Thus the image of man has suffered complete fragmentation in personal and spiritual qualities, and complete objectification in sub-human and quasi-mechanistic powers.

Thus, the MCC would not complete road construction.

Thus in 565 or 566 Justinian's successor Justin II sent his son-in-law Baduarius as magister militum ( field commander ) to lead a Byzantine army against Alboin in support of Cunimund, ending in the Lombards ' complete defeat.

) Thus, when Odo returned, he was able to launch a near complete surprise attack on the besieging force, scattering it at the first attack, and slaughtering units caught resting or that fled without weapons or armour.

Thus, complete meaning is always " differential " and postponed in language ; there is never a moment when meaning is complete and total.

Thus began one of the most productive periods in Telemann's life: during his tenure at Eisenach he composed a wealth of instrumental music ( sonatas and concertos ), and numerous sacred works, which included four or five complete annual cycles of church cantatas, 50 German and Italian cantatas, and some 20 serenatas.

Thus, a nearly complete separation of zirconium and hafnium is necessary for their use in nuclear power.

Thus the axon undergoes complete fragmentation.

Thus, lack of complete information on the part of survey participants may have skewed the results.

Thus DA means that a cocking action separate from the trigger pull is unnecessary ; and every trigger pull will result in a complete cycle.

Thus, not all sound deductive systems are complete in this special sense of completeness, in which the class of models ( up to isomorphism ) is restricted to the intended one.

Thus, the vocoder dramatically reduces the amount of information needed to store speech, from a complete recording to a series of numbers.

Thus, the thinking of those who follow the waterfall process goes, make sure each phase is 100 % complete and absolutely correct before proceeding to the next phase.

Thus a Lab Total double the Level of Effect allows you to complete the project in a single season.

Thus, despite ongoing research, a complete understanding of the causes of mental disability in Graves ’ disease awaits a full description of the effects on neural tissue of thyroid hormones, as well as of the underlying autoimmune process.

Thus, as the Pharisees argued that all Israel should act as priests, the Rabbis argued that all Israel should act as rabbis: " The rabbis furthermore want to transform the entire Jewish community into an academy where the whole Torah is studied and kept .... redemption depends on the " rabbinization " of all Israel, that is, upon the attainment of all Jewry of a full and complete embodiment of revelation or Torah, thus achieving a perfect replica of heaven.

Thus Mithraism is thought to have something to do with the changing ages within the precession cycle or Great Year ( Plato's term for one complete precession of the equinox ).

Thus, Brutus ’ s army could not reform, which made the triumvirs ’ victory complete.

Thus, during the early 1960s, Pontiacs featured the controversial " X " frame used on the big Chevys, as well as the complete Chevy lineup of OHV straight Sixes, small-block 283 and 327 cubic inch V8s, and the big-block 348 and 409 V8s.

Thus he has been interpreted as being the ' complete one ' and also the finisher of the world, which he returns to watery chaos at the end of the creative cycle.

Thus, inheritance could be traced to the male line only, to the complete exclusion of females.

Thus, impeding all fish species needing to migrate to their freshwater habitats, in order to complete their lifecycles.

Thus far, Professor Skousen has published complete transcripts of the Original and Printer ’ s Manuscripts, as well as a six-volume analysis of textual variants.

Thus all the sets comprise a general directed graph ( ownership defines a direction ), or network construct.

Thus, it was not until two centuries had passed that in 1872 Karl Weierstrass presented the first definition of a function with a graph that would today be considered fractal, having the non-intuitive property of being everywhere continuous but nowhere differentiable.

Thus many maze solving algorithms are closely related to graph theory.

Thus, the hub and leaf nodes, and the transmission lines between them, form a graph with the topology of a star.

Thus in the graph of the supply curve, individual firms ' supply curves are added horizontally to obtain the market supply curve.

Thus in the graph of the demand curve, individuals ' demand curves are added horizontally to obtain the market demand curve.

Thus, a planar graph has genus 0, because it can be drawn on a sphere without self-crossing.

In one direction, the Hamiltonian path problem for graph G is equivalent to the Hamiltonian cycle problem in a graph H obtained from G by adding a new vertex and connecting it to all vertices of G. Thus, finding a Hamiltonian path cannot be significantly slower ( in the worst case, as a function of the number of vertices ) than finding a Hamiltonian cycle.

Thus, the graph forms a subgraph of the intersection graph of the subtrees.

Thus, given a graph G

Thus the graph is now ( c − 1 )- coloured.

Thus, the Petersen graph has crossing number 2.

Thus the permanent of A is equal to the sum of the weights of all perfect matchings of the graph.

Thus the permanent of a 01-matrix is equal to the number of vertex cycle covers of an unweighted directed graph.

Thus, for an implicit function to be a true ( single-valued ) function it might be necessary to use just part of the graph.

Thus, while the old " left-right " line attempted to measure politics along a one-dimensional line, Nolan's graph divided political issues into two dimensions: economic and social.

Thus one can think of the individual data points as the nodes of a graph and the kernel k defining some sort of affinity on that graph.

Thus, their theory establishes fundamental connections between graph minors and topological embeddings of graphs.

More specifically, the running time for testing whether H is a minor of G in this case is O ( n < sup > 3 </ sup >), where n is the number of vertices in G and the big O notation hides a constant that depends superexponentially on H. Thus, by applying the polynomial time algorithm for testing whether a given graph contains any of the forbidden minors, it is possible to recognize the members of any minor-closed family in polynomial time.

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 any countably infinite random graph is almost surely the Rado graph, which for this reason is sometimes called simply the random graph.