Therefore no complete system, i. e. including the electromagnetic modes, can have negative temperatures, since there is no highest energy state, so that the sum of the probabilities of the states would diverge for negative temperatures.

Therefore, since sound is in fact an infinitesimal pressure difference propagating through a fluid, the speed of sound in that fluid can be considered the fastest speed that " information " can travel in the flow.

Therefore, they are subject to counter-party risk, like an ordinary contract, since each counter-party relies on the other to perform.

Therefore, they were un-priced and hence the system would be necessarily inefficient since the central planners would not know how to allocate the available resources efficiently.

Therefore, c divides the initial remainder r < sub > 0 </ sub >, since r < sub > 0 </ sub > = a − q < sub > 0 </ sub > b = mc − q < sub > 0 </ sub > nc = ( m − q < sub > 0 </ sub > n ) c. An analogous argument shows that c also divides the subsequent remainders r < sub > 1 </ sub >, r < sub > 2 </ sub >, etc.

Therefore, the logical basis for the theory is deeply flawed, since it presumes that early Americans, despite being only a slight fraction of the population of industrial era America and armed with rudimentary tools, were many times more destructive than later historic humans who engaged in the often deliberate eradication of species.

" Therefore, although the thesis of the " Mysterium Cosmographicum " was in error, modern astronomy owes much to this work " since it represents the first step in cleansing the Copernican system of the remnants of the Ptolemaic theory still clinging to it.

Therefore, who does this is not forbidden to the priesthood because of harlotry, and a woman is not prohibited to her husband by this, since it is not harlotry.

Therefore, since a non-covered sector exists nearly everywhere, the predictions of the textbook model simply cannot be relied on.

Therefore, the optimal mutation rate for a species is a trade-off between costs of a high mutation rate, such as deleterious mutations, and the metabolic costs of maintaining systems to reduce the mutation rate, such as DNA repair enzymes .< ref name = Sniegowski > Viruses that use RNA as their genetic material have rapid mutation rates, which can be an advantage since these viruses will evolve constantly and rapidly, and thus evade the defensive responses of e. g. the human immune system.

Therefore, they often vary since one is theoretical and the other is experimental.

Therefore, since nature has demonstrated the basic operations needed to perform molecular-level cell repair, in the future, nanomachine based systems will be built that are able to enter cells, sense differences from healthy ones and make modifications to the structure.

Therefore, hexadecimal is more commonly used in programming languages today, since two hexadecimal digits exactly specify one byte.

It is the business of the pope to look after the interests of the Roman empire, since the empire derives its origin and its final authority from the papacy ; its origin, because it was originally transferred from Greece by and for the sake of the papacy ... its final authority, because the emperor is raised to his position by the pope who blesses him, crowns him and invests him with the empire .... Therefore, since three persons have lately been elected king by different parties, namely the youth son of Henry VI, Philip Hohenstaufen, brother of Henry VI, and Otto Brunswick, of the Welf family, so also three things must be taken into account in regard to each one, namely: the legality, the suitability and the expediency of his election ...... Far be it from us that we should defer to man rather than to God, or that we should fear the countenance of the powerful .... On the foregoing grounds, then, we decide that the youth should not at present be given the empire ; we utterly reject Philip for his manifest unfitness and we order his usurpation to be resisted by all .... since Otto is not only himself devoted to the church, but comes from devout ancestors on both sides ..... therefore we decree that he ought to be accepted and supported as king, and ought to be given the crown of empire, after the rights of the Roman church have been secured.

: Therefore, since everything asserted by the inspired authors or sacred writers must be held to be asserted by the Holy Spirit, it follows that the books of Scripture must be acknowledged as teaching solidly, faithfully and without error that truth which God wanted put into sacred writings

Therefore, since the ability to visually see a transmitting antenna ( disregarding the limitations of the eye's resolution ) roughly corresponds to the ability to receive a radio signal from it, the propagation characteristic of high-frequency radio is called " line-of-sight ".

Therefore, the viscosity and friction of the liquid in this model do not play a role, since these quantities would play a role only for a moving fluid.

Therefore, since sperm are antigenically different from self tissue, a male animal can react immunologically to his own sperm.

Therefore, since both the panorama and The Prelude imitate the senses, they are equal and suggest Wordsworth was not entirely opposed to panoramas.

Therefore, aside from that one exception, since 1948 Israeli governments have always comprised coalitions.

Therefore, he was barred from Major League Baseball before, the season that black players were admitted to the Major Leagues for the first time since the 19th century.

To start with, none of the terms a, 2a, ..., ( p − 1 ) a can be congruent to zero modulo p, since if k is one of the numbers 1, 2, ..., p − 1, then k is relatively prime with p, and so is a, so Euclid's lemma tells us that ka shares no factor with p. Therefore, at least we know that the numbers a, 2a, ..., ( p − 1 ) a, when reduced modulo p, must be found among the numbers 1, 2, 3, ..., p − 1.

Therefore the two aircraft were sold in 1986, and followed up by closing its Swedish charter operations in 1988.

Therefore, the general board's November 1986 action was not executed by Bishop J. O. Patterson Sr. until January 29, 1988 at the Bishops ' Conference in Jacksonville, Florida.

Therefore, in order to regain some status, the building underwent a major renovation in 1986 that included a re-glazed exterior and removal of the lighting on its sides.

Therefore, the Thais helped establish ( in March 1986 ) a 10-member provisional military committee without the knowledge of Sutsakhan or Sann.

Therefore, in 1986 Danaher added Qualitrol to its instrumentation unit.

Therefore waters around Tabarca were declared a Marine reserve in 1986, the first of its kind in Spain.

Therefore on February 3, 1986 the Professional Coin Grading Service ( PCGS ) was formed and in 1987 the Numismatic Guaranty Corporation.

Therefore, it is plain that the clear distinctions of the nineteenth century are no longer with us.

Therefore the government wanted no part of him.

Therefore, under our longstanding allocation rules, on some of these channels no station other than the dominant ( class 1 ) -- A ) station is permitted to operate at night, so that the 1, -- A station can render service, interference free, wherever it can be received.

Whereas, John Brown has cheerfully risked his life in endeavoring to deliver those who are denied all rights and is this day doomed to suffer death for his efforts in behalf of those who have no helper: Therefore,

Therefore, the plaintiff must offer evidence that the extent of the limitation caused by the impairment is substantial in terms of his or her own experience ;" a medical diagnosis or physician's declaration of disability is no longer enough.

Therefore, approximants fall between fricatives, which do produce a turbulent airstream, and vowels, which produce no turbulence.

Therefore, it is necessary to have the existence of a conflict in public law without any constitutional aspects and no assignment to another jurisdiction.

Therefore, when a runner on first or second base tags on a fly ball and advances no further than third base, no sacrifice is given and the batter is charged with an at-bat.

Therefore it is no great thing if his ministers also transform themselves into ministers of righteousness, whose end will be according to their works.

Therefore, the concept of concubinage stands as permitted ( Halal ) although concubines are no longer permitted.

Therefore, it is clear there is no real consensus of what the term crannog actually implies, although the modern adoption in the English language broadly refers to a partially or completely artificial islet which saw use from the prehistoric to the Post-Medieval period in Ireland and Scotland.

Therefore there will be no correlation between key closeness and similar popularity of data as there might be if keys did exhibit some semantic meaning, thus avoiding bottlenecks caused by popular subjects.

More precisely, he showed that a random graph on vertices, formed by choosing independently whether to include each edge with probability has, with probability tending to 1 as goes to infinity, at most cycles of length or less, but has no independent set of size Therefore, removing one vertex from each short cycle leaves a smaller graph with girth greater than in which each color class of a coloring must be small and which therefore requires at least colors in any coloring.

" Therefore, scholars are no longer looking for the identity of a single writer but for numerous authors whose authorship has been absorbed into the gospel's development over a period of time and in several stages.

Therefore any electron can interchange with another one with no observable physical change of the system at all.

* Therefore regard every living being as you do yourself, harming no one and being kind to all living beings.

Therefore, the federal government had no right to exercise powers not specifically delegated to it.

Therefore, if the determinant equals zero then the parallelogram has no area, and that will happen when two vectors are on the same line.

Therefore, the null hypothesis, the hypothesis that there was no aether wind, could not be rejected.

: Therefore, no intruder was detected by the watch-dog.

Therefore, the Manichaean worldview explained the existence of evil with a flawed creation God took no role in forming and was the result of Satan striking out against God.

Therefore, there is no safe side from which to approach.