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Thus a particular coordinate system ( equinox and equator / ecliptic of a particular date, such as J2000. 0 ) could be used forever, but a set of osculating elements for a particular epoch may only be ( approximately ) valid for a rather limited time, because osculating elements such as those exampled above do not show the effect of future perturbations which will change the values of the elements.
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Thus and particular
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, a Rabbi, a Catholic priest, and an agnostic might agree that, in this particular case, the best approach is to withhold extraordinary medical care, while disagreeing on the reasons that support their individual positions.
" Thus Ambrose refused to be drawn into a false conflict over which particular local church had the " right " liturgical form where there was no substantial problem.
Thus, if people are accustomed to using a particular machine name to access a particular service, their access will break when the service is moved to a different machine.
Thus, anthroposophy considers there to be a being who unifies all religions, and who is not represented by any particular religious faith.
Thus, it determines substancehood empirically by the togetherness of properties rather than by a bare particular or by any other non-empirical underlying strata.
Thus, the license depends on how a particular application that uses Berkeley DB is distributed to the public.
Thus, computing includes designing and building hardware and software systems for a wide range of purposes ; processing, structuring, and managing various kinds of information ; doing scientific studies using computers ; making computer systems behave intelligently ; creating and using communications and entertainment media ; finding and gathering information relevant to any particular purpose, and so on.
In particular, one should think of the condition number as being ( very roughly ) the rate at which the solution, x, will change with respect to a change in b. Thus, if the condition number is large, even a small error in b may cause a large error in x.
Thus a field is a particular type of skew field, and not all skew fields are fields.
Thus if we reason from the statement " Pegasus flies " to the statement " Pegasus exists ", we are not asserting that Pegasus is made up of atoms, but rather that Pegasus exists in a particular worldview, the worldview of classical myth.
Thus, a field due to any particular particle or time-varying electric or magnetic field contributes to the fields present in the same space due to other causes.
Thus, entropy is also a measure of the tendency of a process, such as a chemical reaction, to be entropically favored, or to proceed in a particular direction.
Thus a statement of the form is said to be true, under a particular interpretation, if there is some object in the domain of discourse of that interpretation that satisfies the predicate that the interpretation uses to assign meaning to the symbol Phil.
Thus,,, etc .</ ref > which are particular cases of Diophantine equations.
Thus, Annie's strong drive to take revenge on women scholars in general and on Miss de Vine in particular is perfectly comprehensible, and in fact does not in itself prove her to be mentally deranged.
Thus a resin can be tailored to a particular toxic group.
Thus, the frequency of the vibrations can be associated with a particular bond type.
Thus many equipment manufacturers add on their own particular requirements or tighten the tolerance on a general specification to meet their particular needs ( or doing a different set of tests or using different / own testbed engine ).
Thus, SGML is properly a meta-language, and many particular markup languages are derived from it.
Thus materialism has no definite content independent of the particular theory of matter on which it is based.
Thus, while the probability might be extremely small that any particular universe would have the requisite conditions for life ( as we understand life ) to emerge and evolve, this does not require intelligent design per the teleological argument as the only explanation for the conditions in the Universe that promote our existence in it.
Thus, Wicca in particular is sometimes referred to by its proponents as " The Old Religion ", a term popularised by Margaret Murray in the 1920s, while Germanic neopaganism is referred to in some of its varieties as Forn Sed (" Old Custom ").
Thus and coordinate
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, 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 a line has a dimension of one because only one coordinate is needed to specify a point on it ( for example, the point at 5 on a number line ).
Thus at any point there should be one special coordinate system, " at rest relative to the aether ".
Thus a conservative classification of Sino-Tibetan / Tibeto-Burman would posit several dozen small coordinate families and isolates ; attempts at subgrouping are either geographic conveniences or hypotheses for further research.
Thus, the need to use stars close to the ecliptic (± 9º of latitude ) as a set of observational reference points to help positioning a planet within this ecliptic coordinate system.
Thus, the absence of the ignorable coordinate q < sub > k </ sub > from the Lagrangian implies that the Lagrangian is unaffected by changes or transformations of q < sub > k </ sub >; the Lagrangian is invariant, and is said to exhibit a symmetry under such transformations.
Thus the coordinate systems most used in astronomy need their own date-reference because the coordinate systems of that type are themselves in motion, e. g. by the precession of the equinoxes, nowadays often resolved into precessional components, separate precessions of the equator and of the ecliptic.
Thus that coordinate system can still be used today, even though most comet predictions made originally for 1875 ( epoch
" Thus O ' Rahilly, Sir Roger Casement and Bulmer Hobson worked together to coordinate a daylight gun-running expedition to Howth, just north of Dublin.
Since a given vector v is a finite linear combination of basis elements, the only nonzero entries of the coordinate vector for v will be the nonzero coefficients of the linear combination representing v. Thus the coordinate vector for v is zero except in finitely many entries.
Thus, the tangent half-angle formulae give conversions between the stereographic coordinate t on the unit circle and the standard angular coordinate φ.
Thus, at the level of the final common path, eye movements are encoded in essentially a Cartesian coordinate system.
Thus, each brain structure can be easily assigned a range of three coordinate numbers, which will be used for positioning the stereotactic device.
Thus the name coordinate space because a sequence in an FK-space converges if and only if it converges for each coordinate.
Thus, Alberta's District Nursing Service, created in 1919 to coordinate the province's women's health resources, resulted chiefly from the organized, persistent political activism of UFWA members and only minimally from the actions of professional nursing groups clearly uninterested in rural Canadians ' medical needs.
Thus, intracellular signals must coordinate the synthesis of rRNA with that of other components of protein translation.
Thus, in either coordinate system, the volume element takes the same expression: the expression of the volume element is invariant under a change of coordinates.
Thus, just like vector fields and other geometric quantities, frame fields can be represented in various coordinate charts.
Thus one complex coordinate describes the identification and the other two describe a point in R < sup > 4 </ sup >.
1.041 seconds.