Thus the week cycle is by itself not a full calendar system ; neither is a system to name the days within a year without a system for identifying the years.

Thus, every non-Han dynasty saw itself as the legitimate holder of the " Mandate of Heaven ", which legitimized the dynastic cycle regardless of social or ethnic background as it was moral integrity and benevolent leadership that had been validating the " Mandate of Heaven.

Thus, the cycle repeats to give a reaction that is self-sustaining.

Thus it is not easy to isolate the causes of specific phases of the cycle.

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 there are 3 cavities per housing, all repeating the same cycle.

Thus, any gait can completely be described in terms of the beginning and end of stance phase of three limbs relative to a cycle of a reference limb, usually the left hindlimb.

Thus the Báb taught that with his revelation the end times ended and the age of resurrection had started, and that the end-times were symbolic as the end of the past prophetic cycle.

Thus, the tropical year, measuring the cycle of seasons ( for example, the time from solstice to solstice, or equinox to equinox ), is about 20 minutes shorter than the sidereal year, which is measured by the Sun's apparent position relative to the stars.

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 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, for example, a government budget that is balanced over the course of the business cycle is considered to represent a neutral fiscal policy stance.

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 RNA editing by the cellular enzymes is critical to the virus ’ life cycle because it regulates the balance between viral replication and virion assembly.

Thus, each vertex i in the digraph has a unique " successor " in the cycle cover, and is a permutation on where n is the number of vertices in the digraph.

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

A punitive force sent by the Bulgarians was defeated. Thus we see a continuous cycle of dynastic strife amongst Vlastimir ’ s successors, stirred on by the Byzantine and Bulgarians, who were effectively using the Serbs as pawns.

Thus the root of mathematics and scientific pursuits in Pythagoreanism is also based on a spiritual desire to free oneself from the cycle of birth and death.

Thus the duration of the clock cycle of a moving clock is found to be increased: it is measured to be " running slow ".

Thus begins a vicious cycle which lasts many years.

Thus, by that definition, killing any animal would be a sin: one would be obstructing the natural cycle of birth and death of that creature, and the creature would have to be reborn in that same form because of its unnatural death.

Thus, placing sandtrout on a water-rich planet would allow them to start the complete spice cycle, at the cost of turning the planet into a desert, another Dune.

Thus every cycle c in X is the boundary of some " cone "; one may take the cone to be the image of c under the homotopy.

Thus, he supported funding to the state to assist the expansion of the East Tennessee and Virginia Railroad.

Thus, on January 16, 1997, the Diamondbacks were officially voted into the National League while their expansion counterparts in Tampa Bay were voted into the American League.

Thus Dürer contributed to the expansion in German prose which Martin Luther had begun with his translation of the Bible.

Thus with the expansion of the universe, radiation becomes less dominant than matter.

Thus, the capital of Kazakhstan lent its name to the Alma-Ata Declaration, in which eleven of the fifteen Soviet republics announced the expansion of the thirteen-day-old CIS.

Thus, the fundamental solution may be found by performing the continued fraction expansion and testing each successive convergent until a solution to Pell's equation is found.

Thus the conquest of actual infinity may be considered an expansion of our scientific horizon no less revolutionary than the Copernican system or than the theory of relativity, or even of quantum and nuclear physics.

where D denotes the continuum derivative operator, mapping f to its derivative f. The expansion is valid when both sides act on analytic functions, for sufficiently small h. Thus, T < sub > h </ sub >= e < sup > D </ sup >, and formally inverting the exponential yields

Thus, expansion: pause: contraction: pause.

Thus a better understanding of the possible links between El Niño, Western Pacific Warm Pool, Indonesian Throughflow, wind pattern off western Australia, and ice volume expansion and contraction can be obtained by studying the behaviour of the LC during Quaternary at close stratigraphic intervals.

Thus, in the West, the notion of ethnicity, like race and nation, developed in the context of European colonial expansion, when mercantilism and capitalism were promoting global movements of populations at the same time that state boundaries were being more clearly and rigidly defined.

Thus the sonic boom associated with the passage of a supersonic aircraft is the sound wave resulting from the degradation and merging of the shock wave and the expansion wave produced by the aircraft.

Thus plans were made to build an expansion.

Thus, in the early 1920s the growing University had to look for a more spacious campus as its original site at George Street, Brisbane has limited room for expansion.

Thus the redshift is explained by the fact that the Universe is currently in an expansion phase.

Thus it can be understood that the Zulu Nation's adoption of " Factology vs Beliefs ," was an effort to reorganize the Nation to be more accessible by more people of even more different belief systems, due to the ever expansion of Hip Hop culture worldwide causing a bigger need for a much more universal Hip Hop preservation society.

Thus, the Ayyubids required Nubia to guarantee the protection of Aswan and Upper Egypt, but like their Fatimid predecessors, were discouraged from further expansion by the poverty of the region.

Thus, he wrote: " if 0 is interpreted as falsehood, 1 as truth, and other numbers in the interval 0-1 as the degrees of probability corresponding to various possibilities, a many-valued logic is obtained which is expansion of three-valued logic and differs from the latter in certain details.

Thus, the outcome of a full partial fraction expansion expresses that function as a sum of fractions, where:

Thus the network has registered a sevenfold growth since independence, with the focus of the expansion primarily in rural areas.

Thus, the basic method of navigation using Guide was the expansion button, in which a section was replaced when selected and in which an expansion would provide additional levels of detail.

Thus, for example, if a researcher were interested in US resistance to communist expansion as a theoretical focus, then the Korean War might be taken to be the subject, the lens, the case study through which the theoretical focus, the object, could be viewed and explicated.

Thus began the Commodore's rapid expansion into parts of Indochina, the Middle East and South Africa badged as the Chevrolet Lumina, to Brazil as the Chevrolet Omega 3. 8 V6, and later on with the Monaro to the United States, where it was sold by Pontiac under the GTO nameplate.