Brownian bridge: Difference between revisions

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{{Unreferenced|date=December 2009}}
== in order to indicate the direction ==
In the [[mathematics|mathematical]] theory of [[dynamical systems]], an '''exponential dichotomy''' is a property of an [[equilibrium point]] that extends the idea of [[hyperbolic equilibrium point|hyperbolicity]] to non-[[autonomous system]]s.


==Definition==
This time can be good, the one facing the wall, hands, mouse knife, cut a few people even rub Cengceng belt, rushing pants came down, bare hairy thighs, stunned no one would dare bend waist mention.<br><br>him shoving a security guard's shirt cut injured hand wrapped in a large, wrapped [http://www.dmwai.com/webalizer/kate-spade-8.html 財布 ケイトスペード] in horror found sitting untouched Wang Qian, the lofty, elusive Du Shu master, this time to see the mouse is angry from the heart, lift one foot to kick the old man was Gu Lulu rolled on the ground, the standard is not vent brother tried to stamp his legs, while stamp edge swore:<br><br>'Fuck you had a [http://www.dmwai.com/webalizer/kate-spade-8.html ハンドバッグ ケイトスペード] force, not a good when the gambler, but also play with [http://www.dmwai.com/webalizer/kate-spade-4.html kate spade バッグ] guns knife ...... I play when the police find Liangqian easy it is also special What I inserted a knife.'<br><br>At this point, the advance team has stormed into the building, in order to indicate the direction, out of the mouse to [http://www.dmwai.com/webalizer/kate-spade-7.html ケイトスペード 財布 通販] push the door open, place a few boxes of chips fling, when Lang Lang rolled over the ground, rolling down the stairs down a lot, direct indicates a follow-up team tracking from.<br><br>internal [http://www.dmwai.com/webalizer/kate-spade-11.html バッグ ケイトスペード] security forces is not without foot seven or eight armed guards, just stuck in the hallway,
If
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:<math>\dot{\mathbf{x}} = A(t)\mathbf{x}</math>
== also be sure to want to truly reflect on the organization ==


is a [[linear system|linear]] non-autonomous dynamical system in '''R'''<sup>''n''</sup> with [[fundamental solution matrix]] Φ(''t''), Φ(0) = ''I'', then the equilibrium point '''0''' is said to have an ''exponential dichotomy'' if there exists a (constant) [[matrix (mathematics)|matrix]] ''P'' such that ''P''<sup>2</sup> = ''P'' and positive constants ''K'', ''L'', α, and β such that
Required to truthfully report to the organization ...... last night to now, more than a dozen hours, all what happened in detail after you repeat it again, especially with a horse Shuo contact details. 'Any Red City Road.<br><br>'contact, no, I'm not trying to curry favor with curry favor, give them something to do.' I sin road.<br><br>'gave you bribe is not it?' Any red city once thought. More than sin smiled, the kind Zeixiao, each turned over loot he muttered not happy, either whispered the old: [http://www.dmwai.com/webalizer/kate-spade-8.html 財布 ケイトスペード] 'These, also be sure to want to truly [http://www.dmwai.com/webalizer/kate-spade-15.html ケイトスペード クラッチバッグ] reflect on the organization, handed over in full, all the stolen money, do Do not born [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード バッグ 激安] crooked heart appropriation ah, a lot of Secret Service is [http://www.dmwai.com/webalizer/kate-spade-1.html ケイトスペード 財布 セール] to grasp the severity of a mistake in the above. '<br><br>'Oh, bribery, how turned ah, you ah.' I sin laughed.<br><br>'ah? send you a woman? 'old office was shocked, it seems that the other [http://www.dmwai.com/webalizer/kate-spade-5.html ケイトスペード 財布 ゴールド] side really willing to lower costs.<br><br>'No, sent three.' I sin bristling three fingers, and then facing staggering any way with the old: 'Do not stare at me, I press organizations require full access
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:<math>|| \Phi(t) P \Phi^{-1}(s) || \le Ke^{-\alpha(t - s)}\mbox{ for }s \le t < \infty</math>
== cars and tickets ==


and
The details of the crime than it is to help him recalled, unexpectedly poor results, the time has been a long time, to see how this one Jiunangfandai goods, to remember a beautiful girl approached, he looked good, it almost on a sticky, more wonderful in yes, back to the waiting room did not undress, tigers too drunk himself [http://www.dmwai.com/webalizer/kate-spade-15.html ケイトスペード マザーズバッグ] down, this booing, things anesthesia are saved.<br><br>'then? was not subsequently contact you ...... [http://www.dmwai.com/webalizer/kate-spade-6.html kate spade マザーズバッグ] this cheat.' I sin asked.<br><br>came with [http://www.dmwai.com/webalizer/kate-spade-11.html ケイトスペードニューヨーク 財布] Interpol stunned, Liu Erhu slightly surprised: 'The really contacted, she said to me that the economizer return tickets and car, so I gave her some money, anyway, I do not care which one hundred [http://www.dmwai.com/webalizer/kate-spade-9.html kate spade 財布 ゴールド] and eight thousand Wan's ...... I was on this thing to worry about it, she said [http://www.dmwai.com/webalizer/kate-spade-6.html kate spade マザーズバッグ] I be suspicious, and would talk to her condition, she is also straightforward, said first coal ticket sent to me ...... '<br><br>'So, you get coal ticket?' I asked the crime.<br><br>刘二虎 nodded and continued with: 'ticket to return to the courier to only return to half ...... send her to contact me, and said to her thousands of dollars, cars and tickets, my table , phone Han, are put on board
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:<math>|| \Phi(t) (I - P) \Phi^{-1}(s) || \le Le^{-\beta(s - t)}\mbox{ for }s \ge t > -\infty.</math>
== pulled the quilt off the ground ==


If furthermore, ''L'' = 1/''K'' and β = α, then '''0''' is said to have a ''uniform exponential dichotomy''.
Smug, [http://www.dmwai.com/webalizer/kate-spade-7.html ケイトスペード かごバッグ] in Li jumped out of bed screaming Avon Road with: 'really cool Nima jail but also the value..'<br><br>chestnut Avon vain guarding himself, pulled the quilt off the ground, could not conceal his heart pounding, over the passage of the body that share the pleasure, at this time has turned it into a piece of wet on the sheets, her shame to think, never experienced such intense pleasure, he even looked forward to, the clock back, that pleasure rhythm again.<br><br>rushing to wash the sound of glass bath room where she saw more than [http://www.dmwai.com/webalizer/kate-spade-7.html ケイトスペード 財布 通販] sin, dark skin, of strong physique, she [http://www.dmwai.com/webalizer/kate-spade-8.html ケイトスペード ハンドバッグ] looked stunned, it accidentally, groggy night stand, how will look like this ?<br><br>Soon, more than crime around the towels from the bathroom out, chestnut Avon just stunned the province came from, like a horror like the [http://www.dmwai.com/webalizer/kate-spade-8.html ケイトスペード ハンドバッグ] quilt over his own body, but he found more than sin her cell phone, open the machine, Da Lielie to a place on the quilt, very sternly authentic: 'Do you tell it, I [http://www.dmwai.com/webalizer/kate-spade-7.html ケイトスペード 財布 通販] confessed.'<br><br>'I can not think that way, huh.' Li Avon got up, and be stimulated to hum the sound,
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The constants α and β allow us to define the ''spectral window'' of the equilibrium point, (&minus;α,&nbsp;β).
== and four or five ten days ==


==Explanation==
Reports. 'Lee Dong salute the two, broke and said with:' Captain let us [http://www.dmwai.com/webalizer/kate-spade-6.html kate spade マザーズバッグ] work, let us write checks. '<br><br>this is true, the hole Captains fell silent, daggers eye, I knew the team NAO police ruffian pocketing more than police, be seen today, Lee at the ministries of foreign affairs, but at the bit civilian, that and This ruffian police fought police, watching the two men drank a little confused, and stood still to fight malaria, but their looks are like commit crimes suspects, he was not sure and asked Hung Hing Industry said: 'Kong branch, you determine that they? '<br><br>'come.' Hung Hing industry is unlikely to believe, waving cried Sun Tianming captain, Sun Tianming nodded: 'that the two of them, no, there is a ...... The key is I sin.'<br><br>'Oh, that ...... that person how [http://www.dmwai.com/webalizer/kate-spade-8.html マザーズバッグ ケイトスペード] did not come?' Mr Lee asked.<br><br>stare back Liu Hung Hing industry stars, Liu said the team: 'nobody answered the phone today, [http://www.dmwai.com/webalizer/kate-spade-6.html ケイトスペード 財布 セール] the holiday ...... he really was not intentional, starting before [http://www.dmwai.com/webalizer/kate-spade-9.html ケイトスペードバッグセール] the National Day, to now November 3, and four or five ten days, has [http://www.dmwai.com/webalizer/kate-spade-10.html ケイトスペード バッグ ショルダー] been on In the post, every day is busy. '<br><br>'Do not put the power up, shut
The matrix ''P'' is a projection onto the stable subspace and ''I''&nbsp;&minus;&nbsp;''P'' is a projection onto the unstable subspace.  What the exponential dichotomy says is that the norm of the projection onto the stable subspace of any orbit in the system [[exponential decay|decays exponentially]] as ''t''&nbsp;→&nbsp;∞ and the norm of the projection onto the unstable subspace of any orbit decays exponentially as ''t''&nbsp;→&nbsp;&minus;∞, and furthermore that the stable and unstable subspaces are conjugate (because <math>\scriptstyle P \oplus (I - P) = \mathbb{R}^n</math>).
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<ul>
An equilibrium point with an exponential dichotomy has many of the properties of a hyperbolic equilibrium point in [[autonomous system (mathematics)|autonomous system]]s.  In fact, it can be shown that a hyperbolic point has an exponential dichotomy.
 
 
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Latest revision as of 18:48, 17 July 2014

in order to indicate the direction

This time can be good, the one facing the wall, hands, mouse knife, cut a few people even rub Cengceng belt, rushing pants came down, bare hairy thighs, stunned no one would dare bend waist mention.

him shoving a security guard's shirt cut injured hand wrapped in a large, wrapped 財布 ケイトスペード in horror found sitting untouched Wang Qian, the lofty, elusive Du Shu master, this time to see the mouse is angry from the heart, lift one foot to kick the old man was Gu Lulu rolled on the ground, the standard is not vent brother tried to stamp his legs, while stamp edge swore:

'Fuck you had a ハンドバッグ ケイトスペード force, not a good when the gambler, but also play with kate spade バッグ guns knife ...... I play when the police find Liangqian easy it is also special What I inserted a knife.'

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internal バッグ ケイトスペード security forces is not without foot seven or eight armed guards, just stuck in the hallway, 相关的主题文章:

also be sure to want to truly reflect on the organization

Required to truthfully report to the organization ...... last night to now, more than a dozen hours, all what happened in detail after you repeat it again, especially with a horse Shuo contact details. 'Any Red City Road.

'contact, no, I'm not trying to curry favor with curry favor, give them something to do.' I sin road.

'gave you bribe is not it?' Any red city once thought. More than sin smiled, the kind Zeixiao, each turned over loot he muttered not happy, either whispered the old: 財布 ケイトスペード 'These, also be sure to want to truly ケイトスペード クラッチバッグ reflect on the organization, handed over in full, all the stolen money, do Do not born ケイトスペード バッグ 激安 crooked heart appropriation ah, a lot of Secret Service is ケイトスペード 財布 セール to grasp the severity of a mistake in the above. '

'Oh, bribery, how turned ah, you ah.' I sin laughed.

'ah? send you a woman? 'old office was shocked, it seems that the other ケイトスペード 財布 ゴールド side really willing to lower costs.

'No, sent three.' I sin bristling three fingers, and then facing staggering any way with the old: 'Do not stare at me, I press organizations require full access 相关的主题文章:

cars and tickets

The details of the crime than it is to help him recalled, unexpectedly poor results, the time has been a long time, to see how this one Jiunangfandai goods, to remember a beautiful girl approached, he looked good, it almost on a sticky, more wonderful in yes, back to the waiting room did not undress, tigers too drunk himself ケイトスペード マザーズバッグ down, this booing, things anesthesia are saved.

'then? was not subsequently contact you ...... kate spade マザーズバッグ this cheat.' I sin asked.

came with ケイトスペードニューヨーク 財布 Interpol stunned, Liu Erhu slightly surprised: 'The really contacted, she said to me that the economizer return tickets and car, so I gave her some money, anyway, I do not care which one hundred kate spade 財布 ゴールド and eight thousand Wan's ...... I was on this thing to worry about it, she said kate spade マザーズバッグ I be suspicious, and would talk to her condition, she is also straightforward, said first coal ticket sent to me ...... '

'So, you get coal ticket?' I asked the crime.

刘二虎 nodded and continued with: 'ticket to return to the courier to only return to half ...... send her to contact me, and said to her thousands of dollars, cars and tickets, my table , phone Han, are put on board 相关的主题文章:

pulled the quilt off the ground

Smug, ケイトスペード かごバッグ in Li jumped out of bed screaming Avon Road with: 'really cool Nima jail but also the value..'

chestnut Avon vain guarding himself, pulled the quilt off the ground, could not conceal his heart pounding, over the passage of the body that share the pleasure, at this time has turned it into a piece of wet on the sheets, her shame to think, never experienced such intense pleasure, he even looked forward to, the clock back, that pleasure rhythm again.

rushing to wash the sound of glass bath room where she saw more than ケイトスペード 財布 通販 sin, dark skin, of strong physique, she ケイトスペード ハンドバッグ looked stunned, it accidentally, groggy night stand, how will look like this ?

Soon, more than crime around the towels from the bathroom out, chestnut Avon just stunned the province came from, like a horror like the ケイトスペード ハンドバッグ quilt over his own body, but he found more than sin her cell phone, open the machine, Da Lielie to a place on the quilt, very sternly authentic: 'Do you tell it, I ケイトスペード 財布 通販 confessed.'

'I can not think that way, huh.' Li Avon got up, and be stimulated to hum the sound, 相关的主题文章:

and four or five ten days

Reports. 'Lee Dong salute the two, broke and said with:' Captain let us kate spade マザーズバッグ work, let us write checks. '

this is true, the hole Captains fell silent, daggers eye, I knew the team NAO police ruffian pocketing more than police, be seen today, Lee at the ministries of foreign affairs, but at the bit civilian, that and This ruffian police fought police, watching the two men drank a little confused, and stood still to fight malaria, but their looks are like commit crimes suspects, he was not sure and asked Hung Hing Industry said: 'Kong branch, you determine that they? '

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