Life is further characterized, in antithesis to Piepsam, as animal: the image of a dog, which appears at several places, is first given as the criterion of amiable, irrelevant interest aroused by life considered simply as a spectacle: a dog in a wagon is `` admirable '', `` a pleasure to contemplate '' ; ;

There is one final criterion that Hume thinks gives us warrant to doubt any given testimony, and that is f ) if the propositions being communicated are miraculous.

The primary objective of chemical thermodynamics is the establishment of a criterion for the determination of the feasibility or spontaneity of a given transformation.

An alternative and equivalent definition of Carmichael numbers is given by Korselt's criterion.

In 1970, then-House Minority Leader Gerald R. Ford defined the criterion as he saw it: " An impeachable offense is whatever a majority of the House of Representatives considers it to be at a given moment in history.

For the and cases, a necessary and sufficient criterion for separability is given by the famous Positive Partial Transpose ( PPT ) condition.

By this I mean the principle that, in deciding what is good and what is bad for a given individual, the ultimate criterion can only be his own wants and his own preferences .”

In many recent tile-matching games, the matching criterion is to place a given number of tiles of the same type so that they adjoin each other.

After reaching sufficient temperature, given by the Lawson criterion, the energy of accidental collisions within the plasma is high enough to overcome the Coulomb barrier and the particles may fuse together.

Gardner-Medwin argues that the criterion on which a verdict in a criminal trial should be based is not the probability of guilt, but rather the probability of the evidence, given that the defendant is innocent ( akin to a frequentist p-value ).

Instead, Weber suggests that a ground or motive can be given – for religious or affect reasons, for example — that may meet the criterion of explanation or justification even if it is not an explanation that fits the Zweckrational orientation of means and ends.

While Ruffini and Abel established that the general quintic could not be solved, some particular quintics can be solved, such as ( x − 1 )< sup > 5 </ sup >= 0, and the precise criterion by which a given quintic or higher polynomial could be determined to be solvable or not was given by Évariste Galois, who showed that whether a polynomial was solvable or not was equivalent to whether or not the permutation group of its roots – in modern terms, its Galois group – had a certain structure – in modern terms, whether or not it was a solvable group.

The Bohm criterion in its marginal form says that the ion velocity at the sheath edge is simply the sound speed given by

The precise criterion that distinguishes between those equations that can be solved by radicals and those that cannot was given by Évariste Galois and is now part of Galois theory: a polynomial equation can be solved by radicals if and only if its Galois group ( over the rational numbers, or more generally over the base field of admitted constants ) is a solvable group.

The formula for the highest possible resolution of an optical system with a circular aperture is given by the Rayleigh criterion:

The Nyquist frequency should not be confused with the Nyquist rate, which is the lower bound of the sampling frequency that satisfies the Nyquist sampling criterion for a given signal or family of signals.

He adopted a position which may be described as ethical hedonism, according to which the criterion of goodness in any given action is that it produces the greatest possible amount of pleasure.

The linear regression line is the expected value of the criterion given the predictor ( s ) and is equal to the intercept ( the value of the criterion when the predictor ( s ) are equal to zero ) plus the product of the regression coefficient and some given value of the predictor plus some error term-this implies that it is possible for the expected value of the criterion given the value of the predictor to take on any value as the predictor ( s ) ranges from ; however, this is not the case with a dichotomous criterion.

The doctrines included the opposition to all metaphysics, especially ontology and synthetic a priori propositions ; the rejection of metaphysics not as wrong but as having no meaning ; a criterion of meaning based on Ludwig Wittgenstein's early work ; the idea that all knowledge should be codifiable by a single standard language of science ; and above all the project of rational reconstruction, in which ordinary-language concepts were gradually to be replaced by more precise equivalents in that standard language.

The presence or absence of minimal pairs, as mentioned above, is a frequently used criterion for deciding whether two sounds should be assigned to the same phoneme.

Furthermore, the arguments which Good and Maher used to criticize Nicod's criterion ( see Good's Baby, above ) relied on this fact-that " All ravens are black " is highly probable when it is highly probable that there are no ravens.

However these modern units have the goal of treatment and rehabilitation back into society within a short time-frame ( two or three years ) and not all forensic patients ' treatment can meet this criterion, so the large hospitals mentioned above often retain this role.

This is a powerful criterion: for example, all axioms listed above as canonical are ( equivalent to ) Sahlqvist formulas.

The Jacobson radical of R < nowiki ></ nowiki > X < nowiki ></ nowiki > is the ideal generated by X and the Jacobson radical of R ; this is implied by the element invertibility criterion discussed above.

However, as Hamilton's later refinements of his theory make clear, it does not simply predict that genetically related individuals will inevitably recognise and engage in positive social behaviours with genetic relatives: rather, indirect context-based mechanisms may have evolved, which in historical environments have met the inclusive fitness criterion ( see above section ).

In fact, if the " only one American hit " criterion had been strictly applied, a-ha and Falco would not be eligible for the list, as they each actually had two top-20 US hits — although as noted above their second hits were greatly overshadowed in the US by the prior hit.

In other words, the latter statement is evaluable ( in fact, falsifiable ) by an understood (' background ') criterion for mountain height, like ' the summit is so many meters above sea level '.

In the above equations, g ( X ) refers to the logit function of some given predictor X, ln denotes the natural logarithm, is the probability of being a case, is the intercept from the linear regression equation ( the value of the criterion when the predictor is equal to zero ), is the regression coefficient multiplied by some value of the predictor, base e denotes the exponential function.

If the delusions are judged to be bizarre, or hallucinations consist of hearing one voice participating in a running commentary of the individual's actions or of hearing two or more voices conversing with each other, only that symptom is required to meet criterion A above.

It is easy to verify that all examples above except the presheaf of bounded functions are in fact sheaves: in all cases the criterion of being a section of the presheaf is local in a sense that it is enough to verify it in an arbitrary neighbourhood of each point.

Early work on transformations used paraphrase as a heuristic, but Harris recognized that this was inadequate ( e. g. in Harris 1954 ) and, in keeping with the methodological principles noted above in the section on metalanguage issues and earlier, sought a formal criterion for transformational analysis.

See aliasing for a simpler formulation of this Nyquist criterion that specifies the lower bound on sampling rate ( but is incomplete because it does not specify the gaps above that bound, in which aliasing will occur ).

The criterion above leads to the quick conclusion that if P is irreducible and not separable, then P ′( X )= 0.

As noted above, for many, power capabilities were the sole criterion.

Assuming that the degree of does not exceed, the criterion is correct however, and somewhat stronger than the formulation given above, since if is irreducible modulo, it certainly cannot decompose in into non-constant factors.

This shows that he was unaware of two different proofs of this statement that Schönemann had given, one in either part of a two-part article, the second of which being the one based on the criterion cited above ; this is all the more surprising given the fact that two pages further Eisenstein actually refers ( for a different matter ) to the first part of Schönemann's article.

For example, in the case x < sup > 2 </ sup > + x + 2 given above, the discriminant is − 7 so that 7 is the only prime that has a chance of making it satisfy the criterion.

* The action must bring added value over and above what could be achieved by individual or member-state government action alone ( the benefit criterion ).

A recent analysis of SEB bankas says that Lithuania could not adopt the euro before 2013 due to the high rate of inflationwhich reached 11 % in October 2008well above the Maastricht criterion of 4. 2 %.

Students must have at least four GCSEs at grade A or above ( all offers made during Year Eleven are conditional on students fulfilling this criterion ).

Both of the above cases fits the bridging criterion mathematically, however most uses of the term impedance bridging applies only to the first case.