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, there was seen a need for a new law that would ensure the continuance of the succession following the death of the last legal heir under the Bill of Rights, being Princess Anne, guaranteeing the line of succession would continue in the Protestant line, and excluding any possible claims by the deposed James II or his son and daughter, James Francis Edward and Louisa Maria Teresa Stuart.

Thus a construction of the following type could conceivably arise: " It nearly knocked me off me plates — he was wearing a syrup!

Thus, the Sheikh of al-Azhar in Cairo, Muhammad Sayid Tantawy, who is the leading religious authority in the Sunni Muslim establishment in Egypt, alongside the Grand Mufti of Egypt, said the following about fatwās issued by himself or the entire Dar al-Ifta:

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 the following two statements are equivalent:

Thus Antony, as Caesar's key adherent and one of the two men around whom power coalesced following his assassination, was one of the three men chiefly responsible for the fall of the Roman Republic.

Thus in the following days from September 20, 1945, the functions of the OSS were split between the Department of State and the Department of War.

Thus Lenin remained the enfant terrible of the Russian Social Democratic Labour Party, although in this point in the war his following in Russia was as little as 10 000 and he must have seemed no more than the leader of an extremist wing of a bankrupt organization.

Thus the idea of an intellectual or scientific revolution following the Renaissance is — according to the continuity thesis — a myth.

Thus, all the high-mountain stages were grouped one after the other, with one rest day in between, following the climbing time trial.

Thus, upon the conquest of Persia, Alexander the Great sent to Athens 300 suits of Persian armour with the following inscription Alexander, son of Philip, and all the Greeks except the Spartans, give these offerings taken from the foreigners who live in Asia added.

Thus shot noise is more frequently observed with small currents or light intensities following sufficient amplification.

Thus following an opening bid of 1:

Thus, the following will not compile in C #:

Thus in all forms of Judaism following the Oral Law, women are allowed to marry whom they wish, including exogamously, whether they have gained an inheritance or not.

Thus in content and style it was new and modern, opening the way to many writers of the following century.

Thus new wood resulting from pruning will not produce flowers until the following season.

Thus the full route of the Circumferential Highway, as it existed by 1933, is now the following roads:

Thus, Louis-Auguste de Bourbon, Duke of Maine and Louis-Alexandre de Bourbon, Count of Toulouse were officially inserted into the line of hereditary succession following all of the legitimate, acknowledged princes du sang.

Thus Grosseteste concluded, following very much in what Boethius had argued, that mathematics was the highest of all sciences, and the basis for all others, since every natural science ultimately depended on mathematics.

Thus, the passive deaths following custody restraint presumed to be due to positional asphyxia after being secured by mechanical restraints may actually be examples of active restraint asphyxia occurring during the process of placing restraints.

Thus the following year, the first school in Southfield Township was erected in Franklin Village.

Thus, it was Heartbreak Hotel that turned Harrison from a relatively well-mannered schoolboy into a guitar-crazed truant who would audition for John Lennon's Quarrymen the following year.

Thus, the sentence Lisa found her book has the following interpretations:

Thus before the last ranks have fired, the first will have reloaded, as the following diagram shows: these little dots:: show the route of the ranks as they leave after firing.