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 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 the two-dimensional Fourier transform of the initial function is the one variable Fourier transform of the Radon transform of that function.

Thus, Marcel waving produced a two-dimensional wave, by thermal means only and the change was produced by plastic flow of the hair, rather than by any chemical means.

Thus, the two-dimensional Dirichlet problem is essentially the same problem as that of finding a meromorphic extension of a function defined on a boundary.

Thus two indices are used for a two dimensional array, three for a three dimensional array, and n for an n dimensional array.

Thus the record and array data structures are based on computing the addresses of data items with arithmetic operations ; while the linked data structures are based on storing addresses of data items within the structure itself.

Thus, discrepancy of opinion in a wide array of political matters is often directly traceable back to a discrepancy of opinion in the justification for the state.

Thus, X-ray diffraction results from an electromagnetic wave ( the X-ray ) impinging on a regular array of scatterers ( the repeating arrangement of atoms within the crystal ).

Thus, if its inputs are an array x of length N, we can imagine extending this array to ( x, – x < sub > R </ sub >, – x, x < sub > R </ sub >, ...) and so on, where x < sub > R </ sub > denotes x in reverse order.

Thus, a rough estimate for the total number of sensory nerve cells serving the vibrissal array on the face of a rat or mouse might be over 9000.

Thus, a CAM is the hardware embodiment of what in software terms would be called an associative array.

Thus, Aristea ( approximately 56 species ), which has radially symmetric, mostly blue flowers, has three different pollination systems, whereas Sparaxis ( 15 species ), with both zygomorphic and secondarily radially symmetric flowers, in a variety of colors, exhibits five different pollination systems, and Gladiolus, with a similar array of floral types but over two hundred species, exploits seven different pollination systems, some of which have evolved multiple times.

Thus pseudocode such as would set all elements of array A to zero, no matter its size or dimensionality.

Thus, if we have a vector containing elements ( 2, 5, 7, 3, 8, 6, 4, 1 ), and we want to create an array slice from the 3rd to the 6th items, we get ( 7, 3, 8, 6 ).

Thus, they served a vast array of positions from educational and social leaders, to ambassadors, Imperial Secretaries and high priests.

Thus the spatial location of each single flash of fluorescence is reflected as a pattern of voltages within the interconnecting circuit array.

Thus, the array output vector at any time t can be denoted as, where stands for the signal received by the first sensor.

Thus, array element and record field accessors were simply special cases of a doublet function: this was a function that had another function attached as its updater, which was called on the receiving side of an assignment.

Thus, if the variable < tt > a </ tt > contained an array, then

Thus, an array of facilities are provided primarily for residents in the new towns.

Thus to enjoy the largest array of sources requires a good knowledge of both English and French.

Thus, CST is helpful in unravelling an array of human evolutionary puzzles because it can explain wasteful and altruistic behavior.

Thus Waltham's antenna array does not broadcast these two channels in the direction of Sandy Heath and vice versa.

Thus, an array of devices may end up no more robust than its weakest component.