phenomenon.

These can be contrasted as either univocal, or equivocal conceptions of freedom.

These endogenous retroviruses ( ERVs ), contrasted with exogenous ones, now make up 5-8 % of the human genome.

These elements contrasted sharply with the funk and disco influenced outfits, novelty hits, live bands, synthesizers and party rhymes of artists prevalent in 1984, and rendered them old school.

These twins are contrasted in the book by allusions to sets of opposing twins and enemies in literature, mythology and history ; such as Set and Horus of the Osiris story ; the biblical pairs Jacob and Esau, Cain and Abel, and Saint Michael and the Devil – equating Shaun with " Mick " and Shem with " Nick " – as well as Romulus and Remus.

These were close-knit cross-functional groups responsible for the whole vehicle, as contrasted with Chrysler's highly functional structure.

These elements contrasted sharply with the 1970s P-Funk and disco-influenced outfits, live bands, synthesizers and party rhymes of acts prevalent in 1984, rendering them old school.

These were contrasted with about fifteen of the more active members of the assembly, who were more moderate Independents.

These sources are compared and contrasted in the 1995 English Heritage report.

These liberalizing trends can be contrasted with conservative social trends that seek to reverse these patterns of behaviour, with encouragement for young people to choose traditionally accepted roles, beliefs and behaviors, and to exercise sexual abstinence or non-promiscuous lifestyles before marriage.

These can be contrasted to the epistemic vices such as:

These transitions provide an interesting and important view into shock therapy and its consequences, especially when contrasted with China, which began a gradualist transition ( the opposite of the shock therapy approach ) in 1978 under Deng Xiaoping.

" These sentiments may be contrasted with the fact that the band was well thought of by the Beach Boys, to the extent that Brian Wilson co-wrote with Billy Hinsche one of the band's original songs, and their final single, " Lady Love ".

These propositions are also to be contrasted with logically impossible propositions, i. e., propositions which could not possibly be true under any circumstances in any universe because they are formal contradictions.

These convictions were strengthened in her mind by the new favourite Abigail Masham ( a cousin of the Duchess of Marlborough through her mother, and of Harley on her father's side ), whose coaxing contrasted favourably in the eyes of the Queen with the haughty manners of her old friend, the Duchess of Marlborough.

These contrasted with the rather thick, bulbous fins which were common at the time and were an example of Eldorado once again pointing the way forward.

These featured action oriented scripts which contrasted with the documentary style of his work with Selig.

These can be contrasted with the more widely-used selective serotonin reuptake inhibitors ( SSRIs ) which act upon serotonin alone.

These wet-weather conditions contrasted sharply with the droughts and heat waves experienced in the southeastern United States.

These characteristics contrasted with his 11 predecessors, who possessed greater political credentials and a closer relationship to the President.