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Page "Degeneracy (mathematics)" ¶ 12
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Similarly and roots
Similarly, many place-names in areas of Danish and Norwegian settlement have Scandinavian roots.
" Similarly, journalist Brian Doherty has argued that the Ninth Amendment " specifically roots the Constitution in a natural rights tradition that says we are born with more rights than any constitution could ever list or specify.
Níðhöggr gnaws the roots of Yggdrasil in this illustration from a 17th century Icelandic manuscript. Similarly Níðhöggr ( Nidhogg Nagar ) the dragon of Norse mythology eats from the roots of the Yggdrasil, the World Tree.
Similarly to budō, bujutsu is a compound of the roots bu ( 武 ), and jutsu ( 術: じゅつ ), meaning technique Thus, budō is most often translated as " the way of war ", or " martial way ", while bujutsu is translated as " science of war " or " martial craft.
Similarly, an extract from the roots of the Brazilian Petiveria alliacea plant reduced inflammation in a rat model of pleurisy.
Similarly roots of cubic and quartic ( third and fourth degree ) equations can be expressed using arithmetic, square roots, and cube roots, or alternatively using arithmetic and trigonometric functions.
Similarly, cubic equations with three real solutions have an algebraic solution that is unhelpful in that it contains cube roots of complex numbers ; again an alternative solution exists in terms of trigonometric functions of real terms.
* Similarly, each pair of complex conjugate roots contributes an exponentially damped oscillation.
Similarly, the theory of complex multiplication shows that the maximal abelian extension of Q ( τ ), where τ is an imaginary quadratic irrationality, can be obtained by adjoining the special values of ℘( τ, z ) and j ( τ ) of modular functions j and elliptic functions ℘, and roots of unity, where τ is in the imaginary quadratic field and z represents a torsion point on the corresponding elliptic curve.

Similarly and polynomial
Similarly, for a positive integer the polynomial ( which is relevant for solving the Fermat equation ) can be factored over the ring, where is a primitive root of unity.
Similarly, a language is in UP if a given answer can be verified in polynomial time, and the verifier machine only accepts at most one answer for each problem instance.
Similarly, the class L / poly can be defined as deterministic logspace with a polynomial amount of advice.
Similarly MU < sub >*</ sub >( BU ) is isomorphic to the polynomial ring MU < sub >*</ sub >( point ) β < sub > 2 </ sub >, ...
Similarly, just like one can interpret the binomial distribution as the polynomial coefficients of when expanded, one can interpret the multinomial distribution as the coefficients of when expanded.
Similarly, it can be used to construct surgery presentations of triangulated 3-manifolds, although the procedure is not explicitly written as an algorithm in principle it should have polynomial run-time in the number of tetrahedra of the given 3-manifold triangulation.

Similarly and are
Similarly, all the statements listed below which require choice or some weaker version thereof for their proof are unprovable in ZF, but since each is provable in ZF plus the axiom of choice, there are models of ZF in which each statement is true.
Similarly, a character can find any possible universe, but they can spend character points to know of or inhabit shadows which are ( in some sense ) " real " and therefore useful.
Similarly, the silver used in jewelry and the aluminium used as a structural building material are also alloys.
Similarly, the third and fourth rows are shifted by offsets of two and three respectively.
Only then in fact was payment for assembly attendance, the central event of democracy ( Similarly for the period before the Persian wars, but for the very early democracy the sources are very meagre and it can be thought of as being in an embryonic state ).
Similarly, some dishes that are typically considered American have their origins in other countries.
Similarly, there are many works detailing atrocities and malevolence of Communist regimes ( e. g., Nadezhda Mandelstam's Hope against Hope ).
Similarly, in Avery Corman's book The Old Neighborhood ( 1980 ), an upper-middle class white protagonist returns to his birth neighborhood ( Fordham Road and the Grand Concourse ), and learns that even though the folks are poor, Hispanic and African-American, they are good people.
Similarly powerful Mercia kings such as Offa are missed out of the West Saxon Anglo-Saxon Chronicle, which sought to demonstrate the legitimacy of their kings to rule over other Anglo-Saxon peoples.
Similarly, those participants who are recipients of the activities are typically known as bottoms, those who are controlled by their partners as submissives, and those who receive pain as masochists ; again, these are frequently the same person and the terms are sometimes used interchangeably.
Similarly, corporations are often formed under Delaware corporate law, and contracts relating to corporate law issues ( merger and acquisitions of companies, rights of shareholders, and so on.
Similarly, different cultural attitudes, social organizations, economic models and legal frameworks are seen to account for why copyright emerged in Europe and not, for example, in Asia.
Similarly, relatively little energy is used in producing and combining the raw materials ( although large amounts of CO < sub > 2 </ sub > are produced by the chemical reactions in cement manufacture ).
Similarly, the halogens and the noble gases are nonmetals, viewed in the broader sense.
Similarly, Robert Nozick argues for a theory that is mostly consequentialist, but incorporates inviolable " side-constraints " which restrict the sort of actions agents are permitted to do.
Similarly, the Economic and Financial Affairs Council is composed of national finance ministers, and they are still one per state and the chair is held by the member coming from the presiding country.
Similarly, most biochemically significant processes are catalysed.
Similarly, one cannot argue that Western epistemology is unjustly promoted in non-Western societies if one believes that those epistemologies are absolutely correct.
Similarly, fungi that capture microscopic animals are often called carnivorous fungi.

Similarly and said
Similarly the freehold of a benefice, on the death of the incumbent, is said to be in abeyance until the next incumbent takes possession.
Similarly, P is said to satisfy the descending chain condition ( DCC ) if every descending chain of elements eventually terminates, or equivalently if any descending sequence
Similarly, Human Rights Watch pointed out that " the Contras systematically engage in violent abuses ... so prevalent that these may be said to be their principal means of waging war " in a 1989 report.
Similarly, if only the magnetic field () is non-zero and is constant in time, the field is said to be a magnetostatic field.
" Similarly, Roger Ebert, writing of his iconic performance in Last Tango in Paris, said: " This was the greatest movie actor of his time, the author of performances that do honor to the cinema.
Similarly, an organism living in a demersal habitat is said to be a demersal organism, as in demersal fish.
Similarly, in linguo-labial consonants the tongue contacts the upper lip with the upper lip actively moving down to meet the tongue ; nonetheless, in this gesture the tongue is conventionally said to be active and the lip passive, if for no other reason than the fact that the parts of the mouth below the vocal tract are typically active, and those above the vocal tract typically passive.
Similarly, the Charter of Fundamental Rights, codified into law applicable to European Union countries by the passage civil lawsuit, is said to have accrued when the event beginning its time limitation occurs.
Similarly, in later myths, Zeus would swallow Metis when she was pregnant with Athena, because of a prophecy that said she would later give birth to a son who would be more glorious than his father.
" Similarly, on the May 24, 2011 edition of CNBC's Kudlow and Company, host Lawrence Kudlow, discussing a book by former deputy Under-Secretary of Defense Jed Babbin, said " World War IV is the terror war, and war with China would be World War V ."
Similarly, Briseis was said to have regarded Achilles as her husband as well.
Similarly, bin al-Shibh later said that Mohamed Atta had phoned him on the morning of August 29.
Similarly, Pope John Paul II said of the Paul VI revision of the liturgy: " This work was undertaken in accordance with the conciliar principles of fidelity to tradition and openness to legitimate development, and so it is possible to say that the reform of the Liturgy is strictly traditional and ' in accordance with the ancient usage of the holy Fathers '.
Similarly, Fangorn was said to be a dangerous and evil place like Mirkwood where huge spiders roamed the forest and other evil creatures lay, but this was not the case following the events of Lord of the Rings.
Similarly, a parable also resembles a simile, i. e. a metaphorical construction in which something is said to be " like " something else ( e. g. " The just man is like a tree planted by streams of water ").
" Similarly, when Jimmy Page was asked about the development of guitar feedback, he said, " I don't know who really did feedback first ; it just sort of happened.
Similarly Kent Houston, head of Peerless Camera doing the film's special effects said in Madness and Misadventures that they were promised a bonus if they would finish the effects in time, but when they approached the person again when they were done, he was met with the reply, " I'm not gonna pay you, because I don't want to seem to be doing anything that could benefit Terry Gilliam.
Similarly, God has said: “ If two parties among the believers fall into a quarrel, make peace between them ; but if one of them transgresses beyond bounds against the other, then fight against the one who transgresses until he complies with the command of Allah ; then, if he complies, make peace between them with justice, and be fair: for Allah loves those who act fairly ” ( Qur ' an 49: 9 ).
" Similarly, journalist Matt Taibbi has said of Friedman's writing that, " Friedman came up with lines so hilarious you couldn't make them up even if you were trying – and when you tried to actually picture the ' illustrative ' figures of speech he offered to explain himself, what you often ended up with was pure physical comedy of the Buster Keaton / Three Stooges school, with whole nations and peoples slipping and falling on the misplaced banana peels of his literary endeavors.
Similarly, surfers who ride equally well in either stance are said to be surfing " switch-foot ".
" Similarly, in a 1984 interview on BBC Radio 1, Waters said " If somebody said to me now – right – here's a million pounds, go out and play Atom Heart Mother, I'd say you must be fucking joking.
Similarly, it is said to have lowest weight λ if λ is a weight and all its other weights are greater than it.
" Similarly, the amateur historian Bob Atchison said that Anastasia was akin to someone making a film in which " Anne Frank moves to Orlando and opens a crocodile farm with a guy named Mort.

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