Given such a sweeping definition, it is apparent that cognition is involved in everything a human being might possibly do ; that every psychological phenomenon is a cognitive phenomenon.

Given an asymmetric subunit on a triangular face of a regular isosahedron, with three subunits per face 60 such subunits can be placed in an equivalent manner.

Given that a natural language such as English contains, at any given time, a finite number of words, any comprehensive list of definitions must either be circular or rely upon primitive notions.

Given a simple, binary component feed, analytical methods such as the McCabe-Thiele method or the Fenske equation can be used.

Given a subset X of a manifold M and a subset Y of a manifold N, a function f: X → Y is said to be smooth if for all p in X there is a neighborhood of p and a smooth function g: U → N such that the restrictions agree ( note that g is an extension of f ).

Given these connotations, dandyism can be seen as a political protestation against the rise of levelling egalitarian principles, often including nostalgic adherence to feudal or pre-industrial values, such as the ideals of " the perfect gentleman " or " the autonomous aristocrat ", though paradoxically, the dandy required an audience, as Susann Schmid observed in examining the " successfully marketed lives " of Oscar Wilde and Lord Byron, who exemplify the dandy's roles in the public sphere, both as writers and as personae providing sources of gossip and scandal.

Given a left neutral element and for any given then A4 ’ says there exists an such that.

Given good circumstances one might be able to discern the result of some human activity such as the changing of the Netherlands ' coast or the partial drying out of the Aral Sea, but even that would not be easy.

Given both Einstein's equations and suitable equations for the properties of matter, such a solution consists of a specific semi-Riemannian manifold ( usually defined by giving the metric in specific coordinates ), and specific matter fields defined on that manifold.

Given the Greek fleet's unpreparedness resulting from the premature outbreak of the war, such an early Ottoman attack might well have been able to achieve a crucial victory.

Given a set S with a partial order ≤, an infinite descending chain is a chain V that is a subset of S upon which ≤ defines a total order such that V has no least element, that is, an element m such that for all elements n in V it holds that m ≤ n.

Given the toleration of Hinduism, such imperial leeway was not shocking.

Given a complete set of axioms ( see below for one such set ), modus ponens is sufficient to prove all other argument forms in propositional logic, and so we may think of them as derivative.

Given the need for such fine regulation of Ca < sup > 2 +</ sup > signaling, it is perhaps unsurprising that dysregulated mitochondrial Ca < sup > 2 +</ sup > has been implicated in several neurodegenerative diseases, while the catalogue of tumor suppressors includes a few that are enriched at the MAM.

Given its continental origin as a fragment of Zealandia, unlike many of the islands of the Pacific such as the Hawaiian chain, New Caledonia is not of geographically recent volcanic provenance.

* Named entity recognition ( NER ): Given a stream of text, determine which items in the text map to proper names, such as people or places, and what the type of each such name is ( e. g. person, location, organization ).

Given a base for the topology, in order to prove convergence of a net it is necessary and sufficient to prove that there exists some point x, such that ( x < sub > α </ sub >) is eventually in all members of the base containing this putative limit.

Given a field ordering ≤ as in Def 1, the elements such that x ≥ 0 forms a positive cone of F. Conversely, given a positive cone P of F as in Def 2, one can associate a total ordering ≤< sub > P </ sub > by setting x ≤ y to mean y − x ∈ P. This total ordering ≤< sub > P </ sub > satisfies the properties of Def 1.

Given Poseidon's connection with horses as well as the sea, and the landlocked situation of the likely Indo-European homeland, Nobuo Komita has proposed that Poseidon was originally an aristocratic Indo-European horse-god who was then assimilated to Near Eastern aquatic deities when the basis of the Greek livelihood shifted from the land to the sea, or a god of fresh waters who was assigned a secondary role as god of the sea, where he overwhelmed the original Aegean sea deities such as Proteus and Nereus.

Given a preorder on S one may define an equivalence relation ~ on S such that a ~ b if and only if a b and b a.

Given X such that

Given that the authors were the primary developers of the Unix operating system, it is natural that QED had a strong influence on the classic UNIX text editors ed, sed and their descendants such as ex and sam.

Given that in such a case pits the freedom of an innocent child against the freedom of the evil-doer, it is not clear why God would not intervene for the sake of the child.

Given that estimation is undertaken on the basis of a least squares analysis, estimates of the unknown parameters β < sub > j </ sub > are determined by minimising a sum of squares function

Given that John the Baptist was executed before the defeat of Herod by Aretas IV of Nabatea in the AD 36, and based on the scholarly estimates for the approximate date of the marriage of Herod Antipas and Herodias AD 28-35, Josephus establishes a key connection between the time frame of the ministry of Jesus and his execution.

Given estimates of the image gradients, a search is then carried out to determine if the gradient magnitude assumes a local maximum in the gradient direction.

Given reasonable estimates of the time needed to compute the hash, this would take about 1 second to find.

Given that investments are subject to revisions of future expectations the Nerbrand Z utilises uncertainty of consensus estimates to assess how much earnings forecasts can be revised in standard deviation terms before P / E rations return to normalised levels.

Given that this mass is confined inside a 44 million km diameter sphere, this yields a density ten times higher than previous estimates.

Given that it took 46 years of construction, scholarly estimates for the Temple visit in the Gospel of John are around 27-29 AD.

Given the fact that these gestation lengths are only estimates of an average, it is helpful to consider gestation time as a range of dates rather than a single " due date ".

Given the many problems with the record, the dating of Lóegaire's floruit is imprecise, estimates placing it in the second half of the fifth century, circa 450 to perhaps the late 480s.

Given that observational < ref name = tak02 > and modelling of anthropogenic emissions of CO < sub > 2 </ sub > estimates suggest that the ocean is currently responsible for the uptake of approximately 2 Gt C y < sup >− 1 </ sup >, and that these estimates are poor for the shelf regions, the continental shelf pump may play an important role in the ocean's carbon cycle.

Given a simply connected and open subset D of R < sup > 2 </ sup > and two functions I and J which are continuous on D then an implicit first-order ordinary differential equation of the form

Given a first-order logic formula containing a predicate, circumscribing this predicate amounts to selecting only the models of in which is assigned to true on a minimal set of tuples of values.

Given a differentiable manifold, one can unambiguously define the notion of tangent vectors and then directional derivatives.

Given the derivatives, wave – particle duality can be assessed as follows.

Given that the derivatives as Schwartz distributions are symmetric, this kind of example belongs in the ' fine ' theory of real analysis.

Given this equivalence, it is valid to assume “ risk neutrality ” when pricing derivatives.

Given a field tensor, a scalar called the Lagrangian density can be constructed from and its derivatives.

Given the abundance of these different guidance cues it was previously believed that growth cones integrate various information by simply summing the gradient of cues, in different valences, at a given point in time, to making a decision on the direction of growth.