Thus, the Fifth Division was at Al-Ubayyid in Kurdufan ( Central Command ), the Second Division was at Khashm El Girba ( Eastern Command ), the Sixth Division was assigned to Al-Fashir in Darfur ( Western Command ), the First Division was at Juba ( Southern Command ), and the Seventh Division was at As Shajarah just south of Khartoum ( Khartoum Command ).

Thus, as Dika Newlin has pointed out, " in this symphony Mahler returns to the ideal of ' progressive tonality ' which he had abandoned in the Sixth ".

Thus, the third task unit of the fifth task group of the second task force of the Sixth Fleet would be numbered 62. 5. 3.

Thus, the Sixth Amendment calls for trial " by an impartial jury of the State and district wherein the crime shall have been committed.

Thus the Eighth Consciousness is transformed into the Great Perfect Mirror Wisdom, the Seventh Consciousness into the Equality ( Universal Nature ) Wisdom, the Sixth Consciousness into the Profound Observing Wisdom, and First to Fifth Consciousnesses into the All Performing ( Perfection of Action ) Wisdom.

" Thus, the states were allowed to reject the Sixth Amendment, for example, while ratifying all of the other amendments including the Due Process Clause ; in that case, the rights in the Sixth Amendment would not have been incorporated against the federal government.

Thus, procedurally, only a jury can convict a defendant of a serious crime, since the Sixth Amendment jury-trial right has been incorporated against the states ; substantively, for example, states must recognize the First Amendment prohibition against a state-established religion, regardless of whether state laws and constitutions offer such a prohibition.

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

Thus, the red plane shows the points with x = 1, the blue plane shows the points with z = 1, and the yellow plane shows the points with y =− 1.

Thus a 2 × 2 matrix with determinant − 2, when applied to a region of the plane with finite area, will transform that region into one with twice the area, while reversing its orientation.

Thus the width of the plane within the top brittle crust of the Earth can become 50 to 100 km ( Tohoku, 2011 ; Alaska, 1964 ), making the most powerful earthquakes possible.

Thus any two lines in a projective plane intersect in one and only one point.

Thus the area of S < sub > D </ sub > is obtained by integrating the length of the normal vector to the surface over the appropriate region D in the parametric uv plane.

Thus every analytic function corresponds to a steady incompressible, irrotational fluid flow in the plane.

Thus, in the scaleogram of a continuous wavelet transform of this signal, such an event marks an entire region in the time-scale plane, instead of just one point.

Thus, this function is not meromorphic in the whole complex plane.

Thus, to enter an orbit passing over the poles of the Sun, the spacecraft would have to eliminate the 30 km / s speed it inherited from the Earth's orbit around the Sun and gain the speed needed to orbit the Sun in the pole-to-pole plane — tasks that are impossible with current spacecraft propulsion systems alone, making gravity assist maneuvers essential.

Thus the normal affine space is the plane of equation x = a.

Thus the pair of variables and also serve up the plane as do x, y and and.

Thus, for an object in focus, the distance between the lens and image plane, the distance between lens and the object, and the focal length are related by:

Thus, two specific persons riding together on a plane have beaten out all odds to end up in those specific seats.

Thus as the distance from a point source increases, the spherical wavefronts become flatter and closer to plane waves, which are perfectly collimated.

Thus both horizontality and verticality are strictly speaking local concepts, and it is always necessary to state to which location the direction or the plane refers to.

Thus inversive geometry includes the ideas originated by Lobachevsky and Bolyai in their plane geometry.

Thus, the input-plane plane wave spectrum is transformed into the output-plane plane wave spectrum through the multiplicative action of the system transfer function.

Thus, instead of getting the frequency content of the entire image all at once ( along with the frequency content of the entire rest of the x-y plane, over which the image has zero value ), the result is instead the frequency content of different parts of the image, which is usually much simpler.

Thus the Cayley graph of the abelian group with the set of generators consisting of four elements is the infinite grid on the plane, while for the direct product with similar generators the Cayley graph is the finite grid on a torus.

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.