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 Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

Thus, a central conclusion of Keynesian economics is that, in some situations, no strong automatic mechanism moves output and employment towards full employment levels.

Thus, it is a voltage-controlled device, and shows a high degree of isolation between input and output.

Thus, according to Keynesian theory, some individually-rational microeconomic-level actions such as not investing savings in the goods and services produced by the economy, if taken collectively by a large proportion of individuals and firms, can lead to outcomes, wherein the economy operates below its potential output and growth rate.

Thus, the scale and dimensions of the on-screen display in programs such as MacWrite and MacPaint were easily translated to the printed output — if the paper were held up to the screen, the printed image would be the same size as the on screen image, but at a higher resolution.

Thus, power output of a Wankel engine is generally higher than that of a four-stroke piston engine of similar engine displacement in a similar state of tune ; and higher than that of a four-stroke piston engine of similar physical dimensions and weight.

Thus technological innovation and scientific crop management with synthetic nitrogen fertilizer, irrigation and wheat breeding were the main drivers of wheat output growth in the second half of the century.

Thus all of the additional signal power is guided in the same fiber mode as the incoming signal. There is usually an isolator placed at the output to prevent reflections returning from the attached fiber.

Thus, sensitive detection of specific optical frequencies necessitates optical heterodyne detection, in which two different ( close-by ) wavelengths of light illuminate the detector so that the oscillating electrical output corresponds to the difference between their frequencies.

Thus, the time markers of both clocks, at the output of the clocks, occur simultaneously.

Thus, opportunity costs are not restricted to monetary or financial costs: the real cost of output forgone, lost time, pleasure or any other benefit that provides utility should also be considered opportunity costs.

Thus, human capital is a means of production, into which additional investment yields additional output.

Thus, getting even trivial programs to have a reliable output is often a monumental task.

Thus it is the structure of the organization rather than the employees, alone, which holds the key to improving the quality of output.

Thus, the essential description of a component actually comprises only in-and output that are described fully in terms of data types and their meaning ( semantics ).

Thus, when a differential amplifier is used to extract this difference, its output constitutes the low pass filter section.

Thus many PostScript printer drivers have an option to save as EPS, or to add EPS DSC information to their output which you can " print to file ".

Thus, the output voltage is brought back up to its original value.

Thus, the output of the second filter vanishes when the coefficients of the first one are input into it.

Thus the output of an inexpensive car audio amplifier is limited by the voltage of the alternator.

Thus, crowding out is a problem only when the economy is already close to full employment ( say, at about 4 % unemployment ) and the scope for increasing income and saving is blocked by resource constraints ( potential output ).

Thus for every input, both states must have the same output, and both states must have the same successor ( or unspecified successors ), or both must not change.

Thus the costs of producing the marginal unit of output has two components:

Thus the Gibbs phenomenon can be seen as the result of convolving a Heaviside step function ( if periodicity is not required ) or a square wave ( if periodic ) with a sinc function: the oscillations in the sinc function cause the ripples in the output.

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