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Cantor set

2015-01-13T10:02:04Z

85.181.16.77: /* Construction and formula of the ternary set */ An intuitive explanation

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85.181.178.97: /* Problem formulation */

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2014-01-25T12:41:24Z

85.181.53.212: /* Definition and solution of the Model */

{{technical|date=November 2010}}

EMSR stands for Expected Marginal Seat Revenue and is a very popular [[heuristic]] in [[Revenue Management]]. There are two versions: EMSRa<ref>Belobaba, P. P., Air Travel Demand and Airline Seat Inventory Management. Flight Transportation Laboratory. Cambridge, MIT. PhD, 1987</ref> and EMSRb,<ref>Belobaba, P. P., Optimal vs. heuristic methods for nested seat allocation. Presentation at ORSA/TIMS Joint National Meeting, 1992</ref> both of which were introduced by Belobaba. Both methods are for ''n''-class, static, single-resource problems. Because the models are static some assumptions apply: classes are indexed in such a way that the fare for the highest class, <math>r_{1}</math>, is higher than the fare for the next highest class, <math>r_{2}</math>, so <math>r_{1}</math> > <math>r_{2}</math> > ... > <math>r_{n}</math>; demand arrives in a strict low to high order in stages that are indexed with ''j'' as well; demand for class ''j'' is distributed with cdf <math>F_j(x)</math>. For simplicity it is also assumed that demand, capacity and the distributions are continuous, although it is not very difficult to drop this assumption.

==EMSRa==
EMSRa is the first version that Belobaba came up with. The idea behind the heuristic is to add the protection limits that are calculated by applying [[Littlewood's rule]] to successive classes. Suppose that we are in stage ''j+1'' and we want to calculate how much capacity we need to protect for stages ''j, j-1,..., 1''. Then we are actually calculating protection limit <math>y</math>j. To do so we consider every class in ''j, j-1,..., 1'' and compare that class, indexed with ''k'', with ''j+1'' in isolation. For every combination of ''k'' and ''j+1'' we compute the protection level for that class with [[Littlewood's rule]]:

:<math>P ( D_k > y_k^{j+1}) = \frac{r_{j+1}}{r_k}</math>

The idea of EMSRa then is to add all these protection limits to get the protection limit for <math>y_j</math>.

:<math>y_j = \sum_{k=1}^j y_k^{j+1}</math>

However, there is a problem with this method because it does not take the statistical averaging effect into account. Suppose, for example, that classes ''1'' to ''j'' have the same fare ''r'', then EMSRa will calculate the protection limit for <math>y_{j+1}</math> with

:<math> P( D_k > y_k^{j+1}) = \frac{r_{j+1}}{r}</math>

However, because the fare for all these classes is the same they should be aggregated. EMSRa will calculate protection limits that are too conservative. In other words, it will reserve too many seats for the higher fares, thereby rejecting too many low fare bookings. Although having equal fares is not realistic this will also happen if the difference between fares is small. Therefore EMSRb was invented.

==EMSRb==
One of the most widely used RM heuristics is EMSRb. It is simple and produces under certain conditions close to optimal results. Belobaba reports studies in which both EMSRa and EMSRb were compared. He shows that EMSRb is consistently within 0.5 percent of the optimal solution, while EMSRa under certain conditions can deviate more than 1.5 percent from the optimal solution. However, with mixed order of arrival and frequent reoptimization both methods perform well.<ref>Belobaba, P. P., Optimal vs. heuristic methods for nested seat allocation. Presentation at ORSA/TIMS Joint National Meeting, 1992</ref> There is also study by Polt that shows mixed results.<ref>Polt, S., Back to the roots: New results on leg optimization. In 1999 AGIFORS Reservations and Yield Management Study Group Symposium, London, UK, 1999</ref>

EMSRb is also based on an approximation that compares two classes, but it does take the statistical averaging effect into account. Instead of aggregating protection levels, as EMSRa does, it aggregates demand. Suppose we are again in stage <math>j+1</math> and we want to calculate the protection limit <math>y</math>j. Then first all future demand for classes ''j, j-1,…, 1'' is aggregated:

:<math>S_j = \sum_{k=1}^j D_k</math>

and the weighted revenues are calculated:

:<math> \overline{r}_j = \frac{\sum_{k=1}^j r_k \cdot D_k}{\sum_{k=1}^j D_k}</math>

Then, again with Littlewood’s rule, the protection limit for classes ''j'' and higher is calculated such that:

:<math> P( S_j > y_j ) = \frac{r_{j+1}}{\overline{r}_j}</math>

Usually demand is considered to be independent and distributed normally with a mean and a variance . Using that the protection limits can be calculated as:

:<math> y_j = \mu_j + z_\alpha \cdot \sigma_j</math>

with the mean and variance of the demand to come as <math>\mu_j = \sum_{k=1}^j \mu_k</math> and <math>\sigma_j^2 = \sum_{k=1}^j \sigma_k^2</math> respectively. <math>z_\alpha</math> is calculated with the inverse of the normal distribution <math>z_\alpha = \phi^{-1}(1-\frac{r_{j+1}}{\overline{r}_j})</math>. This is done for each j, giving the protection limit for every class.

==References==

{{Reflist}}

==See also==
* [[Yield management]]
* [[Littlewood's rule]]

{{DEFAULTSORT:Expected Marginal Seat Revenue}}
[[Category:Pricing]]

Blancmange curve

2013-03-15T15:16:08Z

85.181.202.32:

In [[abstract algebra]], the '''total quotient ring''',<ref>Matsumura (1980), p. 12</ref> or '''total ring of fractions''',<ref>Matsumura (1989), p. 21</ref> is a construction that generalizes the notion of the [[field of fractions]] of an [[integral domain]] to [[commutative ring]]s ''R'' that may have [[zero divisor]]s. The construction embeds ''R'' in a larger ring, giving every non-zero-divisor of ''R'' an inverse in the larger ring. Nothing more in ''A'' can be given an inverse, if one wants the homomorphism from ''A'' to the new ring to be injective.


== Definition ==

Let <math>R</math> be a commutative ring and let <math>S</math> be the set of elements which are not zero divisors in <math>R</math>; then <math>S</math> is a [[multiplicatively closed set]]. Hence we may [[localization of a ring|localize]] the ring <math>R</math> at the set <math>S</math> to obtain the total quotient ring <math>S^{-1}R=Q(R)</math>.

If <math>R</math> is a [[integral domain|domain]], then <math>S=R-\{0\}</math> and the total quotient ring is the same as the field of fractions. This justifies the notation <math>Q(R)</math>, which is sometimes used for the field of fractions as well, since there is no ambiguity in the case of a domain.

Since <math>S</math> in the construction contains no zero divisors, the natural map <math>R \to Q(R)</math> is injective, so the total quotient ring is an extension of <math>R</math>.

== Examples ==

The total quotient ring <math>Q(A \times B)</math> of a product ring is the product of total quotient rings <math>Q(A) \times Q(B)</math>. In particular, if ''A'' and ''B'' are integral domains, it is the product of quotient fields.

The total quotient ring of the ring of [[holomorphic function]]s on an open set ''D'' of complex numbers is the ring of [[meromorphic function]]s on ''D'', even if ''D'' is not connected.

In an [[Artinian ring]], all elements are units or zero divisors. Hence the set of non-zero divisors is the group of units of the ring, <math>R^{\times}</math>, and so <math>Q(R) = (R^{\times})^{-1}R</math>. But since all these elements already have inverses, <math>Q(R) = R</math>.

The same thing happens in a commutative [[von Neumann regular ring]] ''R''. Suppose ''a'' in ''R'' is not a zero divisor. Then in a von Neumann regular ring ''a''=''axa'' for some ''x'' in ''R'', giving the equation ''a''(''xa''-1)=0. Since ''a'' is not a zero divisor, ''xa''=1, showing ''a'' is a unit. Here again, <math>Q(R) = R</math>.

== Applications ==
*The rational functions over a ring ''R''{{dubious|date=December 2013}} can be constructed from the polynomial ring ''R''[''x''] as a total quotient ring.<ref>{{citation|title=Public-key Cryptography: Theory and Practice|first1=Abhijit|last1=Das|first2=C. E. Veni|last2=Madhavan|publisher=Pearson Education India|year=2009|isbn=9788131708323|page=121|url=http://books.google.com/books?id=fzoiOeUf8fIC&pg=PA121}}.</ref>
*In [[algebraic geometry]] one considers a [[sheaf (mathematics)|sheaf]] of total quotient rings on a [[scheme (mathematics)|scheme]], and this may be used to give one possible definition of a [[Cartier divisor]].

== Generalization ==

If <math>R</math> is a commutative ring and <math>S</math> is any [[multiplicatively closed set|multiplicative subset]] in <math>R</math>, the [[Localization of a ring|localization]] <math>S^{-1}R</math> can still be constructed, but the ring homomorphism from <math>R</math> to <math>S^{-1}R</math> might fail to be injective. For example, if <math>0 \in S</math>, then <math>S^{-1}R</math> is the trivial ring.

==Notes==

<references/>

==References==

*Hideyuki Matsumura, ''Commutative algebra'', 1980
*Hideyuki Matsumura, ''Commutative ring theory'', 1989

[[Category:Commutative algebra]]
[[Category:Ring theory]]

[[de:Lokalisierung_(Algebra)#Totalquotientenring]]

Path integral formulation

2012-08-24T04:38:41Z

85.181.230.67:

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2012-07-24T23:38:49Z

85.181.14.110: /* References */ corrected

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Turbo equalizer

2012-07-01T19:21:48Z

85.181.131.46: /* Turbo Equalization in Practical Systems */

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These Gerber multi tool testimonials will enable you determine which one particular will be finest for you. I've consistently had my hands on these tools for about a decade. As an Eagle Scout and backpacker, I coveted friends' gadget-packed [http://sss.Chaoslab.ru/tracker/mim_plugs/newticket?reporter=anonymous&summary=AttributeError%3A+%27Environment%27+object+has+no+attribute+%27get_db_cnx%27&description=%0D%0A%0D%0AI+wanted+to+examine+the+medium+sized+%5Bhttp%3A%2F%2FDict.Leo.org%2F%3Fsearch%3Dsurvival%2Bvariety+survival+variety%5D+knives+that+are+supplied.++If+you+have+any+thoughts+regarding+wherever+and+how+to+use+%5Bhttp%3A%2F%2Fwww.thebestpocketknifereviews.com%2Fbecker-knives-review%2F+becker+bk2+knife+reviews%5D%2C+you+can+%5Bhttp%3A%2F%2FWww.Sharkbayte.com%2Fkeyword%2Fcontact+contact%5D+us+at+our+own+internet+site.+These+are+not+the+huge+9%22%2B+blades%2C+but+the+ones+in+the+7%22+to+almost+9%22+size.+The+small+belt+knives+like+the+Bravo-1+and+Yard+Keeper+will+be+completed+in+an+additional+comparo.%0D%0A%0D%0AThe+BK2+is+definitely+complete+tang+from+a+glance.+You+can+see+that+the+grivory+scales+are+attached+to+the+tang%2C+which+is+exposed+the+full+length+of+the+knife+from+tip+to+butt.+Also+worth+mentioning+is+the+butt.+It+really+is+got+a+flat+pommel+that+can+even+be+used+to+hammer+nails+or+smash+factors.+In+addition%2C+a+lanyard+hole+is+drilled+by+way+of+this+pommel.+This+just+adds+to+the+confidence+of+the+user+and+enables+you+that+further+small+bit+of+safety+afforded+to+you+by+the+lanyard+hole+if+you+decide+on+to+use+it.+You+cannot+hold+this+knife+in+your+hand+without+the+need+of+being+aware+of+for+sure+that+it%27s+an+very+strong+and+capable+tool.+I+like+that.%0D%0A%0D%0AIn+common%2C+a+full-tang%2C+fixed+blade+is+going+to+be+more+reliable+and+much+less+probably+to+break+than+a+folding+knife+or+partial+tang.+Obtaining+a+complete-tang+knife+%28metal+blade+runs+the+full+length+to+the+finish+of+the+manage%29+will+aid+ensure+the+knife+can+manage+extreme+stress+or+usage+without+having+the+danger+of+breakage.+The+Mora+Companion+is+8.86+inches+all+round+with+a+blade+length+of+3.97+inches.+The+blade+thickness+is+.125%E2%80%B3+and+the+blade+is+created+of+Carbon+Steel+hardened+to+an+RC+of+59-60.+Not+only+do+those+who+have+reviewed+this+fixed+blade+knife+like+it%2C+they+RAVE+about+it.+The+tang+is+longer+in+this+newer+model+Mora+knife+and+the+blade+is+razor+sharp+correct+out+of+the+box.+Click+Here+to+See+Pricing%2C+Ratings%2C+and+Critiques+on++Buck+65+Hood+Punk+Knife+Knife+Thru+Arm%0D%0A%0D%0ABeneath+is+a+chart+showing+the+greatest+KaBar+knives+on+the+site+as+reviewed+by+multiple+customers.+Keep+in+thoughts+that+there+are+numerous+fantastic+KaBar+knives+out+there%2C+but+if+you+can+not+decide+on+one+particular+after+looking+the+web+page%2C+select+a+single+off+this+list+and+we+are+confident+that+you+will+be+happy%21+I+figure+due+to+the+fact+I+didn%27t+truly+want+this+%28as+in%2C+I+didn%27t+consider+I+like+it+it+then+acquire+it%29%2C+it%27s+the+great+opportunity+to+give+an+sincere+critique.+So+more+than+the+subsequent+week+or+so%2C+I+will+post+up+some+pics%2C+my+common+impression%2C+and+attempt+to+beat+the+snot+out+of+it.+I+think+my+ten+will+grow+to+be+my+new+preferred+Becker%2C+followed+by+my+two+then+the+five+with+my+14+and+11%27s+pulling+up+the+rear.+Will+my+ESEE+Knife+rust+and+how+do+I+avert+it%3F+I+can+not+figure+the+sheathing+possibilities+out+for+my+ESEE+knife.%0D%0A%0D%0AThe+KA-BAR+Eskabar+is+a+collaboration+involving+Ka-Bar+Becker+and+ESEE+knives.+The+tang+is+stamped+%22BK%26T+KA-BAR%22+on+1+side+and+%22RANDALL%27S+ADVENTURE+ESEE%22+on+the+other.+on+the+internet+and+ordered+a+BK2+from+the+Becker+Knife+and+Tool+collection.+I+have+a+BK-two+Becker+Campanion.+It%27s+a+Becker%2FKabar+and+is+stamped+BK%26T+Kabar.+This+knife+is+the+actual+deal.+It+is+a+bit+heavy+weighing+in+at+a+tiny+over+a+pound%2C+but+it+is+indestructible.+These+are+Excellent+survival+knives.+You+aren%27t+ready%2C+unless+you+have+a+KA-BAR+at+your+side.+But+do+not+take+my+word%2C+check+for+yourself+how+a+lot+the+Becker+BK2+is+these+days.+Ka-Bar+Becker+Knife+with+Drop+Point%2C+Brief+Ka-Bar+Becker+BK7+Knife+Pros+Ka-Bar+Becker+BK7+Knife+Cons+Kabar+Becker+11+Neck+Knife+Can+I+order+handles+slabs+for+ESEE+knives%3F+Black+%22I%22+by+Gosh%0D%0A%0D%0AThe+fine+texture+of+the+wood+and+it+really+is+solidity%2C+give+a+steady+grip+for+your+knife.+It+need+to+be+noted+that+the+Cocobola+deal+with+is+not+as+%E2%80%9Cgrippy%E2%80%9D+as+some+of+the+artificial+handles+out+there.+Your+hand+isn%27t+going+to+slide+off+if+you%27re+are+getting+cautious+and+not+pushing+the+knife+too+challenging.+On+the+other+hand%2C+if+you+attempt+and+make+the+knife+do+anything+it+really+is+not+created+to+do%2C+or+if+you+are+not+careful+you+could+drop+your+grip.+It+is+not+really+a+problem+if+you%27re+accountable.+The+aesthetic%27s+of+the+Cocobola+handle+far+outway+its+drawbacks+in+my+view.+Final+Thoughts&create=Create Swiss Army] knives from a [http://Server0.net/index.php?title=Best_Folding_Knives_Under_100_Dollars incredibly] young age. I graduated to a Gerber later on, a Leatherman joined me on the trail. As a contractor restoring historic houses, I kept a Leatherman in my tool belt, and it often came through on fast repairs as well effortless for a trip back to the truck. Now, as a homeowner, I maintain multitools in the kitchen and in the car glove box. For rapid fixes about the residence, they are nevertheless capable enough to resolve small problems most of the time. The Wave can be ‘upgraded' with a Tool Adapter kit which is sold separately. This kit comes with a robust as the tools on the Wave. They also never lock into spot with a have as many built-in tools as the Wave or the Swisstool X (reviewed beneath), the In use, the weight of this tool is evident. Though the edges of the handles Black Oxide ten 4.4 Lifetime $ Overview Leatherman Super Tool These are the top things to contemplate when getting your subsequent multitool. The Leatherman New Wave can be bought on the net at . By employing the link beneath to acquire, you can help help , and get this good tool at the identical time for no additional expense!) I actually like this tool. It does not have all the bells and whistles that most of the others have, but it does have the ideal blade. There is much more than one particular multitool out there that can make a particular person content. But for the most tools for the revenue, in a [http://Dallaskoreans.com/index.php?document_srl=358343&mid=Test satisfying style] that leaves nothing out and doesn't compromise on manufacturing high quality, attempt the New Wave—you'll realize the appeal behind Leatherman's most well known tool of all time. The Super Tool 300 feels like a bit of an oddball to me. It fundamentally sits between the Wave and the Surge in terms of size, weight and quantity of tools. On the plus side it is a fair bit less expensive than both of these and I give it significantly credit for that. If you are on the fence between a typical size Wave or the significant boy Surge then maybe the ST300 it the ideal guy for you. 9. Leatherman Skeletool CX (approx. $60) Leatherman Charge TTI Multi-tool LEATHERMAN MUT This field of tools has truly exploded due to the fact the expiration of the Fein Multi-Master patent in 2008 and as cordless tools have grow to be so effective and long [http://Wiki.Studrespublika.com/index.php?title=Best_Classic_Pocket_Knives lasting] the deluge has continued. Makita's XMT03Z separates itself from the pack for delivering lots of power with incredibly little noise. If you loved this short article and you would certainly such as to get more details pertaining to [http://www.thebestpocketknifereviews.com/becker-knives-review/ Becker Knives Bk2 Review] kindly check out the internet site. Overall a quite productive tool that can be integrated with your regular Makita kit that you are going to definitely be glad you have, specifically in these most unexpected scenarios. When deciding the varied solutions for the most effective multitool for you, you should really also take into account the size of the knife. If you are going to be carrying it around with you everywhere, it must be comfortable and straightforward to carry. Multitool knives come in numerous shapes and sizes. If you choose a thing small that can be effortlessly carried in your wallet or on your belt, you will uncover many customized multitools. There are knives shaped like a essential that can be attached to your essential-ring. As talked about ahead of, there are also compact credit card-shaped knives accessible. One particular of the downsides to all compact tools is just that, they are small and compact. It can be a small difficult to get the leverage needed to break the pedal or nut loose. To help remedy this predicament, the inner tools rotate out giving you five.5 inches of leverage. This could possibly not be sufficient for a rusted on or otherwise stubborn nut, but it will give you adequate to give it your finest shot. Also the integrated neoprene cover can be slid over the tool use in use to give a padded deal with. This tool has all the bells and whistles that you might need for creating or working on your AR-15s. Also constructed in is a tool for installing and removing barrel nuts (the front of the tool). This is crucial if you plan to alter the barrel of your AR-15. That is some thing that is likely significantly less typical for your typical at-house armorer, but it's there if you need it. The tool is made of 4140 steel and has a powder coat finish. I've seen shops and manufacturers that have these tools and have made use of them to build 100s of rifles and they nonetheless appear and perform like new. If you break one, you might requireverify out what your carrying out with it, since you may well have the incorrect tool for the job. Summary & Final Thoughts Posted by Roger on 21st Jul 2014 Leatherman Skeletool

Interpretation (model theory)

2011-08-02T10:30:47Z

85.181.179.182: /* Example */

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