Given Otto Frank's crucial declaration that Silberbauer had obviously acted on orders and behaved correctly and without cruelty during the arrest, judicial investigation of Silberbauer was dropped, and he was able to continue in his career as a police officer.

Given Otto Frank's crucial declaration that Silberbauer had behaved correctly and without cruelty during the arrest, the judicial investigation was dropped.

Note: Given an XML markup declaration set and its corresponding data set ( s ), it is possible to create an EXPRESS schema that captures the semantic intent of the data.

Given time, plaque can mineralize along the gingiva, forming tartar.

Given the importance of these concepts in Moral Politics, it is important to consider their meaning along with how each view suggests and is justified by a corresponding view of the nature of child rearing, morality, and justice.

Given that, the Culture had intended all along to use him to discredit the brutality of the Azadian system by publicly giving the lie to the game's representation of social reality.

Formally, the problem of supervised pattern recognition can be stated as follows: Given an unknown function ( the ground truth ) that maps input instances to output labels, along with training data assumed to represent accurate examples of the mapping, produce a function that approximates as closely as possible the correct mapping.

Given the dynamic nature of the seafloor, changes in the location of shoals and bars may cause the locus of beach or cliff erosion to change position along the shore.

Given a hill angle and launch angle as before, it can be shown that the range along the hill forms a ratio with the original range along the imaginary horizontal, such that:

Given an orientable Haken manifold M, by definition it contains an orientable, incompressible surface S. Take the regular neighborhood of S and delete its interior from M. In effect, we've cut M along the surface S. ( This is analogous, in one less dimension, to cutting a surface along a circle or arc.

Given a smooth curve γ on ( M, g ) and a vector field V along γ its derivative is defined by

Given Vanier's physical state, Pearson was hesitant to advise the Queen to act along those lines, but his worry was short lived, as the following day, after hearing the Holy Sacrifice of the Mass and receiving Holy Communion in the chapel, the Governor General died.

Given the unusual form and fabric of Beaker pottery, and its abrupt appearance in the archaeological record, along with a characteristic group of other artefacts, known as the Bell Beaker " package ", the explanation for the Beaker culture until the last decades of the 20th century was to interpret it as a diffusion of one group of people across Europe.

Given a covariant derivative ∇, the parallel transport along a curve γ is obtained by integrating the condition.

Given a function and a vector field X defined on M, the Lie derivative of a function ƒ along a vector field is simply the application of the vector field.

Given a vector at the north pole, one can transport this vector along a curve by rotating the sphere in such a way that the north pole moves along the curve without axial rolling.

Given its widespread touch on the entirety of a major city, it's dubbed one of, along with the Old Firm, the Rome derby and the Istanbul derby, the most heated rivalries in European football.

Given the lack of standardized road signs at the time, it was decided to place distinctive bells along the route, hung on supports in the form of an high shepherd's crook, also described as " a Franciscan walking stick.

The day after the resignation of Cllr Colin Barrow's resignation as Leader of Westminster City Council in January 2012 on the BBC's inaugural Sunday Politics, Field said about the West End parking charges plan: " Given the furore, given the strength of the campaign by the Evening Standard, I would be very surprised if his successor runs along with this.

Given the San Gabriel Valley's burgeoning population of Asian Americans ( specifically Chinese Americans ), several business districts were developed to serve their needs creating a collection of Southern California Chinatowns loosely connected along the Valley Boulevard Corridor.

Given vector fields and lying in the tangent bundle, the affine connection describes how to differentiate the vector field along the direction.

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 the slight numerical and technological advantage of the Luftwaffe over its enemies in 1939-1941, its success during these years can largely be attributed to extensive officer and staff training programs along with the experiences of the Condor Legion in Spain.

Given a perfect normal subgroup of the fundamental group of a connected CW complex, attach two-cells along loops in whose images in the fundamental group generate the subgroup.

: 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 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 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.