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 Boolos and Jeffrey are saying that an algorithm implies instructions for a process that " creates " output integers from an arbitrary " input " integer or integers that, in theory, can be chosen from 0 to infinity.

Thus, most recipes that use bay leaves will recommend their removal after the cooking process has finished.

Thus, what started as an effort to translate between languages evolved into an entire discipline devoted to understanding how to represent and process natural languages using computers.

Thus, entropy is also a measure of the tendency of a process, such as a chemical reaction, to be entropically favored, or to proceed in a particular direction.

Thus, the immensely popular goddess Durga was a pre-Vedic goddess who was later fused with Parvati, a process that can be traced through texts such as Kalika Purana ( 10th century ), Durgabhaktitarangini ( Vidyapati 15th century ), Chandimangal ( 16th century ) etc.

Thus, " discrimination " against ( i. e., negative differential treatment of ) potential insureds in the risk evaluation and premium-setting process is a necessary by-product of the fundamentals of insurance underwriting.

Thus, they feel that " the decisive factor for the birth of typography ", the use of reusable moulds for casting type, might have been a more progressive process than was previously thought.

Within the space of these tendencies there has developed a coherent critique of " orthodox Marxism " that includes not only a rejection of the concept of " the transition " but a reconceptualization of the process of transcending capitalism that has remarkable similarities to ( Peter ) Kropotkin's thinking on this subject ... Thus one of the earliest political tendencies within which this approach appeared after the Russian revolution of 1917 was that of " Council Communism " which saw the " workers councils " in Germany ( see Bavarian Soviet Republic ), or the soviets in Russia, as new organizational forms constructed by the people.

Thus a vented gauge reference pressure sensor should always read zero pressure when the process pressure connection is held open to the air.

Thus the inferior court decision may remain in effect even though it does not obey the superior court decision, as the only way a decision can enter the appeal process is by application of one of the parties bound by it.

Thus the field encompasses water in rivers, lakes, aquifers and to an extent glaciers, in which the field examines the process and dynamics involved in these bodies of water.

Thus, ' sexual selection ' typically refers to the process of choice ( the limiting factor, which is typically females ) over members of the opposite sex ( the non-limited factor, typically males ).

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, the efficiency of the process may be increased by many orders of magnitude.

The absolute number of cancer cases attributed to exposure to gasoline, however, is low, estimated a few cases per year in the U. S. Thus, the decision to require fewer aromatics has been criticized on the grounds of opportunity cost: the hundreds of millions of dollars spent on process redesign could have been spent on other, more fruitful ways of reducing deaths caused by cancer or automobiles.

Thus, committee action is probably the most important phase of the legislative process.

Thus we might also describe reduction as a process analogous to absorption, by which one theory ( or concept, or property, and so on ) is wholly subsumed under another.

Thus, in jurisdictions with due process, there must be an actus reus accompanied by some level of mens rea to constitute the crime with which the defendant is charged ( see the technical requirement of concurrence ).

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, sending a message to another process and waiting for a reply does not result in " losing one's turn " for the CPU.

Thus railroad " deregulation " was a two step process, starting with the 4R Act and concluding with the Staggers Act.

Thus, one may conceive of the " Oral Torah " not as a fixed text but as an ongoing process of analysis and argument in which God is actively involved ; it was this ongoing process that was revealed at Sinai, and by participating in this ongoing process rabbis and their students are actively participating in God's ongoing act of revelation.

Thus, up to the unification of the country, Nepal's recorded history is largely that of the Kathmandu Valley.

Thus after the unification under the Western Jin Dynasty an era of prosperity began as the relocated tribes adopted agriculture and contributed to the revival of the economy.

Thus the unification of the four provinces in the Union of South Africa, the idea of the British Commonwealth of Nations, and, finally, the great whole resulting from the combination of the peoples of the earth in a great league of nations were but a logical progression consistent with his philosophical tenets.

Thus, the main goal of the Sphere was the hakkō ichiu, the unification of the eight corners of the world under the rule ( kōdō ) of the Emperor.

Thus, he took up from Jinul the tradition of unification of Seon and Gyo Buddhism.

Thus attempts at unification within the Maghrib were more often than not the means by which to counterbalance one or both of the region's major powers.

Thus, within twenty four hours of the Republic's announcement, Algeria threatened Tunisia with military intervention if Tunisia went ahead with the unification.

Thus when German unification became realistic, Wagner wanted to go back to Germany proper – a general attitude of Baltic Germans.

Thus, with the sanction of the Church came the unification of communities in various dioceses with the mother-house at Carondelet, now in the city of St. Louis.

Thus, were Han unification perfectly successful, Z-variants would not exist.

Thus a měizhōurén is an American in the generic sense, and a měiguórén is an American in the U. S. sense.

Thus, a number of Allied soldiers received the Bronze Star Medal in World War II, as well as U. N. soldiers in the Korean War, Vietnamese and allied forces in the Vietnam War, and coalition forces in recent military operations such as the Gulf War, Operation Enduring Freedom and the Iraq War.

Thus, much of the spirits used in making a Canadian whisky, prior to aging, may have less grain-derived flavour than typical single malts or U. S. " straight " whiskeys.

Thus, it might be used to challenge the sharp distinction made in U. S. v. E. C. Knight ( 1895 ) between commerce, which was subject to federal regulation, and manufacturing, which was not.

Thus, in Wilson v. U. S. ( 1911 ), he asserted that corporate officers could not resist a subpoena for company records by invoking the Fifth Amendment's privilege against self-incrimination.

The media, in an attempt to explain the ideology of Ayatollah Khomeini and the Iranian Revolution to a Western audience described it as a " fundamentalist version of Islam " by way of analogy to the Christian fundamentalist movement in the U. S. Thus was born the term " Islamic fundamentalist ", which would come to be one of the most common usages of the term in the following years.

Thus commercial lighting alone consumes about four to five million barrels per day ( equivalent ) of petroleum, in line with the alternate rationale above to estimate U. S. lighting energy consumption.

Thus enforcing that part of the treaty which was of interest to the United States, namely, " It granted the U. S. significant transit rights over the Panamanian isthmus "

Thus in four close U. S. elections ( 1824, 1876, 1888, and 2000 ), the candidate with the most popular votes still lost the election.

Thus far, Swiss authorities have blocked about 72 accounts totalling U. S .$ 22. 6 million.

Thus some of the suburbs of most of the developed world are comparable to several inner cities of the U. S. and Canada.

Thus, the Council was to consist of ( 1 ) all U. N. members administering trust territories, ( 2 ) the five permanent members of the Security Council, and ( 3 ) as many other non-administering members as needed to equalize the number of administering and non-administering members, elected by the United Nations General Assembly for renewable three-year terms.

Thus, for example, the Great Seal of the United States, among other uses, appears on the reverse of the one-dollar bill ; and several of the seals of the U. S. states appear on their respective state flags.

Thus, the population in the U. S. is not aging to the extent as those in Europe, Australia, or Canada.

Thus, at his Canadian residence, Rideau Hall, George VI personally accepted and approved the Letter of Credence of the newly appointed U. S. Ambassador to Canada, Daniel Calhoun Roper.

Thus in the UK there is cost shifting from the private sector to the public sector, which again is the opposite of the allegation of cost shifting in the U. S. from public providers such as Medicare and Medicaid to the private sector.

Thus, some of today's auctioneers in the U. S. carry the unofficial title of " colonel ".

Thus, for this short period in LeMay ’ s career, he was technically an officer and enlisted soldier at the same time, a practice no longer permitted in the U. S. military.

Thus, U. S. 101 is treated as a primary, two-digit route with a " first digit " of 10, rather than a spur of U. S. 1.

Thus U. S. Route 101, not U. S. 99, is the westernmost north – south route in the U. S. Highway system.

Thus he developed and strongly supported " Vietnamization ", a program intended to expand, equip, and train South Vietnam's forces and assign to them an ever-increasing combat role, at the same time steadily reducing the number of U. S. combat troops.