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 energy required to break any single pair is related to the energy required to break all of the pairs ( or more than just two electrons ).

Thus the division form of Euclid's algorithm starts with a pair of positive integers and forms a new pair that consists of the smaller number and the remainder obtained by dividing the larger number by the smaller number.

For example, in peas the allele for green pods, G, is dominant to that for yellow pods, g. Thus pea plants with the pair of alleles either GG ( homozygote ) or Gg ( heterozygote ) will have green pods.

Thus, in DNA, the purines adenine ( A ) and guanine ( G ) pair up with the pyrimidines thymine ( T ) and cytosine ( C ), respectively.

Thus, there is a correlation between the results of measurements performed on entangled pairs, and this correlation is observed even though the entangled pair may have been separated by arbitrarily large distances.

Thus a phonemic split has occurred in London English, exemplified by the minimal pair wholly vs. holy.

f. Thus, every pair of ( mutually ) inverse elements gives rise to two idempotents, and ex

Thus to find the median, order the list according to its elements ' magnitude and then repeatedly remove the pair consisting of the highest and lowest values until either one or two values are left.

Thus, what came out in the media: from newspapers, magazines, TV, and the movies, was a product of the stereotypes of the 30s and 40s — though garbled — of a cross between a 1920s Greenwich Village bohemian artist and a Bop musician, whose visual image was completed by mixing in Daliesque paintings, a beret, a Vandyck beard, a turtleneck sweater, a pair of sandals, and set of bongo drums.

( Thus each unicorn can reach only 30 of the board's cubes ; each player's pair, 60.

Thus the pair of variables and also serve up the plane as do x, y and and.

Thus, if the triangle is red, then the (" triangle ", " red ") pair will be in the function, but the pair (" yellow triangle ", " red ") is not.

Thus, many speakers do not differentiate between the vowel sounds ( as in " dress ") and ( as in < trap >), except in cases where a minimal pair such as < bed >/< bad > exists in the vocabulary of the speaker.

Thus, even though White possesses the bishop pair, it is usually advisable for Black to open the game quickly to exploit his lead in development.

Thus, one obtains a form which Taoist texts liken to a pair of fishes nestling head to tail against each other.

Thus the pair of pants is a cobordism between M and N.

Thus, a parent and child pair has a value of r = 0. 5, siblings have a value of r = 0. 5, a parent's sibling has r = 0. 25, and first cousins have r = 0. 125.

Thus the changes in both the initial and the tone were each conditioned by the other, represented by different characters in the fanqie pair.

Thus, only one empirical value is available in a pair of electrodes and it is not possible to determine the value for each electrode in the pair using the empirically obtained galvanic cell potential.

Thus, the standing pair would be King Edward ( in black chaperon, standing on right ) mirroring his wife, Queen Eleanor of Aragon ( standing on left ).

" Thus an interval cycle or pair of cycles may be reducible to a representation of the chromatic scale.

Thus, there is freshness not only in the individual movements of the dance but in the shape of their continuity as well.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus the fictional detective is much more than a simple businessman.

Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus in both types attention is focused on the community itself, and its phenomenological life.

Thus, it is no mystical intuition, but an analyzable conception to say that man and his tradition can `` fall out of existence ''.

Thus human perception and human volition is the immanent cause of all social change and this most truly when the change reaches the civilizational level.

Thus, circular motion is itself one of the essential characteristics of completely perfect celestial existence.

Thus, in no ordinary sense of ' simplicity ' is the Ptolemaic theory simpler than the Copernican.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus science is the savior of mankind, and in this respect Childhood's End only blueprints in greater detail the vision of the future which, though not always so directly stated, has nevertheless been present in the minds of most science-fiction writers.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

Thus there is a clearer division of authority, administrative and legislative.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus technical efficiency is achieved at the expense of actual experience.

Thus, there is an added incentive to stay on the job.

Thus, the Span of its ossification was shortened and the center's ability to `` catch up '' in ossification is demonstrated.

Thus T is not diagonalizable.

Thus Af is divisible by the minimal polynomial P of T, i.e., Af divides Af.

Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus in the three-dice example Af, Af, and the independence assumption imply that the probability that the three dice fall ace, not-ace, ace in that order is Af.

Thus we do not score the number of bull's-eyes, and the random variable is not the number of successes.

Thus Af is also continuous at Af, and in a neighborhood of Af which does not contain a tangent point.