Thus this class of molecules belong to the D < sub > 2d </ sub > point group.

Thus C ' Mell (" The Ballad of Lost C ' Mell ") is cat-derived ; and D ' Joan (" The Dead Lady of Clown Town "), a Joan of Arc figure, is descended from dogs.

Hence, those with less pigmented skin survived and had children at higher rates because their skin allowed more UV light for the production of vitamin D. Thus, the skin of those in the group that left the African continent and went far north gradually developed adaptations for relatively greater translucence compared to equatorial hues.

Thus intuitionists absolutely disallow the blanket assertion: " For all propositions P concerning infinite sets D: P or ~ P " ( Kleene 1952: 48 ).

Thus there will be a way in which the electron travels to C, emits a photon there and then absorbs it again at D before moving on to B.

Thus the area of S < sub > D </ sub > is obtained by integrating the length of the normal vector to the surface over the appropriate region D in the parametric uv plane.

Thus single decade scales C and D range from 1 to 10 across the entire width of the slide rule while double decade scales A and B range from 1 to 100 over the width of the slide rule.

where D denotes the continuum derivative operator, mapping f to its derivative f. The expansion is valid when both sides act on analytic functions, for sufficiently small h. Thus, T < sub > h </ sub >= e < sup > D </ sup >, and formally inverting the exponential yields

Thus a D whistle is fairly apt for playing both G and A, and a C instrument can be used fairly easily for F and G.

Thus, moving from A to D enables you to make one person better off without making anyone else worse off ( Pareto improvement ).

This question has two fundamental physical units: time t and length, and three dimensional variables: distance D, time taken T, and velocity V. Thus there is 3 − 2 = 1 dimensionless quantity.

Thus, imposition of tariffs reduce the quantity of imports from SD to S * D *.

Thus, if the user is initially at a distance D from the target, the remaining distance after the first submovement is rD, and the remaining distance after the nth submovement is r < sup > n </ sup > D.

By using analytic continuation to eliminate removable singularities, meromorphic functions can be added, subtracted, multiplied, and the quotient can be formed unless on a connected component of D. Thus, if D is connected, the meromorphic functions form a field, in fact a field extension of the complex numbers.

Thus D is isomorphic to the quotient group F / N.

Thus the lands that make up the current province came under occupation of these, up to the barbarian invasions of the early V century A. D.

" Thus, Washington D. C .- area's three airports all have radically different codes: IAD for Washington-Dulles ( formerly DIA ), DCA for Reagan National ( District of Columbia Airport ), and BWI for Baltimore ( Baltimore-Washington International ).

Thus, C & S has less of a modern literary influence than D & D which was influenced by Tolkien but also by other authors such as Jack Vance, Fritz Leiber, L. Sprague de Camp and Michael Moorcock.

Thus, the matrix D = ( d < sub > i, j </ sub >) with

Thus, works by Balzac, Flaubert, James Joyce, and D. H. Lawrence were banned based on isolated passages and the effect they might have on children.

Thus, the initial step corresponds to k =

Thus Euclidean geometry corresponds to the choice of the group E ( 3 ) of distance-preserving transformations of the Euclidean space R < sup > 3 </ sup >, conformal geometry corresponds to enlarging the group to the conformal group, whereas in projective geometry one is interested in the properties invariant under the projective group.

Thus, one would expect to find a factor that roughly corresponds to " left " and " right ", as this is the dominant framing for politics in our society, but the basis of Eysenck's " tough / tender-minded " thesis ( the second, " T "- factor ) may well represent nothing beyond an abstract mathematical construct.

Thus every analytic function corresponds to a steady incompressible, irrotational fluid flow in the plane.

Thus, once we settle on any unitary representation of the gammas, it is final provided we transform the spinor according the unitary transformation that corresponds to the given Lorentz transformation.

Thus, sensitive detection of specific optical frequencies necessitates optical heterodyne detection, in which two different ( close-by ) wavelengths of light illuminate the detector so that the oscillating electrical output corresponds to the difference between their frequencies.

Thus, a primary decomposition of ( n ) corresponds to representing ( n ) as the intersection of finitely many primary ideals.

Thus, the DCT-I corresponds to the boundary conditions: x < sub > n </ sub > is even around n = 0 and even around n = N-1 ; similarly for X < sub > k </ sub >.

Thus, the bow room corresponds exactly to the saloon in terms of its importance to the two smaller suites.

Thus, the DST-I corresponds to the boundary conditions: x < sub > n </ sub > is odd around n =- 1 and odd around n = N ; similarly for X < sub > k </ sub >.

Thus 1989 corresponds to Shōwa 64 up to the seventh day of the first month ( 7 January ) and to since the eighth day of the first month ( 8 January ).

Thus, swapping left for right in a sequent corresponds to negating all of the constituent formulae.

Thus " kva ", corresponds to " 10 21 0 ".

Thus, the year 2000 CE corresponds to the year 1922 of the Salivahana Era.

Thus, Mandarin qì ( 氣, ' breath, air, spirit ') corresponds to Japanese ki.

Thus, the Mandarin reading of " Tokyo " ( 東京 ; Eastern ( 東 ) Capital ( 京 )) is Dōngjīng ; this corresponds to Japanese Tōkyō, with sound history for 京 being supposed approximately * kiæŋ -> kyau -> kyō ( for comparison: Southern Min 京 ( colloquial ) is kiaⁿ with a nasal diphthong ).

) Thus Mandarin Rìběn ( 日本, Japan ) corresponds to Japanese Nippon.

Thus, Mandarin Huángbò ( 黄檗 ) corresponds to Japanese Ōbaku, and Rúlái ( 如来 ) to Nyorai.

Thus, Mandarin hànzì ( 漢字 ) corresponds to Japanese kanji, hànwén ( 漢文, Chinese written language ) to kanbun, and zuìhòu ( 最後, last ) to saigo.

Thus J corresponds to multiplication by i on the ( 1, 0 )- vector fields of the complexified tangent bundle, and multiplication by − i on the ( 0, 1 )- vector fields.

Thus, each cell of the matrix corresponds to the strength of the association between the row item and the column item.

Thus at each step one can either go down ( append a (, 1 ) to the end ) or go right ( add 1 to the last number ) ( except the root, which is extra and can only go down ), which shows the correspondence between the infinite binary tree and the above numbering ; the sum of the entries ( minus 1 ) corresponds to the distance from the root, which agrees with the 2 < sup > n − 1 </ sup > nodes at depth n − 1 in the infinite binary tree ( 2 corresponds to binary ).