However, the argument concludes that the conceptual challenge of bare particulars leaves a bundle of properties and nothing more as the only possible conception of an object, thus justifying bundle theory.

In a small neighborhood U in X in which L is trivial, the total space of the line bundle is the product of U and the underlying field k, and the section s restricts to a function U → k. However, the values of s depend on the choice of trivialization, and so they are determined only up to multiplication by a nowhere-vanishing function.

However it is not a trivial fiber bundle, i. e., S < sup > 3 </ sup > is not globally a product of S < sup > 2 </ sup > and S < sup > 1 </ sup > although locally it is indistinguishable from it.

However, in individuals with a pre-existing accessory conduction pathway, such as the bundle of Kent in Wolff-Parkinson-White syndrome, the accessory pathway may conduct activity from the atria to the ventricles at a rate that the AV node would usually block.

However, this terminology is now strongly deprecated, as it conflicts with universally accepted terminology the theory of complex manifolds, where the canonical line bundle of a complex m-manifold is defined to be the bundle

However, later that night, Koukol arrives by the inn and leaves a red bundle for Sarah on the doorstep.

However, this only works when it doesn't cost much to sell extra items in a bundle that are unwanted.

However Alan Feduccia of the University of North Carolina has called the alleged specimen an " unidentifiable bundle of bones " and has taken issue with using one specimen he claims to be possibly misidentified as evidence that the Anseriformes cohabited with dinosaurs.

However, in that proceeding, as a compromise between the FCC Commissioners, the FCC released a Notice of Inquiry requesting comment on the " competitive consequences when providers bundle their legacy services with new services, or " tie " such services together "; that proceeding remains open before the FCC.

However, when bundle blocks are complex and diffuse in the bundle systems, or associated with additional and significant ventricular muscle damage, they may be a sign of serious underlying heart disease.

However, it is often the case that if g: Y → Z is another map, the inverse image functors are not strictly compatible with composed maps: if z is an object over Z ( a vector bundle, say ), it may well be that

However, since every compact manifold can be embedded in, by the Whitney embedding theorem, every manifold admits a normal bundle, given such an embedding.

However, they do demonstrate the presence of large normal pressures in the presence of flat shear fields which were forecast by the theory in the first part of the paper.

However, Montgomery makes little contribution to leadership theory and practice.

However, that particular case is a theorem of Zermelo – Fraenkel set theory without the axiom of choice ( ZF ); it is easily proved by mathematical induction.

However, this theory is undermined by the disproportional fear of spiders in comparison to other, potentially dangerous creatures that were present during Homo sapiens environment of evolutionary adaptiveness.

However, more vital propositions, such as Hume's argument for the role of habit in a theory of knowledge, are retained.

However, invalid formulas ( those that are not entailed by a given theory ), cannot always be recognized.

However, Davy failed to develop a new theory, concluding that " acidity does not depend upon any particular elementary substance, but upon peculiar arrangement of various substances ".

However, the results of BCS theory do not depend on the origin of the attractive interaction.

However, since piston-engined aircraft rely upon magnetos to provide spark to their cylinders rather than a battery powered ignition coil system, this theory is not strongly convincing.

However, the term naive set theory is also used in some literature to refer to the set theories studied by Frege and Cantor, rather than to the informal counterparts of modern axiomatic set theory ; care is required to tell which sense is intended.

However, one could equally well lay out a consequentialist theory that focuses solely on minimizing bad consequences.

However it is important to note that the objects of a category need not be sets nor the arrows functions ; any way of formalising a mathematical concept such that it meets the basic conditions on the behaviour of objects and arrows is a valid category, and all the results of category theory will apply to it.

However, the later edition in 1959 failed to adequately address the problems that appeared to be better understood by molecular orbital theory.

However, the work of Friedrich Hund, Robert Mulliken, and Gerhard Herzberg showed that molecular orbital theory provided a more appropriate description of the spectroscopic, ionization and magnetic properties of molecules.

" However, in the case of the so-called Nilo-Hamitic languages ( a concept he introduced ), it was based on the typological feature of gender and a " fallacious theory of language mixture.

However, spectropolarimetric observations of SN 2009dc showed it had a polarization smaller than 0. 3, making the large asphericity theory unlikely.

However it was only in 1927 that the shakta theory of seven main chakras, that has become most popular in the West, was introduced, largely through the translation of two Indian texts: the Sat-Cakra-Nirupana, and the Padaka-Pancaka, by Sir John Woodroffe, alias Arthur Avalon, in a book titled The Serpent Power.

However, control theory also saw an increasing use in fields such as economics.

However, this political restriction is less confining than it may first appear in that the Marxist historical framework is surprisingly flexible, and a rather simple matter to modify an alternative historical theory to use language that at least does not challenge the Marxist interpretation of history.

However this theory ignores the fact that the Soviet Union had already suffered several important setbacks during “ reactive and defensive strategy ” of “ containment ”.

However, unlike Johnson, Hodge confined the term to exclude those like Asa Gray who combined Christian faith with support for Darwin's natural selection theory, before answering the question posed in the book's title by concluding: " It is Atheism.

However, Russell's theory analyses proper names into a logical structure which makes sense of this problem.

However, one of the consequences of Einstein's theory is that there is no possible physical test that can distinguish between a beam of light as a model of a geometrical line and any other physical model.

However, the jury said it believes `` these two offices should be combined to achieve greater efficiency and reduce the cost of administration ''.

However, Ealdred did not receive the other two dioceses that Lyfing had held, Crediton and Cornwall ; King Edward the Confessor ( reigned 1043 – 1066 ) granted these to Leofric, who combined the two sees at Crediton in 1050.

However, the loss of AppleTalk did not reduce the desire for networking solutions that combined its ease-of-use with IP routing.

However, in the 1930s the French moved it to battalion level and combined it with some tactical fire control.

However, it is also possible to divide the book into three parts rather than four by combining the sections treating David and Solomon, since they both ruled over a combined Judah and Israel, unlike the last section that contains the chronicle of the Davidic kings who ruled the Kingdom of Judah alone.

However, the lack of manoeuvrability of the British forces, combined with lack of open-field tactics to command these numbers, put them at a disadvantage to the Romans, who were skilled at open combat due to their superior equipment and discipline.

However, they are much less toxic than their predecessors, the barbiturates, and death rarely results when a benzodiazepine is the only drug taken ; however, when combined with other central nervous system depressants such as alcohol and opiates, the potential for toxicity and fatal overdose increases.

However, the combined effects of ethnic and religious fractionalization, i. e. the more chance that any two randomly chosen people will be from separate ethnic or religious groups the less chance of a civil war, were also significant and positive, as long as the country avoided ethnic dominance.

However, for Young Religious Unitarian Universalists ( YRUU ) programming in Canada, the " Central " and " Eastern " regions are combined to form a youth region known as " QuOM " ( Quebec, Ontario and the Maritimes ), giving the youth only three regions for their activities.

However, Pfeiffer had little vision for what the combined companies should do, or indeed how the three dramatically different cultures could work as a single entity, and Compaq struggled as a result of a strategy that had the company caught in between the low end and high end.

However, the combined HP-Compaq struggled and fell to second place behind Dell from 2003-2006.

However when combined with land mines, snipers, barbed wire, and air cover, crossfire became a difficult tactic to counter in the early 20th century.

However, a wall would imply the existence of a defensive ditch outside it, so an earlier wall could not be immediately adjacent to site of the tomb, which combined with the presence of the Temple Mount would make the city inside the wall quite thin ; essentially for the traditional site to have been outside the wall, the city would have had to be limited to the lower parts of the Tyropoeon Valley, rather than including the defensively advantageous western hill.

However, his restaurant " Chinois on Main " was named after the term attributed to Richard Wing, who in the 1960s combined French and Chinese cooking at the former Imperial Dynasty restaurant in Hanford, California.

However, declining cocoa production combined with falling cocoa prices, while oil prices soared.

The Hagia Sophia architects innovatively combined the longitudinal structure of a Roman basilica and the central plan of a drum-supported dome, in order to withstand the high magnitude earthquakes of the Marmara Region, “ However, in May 558, little more than 20 years after the Church ’ s dedication, following the earthquakes of August 553 and December 557, parts of the central dome and its supporting structure system collapsed .” The Hagia Sophia was repeatedly cracked by earthquakes and was quickly repaired.

However in terms of modern competition, it was during the 1950s that a Japanese karateka named Tatsuo Yamada first established an outline of a new sport that combined karate and muay thai.

However, untreated venous insufficiency can progress into a combined venous / lymphatic disorder which is treated the same way as lymphedema.

However, when supervenience physicalism and token physicalism are combined, minimal physicalism is met, as will be detailed in the following sections.

However a Jesuits ' college, founded in the city in 1571 during the Counter-Reformation, had the right to award degrees from 1611 until 1773, when it was combined with the Academy.

However, the unlikelihood that the reputable historian Bede invented Ninian without some basis in the historical record, combined with an increased knowledge of Ireland's early saints and Whithorn's early Christian connections, has led to serious scholarly efforts to find Bede's basis.

However, the burst of the dotcom bubble hurt the growth and profitability of the AOL division which in turned dragged down the combined company's performance and stock price.

However, the element that the club continued to lack was a solid pitching staff, whose combined ERA ranked 9th in the A. L.