For more explicit expositions, one must distinguish different types of analyses.

For a chemical process the first of these might involve the concentrations of the different chemical species, and the temperature or pressure of the stream.

For the Greeks, Apollo was all the Gods in one and through the centuries he acquired different functions which could originate from different gods.

For example, the model for a simplified ANOVA with one type of treatment at different levels.

For easy viewing, the middle 2 beads on each wire ( the 5th and 6th bead ) usually are of a different colour from the other eight beads.

For English, this is partly because the Great Vowel Shift occurred after the orthography was established, and because English has acquired a large number of loanwords at different times, retaining their original spelling at varying levels.

For a while there were two different dialects of Irish being spoken on Achill.

For Lie algebras the definition is slightly different.

For example, impurities in semiconducting ferromagnetic alloys lead to different properties, as first predicted by White, Hogan, Suhl, Tian Abrie and Nakamura.

For example the word learn can be signed two different ways.

For instance, antibacterial resistance genes can be exchanged between different bacterial strains or species via plasmids that carry these resistance genes.

For some elements, allotropes have different molecular formulae which can persist in different phases – for example, two allotropes of oxygen ( dioxygen, O < sub > 2 </ sub > and ozone, O < sub > 3 </ sub >), can both exist in the solid, liquid and gaseous states.

For planets, comets and asteroids a different definition of absolute magnitude is used which is more meaningful for nonstellar objects.

For different reasons, various constitutionalists have praised the Act of Settlement: Henry Hallam called the act in the United Kingdom " the seal of our constitutional laws " and David Lindsay Keir placed its importance above the Bill of Rights 1689.

For example, an " anti-realist " who denies that other minds exist ( i. e., a solipsist ) is quite different from an " anti-realist " who claims that there is no fact of the matter as to whether or not there are unobservable other minds ( i. e., a logical behaviorist ).

For example, many different things can be red.

For different applications there are different precise definitions.

For a given pressure, different liquids boil at different temperatures.

For example, an IBM PC might have either a monochrome or a color display adapter ( using different display memory addresses and hardware ), but a single, standard, BIOS system call may be invoked to display a character at a specified position on the screen in text mode.

For about 5 % to 10 % women, their breasts are severely different, with the left breast being larger in 62 % of cases.

For example, the copyright to a Mickey Mouse cartoon restricts others from making copies of the cartoon or creating derivative works based on Disney's particular anthropomorphic mouse, but does not prohibit the creation of other works about anthropomorphic mice in general, so long as they are different enough to not be judged copies of Disney's.

For if the small group notion involves the implicit claim that the phenomena of sociological investigations are of atomic or subatomic proportions, the philosopher needs to know the extent to which such entities are valid.

For example, it has been suggested that, in the early 20th century Shanghai, “ Western food, and in particular identifiably nourishing items like milk, became a symbol of a neo-traditional Chinese notion of family .”

For a set of points on the same line there is no Delaunay triangulation ( the notion of triangulation is degenerate for this case ).

For example, if we form a complete notion of Moses, and superadd to that notion the claim that Moses existed, we are not adding anything to the notion of Moses.

For example, the review falsely accuses Husserl of subjectivizing everything, so that no objectivity is possible, and falsely attributes to him a notion of abstraction whereby objects disappear until we are left with numbers as mere ghosts.

For householders, non-possession is owning without attachment, because the notion of possession is illusory.

For example, switching back to our correct notion of substitution, in the lambda abstraction can be renamed with a fresh variable, to obtain, and the meaning of the function is preserved by substitution.

For example, the Racket language extends the notion of a macro system to a syntactic tower, where macros can be written in languages including macros, using hygiene to ensure that syntactic layers are distinct and allowing modules to export macros to other modules.

For example, in a letter to the rector of Freiburg University of November 4, 1945, Heidegger, inspired by Jünger, tries to explain the notion of “ God is dead ” as the “ reality of the Will to Power .” Heidegger also praises Jünger for defending Nietzsche against a too biological or anthropological reading during the Third Reich.

For polynomials in more than one variable the notion of root does not exist, and there are usually infinitely many combinations of values for the variables for which the polynomial function takes the value zero.

For example: an apparition of John Wayne is a recurring character and serves as a sort of spiritual guide or conscience for Custer ; Monument Valley and The Alamo serve as backdrops to various legs of the journey ; for a time, Jesse acts as the sheriff of a small town in Texas, and must protect the inhabitants from harm ; the image of the Saint of Killers, a reformed bounty hunter-turned-killer-once-more in the tradition of Clint Eastwood's Unforgiven character, William Munny, is a nod to the classic Western notion of nemesis, straight and true and terrible.

For example, the notion of gauge invariance forms the basis of the well-known Mattis spin glasses, which are systems with the usual spin degrees of freedom for i = 1 ,..., N, with the special fixed " random " couplings Here the ε < sub > i </ sub > and ε < sub > k </ sub > quantities can independently and " randomly " take the values ± 1, which corresponds to a most-simple gauge transformation This means that thermodynamic expectation values of measurable quantities, e. g. of the energy are invariant.

For example the axiom of choice implies that when the size under consideration is the ordinary notion of length for subsets of the real line, then there exist sets for which no size exists, for example, the Vitali sets.

For given test functions, the relevant notion of convergence only corresponds to the topology used in C.

For example, in 2011 Mark Wrathall argued that Heidegger pursued and refined the central notion of unconcealment throughout his life as a philosopher.

For intuitionists, infinity is described as potential ; terms synonymous with this notion are becoming or constructive.

For example, Stephen Kleene describes the notion of a Turing machine tape as " a linear tape, ( potentially ) infinite in both directions.

For Perutz, Kuhn's notion that science advances in paradigm shifts that are subject to social and cultural pressures is an unfair representation of modern science.

For example, if one would like an unambiguous notion of differentiation of functions on a manifold, then it is necessary to construct an atlas whose transition functions are differentiable.

For functions on the real line, the Henstock integral is an even more general notion of integral ( based on Riemann's theory rather than Lebesgue's ) that subsumes both Lebesgue integration and improper Riemann integration.

For example, the notion of restricting a morphism to a subset of its domain must be modified.

For Plato, Eros takes an almost transcendent manifestation when the subject seeks to go beyond itself and form a communion with the objectival other: " the true order of going ... to the things of love, is to use the beauties of earth as steps ... to all fair forms, and from fair forms to fair actions, and from fair actions to fair notions, until from fair notions he arrives at the notion of absolute beauty ".

For the same reason the notion of " Aztec civilization " is best understood as a particular horizon of a general Mesoamerican civilization.