Without a precise knowledge of Germanic philology, however, it is debatable whether their use was not more often a source of confusion and error than anything else.

" Without corroboration in surviving texts, this surmise that the Babylonian version of the story is based upon a modified version of an older epic, in which Enlil, not Marduk, was the god who slew Tiamat, is more recently dismissed as " distinctly improbable ", in fact, Marduk has no precise Sumerian prototype.

Without acknowledging that he was aware of the precise nature of the plot, Garnet tried in vain to dissuade Catesby from his course.

Whiteness has so many different definitions that the word is “ nothing less than a moving target .” Arnsen moreover notes that whiteness studies scholars are entirely on the far left of the political spectrum, and suggests that their apparent vitriol towards white Americans is due in part to white workers not fulfilling the predictions of Marxist theory that the proletariat would overcome racial, national and class distinctions to unite and overthrow capitalism ; he cites as an example Roediger ’ s afterword to the seminal < I > Wages of Whiteness </ i > which asserts that the book was written as a reaction to “ the appalling extent to which white male workers voted for Reaganism in the 1980s .” Arnsen also argues that in the absence of supporting evidence, whiteness studies often relies on amateurish Freudian speculation about the motives of white people: “ The psychoanalysis of whiteness here differs from the ' talking cure ' of Freudianism partly in its neglect of the speech of those under study .” Without more accurate scholarship, Arnsen writes that “ it is time to retire whiteness for more precise historical categories and analytical tools .”

Without the precise, angstrom-level alignment of the three slices, the interference results would not be meaningful.

Without a doubt, he played a leading role in the intransigent formulation in the ultimatum of 23 July, the declaration of war on 28 July and the rebuttal of Grey's mediation proposal on 29 July.

See quantum circuit for a more precise formulation.

The precise formulation of what are today recognized as correct statements of the laws of nature did not begin until the 17th century in Europe, with the beginning of accurate experimentation and development of advanced form of mathematics ( see scientific method ).

A precise formulation of local realism in terms of a local hidden variable theory was proposed by John Bell.

Both notions, as described here, are somewhat vague, and indeed the precise formulation of these principles is controversial.

Since the precise notion of " manifold " was not available to Hilbert, there is room for some debate about the formulation of the problem in contemporary mathematical language.

This example illustrates that the conclusion reached from a statistical test may depend on the precise formulation of the null and alternative hypotheses.

This can be made precise in various contexts with slightly different ways of formulation.

The modal-logical treatment of provability helped demonstrate the " intensionality " of Gödel's Second Incompleteness Theorem, meaning that the theorem's correctness depends on the precise formulation of the provability predicate.

The intuition mentioned above ( that constructions that can be carried out in D can be " lifted " to D < sup > C </ sup >) can be made precise in several ways ; the most succinct formulation uses the language of adjoint functors.

A more precise formulation is that if a function is in both L < sup > 1 </ sup >( R ) and L < sup > 2 </ sup >( R ), then its Fourier transform is in L < sup > 2 </ sup >( R ), and the Fourier transform map is an isometry with respect to the L < sup > 2 </ sup > norm.

The precise formulation of the idea is made difficult by the fact that physicists do not yet know how many independent physical constants there are.

A precise mathematical definition of this matrix is given in the article on the formulation of the standard model.

In the idelic formulation of class field theory, one obtains a precise one-to-one correspondence between abelian extensions and appropriate groups of ideles, where equivalent generalized ideal class groups in the ideal-theoretic language correspond to the same group of ideles.

An early table, featuring reinvestment from one period to the next and a geometric series, is found in the tableau économique of the Physiocrats, which is credited as the " first precise formulation " of such interdependent systems and the origin of multiplier theory.

They provide a precise formulation of the relationship between spacetime geometry and the properties of matter, using the language of mathematics.

However, while a number of arguments have been devised which show that some form of the bound must exist in order for the laws of thermodynamics and general relativity to be mutually consistent, the precise formulation of the bound has been a matter of debate.

In the decade and a half prior to the Spanish Civil War ( 1919-1936 ), the Academy managed to consolidate itself as an institution and set about its project of promoting the birth of a standard literary language, although it was unable to provide a precise, solid academic formulation for that aim.

The formulation of more precise versions of the meaning of compactification in this context has been promoted by discoveries such as the mysterious duality.

This is a more precise formulation of the intuition that asset volatility tends to revert to some mean rather than remaining constant or moving in monotonic fashion over time.

Although for technical reasons the precise equations formulated in the original ADM paper are rarely used in numerical simulations, most or all practical approaches to numerical relativity use a " 3 + 1 decomposition " of spacetime into three-dimensional space and one-dimensional time that is closely related to the ADM formulation, because the ADM procedure reformulates the Einstein field equations into a constrained initial value problem that can be addressed encoded on a computer for solution.

The fact that concepts change does not mean that they are arbitrary ; experience can be formulated in many diverse and incompatible ways, but to the extent that they are rooted in experience, each formulation has its own precise relationship to experience.

As such, the term Ringer's lactate should not be equated with one precise formulation.

According to Victor Brochard “ the five tropes can be regarded as the most radical and most precise formulation of skepticism that has ever been given.

Market trade supplies no universal morality of its own, except the law of contract and basic practical requirements to settle transactions, while at the same time legal rules, however precise in their formulation, cannot control every last detail of transactions and the interpretation ( or implications ) thereof.