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.

Idealists are skeptics about the physical world, maintaining either: 1 ) that nothing exists outside the mind, or 2 ) that we would have no access to a mind-independent reality even if it may exist ; the latter case often takes the form of a denial of the idea that we can have unconceptualised experiences ( see Myth of the Given ).

Given a parameterized family of probability density functions ( or probability mass functions in the case of discrete distributions )

Given the structure of the experiment, it may or may not be possible to actually perform it, and, in the case that it is possible for it to be performed, there need be no intention of any kind to actually perform the experiment in question.

Given that propensity to noble rot was a factor in Hungarian vineyard demarcations some 50 years before a messenger was supposedly mugged on his way to Schloss Johannisberg in Germany, the Hungarians probably have a better case.

:: Example: Given this option to reinstate the contract on its original terms when a plan is proposed, it may be anomalous to require the payment of interest at a market rate while a case is pending.

Given a general triangle ABC, the following conditions would need to be fulfilled for the case to be ambiguous:

Given that there is no constitutional office of Deputy Prime Minister, with the position being recreated on a case by case basis, the person who holds the post has no official residence.

Given a case for which the class is unknown, guess that it belongs to the same class as the majority in its immediate neighborhood.

Given that some common statistical packages ( e. g., SAS, SPSS ) do not provide likelihood ratio test statistics, it can be more difficult to assess the contribution of individual predictors in the multiple logistic regression case.

Given its lightning-like success, one could clearly make the case that the Olds 88 with its V-8 was the first ' musclecar '..."

Given a concrete category C, it is often the case that the opposite category C < sup > op </ sup > per se is abstract.

Given that only 2, 000 of the 785, 000 copies sold worldwide were sold in the United Kingdom, this lead numerous scholars to cite the case as an example of libel tourism.

Given these improvements dating back to 1728, a case could be made that Boston Common is in fact the world's first public urban park, since these developments precede the establishment of the earliest public urban parks in England — Derby Arboretum ( 1840 ), Peel Park, Salford ( 1846 ), and Birkenhead Park ( 1847 )— which are often considered the first.

Given the small overall amount of power produced per cubic meter, there is a substantial case for increasing water flow to the natural channel, now that Arnacrusha is producing so small a proportion of ESB's power.

Given that he resorted to cannibalism so near to food supplies, and that he killed and consumed the remains of all those present, it was revealed that Swift Runner's was not a case of pure cannibalism as a last resort to avoid starvation, but rather of a man suffering from Wendigo psychosis.

Given the interpretation via linear mappings and direct sums, there is a special type of block matrix that occurs for square matrices ( the case m = n ).

Given a set of data and the desire to produce some kind of “ model ” of those data ( model, in this case, meaning a function fitted through the data ), there are a variety of functions that can be chosen for the fit.

Given time, these deposits form much like how a stalactite takes shape in a cave, except in this case on a flat surface.

Given that Suzanne's uncle Antonio works for the Count, it seems likely she was hired on his recommendation when the Countess moved into the palace and a maid was needed for her, in which case she and Figaro would have met after the events of The Barber of Seville.

is also true in the case of compact manifolds, due to Yau's proof of the Calabi conjecture: Given a compact, Kähler, holomorphically symplectic manifold ( M, I ), it is always equipped with a compatible hyperkähler metric.

Given this method of scoring, it is possible for the defendant to be found guilty or lose the case but for the defense team to still win the round.

Given source material, Rabin – Karp can rapidly search through a paper for instances of sentences from the source material, ignoring details such as case and punctuation.

Given the apparent impracticality of massive retaliation strategy, Army Chiefs of Staff Matthew Ridgeway and his successor Maxwell Taylor argued within JCS that deterrence, instead of the " worst case " scenario of a full-scale nuclear war, should be the focus.