Thus, knowing the students ' level on a developmental sequence provides information on the kind and level of knowledge they can assimilate, which, in turn, can be used as a frame for organizing the subject matter to be taught at different school grades.

Thus, measurement of the tension in the string identifies the inertial frame: it is the one where the tension in the string provides exactly the centripetal force demanded by the motion as it is observed in that frame, and not a different value.

Thus IPv4 provides an addressing capability of 2 < sup > 32 </ sup > or approximately 4. 3 billion addresses.

Thus Irenaeus provides the earliest witness to the assertion of the four canonical Gospels, possibly in reaction to Marcion's edited version of the Gospel of Luke, which Marcion asserted was the one and only true gospel.

Thus, union density provides a rough picture of union membership only ; it does not account for the circumstance that in some countries, also many persons under education, many unemployed persons, many retired persons and / or many persons who had to leave work due to occupational injuries may also be union members.

Thus, two of the three color channels for each sensor must be interpolated and a so-called N-megapixel camera that produces an N-megapixel image provides only one-third of the information that an image of the same size could get from a scanner.

Thus it provides an upper bound on what can be achieved with rational ( self-interested ) coordination or knowledge of others ' preferences.

Thus a virtual connection, also known as a virtual circuit or byte stream is provided to the end-user by a transport layer protocol, although intermediate network nodes only provides a connectionless network layer service.

Thus STR analysis provides an excellent identification tool.

Thus, opportunity costs are not restricted to monetary or financial costs: the real cost of output forgone, lost time, pleasure or any other benefit that provides utility should also be considered opportunity costs.

Thus fiscal federalism provides the tools for " application of the federal approach to governance which lies in its ability to balance the contrasting forces of centralization and decentralization " ( Sharma, 2005b: 177 ).

) Thus, the group of conformal transformations in spaces of dimension greater than 2 are much more restricted than the planar case, where the Riemann mapping theorem provides a large group of conformal transformations.

Thus they help create a denser dike surface, which in case of storm surges provides less area for the waves to impact.

Thus it provides an intense, detailed exploration of its subject, providing to some degree both the concentrated focus of the short story and the broad scope of the novel.

Thus in most " natural " settings, if a complex number provides a solution to a problem, so does its conjugate, such as is the case for complex solutions of the quadratic formula with real coefficients.

Thus the neutral theory provides a rationale for the molecular clock, although the discovery of a molecular clock predates neutral theory.

Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.

Thus, the trust center maintains both the network key and provides point-to-point security.

Since any vector v is a linear combination ∑ v < sup > j </ sup > e < sub > j </ sub > of its components, df is uniquely determined by df < sub > p </ sub >( e < sub > j </ sub >) for each j and each p ∈ U, which are just the partial derivatives of f on U. Thus df provides a way of encoding the partial derivatives of f. It can be decoded by noticing that the coordinates x < sup > 1 </ sup >, x < sup > 2 </ sup >,... x < sup > n </ sup > are themselves functions on U, and so define differential 1-forms dx < sup > 1 </ sup >, dx < sup > 2 </ sup >, ..., dx < sup > n </ sup >.

Thus, Bluestein's algorithm provides an O ( N log N ) way to compute prime-size DFTs, albeit several times slower than the Cooley – Tukey algorithm for composite sizes.

Thus, a regulation that allows member states to privatise roads would not have direct effect and could not be enforced in the courts, because it provides that states may privatise roads, not must privatise roads.

Thus the connection ∇ defines a way of moving elements of the fibers along a curve, and this provides linear isomorphisms between the fibers at points along the curve:

In such cases, the family relationship between two distant family members A and C can often be demonstrated by finding an additional family member B that shares significant similarity with both A and C. Thus, B provides a connecting link between A and C. Another approach is to examine distant alignments for highly conserved matches.

Thus, the Treaty of Waitangi voided the Declaration for all practical purposes ; the Treaty rather than the Declaration provides the legal foundation of claims for the redress of historical wrongs.

Thus, any transverse velocity of the emitting source plays no part in aberration.

Thus, one can consider data compression as data differencing with empty source data, the compressed file corresponding to a " difference from nothing ".

Thus Sophia ’ s power becomes enclosed within the material forms of humanity, themselves entrapped within the material universe: the goal of Gnostic movements was typically the awakening of this spark, which permitted a return by the subject to the superior, non-material realities which were its primal source.

Thus Engset's equation should be used when the source population is small ( say less than 200 users, extensions or customers ).

Thus in saturation mode, the FET behaves as a constant-current source rather than as a resistor and can be used most effectively as a voltage amplifier.

Thus magnesium powder ( flash powder ) was used as a source of illumination in the early days of photography.

Thus, seawater flow is eastward in the Strait's surface waters, and westward below ; once in the Atlantic, this chemically distinct Mediterranean Intermediate Water can persist thousands of kilometres away from its source.

Thus, oscillations tend to decay with time unless there is some net source of energy into the system.

Thus, they claim, to conceive of a particular apple and its redness is not to conceive of applehood or redness-in-general, so they question the source of the concept.

Thus, more power can be extracted from a water source with high-pressure and low-flow than from a source with low-pressure and high-flow, even when the two flows theoretically contain the same power.

Thus creating value for the firm, as Debt is thought to be a cheaper source of finance.

Thus returning himself to the proper relationship with his creator and source of being.

Thus the Green's function describes the influence at of the data f and g. For the case of the interior of a sphere of radius a, the Green's function may be obtained by means of a reflection ( Sommerfeld, 1949 ): the source point P at distance ρ from the center of the sphere is reflected along its radial line to a point P that is at a distance

Thus the strength of the field is inversely proportional to the square of the distance from the source.

Thus it doesn't make sense to talk about the noise temperature of a capacitor or of a voltage source.

Thus, a large positive return loss indicates the reflected power is small relative to the incident power, which indicates good impedance match from source to load.

Thus the unconscious mind can be seen as the source of dreams and automatic thoughts ( those that appear without any apparent cause ), the repository of forgotten memories ( that may still be accessible to consciousness at some later time ), and the locus of implicit knowledge ( the things that we have learned so well that we do them without thinking ).

Thus, the emf has the same value but opposite sign as the integral of the electric field aligned with an internal path between two terminals A and B of a source of emf in open-circuit condition ( the path is taken from the negative terminal to the positive terminal to yield a positive emf, indicating work done on the electrons moving in the circuit ).

Thus the Shekinah is associated with the transformational spirit of God regarded as the source of prophecy:

Thus, the relative difference in velocity between a source and an observer is what gives rise to the doppler effect.

Thus, owing to an argument between the two in regard to the source or cause of the electricity, Volta built the first battery in order to specifically disprove his associate's theory.

Thus, preserving the telecasts on tape was not seen as a priority by the networks when another source was available – though the sportscasters ' play-by-play comments, as a result, were lost.

Thus, with all Hindus, there is a strong belief in all paths being true religions that lead to one God or source, whatever one chooses to call the ultimate truth.