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Page "Algebraic topology" ¶ 7
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They and defined
They use Eight-to-Fourteen Modulation, CIRC error correction plus the third error correction layer defined for CD-ROM.
They are being legally defined as different languages from Sardinian by the Sardinian government.
They describe what is needed to be defined in a database for any specific application.
They were originally identified as outliers to a general trend of decreasing extinction rates during the Phanerozoic, but as more stringent statistical tests have been applied to the accumulating data, the " Big Five " cannot be so clearly defined, but rather appear to represent the largest ( or some of the largest ) of a relatively smooth continuum of extinction events.
They are defined by the IEEE 1101. 2-1992 ( 2001 ) standard.
They argue that nations and races must purge themselves of socially and biologically weak or degenerate people, while simultaneously promoting the creation of strong people, in order to survive in a world defined by perpetual national and racial conflict.
They are defined by the set of light cones ( see the image on the left ).
They believed state monopoly capitalism ( defined as a state-sponsored monopoly ) prevented labor from being fully rewarded.
They are defined as non-homogenous array structure.
They have a different type of border, in principle defined only by the area of settlement of the national group, although many nation states also sought natural borders ( rivers, mountain ranges ).
" By the eighteenth century these unorthodox religious and philosophical concerns were well defined as ' occult ', inasmuch as they lay on the outermost fringe of accepted forms of knowledge and discourse ," They were, however, preserved by antiquarians and mystics.
They may view the occult as being anything supernatural or paranormal which is not achieved by or through God ( as defined by those religious denominations ), and is therefore the work of an opposing and malevolent entity.
They argue, for example, that physical magnitudes such as electrical charge cannot be explicitly defined either, in terms of more basic things, but only in terms of what they do ( such as attracting and repelling other electrical charges ).
They defined Reptilia as all amniotes closer to Lacerta agilis and Crocodylus niloticus than to Homo sapiens.
They defined parts of speech, analyzed poetry, parsed close synonyms, invented argumentation strategies, and debated the nature of reality.
* They deny that they implicitly repudiate the dogma of papal infallibility as defined at the First Vatican Council, and maintain that, on the contrary, they are the fiercest defenders of this doctrine, since they teach that the Apostolic See of Peter, under the rule of a true Pope, cannot promulgate contradictory teachings.
They were the biggest popular cultural icons of the 1990s, according to a survey carried out by Trivial Pursuit, winning by 80 percent in a poll of 1, 000 people, stating that " Girl Power " defined the decade.
They state that lack of definition of obscenity in the statutes, coupled with the existence of hypothetical entities and standards as ultimate arbiters within the Miller Test ( hypothetical " reasonable persons " and " contemporary community standards ") proves that federal obscenity laws are in fact not defined, do not satisfy the vagueness doctrine, and thus are unenforceable and legally dubious.
They are also defined in international human rights instruments, such as the 1948 Universal Declaration of Human Rights and the 1966 International Covenant on Civil and Political Rights.
They included G. 707 to G. 709, and I. 121 which defined the principal aspects of B-ISDN, with many others following through the 1990s.
They also run under clearly defined Home Office rules.
They are called " invariants " because they are defined in such a way that they do not change if the space is subjected to some deformation.
( They defined duct tape as any fabric-based tape with rubber adhesive.
They give a highly idealised depiction of the forms represented, and the compositions, though very carefully conceived in drawings, achieve " sprezzatura ", a term invented by his friend Castiglione, who defined it as " a certain nonchalance which conceals all artistry and makes whatever one says or does seem uncontrived and effortless ...".

They and homology
They have a diverticulum of the foregut called a stomochord, previously thought to be related with the chordate notochord, but this is most likely the result of convergent evolution rather than homology.
They are common experimental animals in biology and psychology, primarily because they are mammals, are relatively easy to maintain and handle, reproduce quickly, and share a high degree of homology with humans.
They furthermore showed that the intersection of an i-and an ( n − i )- dimensional allowable cycle gives an ( ordinary ) zero-cycle whose homology class is well-defined.
They were the first known examples of 3-manifolds which were not determined by their homology and fundamental group alone, and the simplest examples of closed manifolds whose homeomorphism type is not determined by their homotopy type.
They are approximately 20-50 % identical to each other ; that is, they share gene sequence and amino acid sequence homology.
They also provide an appropriate algebraic framework for many knot invariants ( in particular the Jones polynomial ), and have been used in describing the properties of Khovanov homology with respect to tangle composition.

They and cohomology
They relate to the Galois action on the l-adic cohomology of an algebraic variety, identifying a space of ' Tate cycles ' ( the fixed cycles for a suitably Tate-twisted action ) that conjecturally picks out the algebraic cycles.
They satisfy a form of Poincaré duality on non-singular projective varieties, and the ℓ-adic cohomology groups of a " reduction mod p " of a complex variety tend to have the same rank as the singular cohomology groups.
They are significant both as applied to several complex variables, and in the general development of sheaf cohomology.
They represent ( at least if K is a perfect field ) Galois cohomology classes in
They have been used to study Hopf algebras, coding theory, and cohomology rings of compact oriented manifolds.

They and equipped
They are more heavily armed and equipped ( including power armors like the K-11 and K-12 ) than a normal police force, but more lightly than a military organization.
They are equipped with a TERCOM system which allows them to cruise at an altitude lower than 110 meters at subsonic speeds while obtaining a CEP accuracy of 15 meters with an Inertial navigation system.
They quickly gained air superiority over the Allies, who at this stage of the war were often disorganized, under-trained and poorly equipped, and Japanese air power contributed significantly to their successes in the Philippines, Malaysia and Singapore, the Dutch East Indies and Burma.
They were equipped as heavy cavalry, with three or four horses and one or two squires.
They were either equipped as light cavalry with a single horse or served in other ways such as administering the property of the Order or performing menial tasks and trades.
They also appeared unwilling to incur the cost of maintaining a large well equipped army.
They are also equipped with front-line ambulances, and personnel have first-aid and paramedic training.
They are trained and equipped to modify physical disease states and the actual cytoarchitecture and functioning of the central nervous and related systems using psychological and pharmacological techniques ( when allowed by statute ), and to provide prevention for the progression of disease having to do with poor personal and life-style choices and conceptualization, behavioral patterns, and chronic exposure to the effects of negative thinking, choosing, attitudes, and negative contexts.
They can be inexpensive: some variants can cost as little as US $ 1000, though more sophisticated mines can cost millions of dollars, be equipped with several kinds of sensors, and deliver a warhead by rocket or torpedo.
They can also be equipped with non-lethal ( more accurately known as " less than lethal " or " less-lethal ") weaponry, particularly for riot control.
They must also fulfill the requirement of Ministry of Housing and Local Government, where the pawn counter is not higher than 4 feet, bullet-proof and stainless steeled counters, stainless steeled doors, strong rooms with automatic locks, safes, equipped with fully computerized system, CCTV, Alarm and Pawnbroker Insurance.
They were therefore equipped with a 32KB L1 cache ( double that of pre-P55C Pentium CPUs ).
They were usually equipped with Apple's newest technologies, and commanded the highest prices among Apple desktop models.
They are equipped with a red light and a license plate.
They are responsible, and therefore liable, only for matters that they are best equipped and prepared to manage.
They have now a thoroughly organised army equipped with guns which one of their own officers has invented and which is said to be second to none.
They were often equipped with a vamplate, a small circular plate to prevent the hand sliding up the shaft upon impact.
They commonly can accommodate both wet and dry soilage ; some are also equipped with a switch or exhaust port for reversing the airflow, a useful function for everything from clearing a clogged hose to blowing dust into a corner for easy collection.
They were carefully constructed to create optimum recording conditions, and were equipped with the latest and best recording equipment and top-quality microphones, as well as electronic amplification gear and musical instruments.
They were equipped with one Rolls-Royce Olympus TMB3 gas turbine and three Wärtsilä marine diesels for slower speeds.
They had been hastily trained, poorly equipped, and only a minority of them had functional muskets.
They were not given a warm welcome and the hotel rooms they stayed in were equipped with anti-American pamphlets.
They are equipped with high visibility driving cabs to enable the operator to see the terrain and more easily manipulate mounted tools.
They can be equipped with a backhoe, front loader, or other contracting equipment.

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