Formic acid (data page): Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
en>ChrisGualtieri
m General Fixes + MOS + DMY changes using AWB
en>Octalz
m removed broken link to SIRI, added MSDS from FLUKA
 
Line 1: Line 1:
In mathematics, '''Property FA''' is a property of [[group (mathematics)|group]]s first defined by [[Jean-Pierre Serre]].
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 enjoyed this post and you would such as to get more facts pertaining to [http://www.youtube.com/watch?v=90z1mmiwNS8 dentist DC] kindly visit our web-site.
 
A group ''G'' is said to have property FA if every [[group action|action]] of ''G'' on a [[tree (graph theory)|tree]] has a global [[Fixed point (mathematics)|fixed point]]. 
 
Serre shows that if a group has property FA, then it cannot split as an [[amalgamated product]] or [[HNN extension]]; indeed, if ''G'' is contained in an amalgamated product then it is contained in one of the factors. In particular, a [[Generating set of a group|finitely generated]] group with property FA has finite [[Derived group|abelianization]].
 
Property FA is equivalent for [[Countable set|countable]] ''G''  to the three properties: ''G'' is not an amalgamated product; ''G'' does not have '''Z''' as a [[quotient group]]; ''G'' is [[Finitely generated group|finitely generated]]. For general groups ''G'' the third condition may be replaced by requiring that ''G'' not be the union of a strictly increasing sequence of subgroup.
 
Examples of groups with property FA include SL<sub>3</sub>('''Z''') and more generally ''G''('''Z''') where ''G'' is a simply-connected simple [[Chevalley group]] of rank at least 2. The group SL<sub>2</sub>('''Z''') is an exception, since it is isomorphic to the amalgamated product of the cyclic groups ''C''<sub>4</sub> and ''C''<sub>6</sub> along ''C''<sub>2</sub>.
 
Any [[quotient group]] of a group with property FA has property FA. If some subgroup of finite [[Index of a subgroup|index]] in ''G'' has property FA then so does ''G'', but the converse does not hold in general. If ''N'' is a [[normal subgroup]] of ''G'' and both ''N'' and ''G''/''N'' have property FA, then so does ''G''.
 
It is a theorem of Watatani that [[Kazhdan's property (T)]] implies property FA, but not conversely. Indeed, any subgroup of finite index in a T-group has property FA.
 
==Examples==
The following groups have property FA:
* A finitely generated torsion group;
* SL<sub>3</sub>('''Z''');
* The Schwarz group <math>\left\langle{ a,b : a^A = b^B = (ab)^C = 1 }\right\rangle</math> for integers ''A'',''B'',''C'' ≥ 2;
* SL<sub>2</sub>(''R'') where ''R'' is the ring of integers of an [[algebraic number field]] which is not '''Q''' or an [[imaginary quadratic field]].
 
The following groups do not have property FA:
* SL<sub>2</sub>('''Z''');
* SL<sub>2</sub>(''R''<sub>''D''</sub>) where ''R''<sub>''D''</sub> is the ring of integers of an imaginary quadratic field of discriminant not −3 or −4.
 
==References==
* {{cite book | title=Proceedings of the Second International Conference on the Theory of Groups | chapter=Amalgames et points fixes | language=French | first=Jean-Pierre | last=Serre | authorlink=Jean-Pierre Serre | series=Lecture Notes in Mathematics | volume=372 | year=1974 | pages=633–640 | zbl=0308.20026  | mr=0376882 }}
* {{cite book |  title=Arbres, amalgames, SL<sub>2</sub> | language=French | first=Jean-Pierre | last=Serre | authorlink=Jean-Pierre Serre | series=Astérisque | volume=46 | publisher=Société Mathématique de France | year= 1977 | zbl=0369.20013 }}  English translation: {{cite book | title=Trees | first=Jean-Pierre | last=Serre | authorlink=Jean-Pierre Serre | publisher=Springer | year=2003 | isbn=3-540-44237-5 | zbl=1013.20001 }}
* {{cite journal | first=Yasuo | last=Watatani | title=Property T of Kazhdan implies property FA of Serre. | journal=Math. Japon. | volume=27 | pages=97–103 | year=1981 | zbl=0489.20022 | mr=MR649023 }}
 
{{DEFAULTSORT:Serre's Property Fa}}
[[Category:Group theory]]
[[Category:Trees (graph theory)]]

Latest revision as of 06:16, 22 April 2014

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.

Here are some common dental emergencies:
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.

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.

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.

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.

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.

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.

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.

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.

If you enjoyed this post and you would such as to get more facts pertaining to dentist DC kindly visit our web-site.