Thus the cocktail party would appear to be the ideal system, but there is one weakness.

Thus, Margenau remarks: `` A large number of unrelated epicycles was needed to explain the observations, but otherwise the ( Ptolemaic ) system served well and with quantitative precision.

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

Thus the Congress marks a formal recognition of the political system that was central to world politics for a century.

Thus if the gyro and platform-controller combination maintains the platform with zero angular deviation about the **yf axis, the system can be rotated with an angular velocity Af if a torque is supplied to the gyro output axis Aj.

Thus, an algorithm can be considered to be any sequence of operations that can be simulated by a Turing-complete system.

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

Thus flight test program was set to integrate the AARGM onto Tornado ECR's weapon system.

Thus, Walsh modified the vertical passing scheme he had learned during his time with the Raiders, designing a horizontal passing system that relied on quick, short throws-often spreading the ball across the entire width of the field.

Thus, a robust surveillance system involving human clinicians and veterinarians may identify a bioweapons attack early in the course of an epidemic, permitting the prophylaxis of disease in the vast majority of people ( and / or animals ) exposed but not yet ill.

Thus natural languages are mainly oral, while Blissymbols is just a writing system dealing with semantics, not phonetics.

Thus the week cycle is by itself not a full calendar system ; neither is a system to name the days within a year without a system for identifying the years.

Thus, the sum of all applied forces and torques ( with respect to the origin of the coordinate system ) in the body can be given by

Thus, though often de facto the case, Conservative Judaism's halakhic system does not inherently see Orthodox halakhic practice as acceptable and legitimate halakhic practice for a Conservative Jew.

Thus the Sidewinder team replaced a potentially complex control system with a simple mechanical solution.

Thus the CGS system never gained wide general use outside the field of science.

Thus, u < sub > ρ </ sub > and u < sub > θ </ sub > form a local Cartesian coordinate system attached to the particle, and tied to the path traveled by the particle.

Thus, instead of streamlining the system, Gorbachev's decentralization caused new production bottlenecks.

Thus, the larger the aperture of the lens, and the smaller the wavelength, the finer the resolution of an imaging system.

Thus, the only logical possibilities are to accept non-Euclidean geometry as physically real, or to reject the entire notion of physical tests of the axioms of geometry, which can then be imagined as a formal system without any intrinsic real-world meaning.

Thus, it has been argued that a voucher system would lead students who do not belong to a preferred religious or ethnic group, or those with disabilities, to become concentrated within the public school system.

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, 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.