Moreover, the Banach fixed point theorem states that every contraction mapping on a nonempty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x, f ( x ), f ( f ( x )), f ( f ( f ( x ))), ... converges to the fixed point.

Moreover, the finds were unique.

Moreover every homomorphism between Lie algebras lifts to a unique homomorphism between the corresponding simply connected Lie groups.

Moreover, for each number of cities there is an assignment of distances between the cities for which the nearest neighbor heuristic produces the unique worst possible tour.

Moreover, every irrational number α is the value of a unique infinite continued fraction, whose coefficients can be found using the non-terminating version of the Euclidean algorithm applied to the incommensurable values α and 1.

Moreover, the biography progresses backwards in time, as a reminder that it is less history than fiction, and as an example of Pindar's unique literary methodshe often demonstrated particular themes by narrating episodes from traditional myths, sometimes in reverse chronological order: an aspect of his risk-taking approach.

Moreover, Salinator was not unique to the Livii ; L. Oppius Salinator wore it, whether by marriage, adoption or independent assignment.

Moreover, V has a unique unitary extension if and only if the both deficiency indices are zero.

Moreover, if such a lift g of f exists, it is unique.

Moreover the morphism q must be universal for this diagram, i. e. any other such q ′: Y → Q ′ can be obtained by composing q with a unique morphism u: Q → Q ′:

More explicitly, a coequalizer can be defined as an object Q together with a morphism q: Y → Q such that q ∘ f = q ∘ g. Moreover, the pair ( Q, q ) must be universal in the sense that given any other such pair ( Q ′, q ′) there exists a unique morphism u: Q → Q ′ for which the following diagram commutes:

" Moreover, he was " extremely critical of student tactics, believing that they were based on irrational romantic ideas, rather than sensible plans for achievable change, that they undermined the unique status of the university, as an institutional bastion of free thought, and that they were bound to provoke a political reaction from the right ".

Moreover, for many white Americans in that era who were not living in areas that were racially diverse, Soul Train provided a unique window into African-American culture.

Moreover every irreducible representation on a complex vector space can be constructed from a unique irreducible representation on a real vector space in one of the three ways above.

Moreover, the conjugate of if it exists, is unique up to an additive constant.

Moreover, the University of Arkansas ' unique sports cheer is known as " Calling the Hogs ".

Moreover, the fact that wormwood and garlic are not found in ancient Chinese herbology shows that traditional Korean medicine developed unique practices.

Moreover the primary submodules associated to the minimal or isolated associated primes ( those not containing any other associated primes ) are also unique.

Moreover, for every vector norm on, there exists a unique positive real number such that is a sub-multiplicative matrix norm for every.

Moreover, the solution of order 3 is essentially unique .< ref >< Trigg, C. W. " A Unique Magic Hexagon ", Recreational Mathematics Magazine, January – February 1964.

Extracts of Scrophularia have been shown to reduce edema, cell infiltration and proliferation of activated T-lymphocytes in joint tissues. Additionally, Scrophularia has been shown to inhibit a number of inflammatory factors, including prosta-glandin E2, leukotriene B4, NO, interleukin-1beta, interleukin-2, interleukin-4 and interferon-gamma, but with no negative effect on the production of interleukin-10, a powerful cytokine involved in the regulation of inflammatory responses. Moreover, Scrophularia is the source of a unique glycoterpenoid, Verbascosaponin A, which is twice as potent as indomethacin for relieving inflammation and pain.

Moreover, during the fifth cutscene of the Allied campaign, a news announcer reporting on the Allies ' loss of Greece is suddenly heard stating that the United Nations are in the process of bringing about a unique military task force aimed at preventing future globalized conflicts.

Moreover, distinctions made between the creation of foreign people groups and the tribe or ethnic group to which the creation myth pertains served to reinforce tribal or ethnic unity, the need to exercise wariness and caution when dealing with outsiders, or the unique nature of the relationship between that tribe and the deities of their religious system.

Moreover, taking G = H it shows that the commutator subgroup is stable under every endomorphism of G: that is, is a fully characteristic subgroup of G, a property which is considerably stronger than normality.

Moreover, orchestral and contrapuntal innovation is characteristic of his style: for instance, the strings producing a rapid ascending scale in Monterone's scene in Rigoletto accentuate the drama, and, in the same opera, the chorus humming six closely grouped notes backstage portrays, very effectively, the brief ominous wails of the approaching tempest.

Moreover, there is a characteristic distribution of letters that is roughly the same for almost all samples of that language.

Moreover, it was a watershed ushering out the commitment to government anti-poverty programs and affirmative action characteristic of the Great Society.

Moreover, at that time the immigration of numbers of monks from Burma was introducing the more rigorous discipline characteristic of the Mon sangha.

Moreover, the essay is an early analysis of speculative fiction by one of the most important authors in the genre.

Moreover, argues Rico, the structure of the novel is radically different from previous works of the picaresque genre: Quevedo uses the conventions of the picaresque as a mere vehicle to show off his abilities with conceit and rhetoric, rather than to construct a satirical critique of Spanish Golden Age society.

Moreover, the law of the land is not irrevocable ; ;

Moreover its posture of stubborn but simple resistance is doomed to failure because of the metaphysical weakness of the existent form of order, once the activation of change has reached visible proportions.

Moreover, if the critic instructs his audience in what to see in a work, he is contributing to this pseudo-thinking ; ;

Moreover, the hearing officer's report is but intradepartmental, is directed to the Attorney General and, of course, is not the recommendation of the Department.

Moreover, the piece is written in five movements, rather than the conventional four of most quintets, and this gives the opus a serenade or divertimento flavor.

Moreover, it will be asymmetric until a certain critical Af distance is reached, below which it will become symmetric.

Moreover, the responsiveness of the hypothalamus to nociceptive stimulation is greatly increased under these conditions.

Moreover, from the definitive transformation of intercepts on the generators of Af, it is clear that the only points of Q at which a line can meet its image are the points of Aj.

Moreover, in this involution there is a cone of invariant lines of order Af, namely the cone of secants of **zg which pass through P.

Moreover, the current information on what types of training are needed and possible is too limited and fragmentary.

Moreover, the taunt concerning the `` sophisticated '' echelon and its alleged erudition is put to test during every campaign, and accrues only upon results ; ;

Moreover, it is likely that Federal policies aimed at stimulating a faster rate of economic growth of the country, to keep ahead of the Communist countries and to demonstrate that our free economic system is better than theirs, will lead to rising Federal spending in certain areas such as education, housing, medical aid, and the like.

Moreover, it is too readily forgotten that in the Republic what gave the initial impetus to Plato's excursus into the construction of an imaginary commonwealth with its ruling-class communism of goods, wives, and children, was his quest for a canon for the proper ordering of the individual human psyche ; ;

Moreover, the cost of operations is always high in any new store, as the conservative bankers who act as controllers for retail giants are beginning to discover.

Moreover, the President is meeting the Soviet leader at a time when the Administration has still not decided on the scope of America's firm foreign policy commitments.

Moreover, there is the 1908 theory that America derives from Richard Amerike of Bristol, England, financier of John Cabot's 1497 expedition.

Individuals who survived to this, the latest and highest stage of evolutionary progress would be “ those in whom the power of self-preservation is the greatest — are the select of their generation .” Moreover, Spencer perceived governmental authority as borrowed from the people to perform the transitory aims of establishing social cohesion, insurance of rights, and security.

Moreover, if any coefficient is a fixed power of 2, the multiplication can be replaced by bit shifting.

Moreover they argued that some species have been created for the purpose of being sacrificed and eaten by humans, that it is normal for animals to kill and eat other animals, that agriculture, too, inevitably leads to the death of many animals, that plants are living beings as well and must still be destroyed, that we unintentionally and unknowingly destroy life forms all the time, and that a hunted animal has a fair chance to survive by killing the hunter.

Moreover, oxidative stress is both the cause and the consequence of disease.

Moreover, frequent smashing can be exhausting in singles where the conservation of a player's energy is at a premium.

Moreover, Frederick A. Tatford in Prophet of Edom ’ s Doom says that Obadiah ’ s prophecy is fulfilled today as there is currently no trace of anyone who may be identified as an Edomite.