Thus, there has come into being a situation in which the state must raise all of its own revenues and, in addition, must give assistance to its local governments.

Thus Af denotes the state of the feed to the R-stage process, and Af the state of the product from the last stage.

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

Thus the necessary and sufficient conditions for the truth of a proposition of law simply involved internal logic and consistency, and that the state's agents used state power with responsibility.

Thus a description of the cat during the course of the experiment — having been entangled with the state of a subatomic particle — becomes a " blur " of " living and dead cat.

Thus, texts like the Annals will often state whether the calendar they use ( the calendar of Lu ) is in phase with the Royal calendar ( used by the Zhou kings ).

Thus, culture has replaced the state as the locus of war.

Thus dubnium is expected to form a stable + 5 state.

Thus, it is easier to state what God is not, than to state what God is:

Thus, the law of " interpenetrating opposites " records the inextricable interdependence of components: the " transformation of quantity to quality " defends a systems-based view of change that translates incremental inputs into alterations of state ; and the " negation of negation " describes the direction given to history because complex systems cannot revert exactly to previous states.

Thus, while a permit to fill non-federal wetlands might require a permit from a single state agency, larger and more complex endeavors — for example, the construction of a coal-fired power plant — might require approvals from numerous federal and state agencies.

Thus, if the rate of any pathway changes, both the excited state lifetime and the fluorescence quantum yield will be affected.

Thus, a piece of iron in its lowest energy state (" unmagnetized ") generally has little or no net magnetic field.

Thus in diplomatic affairs, heads of state are often the first person to greet an important foreign visitor.

Thus in March 1979 Colonel Muammar Gaddafi, who kept absolute power ( until his overthrow in 2011 referred to as " Guide of the Revolution "), after ten years as combined Head of State and Head of government of the Libyan Jamahiriya (" state of the masses "), styled Chairman of the Revolutionary Command Council, formally transferred both qualities to the General secretaries of the General People's Congress ( comparable to a Speaker ) respectively to a Prime Minister, in political reality both were his creatures.

Thus, the nearest formal oxidation state of iron in Hb-O < sub > 2 </ sub > is the + 3 state, with oxygen in the-1 state ( as superoxide. O < sub > 2 </ sub >< sup >-</ sup >).

Thus, even when the Electors of Saxony were Catholics during the eighteenth century, they continued to preside over the corpus evangelicorum, since the state of Saxony was officially Protestant.

Thus, the first East Slavic state, Kievan Rus ', emerged in the 9th century along the Dnieper River valley.

Thus the argument also involved the issue of the proper relationship between church and state.

Thus a number of operations of the order of Af are required.

Thus, during the abdication crisis of 1936, caused by Edward VIII's desire to marry Wallis Simpson, the consent of all realms concerned, along with, in some cases, new acts of parliament, was required in Britain and throughout the British Dominions to allow for Edward's stepping aside and to ensure that if he had any children they would have no claim to the thrones.

Thus, the energy required to break any single pair is related to the energy required to break all of the pairs ( or more than just two electrons ).

Thus his calculations should have required an additional year, ending in 1967.

Thus it has been alleged that many credentes would eventually receive the consolamentum as death drew near — performing the ritual of liberation at a moment when the heavy obligations of purity required of Perfecti would be temporally short.

Thus miniatures were no longer required for game play, although some players continued to use them as a visual reference.

Thus, they required that the Estates be arranged as in 1614.

Thus, numerical mathematical methods are required, even to solve the system of one nucleus and two electrons.

Thus the tonewheel assembly generates 91 frequencies, which are all that are required for the entire organ.

Thus, the Holy Alliance needed Russia to supply the required armies.

Thus, he saw private property as both essential to liberty and a road to tyranny, the former when it resulted from labour and was required for labour and the latter when it resulted in exploitation ( profit, interest, rent, tax ).

Thus, reflection in a resonant cavity is usually required for a laser, but is not absolutely necessary.

Thus ingot casting, foundry techniques, blast furnace extraction, and electrolytic extraction are all part of the required knowledge of a metallurgist / engineer.

Thus, while dialectical methods are necessary to find truth in theoretical matters, rhetorical methods are required in practical matters such as adjudicating somebody's guilt or innocence when charged in a court of law, or adjudicating a prudent course of action to be taken in a deliberative assembly.

Thus to calculate the stoichiometry by mass, the number of molecules required for each reactant is expressed in moles and multiplied by the molar mass of each to give the mass of each reactant per mole of reaction.

Thus, many modern pumps have a molecular drag stage such as a Holweck or Gaede mechanism near the exhaust to reduce the size of backing pump required.

Thus, it is easy to convert from a vector file to a range of bitmap / raster file formats but it is much more difficult to go in the opposite direction, especially if subsequent editing of the vector picture is required.

Thus no special modifications are required to be made to operating systems which would otherwise not know about them.

Thus such studies undermine the broad consensus required for good science by excluding certain people, and so proving themselves in the end to be unscientific.

Thus, according to Coule, an Alcubierre Drive is required in order to build an Alcubierre Drive.

Thus, Electronic Support provides a source of information required for decisions involving Electronic Protection ( EP ), Electronic Attack ( EA ), avoidance, targeting, and other tactical employment of forces.

Thus, a proactive and comprehensive approach to HD is required for US's response.

Thus the amount of the test substance required to produce the same biological effect as a given quantity the unit of a standard preparation is compared and the potency of the unknown is expressed as a % of that of the standard by employing a simple formula.