Thus the analysis using Newton's laws of motion can proceed as if the reference frame was inertial, provided the fictitious force terms are included in the sum of external forces.

Thus, the wise course on the eleventh spin would be to bet on red, not on black: exactly the opposite of the layman's analysis.

Thus Weber's methodology emphasises the use of comparative historical analysis.

Thus the reverse procedure, though originally uncommon, enabled northern analysis to evolve into gene expression profiling, in which many ( possibly all ) of the genes in an organism may have their expression monitored.

Thus the welfare analysis of oligopolies is sensitive to the parameter values used to define the market's structure.

Thus followed the line of Lomonosov and the contributions of the Russian school became more frequent through his disciples, and in the nineteenth century we have great geographers as Vasily Dokuchaev who performed works of great importance as a " principle of comprehensive analysis of the territory " and " Russian Chernozem " latter being the most important where introduces the geographical concept of soil, as distinct from a simple geological strata, and thus founding a new geographic area of study: the Pedology.

Thus the solution is 2, not ½ as would be the result of an incorrect analysis.

Thus my analysis suggests that this response to the paradox the Standard Bayesian one cannot be correct.

Thus a more detailed analysis of the bubble's motion is needed beyond Rayleigh-Plesset to explore the additional energy focusing that an internally formed shock wave might produce.

Thus STR analysis provides an excellent identification tool.

There is no sustained, mature analysis of the notion ..." Thus, some critics object, it would be acceptable to torture one person if this would produce an amount of happiness in other people outweighing the unhappiness of the tortured individual.

Thus, Charles S. Maier suggests that a political economy approach: " interrogates economic doctrines to disclose their sociological and political premises .... in sum, regards economic ideas and behavior not as frameworks for analysis, but as beliefs and actions that must themselves be explained.

Thus, under this analysis, the commodity produced by an unskilled worker would be more valuable than the same commodity produced by the skilled worker.

Thus Fourier analysis might be used to decompose a sound into a unique combination of pure tones of various pitches.

Thus, the definition or analysis of " bachelor " is thought to be an unmarried male.

Thus locally compact spaces are as useful in p-adic analysis as in classical analysis.

Thus, regular spaces are usually studied to find properties and theorems, such as the ones below, that are actually applied to completely regular spaces, typically in analysis.

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 hermeneutics expanded from its medieval role explaining the correct analysis of the Bible.

Thus it holds that technical analysis cannot be effective.

Thus, the RPD model is a blend of intuition and analysis.

Thus far, Professor Skousen has published complete transcripts of the Original and Printer ’ s Manuscripts, as well as a six-volume analysis of textual variants.

Thus, his analysis yields four sections, variations 1 – 7, 9 – 13, 15 – 19 and 21 – 33.

Thus far, genetic analysis of the Kalmyks supports their Mongol roots that also shows that entire families of Kalmyks moved to Volga region and not simply males as is generally the case with most nomadic tribal groups.

Thus, the copying of any dataset might be called a ' brain dump ' if its contents could be colloquially referred to as a ' brain '.

Thus, in applied statistics, a portmanteau test provides a reasonable way of proceeding as a general check of a model's match to a dataset where there are many different ways in which the model may depart from the underlying data generating process.

Thus no form of justification will rationally warrant our inductive inferences.

Thus our expression simplifies to:

Thus, it has generally been used to describe something which, while unreal, is so in a very specific or unusual fashion, usually one emphasizing not just the " not real ," but some form of estrangement from our generally accepted sense of reality.

" Thus irreal works such as Italo Calvino's Cosmicomics and Jorge Luis Borges ' Ficciones can be seen as an attempt to find a new allegorical language to explain our changed perceptions of the world that have been brought about by our scientific and technical culture, especially concepts such as quantum physics or the theory of relativity.

Thus Kant defines idealism as " the assertion that we can never be certain whether all of our putative outer experience is not mere imagining ".

Thus Plato and Gottfried Leibniz affirm an objective and knowable reality transcending our subjective awareness — a rejection of epistemological idealism — but propose that this reality is grounded in ideal entities, a form of metaphysical idealism.

Thus God's time must be aligned with our time if human activities are relevant to God's purpose.

" Thus we " make up our minds ," " change our minds " or are " of two minds " about something.

Thus, in Surah 3: 52 of the Qur ' an, Jesus ’ disciples tell Jesus, " We believe in God ; and you be our witness that we are Muslims ( wa-shahad be anna muslimūn ).

Thus in 2008, enabling the National Executive Way, published by Law Rank, Value and Force of Organic Law of the Bolivarian Armed Forces, leading to a new organization, adapted to new requirements, with a geopolitical vision oriented to a social state, peace-loving defender of human rights and solidarity with our sister nations of the American continent, within the ideology of the Liberator Simón Bolívar.

Thus, while the probability might be extremely small that any particular universe would have the requisite conditions for life ( as we understand life ) to emerge and evolve, this does not require intelligent design per the teleological argument as the only explanation for the conditions in the Universe that promote our existence in it.

Thus the Loyal Toast in the Channel Islands is La Reine, notre Duc (" The Queen, our Duke ").

Thus we can conceive of a “ noumenal ” world ( noumenal meaning " object of thought ") which exists only as a heuristic for our cognitive capacities and not as something directly accessible to experience.

Thus Kant effects his “ Copernican ” revolution of knowledge by changing our perspective on knowledge from a question of “ what can truly be known ” ( i. e. how can we actually come to know universals ), to a question of “ how does the knowing mind operate .”

Thus, in place of God's role as guarantor of the coherence of the world, Kant posits a faculty of reason structured by the forms of our intuition ( our sense of time and space ) and the categories of our understanding ( like the notion of cause and effect ).

Thus, one would expect to find a factor that roughly corresponds to " left " and " right ", as this is the dominant framing for politics in our society, but the basis of Eysenck's " tough / tender-minded " thesis ( the second, " T "- factor ) may well represent nothing beyond an abstract mathematical construct.

Thus, in the story " Ivory, and Apes, and Peacocks ", the Time Patrol's resident agents in the Tyre of King Hiram are a twentieth century Israeli couple, who express their wish to help the ancient Tyrians " in order to compensate a bit for what our country is going to do here.

Thus republicanism entered our Romanic / Germanic world .... Up to this point, the conviction had prevailed in Europe that monarchy best served the interests of the nation.

Thus we placed our energies at the disposal of the revolution, of the proletariat and its struggles, and defined our attitude towards the colonial problem, and hence towards the colour question.

Thus, some authors see arguments appealing to demons or the fall of man as indeed logically possible, but not very plausible given our knowledge about the world, and so see those arguments as providing defences but not good theodicies.