Lefschetz hyperplane theorem - Revision history

en>K9re11: /* Hard Lefschetz theorem */

2015-01-01T02:01:16Z

Hard Lefschetz theorem

← Older revision		Revision as of 04:01, 1 January 2015
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	~~{{Unreferenced\|date=December 2009}}~~		Nice to satisfy you, I am Marvella Shryock. One of the very very best issues in the globe for me is to do aerobics and now I'm attempting to earn money with it. She is a librarian but she's always wanted her own business. North Dakota is our birth location.<br><br>My blog :: [http://btcsoc.com/index.php?do=/profile-4621/info/ home std test kit]
	~~If an [[electrical network\|electric circuit]] has a well-defined output terminal~~, ~~the circuit connected to this terminal (or its input [[impedance]]) is the ''load''~~. ~~(The term 'load' may also refer to the [[Electric power\|power]] consumed by a circuit; that topic is not discussed here.)~~

	~~Load affects the performance~~ of circuits that output [[volt]]ages or [[Current (electricity)\|current]]s, such as [[sensor]]s, [[voltage source]]s, and [[amplifier]]s. [[Mains electricity\|Mains]] [[Domestic AC power plugs and sockets\|power outlet]]s provide an easy example: they supply power at constant voltage, with [[electrical appliance]]s connected to the ~~power circuit collectively making up the load. When a high-power appliance switches on, it dramatically reduces the load [[Electrical impedance\|impedance]].~~

	~~If the load impedance is not~~ very ~~much higher than~~ the ~~power supply impedance, the voltage will drop. In a domestic environment, switching on a heating appliance may cause [[incandescent light]]s to dim noticeably.~~

	~~==A more technical approach==~~
	~~When discussing the effect of load on a circuit, it~~ is ~~helpful~~ to ~~disregard the circuit's actual design~~ and ~~consider only the [[Thévenin equivalent]]. (The [[Norton~~'~~s theorem\|Norton equivalent]] could be used instead,~~ with ~~the same results~~.~~) The Thévenin equivalent of~~ a ~~circuit looks like this:~~

	~~[[image:Electric load0~~.~~png\|center\|thumb\|322px\|The circuit~~ is ~~represented by an ideal voltage source ''Vs'' in series with an [[internal resistance]] ''Rs''~~.]]

	~~With no load (open-circuited terminals), all of~~ <~~math~~>~~V_S~~<~~/math~~> falls across the output; the output voltage is <math>V_S</math>. However, the circuit will behave differently if a load is added. We would like to ignore the details of the load circuit, as we did for the power supply, and represent it as simply as possible. If we use an [[Input impedance\|input resistance]] to represent the load, the complete circuit looks like this:

	[[~~image~~:~~Electric load1.png\|center\|322px\|thumb\|The input resistance of the load stands in series with ''Rs''.]]~~

	~~Whereas the voltage source by itself was an [[open circuit]], adding the load makes a [[closed circuit]] and allows current to flow. This current places a voltage drop across <math>R_S<~~/~~math>, so the voltage at the output terminal is no longer <math>V_S<~~/~~math>~~. ~~The output voltage can be determined by the [[Voltage divider rule\|voltage division]] rule:~~

	~~:<math>V_{OUT} = V_S \cdot \frac{R_{L}}{R_{L} + R_S}<~~/~~math>~~

	~~If the source resistance is not negligibly small compared to the load impedance, the output voltage will fall~~.

	~~This illustration uses simple [[electrical resistance\|resistances]], but similar discussion can be applied in [[alternating current]] circuits using resistive, capacitive and inductive elements.~~

	=~~=See also==~~
	* [[Dummy load]]

	~~{{DEFAULTSORT:Electrical Load}}~~
	~~[[Category:Electrical circuits]~~]

en>Addbot: Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q6516731

2013-03-15T00:24:09Z

Bot: Migrating 1 interwiki links, now provided by Wikidata on d:q6516731

← Older revision		Revision as of 02:24, 15 March 2013
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	~~Hi there~~. ~~Allow me begin~~ by ~~introducing~~ the ~~writer~~, ~~her title~~ is ~~Myrtle Cleary~~. ~~Puerto Rico~~ is ~~where he~~'s ~~been residing for many years~~ and ~~he will never transfer~~. ~~My day job~~ is a ~~meter reader~~. ~~Doing ceramics is what her family~~ and ~~her enjoy~~.<br><br>~~Also visit my web blog -~~ at ~~home std test (~~[~~http~~:/~~/www~~.~~pornextras~~.~~info/blog/187567 Continue Reading~~])		{{Unreferenced\|date=December 2009}}
			If an [[electrical network\|electric circuit]] has a well-defined output terminal, the circuit connected to this terminal (or its input [[impedance]]) is the ''load''. (The term 'load' may also refer to the [[Electric power\|power]] consumed by a circuit; that topic is not discussed here.)

			Load affects the performance of circuits that output [[volt]]ages or [[Current (electricity)\|current]]s, such as [[sensor]]s, [[voltage source]]s, and [[amplifier]]s. [[Mains electricity\|Mains]] [[Domestic AC power plugs and sockets\|power outlet]]s provide an easy example: they supply power at constant voltage, with [[electrical appliance]]s connected to the power circuit collectively making up the load. When a high-power appliance switches on, it dramatically reduces the load [[Electrical impedance\|impedance]].

			If the load impedance is not very much higher than the power supply impedance, the voltage will drop. In a domestic environment, switching on a heating appliance may cause [[incandescent light]]s to dim noticeably.

			==A more technical approach==
			When discussing the effect of load on a circuit, it is helpful to disregard the circuit's actual design and consider only the [[Thévenin equivalent]]. (The [[Norton's theorem\|Norton equivalent]] could be used instead, with the same results.) The Thévenin equivalent of a circuit looks like this:

			[[image:Electric load0.png\|center\|thumb\|322px\|The circuit is represented by an ideal voltage source ''Vs'' in series with an [[internal resistance]] ''Rs''.]]

			With no load (open-circuited terminals), all of <math>V_S</math> falls across the output; the output voltage is <math>V_S</math>. However, the circuit will behave differently if a load is added. We would like to ignore the details of the load circuit, as we did for the power supply, and represent it as simply as possible. If we use an [[Input impedance\|input resistance]] to represent the load, the complete circuit looks like this:

			[[image:Electric load1.png\|center\|322px\|thumb\|The input resistance of the load stands in series with ''Rs''.]]

			Whereas the voltage source by itself was an [[open circuit]], adding the load makes a [[closed circuit]] and allows current to flow. This current places a voltage drop across <math>R_S</math>, so the voltage at the output terminal is no longer <math>V_S</math>. The output voltage can be determined by the [[Voltage divider rule\|voltage division]] rule:

			:<math>V_{OUT} = V_S \cdot \frac{R_{L}}{R_{L} + R_S}</math>

			If the source resistance is not negligibly small compared to the load impedance, the output voltage will fall.

			This illustration uses simple [[electrical resistance\|resistances]], but similar discussion can be applied in [[alternating current]] circuits using resistive, capacitive and inductive elements.

			==See also==
			* [[Dummy load]]

			{{DEFAULTSORT:Electrical Load}}
			[[Category:Electrical circuits]]

en>Phil Boswell: /* Bibliography */convert dodgy URL to ID using AWB

2012-07-18T20:22:10Z

Bibliography: convert dodgy URL to ID using AWB

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Hi there. Allow me begin by introducing the writer, her title is Myrtle Cleary. Puerto Rico is where he's been residing for many years and he will never transfer. My day job is a meter reader. Doing ceramics is what her family and her enjoy.<br><br>Also visit my web blog - at home std test ([http://www.pornextras.info/blog/187567 Continue Reading])