Although the terms adiabatic and isocaloric can often be interchanged, adiabatic processes may be considered a subset of isocaloric processes ; the remaining complement subset of isocaloric processes being processes where net heat transfer does not diverge regionally such as in an idealized case with mediums of infinite thermal conductivity or non-existent thermal capacity.

Although symmetric groups can be defined on infinite sets as well, this article discusses only the finite symmetric groups: their applications, their elements, their conjugacy classes, a finite presentation, their subgroups, their automorphism groups, and their representation theory.

In The History of Mathematics, Burton writes, " Although Zeno's argument confounded his contemporaries, a satisfactory explanation incorporates a now-familiar idea, the notion of a ' convergent infinite series.

Although Jasenovac was expanded, officials were told that " Jasenovac concentration and labor camp cannot hold an infinite number of prisoners ".

Although the Halting problem is not computable, it is possible to simulate program execution and produce an infinite list of the programs that do halt.

Although even in said contexts the phrases " perfect goodness " or " moral perfection " are often preferred because of the difficulties in defining what exactly constitutes ' infinite benevolence '.

Although colored quarks are attached to a QCD string and have infinite mass, the spin-statistics relation for quarks can be proved in the short distance limit.

Although the diversity of organic structures is infinite, the number of basic fragments is rather limited.

Although the number of states in all of the bands is effectively infinite, in an uncharged material the number of electrons is equal only to the number of protons in the atoms of the material.

Although Protectors have a vastly extended lifetime, it is not infinite ; during the original half million year journey to Earth some protector colonists did die from old age.

Although each such isolated configuration has infinite energy, it labels superselection sectors where the difference in energy between two states is finite.

Although the amplitude of these fluctuations is bounded in 3D structures ( even in the limit of infinite size ), the Mermin-Wagner theorem shows that the amplitude of long-wavelength fluctuations will grow logarithmically with the scale of a 2D structure, and would therefore be unbounded in structures of infinite size.

Although bullets do not move at ' infinite speed ' via perfectly straight trajectories in life, they move fast enough that a hitscan solution is ' good enough ' to simulate their behaviour for the layman.

Although every proper subgroup of a finite group is contained in a maximal subgroup, there are infinite Abelian groups that contain no maximal subgroups, for example the Prüfer group.

Although it was becoming evident that water could no longer be considered an infinite resource, as had been the case in the 1950s when there were fewer people on the planet, no one knew just how scarce the resource was.

Although this is usually said somewhat jokingly, children certainly enjoy playing with boxes, using their imagination to portray the box as an infinite variety of objects.

Although there have been no new entrants into the fixed line industry, the government issued three licenses under the new regime to cellular telephone service providers.

Although Spartiate was outnumbered, it had been supported by the next in line Aquilon, which uniquely of the French van squadron was fighting only one opponent, Minotaur.

Although the rest of the northern line is still in place, it is in a state of serious disrepair.

Although the word " chalcogen " is literally taken from Greek words being " copper-former ", the meaning is more in line with " copper-ore former " or more generally, " ore-former ".

Although all of these behaviors merge into each other seamlessly in various bonding situations so that there is no clear line to be drawn between them, nevertheless behaviors of atoms become so qualitatively different as the character of the bond changes quantitatively, that it remains useful and customary to differentiate between the bonds that cause these different properties of condensed matter.

Although Cantor himself defined the set in a general, abstract way, the most common modern construction is the Cantor ternary set, built by removing the middle thirds of a line segment.

Although the Alpha processor family met both of these goals, and, for most of its lifetime, was the fastest processor family on the market, it did little to affect the bottom line or repair the company's status.

Although there is a downward population curve, explained by a larger death than birth rate, as well as a larger number of emigrants than immigrants, the line graph of the natural population increase shows the rate of population decrease was slowly diminishing.

Although elves could be considered to be beautiful and potentially helpful beings in some sections of English-speaking society throughout its history, Old English evidence also attests to alignments of elves with demons, as for example in line 112 of Beowulf.

Although genealogy information described in Shaku Nihongi leaves room for discussion, many scholars acknowledge the blood relationship with the Okinaga clan, a powerful local ruling family or the collateral line of the Imperial family-governed Oumi region ( a part of present-day Shiga Prefecture ).

Although Johnson would attest in a 1984 radio interview that the " two tribes " of the song potentially represented any pair of warring adversaries ( giving the examples of " cowboys and Indians or Captain Kirk and Klingons "), the song does contain the line " On the air America / I modelled shirts by Van Heusen ", a clear reference to then US President Ronald Reagan, who had advertised for Phillips Van Heusen in 1953 ( briefly reviving the association in the early 1980s ), and whose first film had been titled Love Is On The Air.

Although the Social Democrats showed strong support for the expellees especially under Kurt Schumacher and Erich Ollenhauer, social democrats in more recent decades have traditionally been less supportive — and it was under Willy Brandt that West Germany recognized the Oder-Neisse line as factual as part of his Ostpolitik.

Although it is north of the tree line there are still shrubs that are classed, locally, as trees.

Although Infocom started out with Zork, and although the Zork world was the centerpiece of their product line throughout the Zork and Enchanter series, the company quickly branched out into a wide variety of story lines: fantasy, science-fiction, mystery, horror, historical adventure, children's stories, and others that defied categories.

Although use of the script was rather free-form, the line about Hanna was ordered dropped as soon as Hamlin got word of his death in 1904.

Although the brand originates from the original 1947 model, Land Rover as a company has only existed since 1978, prior to this it was a product line of the Rover Company which was subsequently absorbed into the Rover-Triumph division of the British Leyland Motor Corporation ( BL ) following Leyland Motor Corporation ’ s takeover of Rover in 1967.

( Although this poetry is in fact specified using feet, each " foot " is more or less equivalent to an entire line.

Although the name " Maginot Line " suggests a rather thin linear fortification, the line was quite deep, varying in depth ( i. e., from the border to the rear area ) from between.

Although the figures given to the United Nations ( UN ) might have been purposely distorted, it appears that in line with other attempts to open itself to the outside world, the North Korean regime has also opened somewhat in the demographic realm.

Although rare now, in the past there were bowlers who used the off-break action who deliberately did not impart any considerable spin on the ball but relied on line and length to frustrate batsmen.

Although uncommon, polygonal rifling is still used in some weapons today with one example being the Glock line of pistols ( which fire standard bullets ).

Although the reported phone line teledensity is 16. 6 ( 2004 ) fixed phone line teledensity remains as low as 5. 1, where cellular teledensity is 11. 4.

Although all of the western branches of the District and Piccadilly lines were included for the first time in 1933 with Harry Beck's first map, the portion of the Metropolitan line beyond Rickmansworth did not appear until 1938 and the eastern end of the District line did not appear on the map until the mid-1950s.

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.