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, Harlan ’ s arguments can be constructed in three major points: First, states ( California ) cannot censor their citizens in order to make a “ civil ” society.

Thus, the decision makes it illegal to censor material on basis of explicit homosexual content, but such material could be censored if it could be shown to harm women.

Thus though Sikander was approved by the Bombay censor board, it was later banned from some of the theatres serving British Indian Army cantonments.

If a description of s, d ( s ), is of minimal length ( i. e. it uses the fewest number of characters ), it is called a minimal description of s. Thus, the length of d ( s ) ( i. e. the number of characters in the description ) is the Kolmogorov complexity of s, written K ( s ).

Thus, the license depends on how a particular application that uses Berkeley DB is distributed to the public.

Thus a statement of the form is said to be true, under a particular interpretation, if there is some object in the domain of discourse of that interpretation that satisfies the predicate that the interpretation uses to assign meaning to the symbol Phil.

Thus the cache that exists on the International Space Station, GC1BE91, uses the launch area Baikonur in Kazakhstan as its position.

Thus, LED technology may be a good replacement in uses such as supermarket freezer lighting and will last longer than other technologies.

Thus, while most organic acids are deprotonated by the ionization of a polar hydrogen-to-oxygen bond, usually accompanied by some form of resonance stabilization ( resulting in a carboxylate ion ), uric acid is deprotonated at a nitrogen atom and uses a tautomeric keto / hydroxy group as an electron-withdrawing group to increase the pK < sub > 1 </ sub > value.

Thus it uses a much more complex ruleset for coding than its predecessor ; for example, it tests for approximately 100 different contexts of the use of the letter C alone.

Thus, for example, the Great Seal of the United States, among other uses, appears on the reverse of the one-dollar bill ; and several of the seals of the U. S. states appear on their respective state flags.

Thus, no matter what type of indexing method any implementation of the element uses, it will have the appropriate Iterator.

Thus, a hexagonal structure uses the least material to create a lattice of cells within a given volume.

Thus, a program will achieve greater performance if it uses memory while it is cached in the upper levels of the memory hierarchy and avoids bringing other data into the upper levels of the hierarchy that will displace data that will be used shortly in the future.

Thus, Hemingway uses the archaic " thou " ( particularly in its oblique and possessive form ) to parallel the Spanish pronominal " tú " ( familiar ) and " Usted " ( formal ) forms.

Thus, the Council annexed several thousand acres, which now host commercial, residential and agricultural uses.

Thus it has been more recently proposed that, for example, the pipe organ ( even if it uses electric key action to control solenoid valves ) remain in the aerophones category, and that the electric guitar remain in the chordophones category, etc ..

Thus it has been more recently proposed that, for example, the pipe organ ( even if it uses electric key action to control solenoid valves ) remain in the aerophones category, and that the electric guitar remain in the chordophones category, and so on.

Thus it can be seen that, according to Taimni's interpretation of the Yoga Sutras, samadhi is the main tool the yogin uses to achieve the end goal of yoga, the joining of the individual self with the Universal Absolute.

Thus, we can interpret Boltzmann's constant as being simply the expression ( in terms of more standard physical units ) of the abstract logarithmic unit that is needed to convert the dimensionless pure-number quantity ln W ( which uses an arbitrary choice of base, namely e ) to the more fundamental pure logarithmic quantity Log ( W ), which implies no particular choice of base, and thus no particular choice of physical unit for measuring entropy.

Thus, if the perpetrator uses the prybar to pry open the window and then used his hands to lift the partially opened window, an " entry " would have taken place when he grasped the bottom of the window with his hands.

Thus a unitary structure can be seen as an orthogonal structure, a complex structure, and a symplectic structure, which are required to be compatible ( meaning that one uses the same J in the complex structure and the symplectic form, and that this J is orthogonal ; writing all the groups as matrix groups fixes a J ( which is orthogonal ) and ensures compatibility ).

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, the 3 / 8 rule is about twice as accurate as the standard method, but it uses one more function value.

Thus in classical analysis, which uses classical logic, in order to prove the full IVT, it is sufficient to prove the constructive version.

Thus Johnston uses, " potentially hundreds of pitches per octave ," in way that is, " radical without being avant-garde ," and not for the creation of, " as-yet-unheard dissonances ," but in order to, " return ... to a kind of musical beauty ," he perceives as diminished in Western music since the adoption of equal-temperament ( Gann 1995, 1 ).

Thus the three-phase system transmits 73 % more power but uses only 50 % more wire.