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 spinor rotation γ ( ψ ) = γψ ( ordinary quaternionic multiplication ) will rotate the spinor ψ through an angle one-half the measure of the angle of the corresponding vector rotation.

Thus a metric connection is any connection Γ such that, for any two vectors X, Y ∈ T < sub > γ ( s )</ sub >

Thus, if the curvature of γ is strictly monotonic, then

Thus the discriminant is the original curve and its tangent line at γ ( 0 ):

Thus, 1 γ = 1 nT ( nanotesla )

Thus the base angles of ΔAZY are 60 °+ β and 60 °+ γ.

The two different extensions of γ on each ball now becomes a map S³ → G. However, the homotopy group π < sub > 3 </ sub >( G ) = Z for any compact, connected simple Lie group G. Thus we have

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, many users of a given BBS usually lived in the same area, and activities such as BBS Meets or Get Togethers were common, where users of the board would gather at a local restaurant, the SysOp ’ s home or similar venue and meet face to face.

Thus, the digitalis plants have earned several, more sinister, names: dead man ’ s bells and witch's gloves.

Thus Sophia ’ s power becomes enclosed within the material forms of humanity, themselves entrapped within the material universe: the goal of Gnostic movements was typically the awakening of this spark, which permitted a return by the subject to the superior, non-material realities which were its primal source.

Thus their understanding of the Demiurge is similarly flawed in comparison to Plato ’ s original intentions.

Thus, with a bus frequency of 100 MHz, DDR SDRAM gives a maximum transfer rate of 1600 MB / s.

Thus the DTFT of the s sequence is also the Fourier transform of the modulated Dirac comb function .< ref group =" note "> We may also note that:

Thus we have the important result that when a discrete data sequence, s, is proportional to samples of an underlying continuous function, s ( t ), one can deduce something about the continuous Fourier transform, S ( ƒ ).

Thus Joseph ’ s half brothers were jealous of him and they ridiculed him often.

Thus, although the joule has the same dimensions as the newton-metre ( 1 J = 1 N · m = 1 kg · m < sup > 2 </ sup >· s < sup >− 2 </ sup >), these units are not interchangeable as the newton-metre ( N · m ) is the unit of torque and joule the unit of energy.

Thus the base-words in these examples are fákr and marr “ steed ”, the determinants báru “ wave ’ s ” and gjálfr “ sea ”.

Thus the sky might be called naturalistically él-ker “ squall-vat ” ( Markús Skeggjason: Eiríksdrápa 3 ) or described in mythical terms as Ymis haus “ Ymir ’ s skull ” ( Arnórr jarlaskáld: Magnúsdrápa 19 ), referring to the idea that the sky was made out of the skull of the primeval giant Ymir.

Thus, Bavarian candidate ( s ) emerged to take over the Duchy of Luxembourg, but this plan led to nothing permanent.

Thus, in Bakunin ’ s words: “ All that individuals can do is to clarify, propagate, and work out ideas corresponding to the popular instinct ”.

Thus for each unit the seller tries to set the price equal to the consumer ’ s reservation price.

Thus, Nathanael ’ s question, “ Can anything good come out of Nazareth ?” is consistent with a negative view of Nazareth in the canonical gospels, and with the Johannine proclamation that even his brothers did not believe in him.