Extending the pa so that it could interpret standard first-order logic has yet to be done, but Peirce's beta existential graphs suggest that this extension is feasible.

Extending these deep ideas of Riemann, two proofs of the asymptotic law of the distribution of prime numbers were obtained independently by Jacques Hadamard and Charles Jean de la Vallée-Poussin and appeared in the same year ( 1896 ).

Extending this tradition, other groups and individuals create more ribbons for use at the convention ; these may be serious or silly.

Extending these experiments, Ampère published his own successful model of magnetism in 1825.

Extending this to circles immersed in the plane – the immersion condition is precisely the condition that the derivative does not vanish – the Whitney – Graustein theorem classified these by turning number by considering the homotopy class of the Gauss map and showing that this satisfies an h-principle ; here again order 0 is more complicated.

Extending these results to the study of pain causes by the stimulus of the nervous system, he made discoveries about the reception of such signals in the brain and spatial distribution of the sensory areas of the cerebral cortex in different animals.

Extending these systems to support remote procedure calls behind the scenes was seen as a natural evolution, providing a solution to the client / server programming problem.

Extending the bradyon, luxon, tachyon classification from the representation theory of the Poincaré ' group to an analogous classification, here, one may term these states as synchrons.

Extending from the southern end of the Champlain Bridge to Magog, the highway replaced the old Quebec Route 1 ( now Route 112 ) as the main road link between these two points.

Extending the telephoto range, the Canon EF-S 55-250mm lens is a telephoto zoom that picks up at 55mm ( 88mm equivalent ), and together these cover the 18 – 250mm range ( 28. 8 – 400mm equivalent ).

Extending north south along the western edge of the Mescalero Escarpment lies a vast sand sheet called the Mescalero Sands, named for the Mescalero Apaches who once hunted in these sandhills.

Extending these results is an open problem.

Extending by continuity defines f ( T ) for a continuous function f on the spectrum of T. The Riesz-Markov theorem then allows us to pass from integration on continuous functions to spectral measures, and this is the Borel functional calculus.

Extending further south, Lewisham East then takes in some areas of high social deprivation fairly close to Lewisham town centre, and part of Rushey Green, a traditional working class area famous for opening one of the first indoor shopping malls in England.

Extending the definition of separability from the pure case, we say that a mixed state is separable if it can be written as

Extending the definition of remainder for real numbers as described above is not of theoretical importance in mathematics ; however, many programming languages implement this definition — see modulo operation.

Extending this concept to all sentient beings, one can measure a range of consciousness based on how many and how powerfully neurons are actually firing, varying from worms to humans.

Extending responsibility for public order to include the police, military, and citizenry proved to be a highly effective arrangement, and the concept was written into the Common Program that preceded the 1954 state constitution.

Extending the collaboratory concept to include both social and behavioral research as well as more scientists from the developing world could potentially strengthen the concept and provide opportunities of learning more about the social and technical factors that support a distributed knowledge network ( Cogburn, 2003 ).

Extending this concept, Barry relates all chord alterations ( flat and sharp 9 ’ s, sharp 11 ’ s, flat 13 ’ s, etc.

Remaking the concept of aptitude: Extending the legacy of Richard E. Snow.

Extending IMF and WTO voting rights to developing countries, along with public accountability, would be a good start.

Extending until the station at Alcântara-Mar, in 1891 the rail-line was completed after public sanitation works along the beach in Alcântara ( 1876 ), which resulted in the recovery of an additional 500 meters of land from the Tagus River, which were quickly expropriated by factories, docks and warehouses.

* Extending product life cycles

Extending the life of desktop machines will reduce the incursion of off-spec machines later in the life-cycle, improving standardization, reducing support costs, minimizing e-waste.

Extending the useful life of a structure also reduces waste – building materials such as wood that are light and easy to work with make renovations easier.

Extending this idea, he posited that, if training in karate in a natural way leads one to mastery of one's body, knowledge and experience are vastly increased and the foundation for naturally living a moral life is established. For this reason Konishi named his own style Shindo Jinen Ryu (" godly, natural style, complete empty-handed way ").

Extending this meaning, the shastra is commonly used to mean a treatise or text written in explanation of some idea, especially in matters involving religion.

Extending this meaning, the shastra is commonly used to mean a treatise or text written in explanation of some idea, especially in matters involving religion.

Extending over 125 acres ( 500, 000 m² ) of land, it has one of the most spacious campuses in the country.

Extending this convention to the clausal categories occurred in the interest of the consistent use of labels.

Extending the Monroe Doctrine, it set forth the policy that no foreign power, including the United States, could use force against an American nation to collect debt.

Extending SLE service would require negotiations with the US Coast Guard, the Marine Trades Association, and other stakeholders for increased use of the Thames River Bridge and the Mystic River bridge.

Extending this original usage, James C. Scott's writings use " high modernism " as a disparaging label for a cluster of beliefs revolving around faith in " progress " that he finds distastefully technocratic and authoritarian.

Extending her fingers another inch, she caught up the shorts, and swiftly left the room.

Extending entirely across the state of Alabama for about south of its northern boundary, and in the middle stretching farther south, is the Cumberland Plateau, or Tennessee Valley region, broken into broad tablelands by the dissection of rivers.

Extending from the Gulf northward for about 150 miles ( 240 km ) is the outer belt of the Coastal Plain, also called the Timber Belt, whose soil is sandy and poor, but responds well to fertilization.

Extending one night into three, Zeus slept with Alcmene ( his great-granddaughter ) ( thereby conceiving Heracles ) and recounted Amphitryon's victories against the Teleboans.

Extending the capabilities of SAT solving algorithms is an ongoing area of progress.

Extending voting rights to excluded groups ( such as convicted felons, members of certain minorities, and the economically disadvantaged ) continues to be a goal of voting rights advocates.

Extending the compiler only requires writing a new word, instead of modifying a grammar and changing the underlying implementation.

Extending this work, Nirenberg and Philip Leder revealed the triplet nature of the genetic code and deciphered the codons of the standard genetic code.

Extending outward from the bulge are relatively bright arms.

* Extending the file system metaphor, such as searches.

Extending from 18-10, 500 BC, the Kebaran culture shows clear connections to the earlier Microlithic cultures using the bow and arrow, and using grinding stones to harvest wild grains, that developed from the c. 24, 000-17, 000 BC Halfan culture of Egypt, that came from the still earlier Aterian tradition of the Sahara.

Extending on the example outlined, the same apple dropped within a zero gravity environment such as a spacecraft circling around earth, will float in its place.

Extending approximately 15, 500 kilometres ( 9, 600 mi ) from the Bering Sea in the Arctic to the northern extent of the circumpolar Southern Ocean at 60 ° S ( older definitions extend it to Antarctica's Ross Sea ), the Pacific reaches its greatest east-west width at about 5 ° N latitude, where it stretches approximately 19, 800 kilometres ( 12, 300 mi ) from Indonesia to the coast of Colombia – halfway across the world, and more than five times the diameter of the Moon.

Extending across the whole of northern Asia and most of eastern Europe, Russia spans nine time zones and incorporates a wide range of environments and landforms.

Extending for, the Russian border is the world's longest, a source of substantial concern for national security in the post-Soviet era.

See Extending and Embedding the Python Interpreter.

Extending in a north-south orientation, the climate and ecology varies strongly across the Americas, from arctic tundra of Canada, Greenland, and Alaska, to the tropical rain forests in Central America and South America.

Extending their authority into Hispania at the expense of the Suevi and Vandals, their rule in Gaul was ended by the Franks under Clovis I at the Battle of Vouillé in 507.

Extending 5ESS-2000.

Extending the arms and free leg checks the rotation and allows the skater to flow out of the jump on a strong edge.