Kantowski-Sachs metric: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
I deleted the 'and inhomogeneous cosmology' because the Kantowski-Sachs solution is clearly not spatially inhomogeneous. It differs from standard 'Friedmann-Robertson-Walker' solutions in that it is spatially *anisotropic*.
en>Sol1
 
Line 1: Line 1:
{{disputed|date=May 2012}}
There are three options in a circuit for current. It can be '''leading''', '''lagging''', or in phase with voltage. These can all be seen when one maps current and voltage of alternating (AC) circuits against time. The only time that the voltage and current are in phase together is when the load is resistive. If at some point in the phase shift the current leads the voltage by more than 90 degrees, it can then be stated that the current lags that voltage by 180 degrees minus the phase shift. Ninety degrees phase shift is the determining point if the current is either leading or lagging the voltage.<ref>Gilmore, Besser p. 19</ref>


Each of the main components of a circuit ([[resistor]], [[capacitor]], and [[inductor]]) can be seen as an impedance. All of them produce resistance in either fractional or exponential ways. Here are their complex number forms:


* Resistor, R = R<ref>Bowick, Blyler, Ajluni 2008, pg. 25</ref>
As head of Louis Vuitton, Yves Carcelle, who has died at the age of 66, built the French fashion house into one of the world's leading luxury brands.<br>Though it is only one of around 60 such brands owned by LVMH, Louis Vuitton is the conglomerate's driving force, and Carcelle expanded its appeal into areas such as eyewear and jewellery while travelling the world looking for new areas to colonise. One of his key decisions came in 1997 when he hired as creative director the then up-and-coming designer Marc Jacobs, whose introduction of the company's first ready-to-wear line helped seal its place at or near the top of fashion's premier league.<br><br><br>Born in 1948 in Paris, Carcelle graduated in mathematics from the city's �cole Polytechnique then gained a masters in business administration from the business school, Insead. His first job was as a salesman for Spontex a maker of household cleaning products, which he said was excellent training for a career in fashion: "You have to be a good salesmen, if nothing else," he said.<br><br>"And you have to know how to deal with people,"<br>The renowned fashion journalist Suzy Menkes wrote: "My favourite Yves Carcelle story - one he liked to tell with a glass of champagne in hand, perhaps at a private party at home in front of a bold Gilbert & George painting, with his then wife Rebecca at his side and with his boys listening in - was about his early days as a fledgling travelling salesman. Taking to the road with a girlfriend, the young Yves would send her into a hardware store asking with a flirtatious enthusiasm for a new product he was hoping to sell. Ten minutes later, he would be knocking on the same store door, offering to supply the goods. The success was instant."<br><br>Following his stint at Spontex, in 1974 he joined Blenda Pharm laboratories, then five years later was appointed director of the Absorba clothing brand at Poron. In 1985 he became president of the textiles firm Descamps, and his success in turning the company around led to his recruitment by Bernard Arnault as LVMH's director of strategy in 1989.<br><br>The following year he became chairman and CEO, then in 1998 head of the LVMH fashion division, which as well as Louis Vuitton includes such brands as Givenchy, Donna Karan, Christian Dior, [http://www.pcs-systems.co.uk/Images/celinebag.aspx Celine UK], Fendi, the jewellers Bulgari and cognac maker Hennessy.<br>Colleagues said Carcelle knew little about luxury when he joined Louis Vuitton. But he quickly won Arnault's trust and became one of his most respected lieutenants. "There was a lot of mutual respect between the two men even though they had very different personalities," an LVMH executive.<br><br>"Carcelle was very different from Arnault. Arnault is cold and not really somebody who easily gets excited about something, while Carcelle was very spontaneous and open."<br>Carcelle quadrupled Louis Vuitton's network of stores to just under 470, many of them in strategically important emerging markets such as China. He showed great skill in spreading the Louis Vuitton gospel: a rival told Suzy Menkes how when he and Carcelle would arrive in an often [https://www.vocabulary.com/dictionary/remote+Chinese remote Chinese] town, Carcelle would hand out beautifully wrapped small leather goods as gifts to the city's mayor and each member of his family.<br><br>In 2001 he went back to his old job following the departure of Marcello Bottoli after only 18 months. "It's not always easy to sum up what our brand means to people, but let me try," he said in 2004. "It's about reliability, quality, style, innovation and authenticity."<br>Carcelle became an expert in easing Louis Vuitton into new markets. When he wasn't globe-trotting, Carcelle was usually in his Paris office by 6am. Though he was softly-spoken, he could raise his voice when necessary - as he did when he let fly at a French government official who went to a Louis Vuitton store opening in Bangkok carrying a fake Vuitton bag.<br><br>Carcelle, who died of renal cancer, stepped down at the end of 2012 as Louis Vuitton's sales growth was starting to slow down after years of double-digit increases. There were calls for a change in management, particularly as Carcelle was in his early 60s. He stayed on as part of the LVMH executive committee and as vice president of the Fondation Louis Vuitton museum, designed by Frank Gehry on the Bois de Boulogne and due to open next month.<br><br>A keen sailor, he was an enthusiastic follower of the Louis Vuitton Cup, which until last year served as the eliminator series for the Americas Cup. Just before the onset of the global financial crisis he was asked if he was worried that his company could suffer.<br>"Not really," he replied. "The great thing about our business is that our customers are very rich - and then they are a bit less rich, but still rich, right?"<br><br>Yves Carcelle, businessman: born Paris 18 May 1948; Chevalier de la L�gion d'honneur 2014; twice married (five children); died 31 August 2014.
* Capacitor, Z<sub>c</sub> = {{math|1/jωC}}<ref>Bowick, Blyler, Ajluni 2008, pg. 25</ref>
* Inductor, Z<sub>l</sub> = {{math|jωL}}<ref>Bowick, Blyler, Ajluni 2008, pg. 25</ref>
* ω={{math|2πf}}<ref>Bowick, Blyler, Ajluni 2008, pg. 25</ref>
 
 
==Angle notation==
[[Angle notation]] can easily determine leading and lagging current:
 
&nbsp;<math>A \ang \theta.</math><ref>Nilsson p. 338</ref>
 
In this equation, the value of theta is the important factor for leading and lagging current.  Using [[complex number]]s is a way to simplify analyzing certain components in [[RLC circuits]]. It is also one of the quickest ways to notice right away if the current is leading or lagging in the circuit. For example, it is very easy to convert these between polar and rectangular coordinates. Starting from the polar notation, &nbsp;<math>\ang \theta </math> can represent either the [[Euclidean vector|vector]] &nbsp;<math>(\cos \theta, \sin \theta)\,</math>&nbsp; or the rectangular notation &nbsp;<math>\cos \theta + j \sin \theta = e^{j\theta},\,</math>&nbsp; both of which have magnitudes of 1.
 
==Lagging Current==
 
&nbsp;<math>A \ang \theta =A \ang \delta - \beta</math>
 
Lagging current can be formally defined as “an alternating current that reaches its maximum value up to 90° behind the voltage that produces it”.<ref>"Lagging Current".</ref>  This means that current lags the voltage when &nbsp;<math>\beta</math> is less than &nbsp;<math>\delta</math>. This can also be stated as the voltage and current being out of phase.
 
For an inductor, current lags the voltage. This characteristic carries over into circuits with primarily inductive loads, in which current lags the voltage.
 
==Leading Current==
 
&nbsp;<math>A \ang \theta =A \ang \delta - \beta</math>
 
Leading current can be formally defined as “an alternating current that reaches its maximum value up to 90° ahead of the voltage that produces it”.<ref>"Leading Current".</ref> This means that the current leads the voltage when &nbsp;<math>\beta</math> is greater than &nbsp;<math>\delta</math>. They are both out of phase from each other.
 
In a purely capacitive circuit, current will be at its maximum phase shift and leading the voltage.
 
==Visualizing Leading and Lagging Current==
A simple [[phasor]] diagram with a two dimensional Cartesian coordinate system and phasors can be used to visualize leading and lagging current.
 
==Historical Documents Regarding Leading and Lagging Currents==
An early source of data is an article from the 1911 [[American Academy of Arts and Sciences]] by A.E. Kennelly.  Kennelly uses traditional methods in solving vector diagrams for oscillating circuits, which can also include alternating current circuits as well. The math goes way beyond the simplification of how people today mathematically solve for different components using vector math for circuits.
 
For a capacitor, current leads the voltage. This characteristic carries over into circuits with primarily capacitive loads, in which current leads the voltage.
 
==See also==
* [[Alternating current]]
* [[Angle notation]]
* [[Complex numbers]]
* [[Electrical impedance]]
* [[Ohm's Law]]
* [[Phase (waves)#Phase shift]]
* [[Phasor]]
* [[Power factor]]
* [[RLC circuits]]
 
== Notes ==
References: {{reflist}}
 
== References ==
*Bowick, Chris, John Blyler, and Cheryl J. Ajluni. RF Circuit Design. 2nd ed. Amsterdam: Newnes/Elsevier, 2008. Print.
 
*Gaydecki, Patrick. Foundations of Digital Signal Processing: Theory, Algorithms and Hardware Design. 2nd ed. London: Institution of Electrical Engineers, 2004. Print
 
*Gilmore, Rowan, and Les Besser. Passive Circuits and Systems. Boston [u.a.: Artech House, 2003. Print.
 
*Hayt, W. H., and J. E. Kemmerly. Engineering Circuit Analysis. 2nd ed. New York: McGraw-Hill, 1971. Print.
 
*Kennelly, A. E. "Vector-Diagrams of Oscillating-Current Circuits." American Academy of Arts & Sciences 46.17 (1911): 373-421. Jstor. ITHAKA. Web. 1 May 2012. <http://www.jstor.org/stable/20022665>.
 
*"Lagging Current." TheFreeDictionary.com. Web. 1 May 2012. <http://encyclopedia2.thefreedictionary.com/lagging_current>.
 
*"Leading Current." TheFreeDictionary.com. Web. 1 May 2012. <http://encyclopedia2.thefreedictionary.com/leading_current>.
 
*Nilsson, James William; Riedel, Susan A. (2008). Electric circuits (8th ed.). Prentice Hall. p.&nbsp;338. ISBN 0-13-198925-1., Chapter 9, page 338
 
*Smith, Ralph J. Circuit Devices and Systems. 3rd ed. New York: John Wiley & Sons, 1976. Print.
 
[[Category:Electrical parameters]]
[[Category:Electric power]]
[[Category:Electrical engineering]]

Latest revision as of 02:19, 22 June 2014


As head of Louis Vuitton, Yves Carcelle, who has died at the age of 66, built the French fashion house into one of the world's leading luxury brands.
Though it is only one of around 60 such brands owned by LVMH, Louis Vuitton is the conglomerate's driving force, and Carcelle expanded its appeal into areas such as eyewear and jewellery while travelling the world looking for new areas to colonise. One of his key decisions came in 1997 when he hired as creative director the then up-and-coming designer Marc Jacobs, whose introduction of the company's first ready-to-wear line helped seal its place at or near the top of fashion's premier league.


Born in 1948 in Paris, Carcelle graduated in mathematics from the city's �cole Polytechnique then gained a masters in business administration from the business school, Insead. His first job was as a salesman for Spontex a maker of household cleaning products, which he said was excellent training for a career in fashion: "You have to be a good salesmen, if nothing else," he said.

"And you have to know how to deal with people,"
The renowned fashion journalist Suzy Menkes wrote: "My favourite Yves Carcelle story - one he liked to tell with a glass of champagne in hand, perhaps at a private party at home in front of a bold Gilbert & George painting, with his then wife Rebecca at his side and with his boys listening in - was about his early days as a fledgling travelling salesman. Taking to the road with a girlfriend, the young Yves would send her into a hardware store asking with a flirtatious enthusiasm for a new product he was hoping to sell. Ten minutes later, he would be knocking on the same store door, offering to supply the goods. The success was instant."

Following his stint at Spontex, in 1974 he joined Blenda Pharm laboratories, then five years later was appointed director of the Absorba clothing brand at Poron. In 1985 he became president of the textiles firm Descamps, and his success in turning the company around led to his recruitment by Bernard Arnault as LVMH's director of strategy in 1989.

The following year he became chairman and CEO, then in 1998 head of the LVMH fashion division, which as well as Louis Vuitton includes such brands as Givenchy, Donna Karan, Christian Dior, Celine UK, Fendi, the jewellers Bulgari and cognac maker Hennessy.
Colleagues said Carcelle knew little about luxury when he joined Louis Vuitton. But he quickly won Arnault's trust and became one of his most respected lieutenants. "There was a lot of mutual respect between the two men even though they had very different personalities," an LVMH executive.

"Carcelle was very different from Arnault. Arnault is cold and not really somebody who easily gets excited about something, while Carcelle was very spontaneous and open."
Carcelle quadrupled Louis Vuitton's network of stores to just under 470, many of them in strategically important emerging markets such as China. He showed great skill in spreading the Louis Vuitton gospel: a rival told Suzy Menkes how when he and Carcelle would arrive in an often remote Chinese town, Carcelle would hand out beautifully wrapped small leather goods as gifts to the city's mayor and each member of his family.

In 2001 he went back to his old job following the departure of Marcello Bottoli after only 18 months. "It's not always easy to sum up what our brand means to people, but let me try," he said in 2004. "It's about reliability, quality, style, innovation and authenticity."
Carcelle became an expert in easing Louis Vuitton into new markets. When he wasn't globe-trotting, Carcelle was usually in his Paris office by 6am. Though he was softly-spoken, he could raise his voice when necessary - as he did when he let fly at a French government official who went to a Louis Vuitton store opening in Bangkok carrying a fake Vuitton bag.

Carcelle, who died of renal cancer, stepped down at the end of 2012 as Louis Vuitton's sales growth was starting to slow down after years of double-digit increases. There were calls for a change in management, particularly as Carcelle was in his early 60s. He stayed on as part of the LVMH executive committee and as vice president of the Fondation Louis Vuitton museum, designed by Frank Gehry on the Bois de Boulogne and due to open next month.

A keen sailor, he was an enthusiastic follower of the Louis Vuitton Cup, which until last year served as the eliminator series for the Americas Cup. Just before the onset of the global financial crisis he was asked if he was worried that his company could suffer.
"Not really," he replied. "The great thing about our business is that our customers are very rich - and then they are a bit less rich, but still rich, right?"

Yves Carcelle, businessman: born Paris 18 May 1948; Chevalier de la L�gion d'honneur 2014; twice married (five children); died 31 August 2014.