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

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 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 imports declined sharply to an average of only US $ 50 million annually between 1985 and 1987, presumably as a result of a dramatic reduction in oil revenues and the precipitous drop in the value of the sucre, which made imported arms extremely expensive.

These laws sharply circumscribe any non-governmental political activity: street demonstrations, non-approved political organizations, and un-registered financial donations are formally banned.

These suspicions of illegitimacy, along with the continued publication of the libelles, a never-ending cavalcade of court intrigues, the actions of Joseph II in the Kettle War, and her purchase of Saint-Cloud combined to turn popular opinion sharply against the queen, and the image of a licentious, spendthrift, empty-headed foreign queen was quickly taking root in the French psyche.

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 categories, which attempt to bridge the gap between ontological and sociological structures, are sharply delineated.

These events sharply contrast with the rigid power structures of the 18th century.

These events sharply contrast with the rigid power structures of the 18th century, when no major European capital was ever held by an enemy army.

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 doors were not finished until 1469 ; their reliance on a few figures placed in simple, orderly compositions against a flat ground, contrasts sharply with the elaborate pictorial effects of Lorenzo Ghiberti's more famous Baptistery doors.

These studies have shown that in their natural environments, the nonhuman hominoids show sharply varying social structure: gibbons are monogamous, territorial pair-bonders, orangutans are solitary, gorillas live in small troops with a single adult male leader, while chimpanzees live in larger troops with bonobos exhibiting promiscuous sexual behaviour.

These dampened out the unfavorable acoustics, but required massive use of electronic amplification to reach the full audience, particularly since the background noise level had risen sharply since the 1920s.

John Muir said of them, " These workhorses featured a mast that angled, or raked, forward sharply, and a large triangular sail hanging down from a long, two-piece yard ".

These could differ sharply from place to place.

These improvements to the airport sharply increased passenger volumes.

These houses sharply contrast with the relatively undeveloped roads ( some unsealed ) and infrastructure of the area.

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

These in turn seem to contrast quite sharply with the very dark maria, which were once believed to be seas of liquid hydrocarbons, but are now thought to be plains.

These James Bay geese should be sharply distinguished from the stay-at-home geese that have learned how not to migrate.

These were after-market car headlamps mounted in the plated-over nose doors, to provide extra visibility to users of level crossings on sharply curved branch lines.

These measures contrasted sharply with the pardon that Martín de Álzaga and others had received after a short time in prison, and the resentment of criollos against the peninsulars deepened.

These numerous peasants were required to pay even further taxes for disrupting the system, but still, the population increased in large cities and unemployment rate increased sharply.

These views were sharply criticized by Joseph Stalin as " defence of the kulaks ".

These painstakingly realistic works paint an overwhelmingly positive picture of Soviet society, which must have contrasted sharply with the everyday realities of life for many people.

These ( Figure 4B ) are opposite in arrangement ( i. e., produced in pairs along the stems ), generally 5 – 15 x 2 – 6 cm, in outline generally elliptic or often widest above the middle, usually sharply angled at base and apex, papery in texture, overall smooth or infrequently with microscopic plant hairs on the lower surface, have 5 – 10 pairs of secondary veins, and on the lower surface usually have foveolae ( see next item ).