Vasco Núñez de Balboa and Laplace transform: Difference between pages
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The '''Laplace transform''' of a [[function]] ''f''(''t'') defined for all [[real number|real numbers]] ''t'' ≥ 0 is the function ''F''(''s''), defined by: |
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'''Vasco Nuñez de Balboa''' (ca. 1475-1519) was a Spanish [[conquistador]] who was the father of the colony of [[Darien|Darién]] in [[Panama]], the oldest still-existing European settlement in mainland [[America]]. |
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Balboa sailed to [[Hispaniola]] in 1501 on an expedition under [[Rodrigo de Bastidas]] and [[Juan de la Cosa]]. |
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During this voyage they crossed the [[Gulf of Uraba|Gulf of Urabá]] (on the coast of present-day [[Columbia]]), and saw |
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the indian village of [[Darien|Darién]] in present-day [[Panama]]. In Hispaniola, Balboa settled down as a planter. |
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However, he soon amassed a large amount of debts, and to escape from his creditors he hijacked on |
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a supplyship headed for San Sebastian on the Gulf of Uraiba, hidden in a cask. The ship was |
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commanded by [[Martin Fernandez de Enciso|Martín Fernández de Enciso]]. |
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: ''F''(''s'') = ∫<sub>0</sub><sup>∞</sup> ''e''<sup>-''st''</sup> ''f''(''t'') d''t'' |
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While under way, they met [[Francisco Pizarro]] (the later conqueror of [[Peru]]), who lead the colony in |
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San Sebastian and told them almost all members of the colony had been massacred by indians. |
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Enciso nevertheless decided to go on to San Sebastian, but his ship shipwrecked, the men being |
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rescued by Pizarro, but all supplies and livestock being lost, and the colony was in ashes. Balboa, by |
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now accepted as a crew member of Enciso's, convinced them to try again in the area around |
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Darién. |
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The Laplace transform ''F''(''s'') typically exists for all real numbers ''s'' > ''a'', where ''a'' is a constant which depends on the growth behavior of ''f''(''t''). |
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They subdued the indians, started a colony and built a village. Balboa made the colonists reject both |
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Enciso's authority and that of [[Diego de Nicuesa]], who was sent to Darién as governor after Enciso |
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See also: [[Fourier transform]], [[transfer function]], [[linear dynamic system]]. |
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had sought redress with King [[Ferdinand of Aragon|Ferdinand]]. Balboa became de facto leader of the colony. Both the |
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colony and Balboa himself thrived under his policies, making friends with surrounding indians, and |
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subduing and looting those who did not want to. He heared of a great sea on the other side of the |
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mountains, and a land of great wealth (Birú, the [[Incas|Inca]] empire) to the south of this sea. As he heared |
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that the king wanted to sent him back to be tried for his conduct towards Enciso and Nicuesa, he |
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decided he had to move fast. |
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On [[September 1]], 1513, he sailed to [[San Blas]] (a lucky choice, as it just happens to be the smallest point of the isthmus), and went south across the [[isthmus]]. As before he befriended the indians who were inclined to do so, and captured, tortured and looted those that remained hostile, thus gaining substantial treasure. Finally he reached a top from where he could see the [[Pacific Ocean]]. When the others had joined him a [[Te Deum]] was chanted, a cross erected, and the sea was christened Mar del Sur (South Sea). He pushed on to the edge of the ocean, and Balboa claimed the ocean and all adjacent |
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lands for [[Spain]]. |
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On the road back they captured an indian chief called Tubanama and got a huge ransom, but some |
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members almost died of hunger because they had loaded treasure in preference to provisions. On |
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[[January 18]], 1514, Balboa was back in Darién. |
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While Balboa was away, [[Pedrarias Davila|Pedro Arias de Ávila]] (generally known as Pedrarias) had been sent to Darién as a governor. Although this time Balboa did not oppose him openly, tension between them |
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remained, Pedrarias being envious because Balboa was much more popular than himself. Balboa |
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embarked on a new, courageous expedition by building ships on the Pacific coast. The transport of |
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the materials across the isthmus cost the lives of many indian slaves. Balboa made one expedition |
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with the ships, to the [[Pearl Islands]] in the [[Gulf of Panama]]. He tried to head south from there, but |
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found the wind unfavorable. |
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Pedrarias, being convinced that Balboa wanted to establish a government of his own on the west |
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coast, had him arrested and tried for treason. Under pressure of Pedrarias Balboa was convicted |
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and sentenced to death, and on [[January 21]], 1519 Balboa was beheaded. |
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---- |
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[http://www.win.tue.nl/~engels/discovery/balboa.html Original version] (copied with permission) |
Revision as of 01:53, 29 January 2002
The Laplace transform of a function f(t) defined for all real numbers t ≥ 0 is the function F(s), defined by:
- F(s) = ∫0∞ e-st f(t) dt
The Laplace transform F(s) typically exists for all real numbers s > a, where a is a constant which depends on the growth behavior of f(t).
See also: Fourier transform, transfer function, linear dynamic system.