Thus, what happens physically is that the energy level of the bottom of the conduction band of body " A " ( and, hence, the whole band structure of body " A ") moves up in energy, relative to the Fermi level of the Earth, as the temperature of body " A " increases.

Thus a noninteracting Fermi gas, unlike a Bose gas, is prohibited from condensing into a Bose-Einstein condensate, although interacting Fermi gases might.

Thus, there is a one-to-one correspondence between the elementary excitations of a Fermi gas system and a Fermi liquid system.

Thus we can say that the lifetime of particles at the Fermi surface goes to infinity.

Drexler supports a form of the Fermi paradox, arguing that as there is no evidence of alien civilizations, " Thus for now, and perhaps forever, we can make plans for our future without concern for limits imposed by other civilizations.

Thus, diverges as V approaches 0, preventing investigation of the local electronic structure near the Fermi level.

Thus 6th century Gallo-Romans of Gregory's class, surrounded by the ruins of Roman temples and public buildings, attributed the destruction they saw to the plundering raids of the Alemanni.

" Thus, Poole's critique might better be understood as aimed at Calef, Mather's contemporary, who saw fit to ascribe to him, and his influence, the largest portion of blame.

Thus, every non-Han dynasty saw itself as the legitimate holder of the " Mandate of Heaven ", which legitimized the dynastic cycle regardless of social or ethnic background as it was moral integrity and benevolent leadership that had been validating the " Mandate of Heaven.

Thus, he saw private property as both essential to liberty and a road to tyranny, the former when it resulted from labour and was required for labour and the latter when it resulted in exploitation ( profit, interest, rent, tax ).

Thus many admirers ( though not necessarily Brahms himself ) saw him as the champion of traditional forms and " pure music ", as opposed to the " New German " embrace of programme music.

Within the space of these tendencies there has developed a coherent critique of " orthodox Marxism " that includes not only a rejection of the concept of " the transition " but a reconceptualization of the process of transcending capitalism that has remarkable similarities to ( Peter ) Kropotkin's thinking on this subject ... Thus one of the earliest political tendencies within which this approach appeared after the Russian revolution of 1917 was that of " Council Communism " which saw the " workers councils " in Germany ( see Bavarian Soviet Republic ), or the soviets in Russia, as new organizational forms constructed by the people.

Professional dance teachers in the US saw this approach to dancing as " extreme ", " undisciplined ", and thus, deemed it necessary to standardize the dance to present it as a sell-able commodity for the social or ballroom market Thus, compared to the mambo in Cuba, mambo had a different movement sequence in the United States and elsewhere, as it was popularized internationally.

The narrator relates two facts: ( 1 ) Noah became inebriated when he “ uncovered himself within his tent ” and ( 2 ) Ham “ saw his father ’ s nakedness .” Thus, these passages revolve around sexuality and the exposure of genitalia as compared with other Hebrew bible texts, such as Habakkuk 2: 15 and Lamentations 4: 21.

Thus, Rand saw reason and freedom as correlates, just as she saw mysticism and force as corollaries.

Thus, Nicolas Fabri de Peiresc saw the pagan religions of Africa of his day as relicts that were in principle capable of shedding light on the historical Paganism of Classical Antiquity.

Thus, although Enlightenment philosophers saw the Roman Republic as an ideal system, it included no systematic separation of powers, and depended on slave labor.

Thus, instead of expecting a single Antichrist to rule the earth during a future Tribulation period, Martin Luther, John Calvin and the other Protestant Reformers saw the Antichrist as a present feature in the world of their time, fulfilled in the papacy.

Thus the 1980s and 1990s saw a rise in both budgets and the number of sequels a film could generally have.

Thus, the 19th century saw a new group of monarchs titled grand duke all around Central Europe.

Thus, the Samis saw no change or a transformation of their name, for example: some Sire became Siri, Hætta Jáhkoš Ásslat became Aslak Jacobsen Hætta — as it was the norm until recently, when integration into the EU and accelerated international exchanges pushed many people to reverse the order of their full name to given name-surname, so that they are not called Ms. Rauha ( a first name ), just like Japanese, some Koreans, Chinese or some Vietnamese do, for the same reason.

Thus, both pre-20th century disciplines were labelled " classical " and modern movements in art which saw themselves as aligned with light, space, sparseness of texture, and formal coherence.

Thus, his opposition was based on a practical fear of Jews turning to the false messianism of Napoleon as he saw it.

Thus Velázquez saw none of the riches which came from Mexico.

Thus, what man saw as evil, such as wars, epidemia and natural disasters, was in fact only an effect of his perception ; if one adopted God's view, this evil event in fact only took place in the larger divine plan.

Thus over the 250 years ( approximately ) that the rating system of the Royal Navy held sway, only a relatively small number of first rates saw service.

Thus, the same day as the rescript was issued, General Douglas MacArthur announced that he was very much pleased with the Emperor's statement, which he saw as his commitment to lead his people in the democratization of Japan.

Thus the manager will read from the same copy that the first reader saw, and be aware of any volume and deadline pressures the first reader was under, and can directly observe the individual in real time.

Thus, the Spaniards called the land Negros after the black natives they saw on their arrival on the island in April 1565.

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

Thus while his theory or technique may not be oversubscribed, it is commonplace for bullish and bearish positions to become temporarily over-subscribed.

Thus, theory and doctrine applicable among the great nations and the smaller European states did not really comfortably fit less developed and less powerful societies elsewhere.

Thus, while altruistic persons may under some circumstances be outcompeted by less altruistic persons at the individual level, according to group selection theory the opposite may occur at the group level where groups consisting of the more altruistic persons may outcompete groups consisting of the less altruistic persons.

" Thus Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

Thus the axiom of choice is not generally available in constructive set theory.

Thus aesthetic judgments might be seen to be based on the senses, emotions, intellectual opinions, will, desires, culture, preferences, values, subconscious behavior, conscious decision, training, instinct, sociological institutions, or some complex combination of these, depending on exactly which theory one employs.

Thus, the theory asserts that the apple is no more than the collection of its properties.

Thus, the Big Bang theory cannot and does not provide any explanation for such an initial condition ; rather, it describes and explains the general evolution of the universe going forward from that point on.

Thus, while Nozick's side-constraints are absolute restrictions on behavior, Amartya Sen proposes a theory that recognizes the importance of certain rules, but these rules are not absolute.

Thus, in an agent-neutral theory, an actor's personal goals do not count any more than anyone else's goals in evaluating what action the actor should take.

Thus literary criticism became highly theoretical and some of those practicing it began referring to the theoretical dimension of their work as " critical theory "-a philosophically inspired theory of literary criticism.

Thus, theory has its roots in the materiality of social existence.

Thus, though knowledge requires justification, truth, and belief, the word " knowledge " can't be, according to Williamson's theory, accurately regarded as simply shorthand for " justified true belief.

Thus, Gibbs ' theory becomes

Thus the aqua cations behave as acids in terms of Brønsted-Lowry acid-base theory.

" Thus irreal works such as Italo Calvino's Cosmicomics and Jorge Luis Borges ' Ficciones can be seen as an attempt to find a new allegorical language to explain our changed perceptions of the world that have been brought about by our scientific and technical culture, especially concepts such as quantum physics or the theory of relativity.

Thus, according to Keynesian theory, some individually-rational microeconomic-level actions such as not investing savings in the goods and services produced by the economy, if taken collectively by a large proportion of individuals and firms, can lead to outcomes, wherein the economy operates below its potential output and growth rate.

Thus three major themes in 19th century mathematics were combined by Lie in creating his new theory: the idea of symmetry, as exemplified by Galois through the algebraic notion of a group ; geometric theory and the explicit solutions of differential equations of mechanics, worked out by Poisson and Jacobi ; and the new understanding of geometry that emerged in the works of Plücker, Möbius, Grassmann and others, and culminated in Riemann's revolutionary vision of the subject.

Thus for a theory " T ", " G " is true, but not provable in " T ".

Thus, both the statement " Murder is bad " and the statement " Murder is good " are false, according to an error theory.

Thus in theory, if law enforcement officials decline to offer a Miranda warning to an individual in their custody, they may still interrogate that person and act upon the knowledge gained, but may not use that person's statements to incriminate him or her in a criminal trial.