Thus, the study of the solutions to the equation Af is reduced to the study of the space of solutions of a differential equation of the form Af.

Thus for example Heraclitus ' The Allegorist ' quoted fr. 326 and part of fr. 6, about ships in a storm, in his study on Homer's use of allegory.

Thus, study of this Barnum / Forer effect has been mostly focused on the level of acceptance of fake horoscopes and fake astrological personality profiles.

Thus, by monitoring eye movements, we can study what information is being processed at a given time.

Thus this study suggests that full sleep may not be important for optimal performance of memory.

Thus differential geometry may study differentiable manifolds equipped with a connection, a metric ( which may be Riemannian, pseudo-Riemannian, or Finsler ), a special sort of distribution ( such as a CR structure ), and so on.

Thus, it is on the one side, the study of wealth and on the other and more important side, a part of the study of man.

Thus, the search for extrasolar planets also includes the study of planetary habitability, which considers a wide range of factors in determining an extrasolar planet's suitability for hosting life.

Thus, the overall findings of the study are clear and require that even we skeptics, who have long doubted parental claims of the effects of various foods on the behavior of their children, admit we might have been wrong.

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 other than the prophets mentioned in the Quran, Ahmadis, with support from theological study also recognize Buddha, Krishna, founders of Chinese religions to be divinely appointed individuals.

Thus both fields of study are useful.

Thus much of WMCF is, in effect, a study of the epistemological foundations of the calculus.

Thus, genomics is the study of all the genes of a cell, or tissue, at the DNA ( genotype ), mRNA ( transcriptome ), or protein ( proteome ) levels.

Thus biography can form one part of the larger study of the cultural significance, underlying program, or agenda of a work ; a study which gained increasing importance in the 1980s and early 1990s.

Thus, E-Language is not itself a coherent concept, and Chomsky argues that such notions of language are not useful in the study of innate linguistic knowledge, i. e., competence, even though they may seem sensible and intuitive, and useful in other areas of study.

Thus, it cannot be concluded to what extent this study had an effect on " Little Albert's " life.

Thus the study of racism can be seen, at least superficially, as the study of the ways that people with a certain skin color and cultural background are systematically mistreated by society at large.

Thus, he notes that hiring decisions at Hitachi, during the time of his study, were " regulated by very strict qualification standards ", and not very significantly influenced by ascribed characteristics.

" ( 7 ), Thus, Frye launched the pursuit which was to occupy the rest of his career — that of establishing criticism as a " coherent field of study which trains the imagination quite as systematically and efficiently as the sciences train the reason " ( Hamilton 34 ).

Thus, as a simple instance posed by Hume, we cannot know with certainty by inductive reasoning that the sun will continue to rise in the East, but instead come to expect it to do so because it has repeatedly done so in the past.

* " Then opened he their understanding, that they might understand the scriptures, And said unto them, Thus it is written, and thus it behooved Christ to suffer, and to rise from the dead the third day: And that repentance and remission of sins should be preached in his name among all nations, beginning at Jerusalem.

Thus the 1980s and 1990s saw a rise in both budgets and the number of sequels a film could generally have.

f. Thus, every pair of ( mutually ) inverse elements gives rise to two idempotents, and ex

Thus, an increase in demand deposits will indicate expectations that inflation will rise, resulting in a decrease in bank lending and an increase in savings.

Thus, the relative difference in velocity between a source and an observer is what gives rise to the doppler effect.

Thus, Tuna-roa gave rise to all eels.

Thus, in some situations, a rise in the membrane potential can cause ion channels to open, thereby causing a further rise in the membrane potential.

Thus, soft power is often associated with the rise of globalization and neoliberal international relations theory.

Thus, he created a system in which people with talent could rise to the top of the bureaucracy, regardless of their background or rank.

Thus, there was a global rise of religious nationalism in the wake of the end of the cold war, but also as postcolonial politics ( facing considerable developmental challenges, but also dealing with the reality of colonially-defined – and therefore somewhat artificial borders ) become challenged.

Thus for a diameter glass tube in lab conditions given above ( radius ), the water would rise an unnoticeable.

Thus, the term " booby trap " gives rise to the idea that an individual with the misfortune to be caught in the trap does so because the individual is a " booby ", or that an individual who is caught in the trap thereby becomes a " booby ".

Thus a rise and a tread exactly meets this code.

Thus, it is clear that the factor v ( f ) in the exponent of the theoretical equation ( 30 ) gives rise to additional V-dependence in the pre-exponential of the empirical equation.

Thus, given an eigenvalue λ, its corresponding Jordan block gives rise to a Jordan chain.

Thus, every such type of algebra gives rise to a monad on the category of sets.

Thus the architects and planners have avoided not only the clichés of ´ high rise ´ building but the dreary prisonlike order that results from forgetting the very purpose of housing and the necessities of neighbourhood living.

Thus, a rise in income of the consumer may lead his demand for a good to rise, fall or not change at all.

Thus, the primary spermatocyte gives rise to two cells, the secondary spermatocytes, and the two secondary spermatocytes by their subdivision produce four spermatozoa.

Thus, any activating mutation downstream of SOS1 may be subject to less regulation that may mitigate the consequence of such mutations giving rise to the phenotypic differences seen between these syndromes.

Thus, production can be increased without much in the way of diminishing returns and the average price level need not rise much ( if at all ) to justify increased production.