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.

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, even though some of the states cannot be controlled ( as determined by the controllability test above ) all the states will still remain bounded during the system's behavior.

Intuitively, the continuous operator A never " lengthens " any vector more than by a factor of c. Thus the image of a bounded set under a continuous operator is also bounded.

Thus, a function does not need to be " nice " in order to be bounded.

Thus h can be extended to an entire bounded function which by Liouville's theorem implies it is constant.

Thus, it is bounded caudally by the inferior precentral sulcus ( H ) and rostrally by the anterior ascending limb of lateral sulcus ( H ).

Thus I < sup > α </ sup > defines a bounded linear operator from L < sup > p </ sup >( a, b ) to itself.

Thus, such network flow problems with bounded integer capacities have an integral optimal value.

Thus any bounded complete finite poset trivially is a Scott domain.

Much of this depended on Herbert A. Simon ’ s work in the 1950s concerning behaviour in situations of uncertainty, which argued that “ people possess limited cognitive ability and so can exercise only ‘ bounded rationality ’ when making decisions in complex, uncertain situations .” Thus individuals and groups tend to ‘ satisfice ’— that is, to attempt to attain realistic goals, rather than maximize a utility or profit function.

Thus, boundedness of T < sup >∗</ sup > on its domain does not imply boundedness of T. On the other hand, if T < sup >∗</ sup > is defined on the whole space then T is bounded on its domain and therefore can be extended by continuity to a bounded operator on the whole space .< ref > Proof: being closed, the everywhere defined T < sup >∗</ sup > is bounded, which implies boundedness of T < sup >∗∗</ sup >, the latter being the closure of T. See also for the case of everywhere defined T .</ ref > If the domain of T < sup >∗</ sup > is dense, then it has its adjoint T < sup >∗∗</ sup >.

is bounded above by t. Thus, the constant N used in the summation above is given by

Thus, their error-rate performance is lower bounded by the one of orthogonal rate 1 STBCs, that provide ISI free transmissions due to orthogonality.

Thus its channels are strictly bounded with blocking writes.

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

Thus, reswitching implies the rejection of a simple ( monotonic ) non-increasing relationship between capital intensity and either the rate of profit, sometimes confusingly referred to as the rate of interest.