Thus, a practical fallout shield is ten halving-thicknesses of packed dirt, reducing gamma rays by approximately 1024 times ( 2 < sup > 10 </ sup >).

Thus, an additional 6 % of the total energy of fission is also released eventually as non-prompt ionizing radiation, and this is about evenly divided between gamma and beta ray energy.

Thus, small < sup > 169 </ sup > Yb samples ( which emit gamma rays ) act like tiny X-ray machines useful for radiography of small objects.

Thus the presence or absence of gamma rays in a borehole is an indication of the amount of shale or clay in the surrounding formation.

Thus, gamma photoelectric effect electron emission may also cause high-speed electrons to be emitted from radioactive atoms without beta decay.

Thus to apply a linear filter, one must first gamma decode the values – and if resampling, one must gamma decode, resample, then gamma encode.

Thus " gamma ut " ( two Gs below middle C ) was the tip of the thumb, A (" A re ") was the inside of the thumb knuckle, B (" B mi ") was the joint at the base of the thumb, C (" C fa ut ") was the joint at the base of the index finger, and so on, spiraling around the hand counterclockwise past middle C (" C sol fa ut ") until the D a ninth above middle C (" D la sol ") ( the middle joint of the middle finger ) and the E above that (" E la ") ( the back of that joint, the only note on the back of the hand ) were reached.

Thus if E is sufficiently small, there can be only one intersection of C and Af near Q, for if there were more than one intersection for every E then the difference between C and Af near Q would not be a monotone function.

Thus, if public pressure sets the effective limit to the price that the industry may charge, this pressure is itself a function of the wage rate.

Thus the negation of the axiom of choice states that there exists a set of nonempty sets which has no choice function.

Thus, the function of antioxidant systems is not to remove oxidants entirely, but instead to keep them at an optimum level.

Thus the Bauhaus style, also known as the International Style, was marked by the absence of ornamentation and by harmony between the function of an object or a building and its design.

Thus the function cannot access memory out-of-bounds.

Thus any non-constant entire function must have a singularity at the complex point at infinity, either a pole for a polynomial or an essential singularity for a transcendental entire function.

Thus, it was not until two centuries had passed that in 1872 Karl Weierstrass presented the first definition of a function with a graph that would today be considered fractal, having the non-intuitive property of being everywhere continuous but nowhere differentiable.

Thus, any periodic summation in the frequency domain can be represented by a Fourier series, whose coefficients are samples of a related continuous time function:

Thus the DTFT of the s sequence is also the Fourier transform of the modulated Dirac comb function .< ref group =" note "> We may also note that:

Thus we have the important result that when a discrete data sequence, s, is proportional to samples of an underlying continuous function, s ( t ), one can deduce something about the continuous Fourier transform, S ( ƒ ).

Thus, we would say that the function is decomposed into functions.

Thus, the hash function only hints at the record's location — it tells where one should start looking for it.

Thus, a function with a codomain is invertible if and only if it is both injective ( one-to-one ) and surjective ( onto ).

Thus, the statement that f is an idempotent unary operation on S is equivalent to the statement that f is an idempotent element with respect to the function composition operation ∘ on functions from S to S.

Thus, they capture the idea of function composition within a set.

Thus, every MUMPS command or function name could be abbreviated from one to three letters in length, e. g. Quit ( exit program ) as Q, $ P

Thus for map projections we must introduce the concept of point scale, which is a function of position, and strive to keep its variation within narrow bounds.

Thus, the logarithm function is an isomorphism from the group of positive real numbers under multiplication to the group of real numbers under addition, represented as a function:

Thus, the neurochemical alterations which induce psychosis in otherwise healthy people are indicative that the root of the symptoms altered thalamocortical and hippocamalcortical transmission, and corresponding layer 5 / thalamus axis function, altering the crucial ordered cortiocortical layer 3 / 1 and 2 / 3 transmission necessary for rational language self-expression.

Thus, modern automatic rifles overlap to an extent in design and function with machine guns.

Thus, if corporations are not to run away with us, they must become quasi-governmental institutions, subject to public control and needs.

Thus, as a development program is being launched, commitments and obligations must be entered into in a given year which may exceed by twofold or threefold the expenditures to be made in that year.

Thus, there has come into being a situation in which the state must raise all of its own revenues and, in addition, must give assistance to its local governments.

Thus the multiplicity of Af for a given T must be an even number.

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, red wine must, if possible, never be disturbed or shaken ; ;

Thus, moral decision must be entirely deduced backward from the likely eventuality ; ;

Thus he maintained that there must be blackness as well as whiteness in snow ; how otherwise could it be turned into dark water?

Thus linguists must resort to indirect methods to determine what those rules might be, if indeed rules as such exist.

Thus, asymmetric algorithm keys must be longer for equivalent resistance to attack than symmetric algorithm keys.

Thus, to be valid, any law must conform to natural law and coercing people to conform to that law is morally acceptable.

Thus if one chooses an infinite number of points in the closed unit interval, some of those points must get arbitrarily close to some real number in that space.

Thus, he reasoned that existence must be due to an agent cause that necessitates, imparts, gives, or adds existence to an essence.

Thus, according to Aquinas, there must have been a time when nothing existed.

Thus, for example, controversies in physics are limited to subject-areas where experiments cannot be carried out yet, whereas Benford's Law implies that controversy is inherent to politics, where communities must frequently decide on courses of action based on insufficient information.

Thus, humans must be other biological machines created by a life form just as the BETA are.

Thus perceptions must already come parcelled into distinct " bundles " before they can be associated according to the relations of similarity and causality: in other words, the mind must already possess a unity that cannot be generated, or constituted, by these relations alone.

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

Thus, a proper name must have a bearer if it is to be meaningful.

Thus, an applicant must prove discrimination in the enjoyment of a specific right that is guaranteed elsewhere in the Convention ( e. g. discrimination based on sex-Article 14-in the enjoyment of the right to freedom of expression-Article 10 ).

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.

Thus they do not resolve the ambiguities that E-Prime seeks to alleviate without an additional rule, such as that all sentences must contain a verb.