(" the truth-values of our mathematical assertions depend on facts involving platonic entities that reside in a realm outside of space-time ") Whilst our knowledge of concrete, physical objects is based on our ability to perceive them, and therefore to causally interact with them, there is no parallel account of how mathematicians come to have knowledge of abstract objects.

Whilst the magnification of both the field ion and atom probe microscopes is extremely high, the exact magnification is dependant upon conditions specific to the examined specimen, so unlike for conventional electron microscopes, there is often little direct control on magnification, and furthermore, obtained images may have strongly variable magnifications due to fluctuations in the shape of the electric field at the surface.

Whilst there, the Greek army surprised and outmaneuvered Artaphernes, marching to Sardis and burning the lower city.

Whilst there, the Queen met with Bernard of Clairvaux, demanding that he have the excommunication of Petronilla and Raoul lifted through his influence on the Pope, in exchange for which King Louis would make concessions in Champagne, and recognise Pierre de la Chatre as archbishop of Bourges.

Whilst human geography is interdisciplinary, there are a number of journals with a human geography focus.

Whilst there, he staged regular Merz recitals, including a performance of Silence, his first poem in English, but was apparently seen as a somewhat pathetic irrelevant figure by other artists at the camp.

Whilst prices have reduced and availability has increased considerably since the introduction of competition, there is little sign of TPSA's market share being seriously reduced.

Whilst Anglican priests who are members of religious orders must remain celibate ( although there are exceptions, such as priests in the Anglican Order of Cistercians ), the secular clergy – ( bishops, priests, and deacons who are not members of religious orders ) – are permitted to marry before or after ordination.

Whilst on the surface the new Potsdamer Platz appears so far to have lived up to its expectations as a futuristic centre of commerce at the heart of Europe's youngest capital city, there has been much debate as to just how successful it really is.

Whilst the action of rowing and equipment used remains fairly consistent throughout the world, there are many different types of competition.

Whilst there is little evidence to invalidate the letter as a whole, both the recipient ( s ) of the letter and whether such a letter actually nominates Barbastro as the first ' crusade ' are still a matter of dispute.

Bahā ' ad-Dīn writes, " Whilst we were there they brought two Franks to the Sultan ( Saladin ) who had been made prisoners by the advance guard.

Whilst the terms spirituality and religion both relate to a search for an Absolute or God, and thus have much overlap, there are also characteristic differences in their usage.

Also in S6: E5 Whilst the boys are watching the TV there are many cans of soda with the name " ZOOP " on them.

Whilst the styles were similar, there are some notable differences between both Rococo and Baroque architecture, one of them being symmetry, since Rococo emphasised the asymmetry of forms, whilst Baroque was the opposite.

(" the truth-values of our mathematical assertions depend on facts involving platonic entities that reside in a realm outside of space-time ") Whilst our knowledge of concrete, physical objects is based on our ability to perceive them, and therefore to causally interact with them, there is no parallel account of how mathematicians come to have knowledge of abstract objects.

Whilst there his task is a simple assignment to investigate the disappearance of Commander John Strangways, the head of MI6 Station J in Kingston, Jamaica, and his secretary.

Whilst anchored in Cumberland Bay, Robinson Crusoe Island, the Dresden was trapped and forced to scuttle after fighting a battle there with the British.

Whilst there, he met the American composers George Gershwin and Irving Berlin and brought Dédé to Broadway in 1922.

Whilst this elm has little innate resistance to Dutch elm disease, it is not favoured by the vector bark beetles and thus only becomes colonized and infected when there are no other choices, a rare situation in western Europe.

Whilst there, Telemachus is again treated as an honored guest as Menelaus and Helen tell complementary, yet contradictory stories of his father's exploits at Troy.

Whilst working at the Institute, Childe took up residence at Lawn Road Flats near to Hampstead, an apartment block perhaps recommended to him by the popular crime fiction author Agatha Christie ( the wife of his colleague Max Mallowan ), who had lived there during the Second World War.

Whilst there is no specific form of words provided for such proclamations, they must be made ' in the Queen's name '.

Whilst the idea that there is some objective sense in which time is flowing can be denied, the fact that conscious beings feel as though it is in some sense flowing cannot.

" Whilst there, Lumley was hailed ' Daughter of Nepal ' by the crowds of fans at the airport.

Whilst most continuity errors are subtle, such as changes in the level of drink in a character's glass or the length of a cigarette, others can be more noticeable, such as sudden drastic changes in appearance of a character.

Whilst critical theorists usually are defined as Marxist intellectuals, their tendency to denounce Marxist concepts, and to synthesise Marxian analysis with other sociologic and philosophic traditions has been attacked as revisionism, by Classical, Orthodox, and Analytical Marxists, and by Marxist-Leninist philosophers.

" Whilst I agree that it can take a bit of time to see it through carefully, it nevertheless, demonstrates to our regional friends that we are principled in our approach to international relations and diplomacy ," Mataitoga said.

Whilst a few social scientists who draw inspiration from ' organic ' views of society have embraced Gaia philosophy as a way to explain the human-nature interconnections, most professional social scientists are more involved in reflecting upon the way Gaia philosophy is used and engaged with within sub-sections of society.

Whilst the terms are often used interchangeably, branding is more strictly related to the identifying mark or trade name for a product or service, whereas corporate identity can have a broader meaning relating to the structure and ethos of a company, as well as to the company's external image.

Whilst some MUVs might be replicas of European MPVs ( such as the European Ford Fusion ) or American-style minivans ( like the Toyota Innova ), in some cases MUVs are similar to SUVs ( such as the Chevrolet Tavera ).

Whilst bureaucratic operations emphasis business processes and strongly authoritarian hierarchies, these are based on enforcing power relationships rather than an overlying aim of protectionism, sustainability or growth.

Whilst the following example illustrates how a desired sound might be achieved in practice, only the final three stages are really subtractive synthesis and the early stages could be considered to be a form of additive synthesis.

Whilst hierarchy is quickly established between individuals from a single group, this is not the case with organisms from different groups ; these are substantially more aggressive and very rarely climb one another or form aggregates.

Whilst less famous, the An-24, An-26, An-30 and An-32 family of twin turboprop, high winged, passenger / cargo / troop transport aircraft are important for domestic / short-haul air services particularly in parts of the world once led by communist governments.

Whilst they are mainly used in commercial operations, non-electric detonators are still used in military operations.

Whilst Blake is an idealistic freedom fighter, his associates are petty crooks, smugglers and killers.

Whilst a number of viruses can block the effects of TNF and Fas.

Whilst the process of meiosis bears a number of similarities with the ' life-cycle ' cell division process of mitosis, it differs in two important respects:

Whilst this is the largest number in Africa, South Africa's broadband penetration of 4 % is significantly below international standards-largely due to exorbitant costs established by the monopoly enjoyed by Telkom until recently.

Whilst the full number of gods and goddesses found in Mesopotamia is not known, K. Tallqvist, in his Akkadische Götterepitheta ( 1938 ) counted around two thousand four hundred that we now know about, most of which had Sumerian names.

Whilst little has yet been released regarding the successes of the service there have been a number of intelligence failures which have created embarrassment for both the service and the government.

Whilst the British Army has the capability there is no standing UK Corps organisation, forces being allocated through a number of multi-partite arrangements to the North Atlantic Treaty Organisation ( NATO ) and European commitments, providing much of the headquarters capability and framework for the multinational Allied Rapid Reaction Corps.

Whilst the development of Switzerland's road and rail networks has relieved the lake of much of its through traffic, it continues to be used by a considerable number of vessels, both private and public.

Whilst nature documentaries such as Planet Earth are the most familiar part of the 1, 880 annual BBC One hours of factual and learning, this also includes lifestyle-format daytime programmes and a number of reality television formats and the One Life strand.

Whilst some species of procellariid have populations that number in the millions, many species are much less common and several are threatened with extinction.

Whilst this was an issue for monophonic synthesizers, the limited number of oscillators ( typically 3 or fewer ) meant that keeping instruments tuned was a manageable task, often performed using dedicated front panel controls.

Whilst the channel stays at the same usage ( roughly 99 %), the throughput just gets slower and slower due to the number of retries.

Whilst Flybe holds the most flights into and out of Birmingham, Monarch carry the most passengers, which will further be increased over the next 12 months with the introduction of a number of new routes and frequencies.

Whilst the 1989 opening of the improved A361 connection to the motorway network helped in some ways to promote trade, notably weekend tourism, it had a detrimental effect on a number of distribution businesses.

Whilst Richard the Lionheart was away on the Third Crusade, and a great number of English noblemen were away with him, it was said that Nottingham Castle was left derelict and it was occupied by the Sheriff of Nottingham.

Whilst it is a term that has been used in a number of religious and other traditions, Shah's use of it was in the context of Sufi teaching and learning, within which this body of material has been described as the " most valuable of the treasures in the human heritage ".

Whilst there he was one of a number of cadets interviewed for an edition of the BBC's Panorama programme.

Whilst archdeacon he became Rector of Pulham St. Mary ( 1341 ) and acquired a large number of canonries.

Whilst concerned mainly with poetry and theory, Surrealism created a number of works that continued in the French tradition of the Livre d ' Artiste, whilst simultaneously subverting it.

Whilst the term " sound designer " was not is use at this time, a number of stage managers specialised as " effects men ", creating and performing offstage sound effects using a mix of vocal mimicry, mechanical and electrical contraptions and gramophone records.

Whilst generally returns or interest payable in respect of these funds will be subject to local taxation, there are a number of offshore areas in which funds may be placed as bank deposits where the interest and / or the capital gains are paid and kept gross.

Whilst others are starting to carry the number of passengers that was hoped for, Nottingham has exceeded the most optimistic predictions, carrying 9. 7 million people in 2005.

Whilst in some instances, this advice may not have been appreciated in its entirety, in a large number of cases this advice has been used to reach decisions on planning applications.

Whilst maintaining the core provisions which have successfully served the international air transport community for several decades ( i. e. the Warsaw regime ), the new convention achieves the required modernisation in a number of key areas.

Whilst it is difficult to quantify the number of false negative results there have certainly been examples of evaluations suggesting a relatively limited amount of past activity which has had to be upwardly revised during the excavation.