In the field of high-energy particle physics, the fundamental velocity unit is the speed of light c. Thus, dividing energy in eV by the speed of light in vacuum, one can describe the momentum of an electron in units of eV / c.

Thus one has the fundamental groupoid instead of the fundamental group, and this construction is functorial.

Thus, the distinction between micro-and macroevolution is not a fundamental onethe only difference between them is of time and scale.

Thus, theoretical physicists tend to regard these dimensionless quantities as fundamental physical constants.

Thus, one had a theory which combined gravity, quantization and even the electromagnetic interaction, promising ingredients of a fundamental physical theory.

Thus, the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.

Thus, the fundamental frequency of most speech falls below the bottom of the " voice frequency " band as defined above.

This question has two fundamental physical units: time t and length, and three dimensional variables: distance D, time taken T, and velocity V. Thus there is 3 − 2 = 1 dimensionless quantity.

There are 3 fundamental physical units in this equation: time t, mass m, and length l, and 4 dimensional variables, T, M, L, and g. Thus we need only 4 − 3 = 1 dimensionless parameter, denoted π, and the model can be re-expressed as

Thus, by the principal axis theorem, the second fundamental form is

Thus the second fundamental form encodes both the intrinsic and extrinsic curvatures.

Thus the act of measurement induces a fundamental irreversible change on the density matrix ; this is analogous to the " collapse " of the state vector, or wavefunction collapse.

Thus, similar to the definition of other fundamental quantities ( like time and mass ), space is defined via measurement.

Thus, the right to property is no longer a fundamental right, though it is still a constitutional right.

Thus, plural marriage is viewed as an essential and fundamental part of the religion.

Thus, we can interpret Boltzmann's constant as being simply the expression ( in terms of more standard physical units ) of the abstract logarithmic unit that is needed to convert the dimensionless pure-number quantity ln W ( which uses an arbitrary choice of base, namely e ) to the more fundamental pure logarithmic quantity Log ( W ), which implies no particular choice of base, and thus no particular choice of physical unit for measuring entropy.

Thus, in Descartes work, we can see some of the fundamental assumptions of modern cosmology in evidence-the project of examing the historical construction of the universe through a set of quantitative laws describing interactions which would allow the ordered present to be constructed from a chaotic past.

in a ring R. Thus, they can be generated by the standard technique for Pell equations of taking powers of a fundamental solution:

Thus " elementary " refers to " element " ( i. e. state-of-matter ) as well as to something that is fundamental or innate ( physical ).

“ The truth is that there is not enough of the right kind of freedom, the fundamental freedom to choose to be free or not to be free, according to one's preference .... Thus I demand, for each and every member of human society, freedom of association according to inclination and of activity according to aptitude.

Thus the study of the relation between the fundamental groups of X and is not so straightforward.

Thus, these changes conflicted with the Good Neighbor Policy's fundamental principle of non-intervention and resulted in a new wave of American interference into Latin American affairs.

Thus, a legislative measure ( although the role of Parliament is not specified, just that it is not to be dissolved ) which breaches fundamental liberties cannot be appealed against before the Conseil d ' État.

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

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

Thus, in such systems, the Demiurge acts as a solution to the problem of evil.

Thus, a solution requires that no two queens share the same row, column, or diagonal.

Thus, in such systems, the Demiurge acts as a solution to the problem of evil.

Thus, while he recognised the benefits of citrus fruit ( although he weakened the effect by switching to a boiled concentrated or " rob ", the production of which unfortunately destroyed the vitamin C ), he never advocated citrus juice as a single solution.

Thus, Olbers ' paradox can not decide between a finite ( e. g. some variants of the Big Bang model ) and an infinite ( Steady State theory or static universe ) solution.

Thus the solution is 2, not ½ as would be the result of an incorrect analysis.

Thus the interior of the sphere is a lacuna for the solution.

Thus the total pressure above solution of A and B would be

Thus the decision-maker is a satisficer, one seeking a satisfactory solution rather than the optimal one.

Thus he lost two crucial days before finally adopting the solution, however obvious, of his predecessor.

Thus, for a fixed path length, UV / Vis spectroscopy can be used to determine the concentration of the absorber in a solution.

Thus if state vectors, and each solve the linear equation on ψ, then would also be a solution, in which each is a coefficient.

Thus, a salt water solution can be used when a longer period of retention is desired, such as to soften an impaction.

Thus, if the solution is to be said to work, then it is to be said to work solely within the given formal system, and not otherwise.

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, a solution does not generally exist for an arbitrary choice of strain components.

Thus, in this case, the equation bx = a has no solution if a is not equal to 0, and has any x as a solution if a equals 0.

Thus, marketing research may also be described as the systematic and objective identification, collection, analysis, and dissemination of information for the purpose of assisting management in decision making related to the identification and solution of problems and opportunities in marketing.