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 1986 no Dutch judge has any formal competence to impose the death penalty.

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, four loose families of more-efficient light transport modelling techniques have emerged: rasterization, including scanline rendering, geometrically projects objects in the scene to an image plane, without advanced optical effects ; ray casting considers the scene as observed from a specific point-of-view, calculating the observed image based only on geometry and very basic optical laws of reflection intensity, and perhaps using Monte Carlo techniques to reduce artifacts ; and ray tracing is similar to ray casting, but employs more advanced optical simulation, and usually uses Monte Carlo techniques to obtain more realistic results at a speed that is often orders of magnitude slower.

Therefore, even though the relative geometry of the Earth-Sun-Moon system will be nearly identical after a saros, the Moon will be in a different position with respect to the stars.

Therefore, in Euclidean geometry, any two lines that are both perpendicular to a third line are parallel to each other, because of the parallel postulate.

" Therefore any result in Euclidean geometry that follows from these three postulates will hold in elliptic geometry, such as proposition 1 from book I of the Elements, which states that given any line segment, an equilateral triangle can be constructed with the segment as its base.

Therefore, this case is what usually is meant when talking about Hilbert's sixteenth problem in real algebraic geometry.

Therefore, to produce the image which the retina beholds, using projective geometry techniques, it may be convenient to substitute a spherical surface of projection for a plane of projection, i. e., use a " picture sphere " rather than a " picture plane " and place the eye, or " station point ," at the center of the picture sphere.

Therefore distance geometry has immediate relevance where distance values are determined or considered, such as in surveying, cartography and physics.

Therefore, the relative satellite-receiver geometry plays a major role in determining the precision of estimated positions and times.

Therefore, the central atom is predicted to adopt a linear geometry.

Therefore, the predicted geometry is trigonal.

Therefore the multistatic ambiguity function is mostly usefully defined as a function of two-or three-dimensional position and velocity vectors for a given multistatic geometry and transmitted waveform.

Therefore this is also the geometry of a C < sup > 2 </ sup >/ Z < sub > n </ sub > orbifold in string theory after its conical singularity has been smoothed away by its " blow up " ( i. e., deformation ).

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

Therefore, what we must prove or disprove is that there were Saxons, in the broad sense in which we must construe the word, in the area of the Saxon Shore at the time it was called the Saxon Shore.

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.

Therefore, if the target can significantly change its location in something less than 30 minutes, the probability of having destroyed it is drastically lowered.

Therefore, the lumber is bought in planks and ripped to size for battens, etc., on a table saw.

Therefore, neglecting the extreme outbursts, reflected solar radiation is not expected to cause sizable errors in the measurements of planetary radiation in the centimeter- and decimeter-wave-length range.

Therefore, N is inversely proportional to the radius cubed and in fair agreement with the inverse 7/2 power derived from 1958 Alpha and 1959 Eta data.

Therefore, Af is single-valued near Q.

Therefore, for any value of T the number of values of f{t} is equal to the ( finite ) number of tangent points corresponding to the argument T plus an odd number.

Therefore, the congruence of its secants, that is the image of a general plane field of lines, is of order Af and class Af.

Therefore, it is not only a question of honor but of life and death for the Soviet state ''.

Therefore, if the sense of touch is functioning normally and there is a complete absence of spatial awareness in a psychically-blind person when the eyes are closed and an object is handled, the conclusion seems unavoidable that touch by itself cannot focus and take possession of the third-dimensionality of things and that actual sight or visual representations are necessary.

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, a broad concept of over-all submarine defense is needed for co-ordination of the Navy's efforts, for a logical presentation to the public, for industry's guidance, and as a basis for a program to the Congress.

Therefore the second principle of the plan must be that, while providing for all-out hostilities, its effectiveness is not dependent on general war.

Therefore, it is recommended that in such cases the sample be replaced, or if used, the results of dimensional change or dimensional restorability tests be considered as indicative only.

Therefore, her wardrobe is largely mobile, to be packed at a moment's notice and to shake out without a wrinkle.

Therefore, by contraposition, a necessary condition for unit-treatment additivity is that the variance is constant.

Therefore the perfect of these verbs would be ich bin gesessen, ich bin gelegen and ich bin geschlafen respectively ( note: ich bin geschlafen is a very rare form, usually you will hear ich habe geschlafen ; but ich bin eingeschlafen fell asleep is quite normal ).

Therefore, pure antimony is not used to make hard objects: coins made of antimony were issued in China's Guizhou province in 1931, but because of their rapid wear, their minting was discontinued.