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

Therefore, the divergence of is given by

Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

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, Artemis killed Adonis to avenge Hippolytus ’ s death.

Therefore, unbeknown to the French who remained oblivious to the Allies ’ real strength and intentions on the opposite side of the Petite Gheete, Marlborough was throwing his full weight against Ramillies and the open plain to the south.

Therefore, he cannot avoid referring to “ the other side ” of the Doge ’ s figure when discussing his “ royal appearing show ”.

Therefore, in order to preserve the precious mysticism of his materialistic paradigm, he describes the story ’ s setting as empty, vague, and above all enigmatic.

In this approximately 800-word document about methods of franking letters he states, " Therefore, of Mr Hill ’ s plan of a uniform rate of postage … I conceive that the most simple and economical mode … would be by Slips … in the hope that Mr Hill ’ s plan may soon be carried into operation I would suggest that sheets of Stamped Slips should be prepared … then be rubbed over on the back with a strong solution of gum …".

The fact that the PBS is located near the 5 ’ terminus of viral RNA is unusual because reverse transcriptase synthesize DNA from 3 ’ end of the primer in the 5 ’ to 3 ’ direction ( with respect to the RNA template ). Therefore, the primer and reverse transcriptase must be relocated to 3 ’ end of viral RNA.

Therefore, by making one ’ s body uncomfortable, one ’ s soul is uncomfortable.

Therefore, when attempting to understand media ’ s role in the development of teens, it is crucial to be aware of the time teens devote to their shows like reality television due to this strong influence

Therefore, the tendency to give, to cheat, and the response to other ’ s acts of giving and cheating must be regulated by a complex psychology in each individual.

Kleiber ’ s law states that the metabolic rate ( q < sub > 0 </ sub >) of an animal is the mass of the animal ( M ) raise to the 3 / 4 power: q < sub > 0 </ sub >= M < sup > 3 / 4 </ sup > Therefore, the mass of the animal increases at a faster rate than the metabolic rate. There are many types of feeding strategies employed by herbivores.

Therefore, other members of the survivor ’ s family – in particular the spouse and children – are also offered treatment and counselling.

Therefore, in the context of Meyerhoff ’ s research, " eh " can be equated as a device to establish and maintain a group identity.

Therefore, acoelomate organs are not protected from crushing forces applied to the animal ’ s outer surface.

Therefore, single-photon cooling is a physical realization of Maxwell ’ s Demon in the same sense envisioned by Leo Szilard in 1929.

Therefore, it was only natural that this color be used on the " railroad ’ s high school " as well.

Therefore, magic realism's ‘ alternative world ’ works to correct the reality of established viewpoints ( like realism, naturalism, modernism ).

Therefore, one ’ s social identity can have several, qualitatively distinct parts ( for example, one ’ s ethnic identity, religious identity, and political identity ).

Therefore either everything in possible experience isn ’ t predetermined, which contradicts the universality of pure reason, or the freewill is outside the system of causality and can have no effect on it, rendering the will useless.