Thus, current expected inflation reflects a weighted average of all past inflation, where the weights get smaller and smaller as we move further in the past.

Thus, the relative molecular weights of two gases are equal to the ratio of weights of equal volumes of the gases.

Thus, the weights are and, which are normalized distances between the unknown point and each of the end points.

Thus the permanent of A is equal to the sum of the weights of all cycle-covers of the digraph.

Thus the permanent of A is equal to the sum of the weights of all perfect matchings of the graph.

Thus response burden is markedly reduced, accuracy is increased, product description is more specific and point of purchase data are obtained, facilitating the estimation of outlet-type weights.

Thus, Bellman – Ford is used primarily for graphs with negative edge weights.

Thus, the parliament at Ottawa alone can pass laws relating to, amongst other things, the postal service, the census, the military, criminal law, navigation and shipping, fishing, currency, banking, weights and measures, bankruptcy, copyrights, patents, First Nations, and naturalization.

Thus, Bellman – Ford is usually used only when there are negative edge weights.

Thus, even though two robins might begin the day with different weights, they will end the day with similar weights.

Thus he was the first person to give the notion of equivalent weight and to publish a table of equivalent weights of acids and bases.

Thus, a complete graph with equal weights describes a Moran process.

" Thus, his off-season workout pattern of sloughing the weights for discussion of politics and current affairs was troubling, but not challenged because he could outlift most.

Thus we are compelled to face the urbanization of the South -- an urbanization which, despite its dramatic and overwhelming effects upon the Southern culture, has been utterly ignored by the bulk of Southern writers.

Thus, paradoxically, the beat writers resort to `` religious '' metaphors: they are in search of mana, the spiritual, the numinous, but not anything connected with formal religion.

Thus, if corporations are not to run away with us, they must become quasi-governmental institutions, subject to public control and needs.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Thus there are polynomials Af such that Af.

Thus the Af are projections which correspond to some direct-sum decomposition of the space V.

Thus pencils of tangents to Q are transformed into pencils of tangents.

Thus it follows that the secants of **zg are all invariant.

Thus, although the agenda of external assistance in the economic sphere are cumulative, and many of the policies suggested for nations in the earlier stages remain relevant, the basic purpose of American economic policy during the later stages of development should be to assure that movement into a stage of self-sustaining growth is not prevented by lack of foreign exchange.

Thus the first lines of one of Charles Wesley's hymns are as follows.

Thus in his friends are stranger than his sisters' strong stresses are normal for his and sisters', but in his friends are stranger than his sisters strong stresses are normal for friends and sisters.

Thus his persistence values for some stem frequencies per meaning are: stem identical in 8 languages, 100% ; ;

Thus, the white middle and lower classes are arrayed against the Negro middle and lower classes.

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, in the example cited above Fromm rests his whole case on the premise that the workers are being deprived unconsciously, unknowingly, of fulfillment, and then supports this with survey data reporting conscious, experienced frustrations.

Thus, the three main categories of antisubmarine warfare operations are defense of shipping, defense of naval forces, and area defense.

Thus, the most productive areas are not necessarily the most stressed.

Thus a number of operations of the order of Af are required.

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, in `` The Story Of Ruth '' we have Ruth, Naomi, and Boaz and sets that are meticulously authentic.

" 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 although most species in the order are herbaceous, some no more than 15 cm high, there are a number of climbers ( e. g. some species of Asparagus ), as well as several genera forming trees ( e. g. Agave, Cordyline, Yucca, Dracaena ), some of which can exceed 10 m in height.

Thus far, the origins of the word remain inconclusive, as the term is not used outside Mexican-American communities, further indicating that the term is primarily self-identifying.

Thus greenhouses work primarily by preventing convective cooling.

Thus, the state required service from both the old and the new nobility, primarily in the military.

Thus, the convention that Sovereigns do not attend Cabinet meetings was established primarily through royal indifference to the everyday tasks of governance.

Expected to make use of devices with which listeners could press a button to indicate whether they liked or disliked a particular piece of music, Adorno bristled with distaste and astonishment: “ I reflected that culture was simply the condition that precluded a mentality that tried to measure it .” Thus Adorno suggested using individual interviews to determine listener reactions and, only three months after meeting Lasarzfeld, completed a 160-page memorandum on the Project ’ s topic, “ Music in Radio .” Adorno was primarily interested in how the musical material was affected by its distribution through the medium of radio and thought it imperative to understand how music was affected by its becoming part of daily life.

Thus, the most meaningful comparison of advantages and disadvantages is with other forms of local transit, primarily the local bus.

Thus, the creation of Turkish hip hop in Germany ( primarily through such groups as Cartel and Islamic Force ) that sought to address Turkish nationalist identities was born.

" Thus, many long-term investors, even those who buy and hold for decades, may be classified as speculators, excepting only the rare few who are primarily motivated by income or safety of principal and not eventually selling at a profit.

Thus, a financial concept of capital should be adopted if the users of financial statements are primarily concerned with the maintenance of nominal invested capital or the purchasing power of invested capital.

Thus, in regard to stress or injury, the function of adenosine is primarily that of cytoprotection preventing tissue damage during instances of hypoxia, ischemia, and seizure activity.

Thus, in present-day ethnomusicology, an electrophone is considered to be only musical instruments which produce sound primarily by electrical means.

Thus, the elastic modulus of the bilayer is primarily determined by how much extra area is exposed to water when the lipid molecules are stretched apart.

Thus, whether or not the destruction of the press was legal depends primarily on the laws of the state of Illinois and the Nauvoo Charter.

Thus the struggle between metaphysics and scientific world-conception is not only a struggle between different kinds of philosophies, but it is also — and perhaps primarily — a struggle between different political, social and economical attitudes.

“ Since timing and levels of sexual activity are quite similar across France, Canada, Great Britain, and the U. S., the high U. S. rates arise primarily because of less, and possibly less-effective, contraceptive use by sexually active teenagers .” Thus, the cause for the discrepancy between rich nations can be traced largely to contraceptive-based issues.

Thus this particular Protestant ( primarily Methodist ) understanding of theosis is substantially different from that of the Roman Catholic, Orthodox, or Anglican Churches.

Thus the network has registered a sevenfold growth since independence, with the focus of the expansion primarily in rural areas.

Thus, the chansons were primarily an oral medium.

Thus syllabic technique does not — in English — convey a metrical rhythm ; rather it is a compositional device: primarily of importance to the author, perhaps noticed by the alert reader, and imperceptible to the hearer.

Thus, the Company remains primarily as a charitable institution.

Thus, it remains primarily as a charitable institution.

Thus, while appearing to honor his pledge to increase suffrage, Louis-Philippe acted primarily to empower his supporters and increase his hold over the French Parliament.

Thus any algorithm that can be expressed primarily as operations on arrays and matrices can run almost as quickly as the equivalent C code.