Exponential stability - Revision history

en>ClueBot NG: Reverting possible vandalism by 137.151.174.16 to version by Mark viking. False positive? Report it. Thanks, ClueBot NG. (1998410) (Bot)

2014-10-20T19:20:17Z

Reverting possible vandalism by 137.151.174.16 to version by Mark viking. False positive? Report it. Thanks, ClueBot NG. (1998410) (Bot)

← Older revision		Revision as of 21:20, 20 October 2014
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	~~{{Unreferenced\|date=December 2009}}~~		It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you adored this information and you would like to obtain additional info pertaining to [http://www.youtube.com/watch?v=90z1mmiwNS8 dentist DC] kindly go to the page.
	~~In [[control theory]],~~ a ~~'''proper transfer function''' is~~ a ~~[[transfer function]] in which~~ the ~~[[Degree (angle)\|degree]] of~~ the ~~numerator does not exceed~~ the ~~degree~~ of the ~~denominator~~.

	~~A '''strictly proper''' [[transfer function]] is~~ a ~~transfer function where~~ the ~~degree of~~ the ~~numerator is [[less than]]~~ the ~~degree of~~ the ~~denominator~~.

	~~If the degree~~ of ~~the numerator equals the degree~~ of the ~~denominator,~~ the ~~transfer function is '''biproper'''~~.

	~~The difference between~~ the ~~order of the denominator~~ (~~number of poles~~) ~~and order of the numerator~~ (~~number of zeros~~) ~~is the ''relative degree''~~ of the ~~transfer function~~.

	~~==Example==~~
	~~The following transfer function:~~
	:<~~math~~> ~~\textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{s^{4} + n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{s^{4} + d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}~~<~~/math~~>

	~~is '''proper'''~~, ~~because~~
	~~:<math> \deg~~(~~\textbf{N}(s~~)~~) = 4 \leq \deg(\textbf{D}(s)) = 4 </math>~~.

	~~is '''biproper'''~~, ~~because~~
	:<~~math~~> ~~\deg(\textbf{N}(s)) = 4 = \deg(\textbf{D}(s)) = 4~~ <~~/math~~>.

	~~but~~ is ~~'''~~not ~~strictly proper''', because~~
	:<~~math~~> ~~\deg(\textbf{N}(s)) = 4 \nless \deg(\textbf{D}(s)) = 4~~ <~~/math~~>.

	The ~~following transfer function is '''not proper''' (~~or ~~strictly proper)~~
	:<~~math~~> ~~\textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{s^{4} + n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}~~<~~/math~~>
	~~because~~
	:<~~math~~> ~~\deg(\textbf{N}(s)) = 4 \nleq \deg(\textbf{D}(s)) = 3~~ <~~/math~~>.

	The ~~following transfer function is '''strictly proper'''~~
	:<~~math~~> ~~\textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{s^{4} + d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}~~<~~/math~~>
	~~because~~
	~~:<math> \deg(\textbf{N}~~(s)~~) = 3 < \deg(\textbf{D}(s)) = 4 </math>~~.

	~~==Implications==~~
	~~A proper transfer function~~ will ~~never grow unbounded as~~ the ~~frequency approaches infinity:~~
	~~:<math> \|\textbf{G}(\pm j\infty)\| < \infty </math>~~

	A ~~strictly proper transfer function will approach zero as~~ the ~~frequency approaches infinity (which is true for all physical processes):~~
	~~:<math> \textbf{G}(\pm j\infty) = 0 </math>~~

	~~Also,~~ the ~~integral~~ of the ~~real part~~ of ~~a strictly proper transfer function is zero~~.

	~~{{DEFAULTSORT:Proper Transfer Function}}~~
	[[~~Category~~:~~Control theory]~~]

en>Mark viking: Added wl

2013-09-21T04:24:12Z

Added wl

← Older revision		Revision as of 06:24, 21 September 2013
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	~~The author~~ is ~~called Irwin Wunder but it~~'~~s not~~ the ~~most masucline name out there~~. ~~One~~ of the ~~issues she enjoys most~~ is ~~to read comics and she~~'~~ll be starting something else along with it~~. ~~Years in~~ the ~~past he moved to North Dakota~~ and ~~his family loves it~~. ~~Since she was eighteen she~~'s ~~been working as a receptionist~~ but ~~her marketing never arrives~~.<br><br>~~Have a look at my blog post - [http~~://~~www~~.~~nakedsex.tv~~/~~user~~/~~C8514 at home std testing~~]		{{Unreferenced\|date=December 2009}}
			In [[control theory]], a '''proper transfer function''' is a [[transfer function]] in which the [[Degree (angle)\|degree]] of the numerator does not exceed the degree of the denominator.

			A '''strictly proper''' [[transfer function]] is a transfer function where the degree of the numerator is [[less than]] the degree of the denominator.

			If the degree of the numerator equals the degree of the denominator, the transfer function is '''biproper'''.

			The difference between the order of the denominator (number of poles) and order of the numerator (number of zeros) is the ''relative degree'' of the transfer function.

			==Example==
			The following transfer function:
			:<math> \textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{s^{4} + n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{s^{4} + d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}</math>

			is '''proper''', because
			:<math> \deg(\textbf{N}(s)) = 4 \leq \deg(\textbf{D}(s)) = 4 </math>.

			is '''biproper''', because
			:<math> \deg(\textbf{N}(s)) = 4 = \deg(\textbf{D}(s)) = 4 </math>.

			but is '''not strictly proper''', because
			:<math> \deg(\textbf{N}(s)) = 4 \nless \deg(\textbf{D}(s)) = 4 </math>.

			The following transfer function is '''not proper''' (or strictly proper)
			:<math> \textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{s^{4} + n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}</math>
			because
			:<math> \deg(\textbf{N}(s)) = 4 \nleq \deg(\textbf{D}(s)) = 3 </math>.

			The following transfer function is '''strictly proper'''
			:<math> \textbf{G}(s) = \frac{\textbf{N}(s)}{\textbf{D}(s)} = \frac{n_{1}s^{3} + n_{2}s^{2} + n_{3}s + n_{4}}{s^{4} + d_{1}s^{3} + d_{2}s^{2} + d_{3}s + d_{4}}</math>
			because
			:<math> \deg(\textbf{N}(s)) = 3 < \deg(\textbf{D}(s)) = 4 </math>.

			==Implications==
			A proper transfer function will never grow unbounded as the frequency approaches infinity:
			:<math> \|\textbf{G}(\pm j\infty)\| < \infty </math>

			A strictly proper transfer function will approach zero as the frequency approaches infinity (which is true for all physical processes):
			:<math> \textbf{G}(\pm j\infty) = 0 </math>

			Also, the integral of the real part of a strictly proper transfer function is zero.

			{{DEFAULTSORT:Proper Transfer Function}}
			[[Category:Control theory]]

en>MenasimBot: r2.7.2) (Robot: Modifying fr:Stabilité de Lyapunov#Les stabilités

2012-04-03T11:35:28Z

r2.7.2) (Robot: Modifying fr:Stabilité de Lyapunov#Les stabilités

New page

The author is called Irwin Wunder but it's not the most masucline name out there. One of the issues she enjoys most is to read comics and she'll be starting something else along with it. Years in the past he moved to North Dakota and his family loves it. Since she was eighteen she's been working as a receptionist but her marketing never arrives.<br><br>Have a look at my blog post - [http://www.nakedsex.tv/user/C8514 at home std testing]