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 every part and plane of the picture keeps changing place in relative depth with every other part and plane ; ;

Thus, if a publicly traded company specialises in the acquisition of privately held companies, from a per-share perspective there is a gain with every acquisition that falls within these guidelines.

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.

By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.

Thus in Austinian terms a moral code can objectively determine what people ought to do, the law can embody whatever norms the legislature decrees to achieve social utility, but every individual remains free to choose what to do.

Thus, every chlorine is in the middle of a cube formed by caesium atoms and every caesium is in the middle of a cube formed by chlorine.

Thus, body forces are specified by vector fields which are assumed to be continuous over the entire volume of the body, i. e. acting on every point in it.

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, every non-Han dynasty saw itself as the legitimate holder of the " Mandate of Heaven ", which legitimized the dynastic cycle regardless of social or ethnic background as it was moral integrity and benevolent leadership that had been validating the " Mandate of Heaven.

Thus every proposition has three components: the two terms, and the " copula " that connects or separates them.

Thus every module direct summand of R is generated by an idempotent.

Thus we have in the first five centuries such epithets applied to her as " in every respect holy ", " in all things unstained ", " super-innocent " and " singularly holy "; she is compared to Eve before the fall, as ancestress of a redeemed people ; she is " the earth before it was accursed.

Thus it is true in every case above except case 2, because this is the only case when is true but is not.

Thus, every MUMPS command or function name could be abbreviated from one to three letters in length, e. g. Quit ( exit program ) as Q, $ P

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 the number of preorders is the sum of the number of partial orders on every partition.

( Thus we consider something like the winding number of the orientation of the sides, where at every vertex the contribution is between − and winding.

Thus every even perfect number is a pernicious number.

Thus DA means that a cocking action separate from the trigger pull is unnecessary ; and every trigger pull will result in a complete cycle.

Thus, only a small number of computers ( the servers ) need to be rigorously secured, rather than securing every single client computer.

Thus early 1950s historian of fandom Jack Speer began to label successive generations of fans as First Fandom, Second Fandom, Third Fandom, and so forth ... all the way to Seventh Fandom and beyond.

Thus, his historian style has been imitated all through the ages, and had a strong impact in Edward Gibbon and Montesquieu.

Thus he came to sing alongside the great soprano castrato Farinelli, and their meeting on stage ( in the pasticcio Artaserse ) led to a famous incident, reported by the music historian Charles Burney.

Thus, an interval passed between the " first sweep " of Einsatzgruppen massacres in summer and fall, and what American historian Raul Hilberg called the " second sweep ", which started in December 1941 and lasted into the summer of 1942.

Thus the Latin of a theologian like St Thomas Aquinas or of an erudite clerical historian such as William of Tyre tends to avoid most of the characteristics described above, showing its period in vocabulary and spelling alone ; the features listed are much more prominent in the language of lawyers ( e. g. the 11th century English Domesday Book ), physicians, technical writers and secular chroniclers.

Thus, Samuel Usque, also a historian, who had fled from the Inquisition in Portugal, settled in Ferrara ; and Abraham Usque founded a large printing establishment there.

Thus, Malone received considerable though balanced criticism in Thomas Jefferson and Sally Hemings: An American Controversy ( 1997 ), the first book by the historian Annette Gordon-Reed.

Thus, historian Philip Hitti notes, Kafur would be generously rewarded for such loyalty.

Thus Kafur was immortalized in the poetry of al-Mutanabbi-the greatest poet of Kafur's time, according to historian Hitti.

Thus, the two ancient names as Jambhiyagram and Jambubani prove that this district was important as a religious place for Jains and it was also a place of Gupta dynasty in the 19th century, the historian Buchanan also visited this place in 1811 and found the historical facts.