Therefore, φ ( 9 )

Therefore by 5 ) and 4 ), χ ( a < sup > φ ( k )</ sup >)

Therefore, φ is initially a constant as well.

Therefore, φ is a Pisot number.

Therefore ( T *-λ ) φ

Therefore, the change in φ over one oscillation of u ( or, equivalently, one oscillation of r ) equals

Therefore Irenaeus describes man's creation as follows:

: 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, the sum rule can be extended so it " accepts " addition and subtraction as follows:

Therefore the delta-v required for the Hohmann transfer can be computed as follows, under the assumption of instantaneous impulses:

Therefore, if God is sufficient without need of any unethical thing it necessarily follows that He would not choose the unethical based on His knowledge of its immorality.

" 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, instead of a single name and date, there follows a list of significant contributions to the history of the device.

Therefore we suppose S multiplicatively closed in what follows.

Therefore, over the natural numbers, has at most minimal elements, a finite number .< ref > With more care, it is possible to show that one of and is at most, and that there is at most one minimal pair for each choice of one of the coordinates, from which it follows that there are at most minimal elements .</ ref >

( To see this, note that there is some extension field in which f has a root ; necessarily, in E. Therefore, working over E, ( the final equality in the sequence follows from freshman's dream ), and f does not have distinct roots.

Therefore, he took out a page that follows the one in which Tintin has shown Haddock all the bugs and hidden cameras in their villa, and Sponsz has told Alvarez how it was he who framed Castafiore.

Therefore, the Age of Aquarius follows the Age of Pisces.

Since f < sup > 0 </ sup >< sub > k </ sub > is a constant it does not contribute to the error on f. Therefore, the propagation of error follows the linear case, above, but replacing the linear coefficients, A < sub > ik </ sub > and A < sub > jk </ sub > by the partial derivatives, and.

The corresponding set K of vertices in G ( the vertices whose expanded cliques in G * intersect K *) is a clique in G with the property that it intersects every maximum independent set in G. Therefore, the graph formed from G by removing K has clique cover number at most one less than the clique number of G, and independence number at least one less than the independence number of G, and the result follows by induction on this number.

Therefore, if a minimally imperfect graph has a 2-join, it must equal one of its blocks, from which it follows that it must be an odd cycle and not Berge.

Therefore, in order to transmit light through a double ring resonator system, we will need to satisfy the resonant condition for both rings as follows:

Therefore, it follows that the process of adaptation is never finally complete.

" Therefore, what follows is a restrictive clause.

" Therefore, what follows is a non-restrictive clause.

Therefore, this trigonometric identity follows from the Pythagorean theorem.

Therefore, chlorite's structure appears as follows:

Therefore, it follows that our optimal language is universal up to this additive constant.

Therefore, the biography that follows is garnered largely from traditional biographies of Sengcan, mainly the Transmission of the Lamp.

Therefore, the resonance condition ( above ) is rewritten as follows:

Therefore it's a genuine pleasure to tell you about an entirely happy bodybuilder who has never had to train in secret has never heard one unkind word from his parents and never has been taunted by his schoolmates!!

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 employment and education in all the schools in a metropolitan area are related in different ways from those which are characteristic of the comprehensive high school described in my first report.

Therefore they applied for help from Alexander II of Macedon.

Therefore, the goals of an aerodynamicist have shifted from understanding the behavior of fluid flow to understanding how to engineer a vehicle to interact appropriately with the fluid flow.

Therefore, after combining like terms, the coefficient of x < sup > n − 2 </ sup > y < sup > 2 </ sup > will be equal to the number of ways to choose exactly 2 elements from an n-element set.

" Therefore I should infer from analogy that probably all the organic beings which have ever lived on this earth have descended from some one primordial form, into which life was first breathed.

Therefore, native Caymanians do not have any Amerindian heritage from their own islands ; however, a significant number of Jamaicans have settled in the Cayman Islands over the years, so they and their descendants may have some Amerindian blood via Jamaica.

Therefore, most Chicanos do not agree that " Chicano " was ever derived from the word " chicamo ".

Therefore Latinos are Americans who are descendants of the Latin group ( namely Spain, France, Italy and Portugal ) and Hispanic refers to the descendants from the Iberian Peninsula ( also known as Ibero-American ).

Therefore, inherent in systems of power, is always " truth ," which is culturally specific, inseparable from ideology which often coincides with various forms of hegemony.

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, in 1890, Young signed with the Cleveland Spiders, a team which had moved up from the American Association to the National League the previous year.

Therefore, compound crossbows generally use only pulleys that are both round and concentrically mounted, in order to capture the maximum available energy from the relatively short draw length.

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 I propose to the comrades that they devise a way of shifting Stalin from this position and appointing to it another man who in all other respects falls on the other side of the scale from Comrade Stalin, namely, more tolerant, more loyal, more polite and considerate of comrades, less capricious and so forth.

Therefore, some violations like suicide would be punished by separation from the community, such as not being buried in a Jewish cemetery ( in practice, rabbis often rule suicides to be mentally incompetent and thus not responsible for their actions ).

Therefore, judgments from the House of Lords and the Court of Appeal have greater authority than the lower courts such as the High Court and the County Court.

Therefore he publicly disavowed his allies at the United Nations, and used financial and diplomatic pressure to make them withdraw from Egypt.

Therefore, the distillate will not be pure – its composition will be identical to the composition of the vapors at the given temperature and pressure, and can be computed from Raoult's law.

Therefore, a country's ability to learn from the leader is a function of its stock of " human capital ".

Therefore, earthquakes lower the Earth's available elastic potential energy and raise its temperature, though these changes are negligible compared to the conductive and convective flow of heat out from the Earth's deep interior.

Therefore, while Gibbon was pointing out what he perceived as a flaw in Eusebius's work, he also paid him a compliment, where by calling him ' grave ' he was ascribing the quality of sternness and a lack of credulity when it came to sifting out the fantastical from the reliable historical sources.