Thus the diminished seventh chord would be C3 and the augmented triad would be C4.

Thus, because the King and Queen had not made any concessions in return, the prestige of Naples was augmented.

Thus, the name could refer to the similarity between a swollen cheek and a Maultasche.

Thus jazz is transmuted into something holy, the sacred road to integration of being.

Thus the transformation of Adam Smith's ideal entrepreneur into a mythological detective coincides closely with the decline of the real entrepreneur in economic life.

Thus, when the Russians sent up their first sputnik, American chagrin was human enough, and American determination to put American satellites into orbit was perfectly understandable.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, there has come into being a situation in which the state must raise all of its own revenues and, in addition, must give assistance to its local governments.

Thus, the energy transferred from the arc to the anode was partly fed back into the arc.

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

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 at the same time that William Henry Harrison was preparing to pacify the aborigines of Indiana Territory and winning fame at the battle of Tippecanoe, Anglo-Saxon settlement made a great leap into the center of the North American continent to the west of the American agricultural frontier.

For every group G there is a natural group homomorphism G → Aut ( G ) whose image is the group Inn ( G ) of inner automorphisms and whose kernel is the center of G. Thus, if G has trivial center it can be embedded into its own automorphism group.

" Thus Ambrose refused to be drawn into a false conflict over which particular local church had the " right " liturgical form where there was no substantial problem.

Thus we have the story of his riding across a stick ( horse made of stick ) with his children and upon being discovered by a friend desiring that he not mention till he himself were the father of children ; and because of the affection of his son Archidamus ' for Cleonymus, he saved Sphodrias, Cleonymus ' father, from execution for his incursion into the Piraeus, and dishonorable retreat, in 378 BC.

Thus the possibility of re-incorporating Portugal ( up to then Southern Galicia ) into a Kingdom of Portugal and Galicia as before was eliminated and Afonso became sole ruler ( Duke of Portugal ) after demands for independence from the county's church and nobles.

Thus he maintained that there must be blackness as well as whiteness in snow ; how otherwise could it be turned into dark water?

Thus, on January 16, 1997, the Diamondbacks were officially voted into the National League while their expansion counterparts in Tampa Bay were voted into the American League.

Thus, English developed into a " borrowing " language of great flexibility and with a huge vocabulary.

By a theorem of Gelfand and Naimark, given a B * algebra A there exists a Hilbert space H and an isometric *- homomorphism from A into the algebra B ( H ) of all bounded linear operators on H. Thus every B * algebra is isometrically *- isomorphic to a C *- algebra.

Thus, in the Eucharist, gone were the words Mass and altar ; the ' Lord have mercy ' was interleaved into a recitation of the Ten Commandments and the Gloria was removed to the end of the service.

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, a week of Beetle Bailey would arrive at the Lansing State Journal in two sheets, printed much larger than the final version and ready to be cut apart and fitted into the local comics page.

Thus fundamentally in Judaism, one is enjoined to bring holiness into life ( with the guidance of God's laws ), rather than removing oneself from life to be holy.

Thus, living birds were divided into carinates ( keeled ) and ratites ( from ratis, " raft ", referring to the flatness of the sternum ).

Thus perceptions must already come parcelled into distinct " bundles " before they can be associated according to the relations of similarity and causality: in other words, the mind must already possess a unity that cannot be generated, or constituted, by these relations alone.

Thus, an expanded definition for data warehousing includes business intelligence tools, tools to extract, transform and load data into the repository, and tools to manage and retrieve metadata.

Thus, an analog signal is one represented by a continuous stream of data, in this case along an electrical circuit in the form of voltage, current or charge changes ( compare with digital signals below ).

Thus, in the first twenty years of the 20th century many writers, thinkers, and artists broke with the traditional means of organizing literature, painting, and music ; the results were abstract art, atonal music, and the stream of consciousness technique in the novel.

Thus municipalities can use plea bargaining as a revenue stream, regardless if justice is subverted and criminals can pay their way out of an otherwise serious charge.

Thus, “ The Daily Sun " features stories about tokoloshes ( hob-goblins ), ancestral visions and all things supernatural and wildly absurd, together with localised stories and main stream news.

Thus a virtual connection, also known as a virtual circuit or byte stream is provided to the end-user by a transport layer protocol, although intermediate network nodes only provides a connectionless network layer service.

Thus if the primary seal fails, the neutral liquid will leak into the pump stream instead of the dangerous pumped fluid escaping into the atmosphere.

Thus, without being constitutionally obligated to pay compensation, the United States may change the course of a navigable stream, South Carolina v. Georgia, 93 U. S. 4 ( 1876 ), or otherwise impair or destroy a riparian owner's access to navigable waters, Gibson v. United States, 166 U. S. 269 ( 1897 ); Scranton v. Wheeler, 179 U. S. 141 ( 1900 ); United States v. Commodore Park, Inc., 324 U. S. 386 ( 1945 ), even though the market value of the riparian owner's land is substantially diminished.

Thus the Upper Fox grows from a small stream to a small river over its course.

Thus this portion of the stream has variable salinity and electrical conductivity over the tidal cycle.

Thus it imposes conformance rather than checking it, and where the queue is serviced at a fixed rate ( and where the packets are all the same length ), the resulting traffic stream is necessarily devoid of burstiness or jitter.

Thus, high stream flows spread water and nutrients to beyond the stream banks to wide riparian zones when beaver dams are present.

Thus, the intensity of many lighting instruments are often altered with a single fade, especially with newer digital control systems like DMX, which uses a serial data stream to control up to 512 dimmers or other compatible fixtures, via a single twisted pair of wires.

Thus the rights to the revenue stream produced by the land had been farmed by the lessor ( therefore strictly perhaps the " farmor ") and the tenant became the " holder of the farm ", or to coin a word, " farmee ".

Citing these cases, the Kentucky court wrote: " Thus our decision, rather than being the leading edge of change, is but a part of the moving stream.