Therefore a naive algorithm to calculate the estimated variance is given by the following:

Therefore, the divergence of is given by

Therefore, in order to describe a given signal completely, it's necessary to quote the color system and the broadcast standard as capital letter.

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, there exists a contact force density or Cauchy traction field that represents this distribution in a particular configuration of the body at a given time.

Therefore, the velocity field of the continuum is given by

Therefore, in December 1942, several patients with advanced lymphomas ( cancers of certain white blood cells ) were given the drug by vein, rather than by breathing the irritating gas.

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, if an electric field, E < sub > inc </ sub >( x, y ) is incident on the aperture, the field produced by this aperture distribution is given by the surface integral:

Therefore, language, in the absence of translation, comprises a barrier to a worldwide community of debate and opinion, although it is also true that media within any given society may be split along class, political or regional lines.

Therefore, each mirror pair and each non-chiral stereoisomer may be given a specific monosaccharide name.

Therefore, the final velocities are given by

Therefore, the absence of life in Venus, with a somewhat similar composition to Earth's primitive conditions or the absence of life on Mars, given the proposed " resilience " of life in space, damages the panspermia theory, at least based on observations of our own Solar System-the theory suggests that life would be more abundant in the Solar system.

Therefore, when the numbers of atoms in the ground and excited states are equal, the rate of stimulated emission is equal to the rate of absorption for a given radiation density.

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, the percentages mentioned above are taken from the total population that declared their ethnicity, given that the non-declared remainder is thought to have an ethnic composition similar to the declared segment.

Therefore, the shortcut taken in raytracing is to presuppose that a given ray intersects the view frame.

Therefore, if ΔE is larger than the thermal energy of the lattice, given by kT, where k is Boltzmann's constant and T is the temperature, the fluid will not be scattered by the lattice.

Therefore, their salt content is given for the respective ions.

Therefore optical amplification will add power to an incident optical field at frequency at a rate given by:

Therefore, if the equation of the line is given in the form

Therefore, to establish a mathematical statement as a theorem, the existence of a line of reasoning from axioms in the system ( and other, already established theorems ) to the given statement must be demonstrated.

Therefore, heritability is not a measure of phenotypic ( physiognomy and physique ) differences among racial and ethnic groups, but of differences between genotype and phenotype in a given population.

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, any measures taken in peacetime which will decrease force requirements in war will contribute greatly to success when hostilities occur.

Therefore, neither merit the beatific vision, nor yet are subjected to any punishment, because they are not guilty of any personal sin although they have not received baptism, so still bear original sin.

Therefore, any test of a scientific theory must prohibit certain results which will falsify the theory, and expect other specific results which will be consistent with the theory.

Therefore it soon announced and implemented a hostile doctrine against any political dissent, whether inside or outside the party.

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, 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, the diagonal of a 4 x 9 lattice does not intersect any other square lattice | lattice points

Therefore strings beginning with C ( or any other capital letter ) would be sorted before strings with lower-case a, b, etc.

Therefore, just as Christianity does not accept that Mosaic Law has any authority over Christians, Judaism does not accept that the New Testament has any religious authority over Jews.

Therefore an optimizer can replace a string copy with a sequence of word moves without any loops, which will be much faster.

Therefore, as outlined in the example above, neither the EPR experiment nor any quantum experiment demonstrates that faster-than-light signaling is possible.

Therefore, General Niazi and Air Marshal Enamul Haque, Commander of Eastern Air Force Command ( EAFC ), were failed to launch any operation in East Pakistan against Indian or its allies.

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, the first and second rules (" always treat the gun as if loaded ", " never let the muzzle cover non-targets ") apply to any gun, even one loaded with blanks.

Therefore, all this must be kept secret-which rules out any approach to the police or other outside agency.

Therefore, any eigenstate of the electron in the hydrogen atom is described fully by four quantum numbers.

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

Therefore " Liberty will abolish interest ; it will abolish profit ; it will abolish monopolistic rent ; it will abolish taxation ; it will abolish the exploitation of labour ; it will abolish all means whereby any labourer can be deprived of any of his product.

Therefore, before any interrogation begins, the police must advise the suspect that: