Given a DMS ( Degrees, Minutes, Seconds ) coordinate such as W87 ° 43 ′ 41 ″, convert it to a number of decimal degrees using the following method:

Given any coordinate chart about some point on the manifold, the above identities may be written in terms of the components of the Riemann tensor at this point as:

Given a local coordinate system x < sup > i </ sup > on the manifold, the reference axes for the coordinate system are the vector fields

Given a subset V of P < sup > n </ sup >, let I ( V ) be the ideal generated by all homogeneous polynomials vanishing on V. For any projective algebraic set V, the coordinate ring of V is the quotient of the polynomial ring by this ideal.

Given a coordinate system and a metric tensor, scalar curvature can be expressed as follows

Given a decimal longitudinal coordinate such as-87. 728055 it will be necessary to know whether it is a latitudinal or longitudinal coordinate in order to fully convert it.

Given coordinate functions

Using tensor calculus, proper time is more rigorously defined in general relativity as follows: Given a spacetime which is a pseudo-Riemannian manifold mapped with a coordinate system and equipped with a corresponding metric tensor, the proper time experienced in moving between two events along a timelike path P is given by the line integral

: Given such a tangent vector v, let f be the curve given in the x < sup > i </ sup > coordinate system by.

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 current trends in the UMC — with overseas churches growing, especially in Africa, and U. S. churches collectively losing about 1, 000 members a week — it has been estimated that Africans will make up at least 30 % of the delegates at the 2012 General Conference, and it is also possible that 40 % of the delegates will be from outside the U. S. One Congolese bishop has estimated that typical Sunday attendance of the UMC is higher in his country than in the entire United States.

Given: side a = 20, side c = 24, and angle C = 40 °

Given the importance of the seasonal gift-giving to the U. S. economy, one driven largely by consumer spending, and with the music industry making at least 40 percent of its annual revenue in the fourth quarter culminating at Christmas, demands for increased revenues motivates the shift.

# Launched Global Food Crisis Response Program: Given grants to approximately 40 nations for seeds, etc.

Given that syringes are not prohibited in the jurisdiction and their confiscation can only occur as part of an otherwise authorized arrest, almost 40 % of those who reported syringe confiscation were not arrested.

Given 40, the Mertens function returns 0.

Given that average size of a peasant family was 5, land reforms program brought freedom to approximately 9 million people, or 40 % of Iran's population.

Given a Hi of 0. 40, if the H_m is assumed to be 0. 25. then from the equation above RCM count is still high and ANH is not necessary, if BLs does not exceed 2303mL, since the hemotocrit will not fall below H_m.

Given the current energy mixes in other countries, it has been predicted that such emissions would decrease by 40 % in the U. K., and 19 % in China.

Given that the orkz of Warhammer 40, 000 reproduce asexually, through a symbiotic relationship with a type of fungal spore, it is very likely that the two races are in fact one and the same and that the details of this process as outlined in Warhammer 40, 000 background material apply to the Orcs of Warhammer also.

Given the straightforward nature of the climbing ( Alaska Grade 1, snow up to 40 degree slope ), it is possible that an earlier ascent occurred, either by native Aleuts, Russians, or other visitors.

* The song " Memory Gospel " was used in the 2007 film Southland Tales as well as the 2001 film Ali, 40 Days and 40 Nights, Get Carter and Oliver Stone's Any Given Sunday.

From just outside the penalty area, Taylor let one of his specialist direct free kicks fly straight into the top corner with the returning Newcastle goalkeeper, Shay Given, left stranded after 40 minutes.

Given the crowded field, many believed a runoff election was likely between the top two finishers — which polls suggested would be Beshear and Lunsford — if no candidate was able to obtain at least 40 % of the vote.

In 2005 Their second single " You've Given Me Something That I Can't Give Back " made the Top 40, charting at number 38 and In 2006 The band won a ' Vodafone Live Music Award '.

Given the celebrations of 40 years of Maltese independence, the 25 years of the closure of the British Base in Malta, and the anticipated admission of Malta into the European Union, the three Lodges of the Irish Constitution met on 5 September 2003 and resolved to form themselves into a Sovereign Grand Lodge.