Then, in the late 1960s and early 1970s, Vera Rubin, a young astronomer at the Department of Terrestrial Magnetism at the Carnegie Institution of Washington, presented findings based on a new sensitive spectrograph that could measure the velocity curve of edge-on spiral galaxies to a greater degree of accuracy than had ever before been achieved.

Then we could have written a formula of degree k which is equivalent to φ, namely.

Then it would be that by recursion ( using the axiom of countable choice ) that a sequence of polynomials could be found so that, letting of minimal degree.

Then you rank your lists according to the degree in which the phenomenon occurs in each one.

Theorem: Let R be a Dedekind domain with fraction field K. Let L be a finite degree field extension of K and denote by S the integral closure of R in L. Then S is itself a Dedekind domain.

Then, following a degree of reconciliation with Charles, Rupert obtained command of the Royalist fleet himself.

Then the mountains that are the natural boundary of the Chao Praya watershed form a divide, which has, to some degree, historically isolated Thailand from other Southeast Asian civilisations.

Then he went to the University of Illinois for his master of arts degree, which he received in 1921 under the guidance of Professor Carl Marvel.

Then in 1799 he earned a degree in Civil and Canonical lawand a litcentiate degree in Law in 1803.

* Let k be the coordinate ring of the variety V. Then the dimension of V is the transcendence degree of the field of fractions of k over k.

Then the practice was to join the teaching profession with a Bachelors degree either in Arts or Sciences and after four years of teaching in a Secondary school teachers get the One year Post-Graduate Diploma in Education.

Then for an equation to have a solution, we must have ( one constraint ), and in that case the solution space is or equivalently stated, ( one degree of freedom ).

Then he moved to the United States, where he received Master's degree in Applied Mathematics at the University of Kansas City ( now known as the University of Missouri-Kansas City ) in 1951 and Ph. D. in Mathematics from Caltech under the supervision of Robert P. Dilworth in 1955.

Then, for some quotient polynomial Q ( x ) and remainder polynomial R ( x ) with degree ( R ) < degree ( D ),

Then, financed by the GI Bill, he attended and graduated from Columbia Business School in 1949 with a degree in economics.

P is a polynomial of degree n − r. Then we have the following:

Then they can weigh the degree of reliability of the result and make their decision.

1 ) Let L be a finite extension of k of degree s. Then ( Spec L ) = Spec ( k ) and

Then he went to the University of Exeter and graduated with a degree in sports science.

Then, he creates " survey codes " for each pair of the rulers, which contain a number which describes degree of the match of each considered property of two rulers.

Then, in 1978, he obtained both an Master of Science in mechanical engineering and the degree of Ocean Engineer from the Massachusetts Institute of Technology.

Then, he received a master's degree in social and political science from Syracuse University in 1999.

Then the same mapping property assures that continuous-time filters that are minimum-phase are converted to discrete-time filters that preserve that property of being minimum-phase.

Then a curve is a continuous mapping, where is a topological space.

Then for all Riemann mapping functions F ( z )

Then a mapping

If E is a Borel subset of R, and 1 < sub > E </ sub > is the indicator function of E, then 1 < sub > E </ sub >( T ) is a self-adjoint projection on H. Then mapping

Then the squeeze mapping with diagonal elements b and a maps this interval to the standard position hyperbolic angle that runs from ( 1, 1 ) to ( bc, ad ).

Then a Toda field theory is the study of a function φ mapping 2 dimensional Minkowski space satisfying the corresponding Euler-Lagrange equations.

Then K ( A ) is a triangulated category ; the distinguished triangles consist of triangles isomorphic to a morphism with its mapping cone ( in the sense of chain complexes ).

Then the mapping cone C < sub > f </ sub > is homeomorphic to two disks joined on their boundary, which is topologically the sphere S < sup > 2 </ sup >.

The index can be easily defined in the setting of complex analysis: Let f ( z ) be a holomorphic mapping on the complex plane, and let z < sub > 0 </ sub > be a fixed point of f. Then the function f ( z ) − z is holomorphic, and has an isolated zero at z < sub > 0 </ sub >.

Then for all the mapping is a bijection with inverse.

Then he would get to his feet, as though rising in honor of his own remarkable powers, and say almost invariably, `` Gentlemen, this is an amazing story!!

Then, Jesus indicated that God's forgiveness is unlimited.

Certainly, the meaning is clearer to one who is not familiar with Biblical teachings, in the New English Bible which reads: `` Then Jesus arrived at Jordan from Galilee, and he came to John to be baptized by him.

Then it added: `` It is not possible to determine how extensive these ill effects will be -- nor how many people will be affected ''.

Then the words fell into a pattern: `` Mollie the Mutton is scratching her nose, Scratching her nose in the rain.

Then he thought of Aaron Blaustein standing in his rich house saying: `` God is tired of taking the blame.

Then it is marked on the inside where it comes in contact with the transom, frames, keelson and all the battens.

Then it is replaced and fastened.

Then the chines are rounded off and the bottom is rough-sanded in preparation.

Then, a group of eggs is deposited in a cavity in the beebread loaf and the egg compartment is closed.

Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.

Then in 2 we show that any line involution with the properties that ( A ) It has no complex of invariant lines, and ( B ) Its singular lines form a complex consisting exclusively of the lines which meet a twisted curve, is necessarily of the type discussed in 1.

Then, too, the utmost clinical flexibility is necessary in judiciously combining carefully timed family-oriented home visits, single and group office interviews, and appropriate telephone follow-up calls, if the worker is to be genuinely accessible and if the predicted unhealthy outcome is to be actually averted in accordance with the principles of preventive intervention.

Then the editorial added prophetically: `` how far they may reach in Asia is yet undetermined, but they fall far short of our dreams of the war conferences ''.

Then she catapults into `` everything and everybody '', putting particular violence on `` everybody '', indicating to the linguist that this is a spot to flag -- that is, it is not congruent to the patient's general style of speech up to this point.

Then comes the time when the last wire is removed and Susie walks out a healthier and more attractive girl than when she first went to the orthodontist.

Then, with the new affluence, there is actually a sallying forth into the wide, wide world beyond the precincts of New York.

Then, if the middle number is activated to its greatest potential in terms of this square, through multiplying it by the highest number, 9 ( which is the square of the base number ), the result is 45 ; ;