Given this influence, it is unfortunate that many of the details of his life remain shrouded in mystery, perhaps forever ; even the only known picture of him, shown above, is heavily retouched, with a fake tie painted in by hand.

) Given the diffusion of different Piers / Ploughman texts, it is usually not possible to be certain about what someone means to refer to when they mention " Piers Plowman " unless they provide specific identifying details — and most writers do not.

Given that the conduct of conclaves is strictly confidential and that any cardinal revealing such details would face automatic excommunication, no documentary evidence has ever substantiated or disproved the widely claimed rumour.

Given the condition of Ilam Cross, the following details of the faces are included for archive purposes.

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 that the details of characters ' physical appearances are not often given in His Dark Materials ( for example, it is a long time before it is mentioned that the protagonist, Lyra, is blonde ), this is an unusual attention to physical detail.

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 integers a, b and n, the expression a ≡ b ( mod n ) ( pronounced " a is congruent to b modulo n ") means that a − b is a multiple of n, or equivalently, a and b both leave the same remainder when divided by n. For more details, see modular arithmetic.

Given the lack of details and the imprecision contemporary diagnosis and description, Viceroy Revillagigedo's statement official statement that Bodega died " of natural causes " is indisputable.

Given an input test vector some instructions of that algorithm gets covered, ( see code coverage for details ) others do not.

Given how difficult all concerned found discussing the details of the crimes at issue, their language characterizes the questionable activities repeatedly without ever specifying the actions themselves.

Given the details of the mission, Beckett requests that an additional man, a spotter, must come with him.

: Given any set X of pairwise disjoint non-empty sets, there exists at least one set C that contains exactly one element in common with each of the sets in X.

* Given an algebraic number, there is a unique monic polynomial ( with rational coefficients ) of least degree that has the number as a root.

Given two subspaces with, this leads to a definition of angles called canonical or principal angles between subspaces.

While tests have been done to support this with fixed pieces of flat metal, the result is inconclusive with respect to the curved armour of the period. Given the following actions of the archers, it seems likely Froissart was correct.

Given the opportunity, adults eat hatchlings, which may be protected by separating the two groups with a net, breeding box or separate tank.

Love and Erlandson continued to pursue with the band, and released the single " Be A Man "— an outtake from the Celebrity Skin sessions — for the soundtrack of the Oliver Stone film Any Given Sunday ( 1999 ).

Given that many journeys are for relatively short distances, there is considerable scope to replace car use with walking or cycling, though in many settings this may require some infrastructure modification, particularly to attract the less experienced and confident.

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 the bias of the Victorian age, female students were denied direct study in anatomy and could not attend drawing classes with live models ( who were often prostitutes ) until a decade later.

Given the small population of the region ( compared with the Central Canadian provinces or the New England states ), the regional economy is a net exporter of natural resources, manufactured goods, and services.

Given the rigorous admission process it is not surprising that CUNY BA boasts a 70 % graduation rate within an average of 2. 2 years and that 60 % graduate with academic honors.

Given Chrétien's known tendency to create new stories and characters, being the first to mention the hero Lancelot and his love affair with Queen Guinevere for example, the name might also be entirely invented.

Given that the dispute with Pizarro over Cuzco had kept intensifying, Almagro spent a great deal of time and money equipping a company of 500 men for a new exploration south of Peru.

Given Mountbatten's determination, Nehru and Patel's inability to deal with the Muslim League and lastly Jinnah's obstinacy, all Indian party leaders ( except Gandhi ) acquiesced to Jinnah's plan to divide India, which in turn eased Mountbatten's task.

Given this kind of data, the estimated coefficient on Years of Education in the equation above reflects both the effect of education on wages and the effect of other variables on wages, if those other variables were correlated with education.

Given limited defense budgets, air forces tended to be conservative in their aircraft purchases, and biplanes remained popular with pilots because of their agility, and remained in service long after they had ceased to be competitive.

Given Guatemala's large expatriate community in the United States, it is the top remittance recipient in Central America, with inflows serving as a primary source of foreign income equivalent to nearly two-thirds of exports.

Given a trigonometric series f ( x ) with S as its set of zeros, Cantor had discovered a procedure that produced another trigonometric series that had S ' as its set of zeros, where S ' is the set of limit points of S. If p ( 1 ) is the set of limit points of S, then he could construct a trigonometric series whose zeros are p ( 1 ).

Given that Gable and Cukor had worked together before, in Manhattan Melodrama and Gable had no objection to working with him then, and given Selznick's desperation to get Gable for Rhett Butler, if Gable had any objections to Cukor, certainly they would have been expressed before he signed his contract for the film.

Given the differences of opinion within the Lord Aberdeen cabinet over the direction of foreign policy with regard to relations between Britain and the French under Napoleon III, it is not surprising that debate raged within the government as Louis Bonaparte, now assuming the title of Emperor Napoleon III of France.

Given a finite dimensional real quadratic space with quadratic form, the geometric algebra for this quadratic space is the Clifford algebra Cℓ ( V, Q ).

Given the limited amount of good quality agricultural land to begin with, that policy has resulted in continual deforestation and subsequent erosion.

On poverty, Hoover said that " Given the chance to go forward with the policies of the last eight years, we shall soon with the help of God, be in sight of the day when poverty will be banished from this nation ", and promised, " We in America today are nearer to the final triumph over poverty than ever before in the history of any land ," but within months, the Stock Market Crash of 1929 occurred, and the world's economy spiraled downward into the Great Depression.

Given the conceptual context within which ancient thought thrived, how could anyone have questioned this principle??

Given a surface through which a metal wire passes, electrons move in both directions across the surface at an equal rate.

Given also a measure on set, then, sometimes also denoted or, has as its vectors equivalence classes of measurable functions whose absolute value's-th power has finite integral, that is, functions for which one has

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 a binary operation, an idempotent element ( or simply an idempotent ) for the operation is a value for which the operation, when given that value for both of its operands, gives the value as the result.

Given the tendency for real negotiations in Japan to be conducted privately ( in the nemawashi, or root binding, process of consensus building ), the shingikai often represented a fairly advanced stage in policy formulation in which relatively minor differences could be thrashed out and the resulting decisions couched in language acceptable to all.

Given significant distance from the magnetic poles, one can figure which hand is which using a magnetic compass and the sun.

Given two secondary stations, the time difference ( TD ) between the primary and first secondary identifies one curve, and the time difference between the primary and second secondary identifies another curve, the intersections of which will determine a geographic point in relation to the position of the three stations.

Given this assumption, there are four categories in which a firm's profit may be considered to be.

Given the definition of morpheme as " the smallest meaningful unit " Nanosyntax aims to account for idioms where it is often an entire syntactic tree which contributes " the smallest meaningful unit.

Given that different groups in society have different beliefs, priorities, and interests, to which group would the media tailor its bias?

Given the above commonalities there appear to be only two string theories: the heterotic string theory ( which is also the type I string theory ) and the type II theory.

Given the proposition that ' a persons life prospects should not be decided by factors outside of their control or for which a person cannot claim personal credit ' ( i. e. social status, inherited wealth, race and other accidents of birth ) a meritocracy proposes a system where people are rewarded based on their efforts, and if everyone can start on equal footing with the same opportunity to advance, then the results are just.

Given a specific task to solve, and a class of functions, learning means using a set of observations to find which solves the task in some optimal sense.

Given printing practices at the time ( which included type-setting from dictation ), no two editions turned out to be identical, and it is relatively rare to find even two copies that are exactly the same.

" Given, a certain population, with various needs and powers of production, in possession of certain lands and other sources of material: required, the mode of employing their labour which will maximize the utility of their produce.

* Coreference resolution: Given a sentence or larger chunk of text, determine which words (" mentions ") refer to the same objects (" entities ").

* 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 ).

* Topic segmentation and recognition: Given a chunk of text, separate it into segments each of which is devoted to a topic, and identify the topic of the segment.

Given a year to complete the work, Gibson undertook the actual writing out of " blind animal terror " at the obligation to write an entire novel – a feat which he felt he was " four or five years away from ".

Given these issues, Microsoft started to work in parallel on a version of Windows which was more future-oriented and more portable.

Given an arbitrary group G, there is a related profinite group G < sup >^</ sup >, the profinite completion of G. It is defined as the inverse limit of the groups G / N, where N runs through the normal subgroups in G of finite index ( these normal subgroups are partially ordered by inclusion, which translates into an inverse system of natural homomorphisms between the quotients ).