Thus, the avant-garde choreographers have extended the scope of materials available for dance composition.

Thus, many a creativity-oriented aspirant for a career in architecture, drama, or journalism, resigns himself to a real estate business ; ;

Thus a new pattern of days began to develop, for Granny Albright did not die.

Thus, the need for the B-70 as a strategic weapon system is doubtful.

Thus, you avoid headaches when an employee wants off for his fourth cousin's funeral.

Thus it was that Barco, apprehended for mere larceny, now began to suspect that one or another of his murders had been uncovered.

Thus, the dotted line shown in figure 4 was taken as typical for the temperature distribution for all blowing rates.

Thus, for aqueous media, we can think of the idealized organic active as an oleophilic or hydrophobic surface-active agent, and of an idealized builder as a oleophobic or hydrophilic surface-active agent.

Thus, an enemy would probably use this weapon for attack on static population centers such as large cities.

Thus, the alignment of the `` dots '' and `` tips '', respectively, indicate individual variability of the 21 growth centers of each child with respect to the mean values for these boys and girls.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus the multiplicity of Af for a given T must be an even number.

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 the lack of effective recognition of the responsibilities involved in caring for two babies showed signs of becoming a disabling problem.

Thus, the writer decided to hold one experimental section of the functional preparation for marriage course in the spring semester of 1960 exclusively for persons already married -- that is, prerequisite: `` marriage ''.

Thus the films seen as they came in ( coordinated for the regular sections ), were often out of context.

Thus, when more than one distinct form leads to a particular cell in the X-region, a chain of information cells must be created to accommodate the forms, one cell in the chain for each form.

Thus in his friends are stranger than his sisters' strong stresses are normal for his and sisters', but in his friends are stranger than his sisters strong stresses are normal for friends and sisters.

Thus in Mary wrote an account of the trip first strong stress on Mary marks Mary as the first in a series of people who wrote accounts of the trip, strong stress on wrote marks the writing as the first of a series of actions of Mary's concerned with an account of her trip ( about which she may later have made speeches, for example ), and strong stress on trip makes the trip the first of a series of subjects about which Mary wrote accounts.

Thus his persistence values for some stem frequencies per meaning are: stem identical in 8 languages, 100% ; ;

Thus while his theory or technique may not be oversubscribed, it is commonplace for bullish and bearish positions to become temporarily over-subscribed.

Thus, liquid crystal sheets are often used in industry to look for hot spots, map heat flow, measure stress distribution patterns, and so on.

Thus it made sense to not map the memory between programs for IPC, but instead migrate the program code being used into the local space of the program.

Thus the set of all polynomials with coefficients in the ring R forms itself a ring, the ring of polynomials over R, which is denoted by R. The map from R to R sending r to rX < sup > 0 </ sup > is an injective homomorphism of rings, by which R is viewed as a subring of R. If R is commutative, then R is an algebra over R.

Thus the polarization direction can be used to map out the galactic magnetic field.

Thus, a random function can be considered to map each input independently at random to any one of the possible outputs.

Thus, Pondicherry district is made of 12 pockets, some of which are very small ( see map ) and entirely surrounded by the territory of Tamil Nadu.

Thus, G < sub > t </ sub >( V ) = exp ( tV ) is the exponential map of the vector tV.

Thus each orthogonal group falls into two pieces ; and because the projection map splits, O ( n ) is a semidirect product of SO ( n ) by O ( 1 ).

Thus the only two field automorphisms of that leave the real numbers fixed are the identity map and complex conjugation.

Thus, by expressing quantum mechanics in phase space ( the same ambit as for classical mechanics ), the Weyl map facilitates recognition of quantum mechanics as a deformation ( generalization ) of classical mechanics, with deformation parameter ħ / S, where S is the action of the relevant process.

for any vectors v, w and any real number c. This linear map from R < sup > n </ sup > to R is denoted df < sub > p </ sub > and called the derivative of f at p. Thus df < sub > p </ sub >( v ) = ∂< sub > v </ sub > f ( p ).

Thus the requirements of Phase I of the road map were not fulfilled, and the road map has not continued further.

Thus, an important decision in the game is whether to buy a variety of railroads in order to gain access to all areas of the map for oneself, or to buy railroads in a given area in order to monopolize it and collect the valuable use fees from opponents.

Thus we obtain the global reciprocity map from the idele class group to the abelian part of the absolute Galois group of the field.

Thus a covering map p: C → X defines a conjugacy class of subgroups of π < sub > 1 </ sub >( X, x ) and one can show that equivalent covers of X define the same conjugacy class of subgroups of π < sub > 1 </ sub >( X, x ).

Thus a particular kind of map of spaces is well modelled by a particular kind of morphism of groupoids.

Given two tensor bundles E → M and F → M, a map A: Γ ( E ) → Γ ( F ) from the space of sections of E to sections of F can be considered itself as a tensor section of if and only if it satisfies A ( fs ,...) = fA ( s ,...) in each argument, where f is a smooth function on M. Thus a tensor is not only a linear map on the vector space of sections, but a C < sup >∞</ sup >( M )- linear map on the module of sections.

Thus P is a smooth manifold with a smooth map π: P → M which looks locally like the trivial bundle M × H → M. The frame bundle of M is a principal GL ( n )- bundle, while if M is a Riemannian manifold, then the orthonormal frame bundle is a principal O ( n )- bundle.

Specifically, if X and Y are the representation spaces of two linear representations of G then a linear map f: X → Y is called an intertwiner of the representations if it commutes with the action of G. Thus an intertwiner is an equivariant map in the special case of two linear representations / actions.

Thus he drew his famous diagram, looking more like an electrical schematic than a true map, on which all the stations were more or less equally spaced.