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 we will have a society consisting of the planners or conditioners, and the controlled.

Thus in a context in which there has been discussion of snow but mention of local conditions is new, dominant stress will probably be on here in it rarely snows here, but in a context in which there has been discussion of local weather but no mention of snow, dominant stress will probably be on snows.

Thus in it's incredible what that boy can eat dominant stress is likely to be on incredible, and eat will have strong stress also.

Thus, during any given year ( A ) if the revenues from the residential service are $7,000,000, ( B ) if the operating expenses imputed to this class of service come to $5,000,000, and ( C ) if the net investment in ( or value of ) the plant and equipment deemed devoted to this service amounts to $30,000,000, the cost analyst will report that residential service, in the aggregate, has yielded a return of $2,000,000 or 6-2/3 per cent.

Thus, if we are to observe American folklore in the twentieth century, we will do well to establish the relationships between folklore, nationalism and imperialism at the outset.

Thus he will be in a position to disabuse the Soviet leader of any notions he may have about grave Allied disunity.

Thus, while it remains possible that the Babylonians and/or the Pythagoreans may perhaps have had the magic square of three before the Chinese did, more definite evidence will have to turn up from the Middle East or the Classical World before China can lose her claim to the earliest known magic square by more than a thousand years.

Thus, if a two-dimensional array has rows and columns indexed from 1 to 10 and 1 to 20, respectively, then replacing B by B + c < sub > 1 </ sub >-− 3 c < sub > 1 </ sub > will cause them to be renumbered from 0 through 9 and 4 through 23, respectively.

“ Acts, then is a continuation of the Lucan Gospel, not in the sense that it relates what Jesus continued to do, but how his followers carried out his commission under the guidance of his Spirit .” Thus, part of the answer to the purpose of Acts is that Luke is writing to Theophilus, who is also mentioned in Luke 1: 3, in order to explain to him the occurrences that take place in the church that fulfill Jesus ’ promise to his disciples that “ you will be baptized with, the Holy Spirit not many days from now ” ( Acts 1: 5 ).

Thus, if people are accustomed to using a particular machine name to access a particular service, their access will break when the service is moved to a different machine.

Thus aesthetic judgments might be seen to be based on the senses, emotions, intellectual opinions, will, desires, culture, preferences, values, subconscious behavior, conscious decision, training, instinct, sociological institutions, or some complex combination of these, depending on exactly which theory one employs.

Thus, a heretic bearing the name of Sason (= Joy ) once remarked to him, " In the next world your people will have to draw water for me ; for thus it is written in the Bible ( Isaiah 12: 3 ), ' With joy shall ye draw water.

Thus even if the macro "" is not defined to signify non-ANSI compliance, "" will work as shown.

Thus united to them in the fellowship of life, he will both understand the things revealed to them by God and, thenceforth escaping the peril that threatens sinners in the judgment, will receive that which is laid up for the saints in the kingdom of heaven.

Thus, in any use of biological weapons, it is highly likely that animals will become ill either simultaneously with, or perhaps earlier than humans.

Thus the electrons stay paired together and resist all kicks, and the electron flow as a whole ( the current through the superconductor ) will not experience resistance.

Thus, even when family and friends learn to recognize the mood swings, the individual often will deny that anything is wrong.

Thus, Blackwood will not tell you what you want to know: Are we at risk of losing the first two tricks?

Thus, from a consequentialist standpoint, a morally right act ( or omission ) is one that will produce a good outcome, or consequence.

Thus, egoism will prescribe actions that may be beneficial, detrimental, or neutral to the welfare of others.

Thus, a poison that covers surface randomly will tend to reduce the number of uncontaminated large planes but leave proportionally more smaller sites free, thus changing the hydrogenation vs. hydrogenolysis selectivity.

Thus, the material body will occupy different configurations at different times so that a particle occupies a series of points in space which describe a pathline.