Although the symmetric and transitive properties are often seen as fundamental, they can be proved, if the substitution and reflexive properties are assumed instead.

Although aluminium substitutes extensively for silicon in silicates such as feldspars and amphiboles, the substitution occurs only to a limited extent in most pyroxenes.

Although this is sometimes controversial, Canadian cable companies are required by the CRTC to practise simultaneous substitution when a Canadian channel and a non-Canadian channel ( which is usually American ) are airing the same program at the same time.

Although " transition matrix " is often used interchangeably with " substitution matrix " in fields other than bioinformatics, the former term is problematic in bioinformatics.

Although simultaneous substitution was conceived to substitute the signal of a foreign station, the practice has been applied as well to substitute the signal of a non-local Canadian station in a given market.

Although he was suffering a broken toe during the final, Hamann's substitution for Steve Finnan at half time was the catalyst for Liverpool's historic fightback.

Although Paykan was based on an old 1966 model, there were many changes and modifications made to it over the years, notably the substitution, for the original 1725 cc Rootes engine, of a Peugeot 504-derived unit.

Although he was practically a simple magnetiser, he had some influence upon the march of events, especially in the United States, by the doubts he cast upon some of the theories of the magnetisers through his own metaphysical doctrines, and through his substitution of the name “ Psychodunamy ” ( from Psyche soul, and Dunamis power ) for " Animal Magnetism .”

Although some commentators state confidently that the two refer to the same place, others dismiss the substitution of Magdala for Magadan as simply " to substitute a known for an unknown place ".

Although fabricated using measurements and moulds taken from an existing prop, the " goon " Daleks exhibited minor differences from the original Shawcraft builds including the substitution of single dowels neck struts for the trefoil cross section items which were the norm up to this point.

Although triazines are aromatic compounds, the resonance energy is much lower than in benzene and electrophilic aromatic substitution is difficult but nucleophilic aromatic substitution more frequent.

Although mutation and substitution are often used interchangeably, there is a subtle but important difference.

Although he is perfectly willing to cooperate with Scotland Yard, Holmes has nothing but contempt for the intelligence and mentality of the police.

Although we continue to pay our conversational devotions to `` free private enterprise '', `` individual initiative '', `` the democratic way '', `` government of the people '', `` competition of the marketplace '', etc., we live rather comfortably in a society in which economic competition is diminishing in large areas, bureaucracy is corroding representative government, technology is weakening the citizen's confidence in his own power to make decisions, and the threat of war is driving him economically and physically into the ground ''.

Although it is constantly made to look foolish ( too simple to come in out of the rain, people say, who have found in the innocent an impediment ), it does not mind looking foolish because it is not concerned with how it looks.

Although open to the general public it is not overcrowded ; ;

Although we have no measures of its strength or intensity, the heritage of the doctrine of inalienable rights is retained.

Although because of the important achievements of nineteenth century scholars in the field of textual criticism the advance is not so striking as it was in the case of archaeology and place-names, the editorial principles laid down by Stevenson in his great edition of Asser and in his Crawford Charters were a distinct improvement upon those of his predecessors and remain unimproved upon today.

Although Patchen has given previous evidence of an interest in jazz, the musical group that he works with, the Chamber Jazz Sextet, is often ignored by jazz critics.

Although the false glamour surrounding bourbon or other whisky commercials is possibly no more fatuous than the pseudo-sophistication with which TV soft-drinks are downed or toothpaste applied, there is a sad difference between enticing a viewer into sipping Oopsie-Cola and gulling him into downing bourbon.

Although the United States and the U.S.S.R. have been arguing whether there shall be four, five or six top assistants, the most important element in the situation is not the number of deputies but the manner in which these deputies are to do their work.

`` Although it is not the best of which he is capable '', said Shelley as he closed the book, `` it is still poetry of a high order ''.

Although Sam Rayburn affects a gruff exterior in many instances, nevertheless he is fundamentally a man of warm heart and gentle disposition.

Although a similar situs for tangible property is mentioned in the statute, this is cancelled out by the provision that definite kinds of property `` and all other tangible property '' situated or being in any town is taxable where the property is situated.

Although much of the Industrial Division's promotional effort is devoted to securing new locations and expansions by major industries, small business is also afforded considerable attention.

Although Mr. Brown was not himself its inventor ( it was a French idea ), it is typical that his intuition first conceived the importance of mass producing this basic tool for general use.

Although programs can alter the position of the screen in memory, the non-linear format of the display means that vertical scrolling can only be done in blocks of 8 pixels without further work.

Although Louis XIV wanted peace he wanted it on reasonable terms ; for that, he needed victory in the field and to convince the Allies that his resources were by no means exhausted.

Although mechanisation of the Army was considered as a means of avoiding the heavy casualties and indecisive nature of the offensives during the earlier years of the war, no strategic doctrine was evolved to match technical developments.

Although it is usually translated as " element ", the Chinese word xing literally means something like " changing states of being ", " permutations " or " metamorphoses of being ".

Although never formally endorsed by CND nationally, INDEC candidates were generally put up by local CND groups as a means of raising the profile of this issue in public politics.

Although this was regarded as a character flaw in older academic research, his delaying tactics are now viewed as a means of coping with political challenges in far-flung territorial possessions.

Although greatly improved and with many variations, the Fourdriner machine is the predominant means of paper production today.

Although this means fewer clock cycles per instruction compared to the Z80, for instance, the latter's higher resolution state machine allowed clock frequencies 3-5 times as high without demanding faster memory chips, which was often the limiting factor.

Although not free, villeins were by no means in the same position as slaves: they enjoyed legal rights, subject to local custom, and had recourse to the law subject to court charges, which were an additional source of manorial income.

Although a supervised dose costs more than a take-home dose the risk of diversion means clinics / prescribers are often reluctant to provide take-home privileges.

Although stimulus-response mechanisms are the easiest to understand, the nervous system is also capable of controlling the body in ways that do not require an external stimulus, by means of internally generated rhythms of activity.

Although in the English language the term onomatopoeia means the imitation of a sound, in the Greek language the compound word onomatopoeia ( ονοματοποιία ) means " making or creating names ".

Although Pen Saloth's family was of Sino-Khmer descent and Saloth Sar was named accordingly due to his fair complexion (" Sar " means white in Khmer ), the family had already assimilated themselves with mainstream Khmer society by the time Sar was born.

Although the curriculum has transformed in a number of ways, it has generally emphasized the study of principles and rules of composition as a means for moving audiences.

Although Schafkopf literally means " sheepshead ", it has nothing to do with sheep.

Although the British discovered the presence of the Argentine base in 1978, protested and tried to resolve the issue by diplomatic means, no effort was made to remove them by force until after the Falklands War.

) Although these things are true, the government also wanted more tax money from breweries, as using wooden barrels means that a significant amount of sake is lost to evaporation ( somewhere around 3 %), which could have otherwise been taxed.

Although it uses gas more economically, the weight of the rebreathing equipment means the diver carries smaller cylinders.

Although vulcanization is a 19th century invention, the history of rubber cured by other means goes back to prehistoric times.

Although Dirac did not at first fully appreciate what his own equation was telling him, his resolute faith in the logic of mathematics as a means to physical reasoning, his explanation of spin as a consequence of the union of quantum mechanics and relativity, and the eventual discovery of the positron, represents one of the great triumphs of theoretical physics, fully on a par with the work of Newton, Maxwell, and Einstein before him.

Although the means to carry out, motives for, and targets of a DoS attack may vary, it generally consists of the efforts of one or more people to temporarily or indefinitely interrupt or suspend services of a host connected to the Internet.

Although they were first discovered in 1883 by the German zoologist, Franz Eilhard Schulze ( 1840-1921 ) and since the 1970s more systematically analyzed by the German protozoologist, Karl Gottlieb Grell ( 1912-1994 ), a common name does not yet exist for the taxon ; the scientific name literally means " flat animals ".

Although the purpose of all morality plays is to instruct listeners on the means of receiving redemption, morality plays after the Protestant Reformation are of a distinctly different didacticism than the morality plays before the Reformation.

Although Petra is usually identified with Sela which means a rock, the Biblical references refer to it as " the cleft in the rock ", referring to its entrance.