While sovereignty has roots in antiquity, in its present usage it is essentially modern.

While often cited as an Indian legend, the white doe seems to have its roots in English folklore.

While the roots of the game are very casual and laid back the newer generations of players are taking course design as well as the other elements of the game to a new level.

While it is now used to apply to groups of people fascinated with any subject, the term has its roots in those with an enthusiastic appreciation for sports.

While Deep Water Culture involves the plant roots hanging down into a reservoir of water below, the term Bubbleponics describes a top-fed Deep Water Culture ( DWC ) hydroponic system.

While libertarian socialism has roots in both socialism and liberalism, different forms have different levels of influence from the two traditions.

While evidence show that martial arts have roots in prehistory, the earliest evidence of systematic training in specific martial arts traditions emerges in antiquity ( late 1st millennium BC ) in both Asia and Europe.

While stereotyped as rural music, the Country music format is common and popular throughout the United States and in some other countries ( particularly Canada and Australia, both of which share much of the same Anglo-Saxon and Celtic roots as the United States ).

While contemporary biomedicine has distanced itself from its ancient roots in religion and magic, many forms of traditional medicine and complementary and alternative medicine ( CAM ) continue to espouse vitalism in various guises: ' As long as life had its own secret properties, it was possible to have sciences and medicines based on those properties ' ( Grossinger 1980 ).

While the Trento group around Curcio had its main roots in the Sociology Department of the Catholic University, the Reggio Emilia group ( around Franceschini ) included mostly former members of the F G C I ( the Communist youth movement ) expelled from the parent party for extremist views.

While most of the words introduced to the language by the TDK were newly derived from Turkic roots, it also opted for reviving Old Turkish words which had not been used for centuries.

While the roots of democracy were apparent, nevertheless deference was typically shown to social elites in colonial elections.

While gravitropic response of Arabidopsis root organs is their predominant tropic response, specimens treated with mutagens and selected for the absence of gravitropic action showed negative phototropic response to blue or white light, and positive response to red light, indicating the roots also show positive phototropism.

While the fundamental technology underlying the Marathon engine is still considered rather outdated by today's standards, Aleph One has added significant improvements and a more modern polish to its capabilities and ported it to a wide variety of platforms, bringing Marathon and its derivatives far beyond their Mac roots.

While Lower Louisiana had been settled by French colonists since the late 18th century, the Cajuns trace their roots to the influx of Acadian settlers after the Great Expulsion from their homeland during the French and Indian War ( 1754 to 1763 ).

While Ruffini and Abel established that the general quintic could not be solved, some particular quintics can be solved, such as ( x − 1 )< sup > 5 </ sup >= 0, and the precise criterion by which a given quintic or higher polynomial could be determined to be solvable or not was given by Évariste Galois, who showed that whether a polynomial was solvable or not was equivalent to whether or not the permutation group of its roots – in modern terms, its Galois group – had a certain structure – in modern terms, whether or not it was a solvable group.

While all of these People's Republics did not " officially " take power until after World War II ended, they all have roots in pro-Communist war-time governments.

While this has stunted the population growth in a significant way, in the modern day it has meant that many people visit the area to trace their family roots and background.

While usually considered experimental and avant-garde, free jazz has also oppositely been conceived as an attempt to return jazz to its " primitive ", often religious roots, and emphasis on collective improvisation.

# While there is a heap to the left of the current heap and its root is larger than the current root and both of its child heap roots

While the town on the west side of the River was always called Lehigh, the east town was called Slabtown, and a piece of history marks the east side's roots –– a sign that hangs over the playground with the words " Slabtown Traders ," perhaps alluding to the flea market that occurs there every summer during Lehigh River Days.

While Flat Rock is a rapidly growing community today, even with its growth, it remains a unique " small town " with many of its residents having roots reaching back to the 1800s.

While the roots of Sitges ' artsy reputation date back to the late 19th century, when Catalan painter Santiago Rusiñol took up residence there during the summer, the town became a centre for the 1960s counterculture in mainland Spain, then still under the dictatorship of Francisco Franco, and became known as " Ibiza in miniature ".

While most authorities stress the African roots of calypso, in his 1986 book, Calypso from France to Trinidad: 800 Years of History, that veteran calypsonian, The Roaring Lion ( Rafael de Leon ) asserted that calypso descends from the music of the medieval French troubadours.

While not as formalised as the Assassins ' Guild Code of Conduct, Guild thieves are expected to work to certain standards.

While the secret ballot might have had some effect in reducing corruption in British politics, the Corrupt and Illegal Practices Prevention Act 1883 formalised the position and is seen by many to have been the key legislation in the attempts to end electoral corruption.

While propositional logic deals with simple declarative propositions, first-order logic additionally covers predicates and quantification.

While the three formulae above are a direct expression in logic of what is known, they do not suffice to correctly draw consequences.

While some might argue that, by this logic, humans should also express hairy shoulders given that these body parts would putatively be exposed to similar conditions, the protection of the head, the seat of the brain that enabled humanity to become one of the most successful species on the planet ( and which also is very vulnerable at birth ), was arguably a more urgent issue ( axillary hair in the underarms and groin were also retained as signs of sexual maturity ).

While a member of the Senate, Adams also served as a professor of logic at Brown University.

While it is one of the most commonly used concepts in logic it must not be mistaken for a logical law ; rather, it is one of the accepted mechanisms for the construction of deductive proofs that includes the " rule of definition " and the " rule of substitution " Modus ponens allows one to eliminate a conditional statement from a logical proof or argument ( the antecedents ) and thereby not carry these antecedents forward in an ever-lengthening string of symbols ; for this reason modus ponens is sometimes called the rule of detachment.

While Weber shares some of Marx's consternation with bureaucratic systems and maligns them as being capable of advancing their own logic to the detriment of human freedom and autonomy, Weber views conflict as perpetual and inevitable and does not host the spirit of a materially available utopia.

While no longer used much in logic, Polish notation has since found a place in computer science.

While Spock represented " extreme logic, extreme science " and Kirk symbolized " extreme emotion and intuition ", McCoy's role as " a very colorful doctor, essentially a very humanistic scientist " represented the " two extremes that often served as the glue that held the trio together.

; Programming style: While typos in the program code are often caught by the compiler, a bug usually appears when the programmer makes a logic error.

While he was directed by George Birkhoff to work on differential equations, his interests continued to shift to logic.

While variables in mathematics usually take numerical values, in fuzzy logic applications, the non-numeric linguistic variables are often used to facilitate the expression of rules and facts.

While the above kinds of fuzzy logic have traditional syntax and many-valued semantics, in EVŁ is evaluated also syntax.

While both fuzzy logic and probability theory can be used to represent subjective belief, fuzzy set theory uses the concept of fuzzy set membership ( i. e., how much a variable is in a set ), and probability theory uses the concept of subjective probability ( i. e., how probable do I think that a variable is in a set ).

While AltiVec refers to an instruction set, the implementations in CPUs produced by IBM and Motorola are separate in terms of logic design.

While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-order logics.

While his original writings demonstrate that he had a sincere passion for the seven liberal arts ( grammar, rhetoric, logic, mathematics, geometry, music, and astronomy ), his work in Quaestiones naturales illustrated a more encompassing dedication to subjects such as physics, the natural sciences, and possibly even metaphysics.

While the expressive power of combinatory logic typically exceeds that of first-order logic, the expressive power of predicate functor logic is identical to that of first order logic ( Quine 1960, 1966, 1976 ).

While the theorems of Gödel and Gentzen are now well understood by the mathematical logic community, no consensus has formed on whether ( or in what way ) these theorems answer Hilbert's second problem.

He claimed, “ the best sites for ‘ earth art ’ are sites that have been disrupted by industry, reckless urbanization, or nature ’ s own devastation .” While in earlier 18th-century formal characterizations of the pastoral and the sublime, something like a “ gash in the ground ” if encountered by a “ leveling improver ”, as described by Price, would have been smoothed over and the whole composition returned to a more aesthetically pleasing contour For Smithson, however, it was not necessary that the deformation become a visual aspect of a landscape ; by his anti-formalist logic, more important was the temporal scar worked over by natural or human intervention.