Thus, if corporations are not to run away with us, they must become quasi-governmental institutions, subject to public control and needs.

Thus Af if and only if Af.

Thus F satisfies Af if and only if F has the form Af.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus, if public pressure sets the effective limit to the price that the industry may charge, this pressure is itself a function of the wage rate.

Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.

Thus if the gyro and platform-controller combination maintains the platform with zero angular deviation about the **yf axis, the system can be rotated with an angular velocity Af if a torque is supplied to the gyro output axis Aj.

Thus, if one accelerometer is properly aligned, the other is also.

Thus, if we are to observe American folklore in the twentieth century, we will do well to establish the relationships between folklore, nationalism and imperialism at the outset.

Thus, red wine must, if possible, never be disturbed or shaken ; ;

Thus, if what is at issue is whether `` All S is P '', it is indifferent whether `` Some S is not P '' or `` No S is P '', since in either case the judgment in question is false.

Thus most Affidavits now require to be Apostilled if used for cross border issues.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

Thus throwing a rock at someone for the purpose of hitting him is a battery if the rock in fact strikes the person and is an assault if the rock misses.

Thus, a court officer taking possession of goods under a court order may use force if reasonably necessary.

Thus, there is no assault if an ox gores a man.

Thus, if P is a program in L < sub > 2 </ sub > which is a minimal description of s, then InterpretLanguage ( P ) returns the string s. The length of this description of s is the sum of

Thus, if every historian were to claim that there was a solar eclipse in the year 1600, then though we might at first naively regard that as in violation of natural laws, we'd come to accept it as a fact.

Thus the Af are projections which correspond to some direct-sum decomposition of the space V.

Thus, for example, V ← V + 1 is commonly understood to be a shorthand for ( V ,( V ) + 1 ).

Thus for an ion which traverses a 1 m flight path, across a time of 2000 ns, given an initial accelerating voltage of 5000 V and noting that one amu is 1 × 10 < sup >− 27 </ sup > kg, the mass-to-charge ratio ( more correctly the mass-to-ionisation value ratio ) becomes Z amu / charge.

Thus a point y in V is a cluster point of the net if and only if every neighborhood Y of y contains infinitely many elements of the sequence.

Thus K < sub > V </ sub > 1. 3 blockers could be potential immunosuppressants for the treatment of autoimmune disorders ( such as rheumatoid arthritis, inflammatory bowel disease and multiple sclerosis ).

Thus, Charles was the maternal uncle of Charles V of France, who solicited his relative's advice at Metz in 1356 during the Parisian Revolt.

The Battle of Pavia ( 1525 ) marks a watershed in the city's fortunes, since by that time, the former cleavage between the supporters of the Pope and those of the Holy Roman Emperor had shifted to one between a French party ( allied with the Pope ) and a party supporting the Emperor and King of Spain Charles V. Thus during the Valois-Habsburg Italian Wars, Pavia was naturally on the Imperial ( and Spanish ) side.

This question has two fundamental physical units: time t and length, and three dimensional variables: distance D, time taken T, and velocity V. Thus there is 3 − 2 = 1 dimensionless quantity.

Thus the total time is O ( E log E ) = O ( E log V ).

Thus, suppose that ( x < sub > 1 </ sub >,..., x < sub > n </ sub >) is a choice of Cartesian coordinates, in terms of which the coordinates of the vector V are

Thus, G < sub > t </ sub >( V ) = exp ( tV ) is the exponential map of the vector tV.

) Thus the " saturation " voltage of a Darlington transistor is one V < sub > BE </ sub > ( about 0. 65 V in silicon ) higher than a single transistor saturation voltage, which is typically 0. 1-0. 2 V in silicon.

Thus the lands that make up the current province came under occupation of these, up to the barbarian invasions of the early V century A. D.

Thus if U < sub > p </ sub >, V < sub > p </ sub >, Y < sub > p </ sub > are three tangent vectors at p and a and b are real numbers, then

The Chinese words already introduced by his predecessors he did not alter, and in introducing new terms required in the translation of the Mahayana literature, the 大乘 Tasheng or greater development, he uses SH for SH and usually B for V. Thus the city Shravasti was in Pali Savatthi and in Chinese Sha-ba-ti.

Thus let V be a vector space of dimension n over the field of scalars S, and let each of f = ( X < sub > 1 </ sub >,..., X < sub > n </ sub >) and f ' = ( Y < sub > 1 </ sub >,..., Y < sub > n </ sub >) be a basis of V .< ref group =" note "> A basis f may here profitably be viewed as a linear isomorphism from R < sup > n </ sup > to V. Regarding f as a row vector whose entries are the elements of the basis, the associated linear isomorphism is then Also, let the change of basis from f to f ′ be given by

Thus, they were classified as a single species V. cholera: however, Hugh believed the differing features between the two could be of epidmiological importance, so El Tor vibrios were further classified as V. cholerae biotype eltor ( serogroup O1 ).

Thus areas can be measured in square metres ( m < sup > 2 </ sup >), square centimetres ( cm < sup > 2 </ sup >), square millimetres ( mm < sup > 2 </ sup >), square kilometres ( km < sup > 2 </ sup >), square feet ( ft < sup > 2 </ sup >), square yards ( yd < sup > 2 </ sup >), square miles ( mi < sup > 2 </ sup >), and so forth.

Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing B by B + c < sub > 1 </ sub >-− 3 c < sub > 1 </ sub > will cause them to be renumbered from 0 through 9 and 4 through 23, respectively.

Thus this class of molecules belong to the D < sub > 2d </ sub > point group.

Thus, few drops of diamminesilver ( I ) hydroxide ( Ag ( NH < sub > 3 </ sub >)< sub > 2 </ sub > OH ) reacts with terminal alkynes signaled by formation of a white precipitate of the silver acetylide.

Thus, all the antiderivatives of x < sup > 2 </ sup > can be obtained by changing the value of C in F ( x ) = ( x < sup > 3 </ sup >/ 3 ) + C ; where C is an arbitrary constant known as the constant of integration.

Thus, a single " rule ," like mapping every real number x to x < sup > 2 </ sup >, can lead to distinct functions and, depending on whether the images under that rule are understood to be reals or, more restrictively, non-negative reals.

Thus, oxygen is reduced to water and the original electron acceptors NAD < sup >+</ sup > and quinone are regenerated.

Thus, for example, the English form is is an apparent cognate of German ist, Latin est and Russian < nowiki > jest '</ nowiki >, even though the Germanic, Italic, and Slavic language groups split at least three thousand years ago.

Thus, the molecular formula of ethanol may be written in a paper in conformational, three-dimensional, full two-dimensional ( indicating every bond with no three-dimensional directions ), compressed two-dimensional ( CH < sub > 3 </ sub >– CH < sub > 2 </ sub >– OH ), separating the functional group from another part of the molecule ( C < sub > 2 </ sub > H < sub > 5 </ sub > OH ), or by its atomic constituents ( C < sub > 2 </ sub > H < sub > 6 </ sub > O ), according to what is discussed.

Thus ℵ < sub > 0 </ sub > is a regular cardinal.