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Thus, the perturbation introduced to the system is described by a velocity field of infinitesimally small amplitude,.
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Thus and perturbation
Thus, an arbitrarily small perturbation of the current trajectory may lead to significantly different future behavior.
Thus the perturbation can not be considered small in the D subspace and in that subspace the new Hamiltonian must be diagonalized first.
Thus, in the weak field approximation, we can identify with the Newtonian gravitational potential, and we can regard it as controlling a small conformal perturbation from a flat spacetime background.
Thus and introduced
Thus it was the Aeginetans who, within 30 or 40 years of the invention of coinage in Asia Minor by the Ionian Greeks or the Lydians ( c. 630 BC ), introduced coinage to the Western world.
Thus, dark blue jerseys, were introduced with white shorts and the red socks of 1908.
Thus, when the plate is introduced to a compatible printing ink and water mixture, the ink will adhere to the positive image and the water will clean the negative image.
Thus the scutage was introduced, whereby most Englishmen paid to escape their service and this money was used to create a permanent army.
Thus such elements as collage were introduced, arising partly from an ideal of startling juxtapositions as revealed in Pierre Reverdy's poetry.
Thus, the new short dance was introduced at the start of the 2010-11 season.
Thus the B Series, introduced for 1971, offered both car-like comfort in its Sportsman passenger line or expansive room for gear and materials in its Tradesman cargo line.
Thus the large-scale contact with Europeans after 1492 introduced novel germs to the indigenous people of the Americas.
Thus, Hari goes on his " Flight " and is introduced to Dors Venabili by Hummin.
Thus were black magic and death introduced into the world.
Thus it was entirely possible that models introduced in the ' 50s could be fitted with four different wheel types during the span of their inclusion in the series — or even more, since there were further variations ( e. g. knobby or smooth ) besides the color or material.
Thus, Kolmogorov introduced a second hypothesis: for very high Reynolds numbers the statistics of small scales are universally and uniquely determined by the viscosity () and the rate of energy dissipation ().
Thus, while early Jewish literature has few historical works, many notes on the history of Judaism have been introduced into the responsa.
Thus, one conforms to the group standard, but as soon as one does, eliminating this external conflict, internal conflict is introduced ( because one has violated one's own standards ).
The Chinese words already introduced by his predecessors he did not alter, and in introducing new terms required in the translation of the Mahayana literature, the 大乘 Tasheng or greater development, he uses SH for SH and usually B for V. Thus the city Shravasti was in Pali Savatthi and in Chinese Sha-ba-ti.
Thus, the red color was introduced to differentiate from the color pattern of Flamengo of Arcoverde.
Also sprach Zarathustra, literally " Thus Spoke Zarathustra ", is also the title to Nietzsche's most famous work of philosophy, which introduced the Übermensch ( overmen ) and popularized the phrase " God is dead ".
Thus they reproached him because he wrote in Hebrew instead of in the customary Talmudic idiom, because he departed from the Talmudic order and introduced a division and arrangement of his own, and because he dared to sometimes decide according to the Tosefta and the Jerusalem Talmud as against the Babylonian Talmud.
Thus it was decided to follow the Germans ( Leopard 2A4 ) and British ( Challenger 2 ) in their application of a titanium-tungsten system, which was introduced to the Leclerc in 2001, in Batch 10.
Thus, the label of " reconciliation " which de Waal introduced for reunions after fights was questioned at first, but is now fully accepted with respect to animal behavior.
Thus, when the liquor was introduced in 1935, the name was already familiar to Germans and was occasionally called " Göring-Schnapps ".
Thus in order to make house music more appealing to the Singapore crowd, it introduced a blend of music which incorporated pop hits from the 70s and 80s with house music which were to be played every Wednesday night.
Thus, when an electrophilic alkylating agent is introduced to a primary amine, it will preferentially alkylate all the way to a quaternary ammonium cation.
Thus Bishop Georg von Polenz of Pomesania and Samland, who had converted to Lutheranism in 1523, took over and introduced the Protestant Reformation also in the ducal two thirds of Warmia diocese, territorially surrounding the actual prince-episcopal third.
Thus and system
Thus the cocktail party would appear to be the ideal system, but there is one weakness.
Thus, Margenau remarks: `` A large number of unrelated epicycles was needed to explain the observations, but otherwise the ( Ptolemaic ) system served well and with quantitative precision.
Thus, the need for the B-70 as a strategic weapon system is doubtful.
Thus the Congress marks a formal recognition of the political system that was central to world politics for a century.
Thus if the gyro and platform-controller combination maintains the platform with zero angular deviation about the **yf axis, the system can be rotated with an angular velocity Af if a torque is supplied to the gyro output axis Aj.
Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system.
Thus, an axiom is an elementary basis for a formal logic system that together with the rules of inference define a deductive system.
Thus flight test program was set to integrate the AARGM onto Tornado ECR's weapon system.
Thus, Walsh modified the vertical passing scheme he had learned during his time with the Raiders, designing a horizontal passing system that relied on quick, short throws-often spreading the ball across the entire width of the field.
Thus, a robust surveillance system involving human clinicians and veterinarians may identify a bioweapons attack early in the course of an epidemic, permitting the prophylaxis of disease in the vast majority of people ( and / or animals ) exposed but not yet ill.
Thus natural languages are mainly oral, while Blissymbols is just a writing system dealing with semantics, not phonetics.
Thus the week cycle is by itself not a full calendar system ; neither is a system to name the days within a year without a system for identifying the years.
Thus, the sum of all applied forces and torques ( with respect to the origin of the coordinate system ) in the body can be given by
Thus, though often de facto the case, Conservative Judaism's halakhic system does not inherently see Orthodox halakhic practice as acceptable and legitimate halakhic practice for a Conservative Jew.
Thus the Sidewinder team replaced a potentially complex control system with a simple mechanical solution.
Thus the CGS system never gained wide general use outside the field of science.
Thus, u < sub > ρ </ sub > and u < sub > θ </ sub > form a local Cartesian coordinate system attached to the particle, and tied to the path traveled by the particle.
Thus, instead of streamlining the system, Gorbachev's decentralization caused new production bottlenecks.
Thus, the larger the aperture of the lens, and the smaller the wavelength, the finer the resolution of an imaging system.
Thus, the only logical possibilities are to accept non-Euclidean geometry as physically real, or to reject the entire notion of physical tests of the axioms of geometry, which can then be imagined as a formal system without any intrinsic real-world meaning.
Thus, it has been argued that a voucher system would lead students who do not belong to a preferred religious or ethnic group, or those with disabilities, to become concentrated within the public school system.
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