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 a third style, the " curved lip " style was produced, and all official and third-party cartridges during the console's lifespan were released ( or re-released ) using this style.

Thus, the Bayesian statistician needs either to use informed priors ( using relevant expertise or previous data ) or to choose among the competing methods for constructing " objective " priors.

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.

Thus, what started as an effort to translate between languages evolved into an entire discipline devoted to understanding how to represent and process natural languages using computers.

Thus dates can be sorted using simple string comparison algorithms, and indeed by any left to right collation.

Thus the analysis using Newton's laws of motion can proceed as if the reference frame was inertial, provided the fictitious force terms are included in the sum of external forces.

Thus, using Euler's theorem we can say that the solution must be of the form:

Thus most database systems nowadays are software systems running on general-purpose hardware, using general-purpose computer data storage.

Thus, instead of using rules they no longer remember, as knowledge engineers suppose, the expert is forced to remember rules they no longer use.

Thus one must be careful with the notation when using these functions, because various reputable references and software packages use different conventions in the definitions of the elliptic functions.

In a digital implementation, the number of computations performed per sample is proportional to N. Thus the mathematical problem is to obtain the best approximation ( in some sense ) to the desired response using a smaller N, as we shall now illustrate.

Thus, the third phase of the war ( roughly August 1920 – July 1921 ) involved the IRA taking on a greatly expanded British force, moving away from attacking well defended barracks and instead using ambush tactics.

Thus, many typical household applications already in existence like word processing and email were designed specifically to avoid using floating point operations.

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, the effect of using this procedure is to make activity equal to the numerical value of concentration.

Thus studies of different populations using the same contraceptive will yield different values for the index.

Thus, a list of possible rational roots of the equation can be derived using the formula.

Thus, the so-called blub paradox ( after a hypothetical programming language of average complexity called ' Blub ') says that anyone preferentially using some particular programming language will ' know ' that it is more powerful than some, but not that it is less powerful than others.

Thus using as defined above a Scheme implementation would rewrite "" as "", which reduces implementation's task to that of coding procedure instantiations.

Thus far, most DNA sequencing has been performed using the chain termination method developed by Frederick Sanger.

Expected to make use of devices with which listeners could press a button to indicate whether they liked or disliked a particular piece of music, Adorno bristled with distaste and astonishment: “ I reflected that culture was simply the condition that precluded a mentality that tried to measure it .” Thus Adorno suggested using individual interviews to determine listener reactions and, only three months after meeting Lasarzfeld, completed a 160-page memorandum on the Project ’ s topic, “ Music in Radio .” Adorno was primarily interested in how the musical material was affected by its distribution through the medium of radio and thought it imperative to understand how music was affected by its becoming part of daily life.

Thus there is no simple way to find an equivalent in the proleptic Julian calendar of a date quoted using the Roman pre-Julian calendar ( AUC or by reference to consuls ).

Thus, wavelength ratios observed for different ionic species in the absorption spectra of quasi stellar objects ( QSO or quasars ) place a limit on any variation in the fine-structure constant to less than 1 part in 1 million out to a distance in space ( and time ) of z = 3 ( about 6500 megaparsecs or 11. 5 billion light years ); as the fine-structure constant is determined by the relation between the speed of light ( c ), Planck's constant ( h ) and the electron charge ( e ), these physical constants are constrained as well.

Thus the representation of the center of the Heisenberg group is determined by a scale value, called the quantization value ( in physics terms, Planck's constant ), and if this goes to zero, one gets a representation of the abelian group ( in physics terms, this is the classical limit ).

Thus, all the antiderivatives of x < sup > 2 </ sup > can be obtained by changing the value of C in F ( x ) = ( x < sup > 3 </ sup >/ 3 ) + C ; where C is an arbitrary constant known as the constant of integration.

Thus, if ( M, d ) and ( N, d ) are two metric spaces, and, then there is a constant k such that

Thus cannot be too little, less than some constant.

Thus in the system of units in which the fine structure constant is fixed, the observational claim is that the speed of light is time-dependent.

Thus, because of the O ( n log n ) upper bound on heapsort's running time and constant upper bound on its auxiliary storage, embedded systems with real-time constraints or systems concerned with security often use heapsort.

Thus the constant has dimension density < sup >− 1 </ sup > time < sup >− 2 </ sup >.

Thus, positive displacement pumps are " constant flow machines ".

Thus, it follows that all power laws with a particular scaling exponent are equivalent up to constant factors, since each is simply a scaled version of the others.

Thus a is considered to be a parameter: it is less variable than the variable x or y, but it is not an explicit constant like the exponent 2.

Thus, the current standard model of cosmology, the Lambda-CDM model, includes the cosmological constant, which is measured to be on the order of 10 < sup >− 52 </ sup > m < sup >− 2 </ sup >, in metric units.

Its change is equal to the amount of reversible work done on, or obtainable from, a system at constant T. Thus its appellation " work content ", and the designation A from Arbeit, the German word for work.

Thus, in traditional use, the term “ free ” was attached to Gibbs free energy, i. e., for systems at constant pressure and temperature, or to Helmholtz free energy, i. e., for systems at constant volume and temperature, to mean ‘ available in the form of useful work .’ With reference to the Gibbs free energy, we add the qualification that it is the energy free for non-volume work.

Thus, Avogadro's number is a dimensionless quantity and has the numerical value of the Avogadro constant given in base units.

Thus for n cascaded sections all having matching impedances facing each other, the overall propagation constant is given by,

) Thus instrumentation had to be developed to maintain such constant altitudes, such as pressure sensors controlling the release of ballast.

Thus, a 0-ary operation ( or nullary operation ) can be represented simply as an element of A, or a constant, often denoted by a letter like a.

Thus the money supply function is represented as a vertical line-money supply is a constant, independent of the interest rate, GDP, and other factors.

Thus the thermal conductivity of nonmetals is approximately constant at not too low temperatures.

Thus, it states that the product of pressure and volume is a constant for a given mass of confined gas as long as the temperature is constant.

Thus George, tree, tall and blue are examples of well formed constant symbols.