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, Electronic Support provides a source of information required for decisions involving Electronic Protection ( EP ), Electronic Attack ( EA ), avoidance, targeting, and other tactical employment of forces.

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, 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, an axiom is an elementary basis for a formal logic system that together with the rules of inference define a deductive system.

Thus, they are the basis of many software vulnerabilities and can be maliciously exploited.

Thus, for example, on the basis of superficial similarities one might suppose that the Latin verb habere and German haben, both meaning ' to have ', were cognates.

Thus, there is a good basis for affirming the straightforward and traditional claim that the Epistle to Titus was authentically written by Paul.

Thus a conventionally corrected form of Newcomb's formula, to incorporate the corrections on the basis of mean solar time, would be the sum of the two preceding expressions:

Thus, freethinkers strive to build their opinions on the basis of facts, scientific inquiry, and logical principles, independent of any logical fallacies or intellectually limiting effects of authority, confirmation bias, cognitive bias, conventional wisdom, popular culture, prejudice, sectarianism, tradition, urban legend, and all other dogmas.

Thus, a simple way to change gauge is to use different needles, which is the basis of uneven knitting.

Thus far, no system design has been shown to meet this requirement fully on a technical basis alone.

Thus, solid-state physics forms the theoretical basis of materials science.

Thus, on the basis of remarks made by President Kim Il Sung in 1977 concerning school attendance, the population that year was calculated at 17. 2 million persons.

Thus, on the basis of the budget of 1861, tax collection continued for four years.

Thus, while the outcome of any particular hand significantly involves chance, the long-run expectations of the players are determined by their actions chosen on the basis of probability, psychology and game theory.

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, in the predominantly agrarian Qing Dynasty, the " household " was the basis of imperial finance.

Thus, on a weight-for-weight basis they are significantly more energetic than normal condensed explosives.

Jeff Snyder is a spokesman for the view that gun possession is a civil right, and that therefore arguments about whether gun restrictions reduce or increase violent crime are beside the point: " I am not here engaged in ... recommending ... policy prescriptions on the basis of the promised or probable results crime ... Thus these essays are not fundamentally about guns at all.

Thus, many believed that tribes organize links between families ( including clans and lineages ), and provide them with a social and ideological basis for solidarity that is in some way more limited than that of an " ethnic group " or of a " nation ".

Thus, knowledge of paleoecology, palaeogeography, glacial geology and paleoclimatology is important for the recognition and understanding of soil genesis and constitute a basis for predicting the future soil changes.

Thus, the basis of morality is strong moral character, which requires self-reliance and self-discipline.

Thus Tychonoff's theorem joins several other basic theorems ( e. g. that every nonzero vector space has a basis ) in being equivalent to AC.

: Thus, in Bergsland & Vogt ( 1962 ), the authors make an impressive demonstration, on the basis of actual language data verifiable by extra-linguistic sources, that the " rate of change " for Icelandic constituted around 4 % per millennium, whereas for closely connected Riksmal ( Literary Norwegian ) it would amount to as much as 20 %.

Thus in a short time Charles's own cabinet, the Cabal Ministry, went over to the " Dutch " peace party ; Lord Shaftesbury, much shocked by the revelation, even beginning to consider driving out the troublesome House of Stuart entirely and inducing his secretary, John Locke, to further develop the legal concepts which would later be the basis of the Two Treatises of Government, which justified the Glorious Revolution of 1688.

Thus Grosseteste concluded, following very much in what Boethius had argued, that mathematics was the highest of all sciences, and the basis for all others, since every natural science ultimately depended on mathematics.

Thus, solid-state physics forms the theoretical basis of materials science.

Thus, it remains doubtful whether there is any historical basis for the famous ride.