Therefore, given any positive integer n, it produces a string with Kolmogorov complexity at least as great as n. The program itself has a fixed length U. The input to the program GenerateComplexString is an integer n. Here, the size of n is measured by the number of bits required to represent n, which is log < sub > 2 </ sub >( n ).

Therefore, if one is to change the quantity of by, without moving off the indifference curve, one must also change the quantity of by an amount such that, in the end, there is no change in U:

Therefore, these processes are also known as Umklapp ( U ) processes and can only occur when phonons with sufficiently large q-vectors are excited, because unless the sum of q < sub > 2 </ sub > and q < sub > 3 </ sub > points outside of the Brillouin zone the momentum is conserved and the process is normal scattering ( N-process ).

* United States of America – Our Lady of the Immaculate Conception unofficial due to the Establishment Clause of the First Amendment to the Constitution of the United States which states, " Congress ( Therefore the U. S. Government ) shall make no law respecting an establishment of religion ,..."

Therefore, the resulting U and V signals can be substantially " compressed ".

Therefore 80 % of the county residents belong to major denominational churches, compared to 36 % of the total U. S. population.

Therefore, the modern legal education system in the U. S. is a combination of teaching law as a science and a practical skill, implementing elements such as clinical training, which has become an essential part of legal education in the U. S. and in the J. D.

Therefore, 24-gun salutes were fired from military posts and ships, each shot representing a U. S. state.

Therefore, the resulting 5 ' → 3 ' RNA strand is identical to the coding DNA strand with the exception that thymines ( T ) are replaced with uracils ( U ) in the RNA.

Therefore, Hammer was first invited to perform the song " U Can't Touch This ", prior to its release, on The Arsenio Hall Show in 1989.

Therefore, in 1971 MHI sold U. S. automotive giant Chrysler a 15 percent share in the new company.

Therefore, travelers to and from the continental United States and Puerto Rico must clear U. S. customs but do not need to present a passport, and only need proof of U. S. citizenship or nationality.

Therefore about 75 % of the U. S. Divisions were still equipped with the Chauchat-in its original French M1915 version in 8 mm Lebel-at the time of the Armistice of November 11, 1918.

Therefore the price of L must be the same as the price of U minus the money borrowed B, which is the value of L's debt.

* Israeli Settlements: Legitimate, Democratically Mandated, Vital to Israel's Security and, Therefore, in U. S. Interest, The Center for Security Policy, Transition Brief No. 96 ‐ T 130, December 17, 1996

Therefore, the U. S. sent Task Force 67 ( TF 67 )— a large reinforcement and re-supply convoy, split into two groups and commanded by Rear Admiral Richmond K. Turner — to Guadalcanal on 11 November.

Therefore, in 2004, he did not stand for re-election and was instead briefly a candidate in the Republican primary for the U. S. Senate.

:: Therefore U

Therefore during 1847 United States troops invaded central Mexico and occupied the Mexican capital of Mexico City, but still no Mexican government was willing to ratify transfer of the northern territories to the U. S. It was uncertain whether any treaty could be reached.

Therefore, if u and v are non-zero elements of U, there is an element of R that induces an endomorphism of U transforming u to v. The natural question now is whether this can be generalized to arbitrary ( finite ) tuples of elements.

Therefore, even if Iran becomes the most peaceful, secular and progressive, yet still independent state on the planet, the U. S. would be unable to tolerate it.

Therefore, the circle group is canonically isomorphic to U ( 1 ), the first unitary group.

Therefore, in one way Kemble and Lappenberg have been vindicated.

Therefore, it is plain that the clear distinctions of the nineteenth century are no longer with us.

Therefore, what we must prove or disprove is that there were Saxons, in the broad sense in which we must construe the word, in the area of the Saxon Shore at the time it was called the Saxon Shore.

Therefore the government wanted no part of him.

Therefore, he decided he was unfair to the young man and should make an effort to understand and sympathize with his point of view.

Therefore, give Him your affection and store up His love for you.

Therefore, sharp turns in a shelter entrance will reduce radiation intensity inside the shelter.

Therefore, civil defense instructions received over CONELRAD or by other means should be followed.

Therefore, under our longstanding allocation rules, on some of these channels no station other than the dominant ( class 1 ) -- A ) station is permitted to operate at night, so that the 1, -- A station can render service, interference free, wherever it can be received.

Therefore, if the target can significantly change its location in something less than 30 minutes, the probability of having destroyed it is drastically lowered.

Therefore, the lumber is bought in planks and ripped to size for battens, etc., on a table saw.

Therefore, neglecting the extreme outbursts, reflected solar radiation is not expected to cause sizable errors in the measurements of planetary radiation in the centimeter- and decimeter-wave-length range.

Therefore, the only unknown structural feature would appear to be whether the hydrogen atoms are located symmetrically ( 1 ) or asymmetrically ( 3 ).

Therefore, detergents are used.

Therefore, N is inversely proportional to the radius cubed and in fair agreement with the inverse 7/2 power derived from 1958 Alpha and 1959 Eta data.

Therefore, an explanation of this alveolar bronchial artery supply might be the nutritive requirement of an increased amount of supportive tissue, not primarily diffusing in nature, in the region of the alveolus.

Therefore, under independent voting, Af or 0.36 of the couples would cast two votes for picture A, and Af or 0.16 would cast two votes for picture B.

Therefore each binomial trial can be thought of as producing a value of a random variable associated with that trial and taking the values 0 and 1, with probabilities Q and P respectively.

Therefore, Af is single-valued near Q.

Therefore, for any value of T the number of values of f{t} is equal to the ( finite ) number of tangent points corresponding to the argument T plus an odd number.

Therefore, the congruence of its secants, that is the image of a general plane field of lines, is of order Af and class Af.

Therefore, third-grade children were chosen as subjects for this study.

Therefore, it is not only a question of honor but of life and death for the Soviet state ''.

Therefore, if the sense of touch is functioning normally and there is a complete absence of spatial awareness in a psychically-blind person when the eyes are closed and an object is handled, the conclusion seems unavoidable that touch by itself cannot focus and take possession of the third-dimensionality of things and that actual sight or visual representations are necessary.

Therefore, a broad concept of over-all submarine defense is needed for co-ordination of the Navy's efforts, for a logical presentation to the public, for industry's guidance, and as a basis for a program to the Congress.