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# Blowing down exceptional curves
Let X be a Noetherian separated scheme. Let E ⊂ X be an effective Cartier divisor such that there is an isomorphism E → P1k where k is a field. Then we say E is an exceptional curve of the first kind if the normal sheaf of E in X has degree -1 on E over k.
You can get an example of the situation above by starting with a Noetherian separated scheme Y and a closed point y such that the local ring of Y at y is a regular local ring of dimension 2 and taking the blowup b : X → Y of y and taking E to be the exceptional divisor.
Conversely, if E ⊂ X is gotten in this manner we say that E can be contracted.
The following questions have been bugging me for a while now.
Question 1: Given an exceptional curve E of the first kind on a separated Noetherian scheme X is there a contraction of E?
Question 2: Given an exceptional curve E of the first kind on a separated Noetherian scheme X is there a contraction of E but where we allow Y to be an algebraic space?
Question 3: Suppose that Y is a separated Noetherian algebraic space and that y is a closed point of Y such that the henselian local ring of Y at y is regular of dimension 2. Is there an open neighbourhood of y which is a scheme?
Question 4: With assumptions as in Question 3 assume moreover that the blow up of Y in y is a scheme. Then is Y a scheme?
In these questions the answer is positive if we assume that X or Y is of finite type over an excellent affine Noetherian scheme (and I think in the literature somewhere; I’d be thankful for references).
But… it might be interesting and fun to try and find counter examples for the general statements. Let me know if you have one!
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## We had the perfect TW, actually… An optimist’s perspective?
Before the TW and all its attendant terror, the main discussion was, as always, around two things:
• Who had to go, and it was a large number including: Squillaci, Arshavin, Denilson, Djourou, Santos, Bendtner, Chamakh. Opinions were also split on Mannone (not good enough) and Gervinho (too Jekyll and Hyde)
• Who had to come: GK, DM, ST were the main calls, with lesser calls for defenders.
I am thus presenting an optimist’s view, perhaps, although no one can be as optimistic as Glic and his tattoos, which says that this TW was wildly successful. I base this assessment on 3 metrics, like any good engineer, offering a measure of redundancy in my analysis!
1. Net Flow or Team Quality (TQ) – where the goal of the TW is to raise your average quality, admittedly while keeping enough players to make a side. Thus, when an Oiler buys their third national side, the team quality doesn’t go up much, was it worth it? Equally, for Everton, Fellaini out of a strong(er) midfield and Lukaku in is likely a big improvement for them for this year. I fear them more not less now.
2. Risk (R) – will said player achieve vs what is paid, in terms of when you need that achievement at that position. Thus, coverage is included here as well. Suarez was always high quality but the risk of him being out and not delivering was also high. Equally, Fellaini offers little risk to ManU, but little return, leading to…
3. Quality of Return (QR) – what can the players and modified team (potentially) achieve in terms of improving the team’s outcome in placing, cups etc. No sense to pay 100M for no change in cups or outcomes, which makes the risk of say RMs Bale investment somewhat high if they don’t win any more than last year.
So, I think this summer we did great, and here’s why.
Total Quality of TQ: We got rid of all but the world’s greatest striker from our deadwood and both mixed opinions. We added a potentially very good youngster who will play in League Cup perchance (Sanogo), a very good GK with option to buy who will provide the necessary competition for Scez that (somehow!) Fabianski does not, a solid DM with Adamsesque bite and mongrel (for free no less), and possibly the world’s best creator if we let our Cesc blinders slip a bit.
For me, the deadwood out is critical, it frees us now and long term. There was no way Squillaci or Santos was going to play, even if we had only 1 defender left on the squad. You’d have seen JW playing LB first! Thus, why have them?
Finally, we have seen glimpses that OG will become more clinical this year. In fairness, last year he was not so good but with ball to feet he has been very good in front of goal so far. Well may it continue.
I think there is little argument that our TQ is now far, far higher than it was a week or two ago.
Risk or R: There are two aspects, achievement (or player failure) and coverage. First, achievement: I think that the positions with least risk are defenders and creators. Defenders can always fall back on their own physicality, fitness and Presence!, and fit into most systems easily enough. Thus, low risk. Creators, all across the park at any position are equally lower risk, as they rely primarily on ball holding skills that they always have, vision and passing accuracy. Thus, as long as the supporting cast is good their skills transfer anywhere pretty easily, although putting Ozil into Stoke would be a waste! J
Hence, we got one of the world’s best creators in a scheme that favors them, a very good defensive DM, and Sanogo is the long term bet for no money. The GK should also be fine.
Hence, I think there is virtually no risk in our TW activity from an achievement standpoint.
Next, is coverage. The complaint on the various e- and bloggo-spheres is that we didn’t get a defender. In that regard we have:
• Central defender: Per, Koz, TV (when healthy), Sagna, Flamini
• Outside defender: Jenks, Gibbs, Monreal, Sagna, Flamini
There are some youngsters too for the League Cup. Equally, some loan deals also have a mid-year return built in if one has nuclear war type injuries and loses far too many players. I would be surprised if we didn’t have that with Coquelin for example, at a cost of course.
Similarly, we are now relatively well stocked in the more defensive midfield portion as well, and can really offer some teams different “looks”. I am particularly excited about our ability to look very offensive with Ram-Teta, and equally more aggressive with Flam-Sey or Flam-Zorro (warning: I have copyrighted all nicknames! J ). There is also Flam-Shere which would be like Flam-Zorro but with more aggressiveness. Overall, with Zorro, JW, Ramsey and Flamini we are well placed.
It will also allow a full year for Diaby to recover and we may thus have him signed for the third or fourth time next year! One can only hope his outlook improves finally.
Out wide, injuries to Poldi and Ox don’t help but will be recovered. Meanwhile, we have Santi, Theo and JW, as well as Gibbs with Monreal back deeper to help out.
Equally, the Ozil signing frees JW to play both offensively and defensively in various combinations, or even out wide where Poldi, Ox, Theo, Santi, and others roam. We should be able to offer so many different looks of quality that others will fear our overall Presence! in midfield, no matter that they park the bus or play us straight up.
Finally, the ST. I want to point out we still have the world’s best and that he will never play for us. I think not even in League Cup, perhaps. OG is more clinical and I think Ozil will give him great service. Equally, Ozil with Santi and Theo wide should remove 1-2 defenders from clinging to OG and swarming him. Ozil is the one magic player that will make OG even better.
Hence, I think there is very little risk in our TW activity from a coverage standpoint, especially with January and ~40M or more on hand coming soon enough. Injuries, we already have a lot of, but if they get worse, well that’s life. But, I think we are more than well placed to be very confident about two things:
1. Our ability to really stick it to any team we play
2. Our ability to stack up against the best in Europe (1st up is BD in group stages!)
Thus, I think we were actually very low risk
Quality of Return or QR: Finally, I think I’ve said it all, but to repeat shortly:
• Ozil will make Theo, Santi and OG better. He will allow JW to develop. I think he will score ~8-10 goals but have 20+ assists and we will score at least 10-15 more league goals because of him. Given last year’s defense that would allow for something like 3-4 more wins easily and a few more draws (i.e. far less losses), and we would have been at or near ManU.
• Flamini: will add bite and defense within a system and culture he knows well. He offers now so many looks with Ramsey and JW and Arteta that we should be far more organised and full of Presence! down the middle. His experience will also improve Ramsey and JW I think
Sanogo and the GK are the future and competition.
So, our quality for just two players, IMO, the exact right two players by position and choice, are going to make a huge impact on our ability to compete for the EPL, cups and Europe. Injuries always are a risk, but January is soon
Hence, I think we got a very high QR this TW, better than anyone in Europe and far better than some think, both for direct contribution and how those players will impact those around them.
The Future:
In future, I hope for Diaby to come right, or for January or next summer to see us get a more proper long term solution at DM. I’d like a little depth at the backs, but think we are solid now, and can afford to wait on the youngsters to develop.
A SQ striker, … Well, there were actually very few STs moving this year if you look at it. They have the greatest risk of not fitting into a new system and scoring immediately, as we know from history, and with the WC coming, I think many would not move unless they were highly confident of their national team position (eg Bale who’s not really a ST)… From the standpoint of Jovetic, you have to wonder what he’s thinking now… In my opinion we can wait on it and there is always Theo or Poldi when better, as anyone should do well in front of Ozil et al. And if not, there is January or the dreaded Dane.. J
Cheers, I am optimist at heart I guess!
Written by: jgc.
This entry was posted in Uncategorized and tagged , , , , , . Bookmark the permalink.
### 161 Responses to We had the perfect TW, actually… An optimist’s perspective?
1. TotalArsenal says:
Superb post, jgc. 🙂
Well written and structured and a joy to read.
You have added quite a bit of steel towards your positivity and I agree that Flamini and Ozil will add a lot to this team. As said in previous comments, the late arrival of Ozil is likely to mean it will take a while before we will get the full benefit of his addition as he will have to settle in the team and the team will have to get used to him. However, I agree that Flamini will have an instant positive impact and he should help us to grind out results. In the meantime, the German can get settled in the team and we can go from strength to strength.
Up-front is where the worry is, as the likes of Theo, Giroud and Cazorla will have to play a hell of a lot of games with limited back up. Injury prone Pod and inexperienced Sanogo, Gnabry and Ryo are not ideal replacements. This leaves us with an interesting position re Bendtner…. it could be make or break for him, and to a certain extent for us, this year…
Back in a bit.
2. mA says:
great post and i agree with u
only regret is why we didn’t go for a mobile striker. I would have liked someone in the mould of Suarez or Atletico’s D. Costa. We have a pretty good squad, but lacking in depth in some of the positions. If only we can keep all of them injury-free till March (not May). By then we would know the strength of the team and whether it can mount a real challenge for the title.
Gnabry for Gerv. was great business but will Zelalem be unleashed as a substitute for Ozil and Rosicky? Will Arteta, Ramsey, Flamini and Jack fit in? do you remember we have Carzola and…Diaby? That’s a midfield to be proud of and can’t wait for the season to begin once more.
3. TotalArsenal says:
jgc – the games against BD and Napoli, whilst Marseille cannot be underestimated either, will be great tests for this team. I cannot wait for the first CL games but first we have to get trough the inter-lull without players getting injured.
So what if Giroud gets injured and Pod is still not available?
Maybe we could play:
——–Flam—–Arteta/Ramsey———–
Jack—————Ozil——————Santi
———————–Theo——————–
Jack and Santi to interchange with Ozil and with each other regularly……..
4. TotalArsenal says:
5. TotalArsenal says:
6. TotalArsenal says:
MA 🙂
Do you believe Gnabry is ready for first team action?
7. AFC says:
JGC, top post. 🙂
Just a quick point on Bale. In a football way the signing of Bale is very risky but in a marketing way it is not. Real will simply make all of the £85 million with added profit back from shirt sales, sponsorship deals etc. He is a very marketable player.
I have said a lot of what I feel in my post but I guess I can say a bit more. Sanogo, Ryo and Gnabry are not ready yet and I feel it would have been better for them to go on loan to EPL clubs. Palace would have taken Ryo but I’m not sure who would have taken Sanogo. Frimpong and Park are done at Arsenal whereas Bendy still has something to offer. Still quite young and has not entered his prime yet. He should be out second ST in my opinion. Wenger has said he will use him. I feel Bendy can turn it around. Walcott and Podolski will be needed on the wings. Diaby may have to take a pay as you play deal if he wants to stay at Arsenal in the future.
Future signings needed: young CB who can play RB or LB or both; top ST; long term DM replacement. L.Bender will do.
Frimpong, Fabianski, Bendy and Park will all be gone by the end of next season with those who are still on loan.
Flamini is injury-prone so that could be the only risk of us signing him as we have given him a two year contract. Sanogo is one for the future, Viviano could be signed on a permanent deal after this season and Ozil, need I say anything. You know what I”m going to say. 😀
We did not really take any risks in the TW but sometimes in business you do need to take some risks? 😀
8. Glic says:
I have a long journey tomorrow, so will comment on BKs very own Professors post when I get back from Orcland !.
Totes. If you were to look in VCCs Y- Fronts, you would see some more Tumbleweed action !.
Im sure Sergio Leone filmed some scenes about my Emirates day out with Stretch and Vics in a film called………..The Good, The Bald and the Ugly Muvver Fcuker !.
Good night from The Good one !. hahaha
9. TotalArsenal says:
Night Glic and travel safely tomorrow 🙂
10. ProudGooner says:
jgc,
Good post, i agree with most.
On the Sanogo, Gnabry, Ryo and Frimpong. I feel they are ready to play for us, i think loaning them out when we are so low on numbers would have been suicidal Gnabry could play v Sunderland in Podolski position and i would be happy. Sanogo is highly rated by Wenger and i totally trust his judgement , but i feel he may need a few weeks to fully settle, so the international break has probably come at a good time for him. Ryo not as sure about , but i would be happy for him to play again . Arsene has always played and developed players and it is important this continues plus the fact thata player can’t play all the matches its just not pyhically possible. Frimpong may for his chances very few, so he could perhaps of gone on loan but what i have seen at him at Arsenal has been very good. But i feel for sure the players he kept, including Bender were all needed this season.
11. Dylan says:
Fantastic post! 🙂 I totally agree, although I think TGSTEL will play some games. And I think a ST, Winger, and DM. Cesc would be a bonus. As well as a young CB. 🙂
12. TotalArsenal says:
Nice article and I read a similar article on a Dutch professional site – We have got the King of Assists!
http://www.bbc.co.uk/sport/0/football/23958489
13. ProudGooner says:
TA,
Thanks for the tumble weed film, interesting,
Dr Glic,
night
It would not surprise me if Wenger transformed Ryo or Gnabry into a striker ,like he did with Henry and Rvp. As he is doing with Walcott who is ready already . I wanted another striker but i feel there is plenty of goals until the winter window.
14. TotalArsenal says:
Good post but IMHO the initials just were BS and drove me crazy reading it ! lol
16. ProudGooner says:
TA,
Do you think Wenger will free up Arteta to his old Everton days role again for some games now he has Flem-teta possiblities possible lol?
17. Bongo says:
I would have come on sooner, but as a Spurs fan, after last week ends result, have just stopped crying.
I was just wondering how you see the result as Arsenal fans. Did you deserve the win? were you worried? and was it closer than you thought? Or are you just pleased to get a win over us?
Also, does the Ozil transfer mean Wenger is back to his best or is this just a signing to keep you happy for a while while not really strengthening your whole squad? He is a great player though.
Don’t pelt me, I know you won. The world hasn’t ended.
18. AFC says:
TA, Mourinho said he blocked the loan move of Ba because he knew that with Ba and Ozil we would become title contenders. 😦
I can’t actually blame him for doing that. Why help a rival. However we really should have had other targets better than Bendy lined up.
19. ProudGooner says:
So many options our midfield it is defo top 2 of the PL with either city or the chavs , the fact that Jose plays anti-football will hold there offensive play back and city boss well he will need time to get used to everything if he does at all. That is something Wenger needs to take advantage of early on if possible. I have faith in our old owl Wenger.
20. ProudGooner says:
Bongo,
I honestly feel Arsenal deserved the win, we had the most clear cut chance, scored early on and defended as well as i have seen us do in a long time. Spurs had a strong last 10 mins and there was a couple of minutes then when i was a little worried but overal i was confident that we would win. That is the truth of what i thought. But if i was a spurs an i would of taken all them players for Bale any day.
21. AFC says:
Bongo, good to see. 🙂
Ozil is a very good addition and with Flamini and Viviano those signings make me happy for now. In the next few seasons we will need to buy 2-3 more players if we want to become a dominant force and win several trophies. The signing of Ozil is a step in the right direction and is a statement of intent by Wenger. That signing shows we are willing to splash the cash on world class players and are ready to start challenging.
I was a bit worried about our match with you guys but I think the fact that your team is going through a transitional period made us just that bit stronger. I was just happy for the win. I do not know why Sandro didn’t start with Paulinho for you guys or why Lamela did not play as a SS behind Soldado.
You guys have sold a guy for £85 million and you only signed him for a few million. That’s good business considering he is probaly only worth around £40 million. You guys have invested well but I feel you are still missing another ST, RB and LB.
22. ProudGooner says:
The coulple of minutes i was worried was when King rent boy AVB ran down the touch line to coach the lad where to throw the ball, i though the rent-biy was going to run on to the pitch and get on the end of the throw with a bycicle kick. lol
23. ProudGooner says:
This season is going to be a very interesting one, i feel Arsenal, Chelsea, united, Spurs, Liverpool and City 6 teams will all be tighter and closer then ever.
24. Bongo says:
The game could have done with a few more goals I suppose. For what my opinion is worth I am pleased you didn’t put 5 passed us again.
I do think that your squad is too small though for fighting in all competitions and you played us at the right time.
Wouldn’t it be great if it was you and us competing for the title?
Enjoy the international break. I’m off to bed.
25. James Bond says:
all of you best totally agree or agree with my amigo aka JGC – yeah, i’m the one with the gun in my hand if anyone messes with him !
since that’s out of the way, let’s get back to business
cracking article @ JGC – was worth the 2 days and 3 hour and 21 minutes and 19 seconds wait 😉
agreed re- the focal points and the spine of your article.
yes, we are the biggest winners in the TW, not because of the amount of players we were able to shift (both get rid of, sell and loan out) but merely due to keeping hold of our CAPTAIN and not selling him for the 3rd season in a row 🙂
i also, don’t agree with the premise that it may take a little bit time before we get to see, Ozil at his best – that’s the thing with world class players, they often need very little time or no time at all to settle in, i expect Ozil to come straight in and start firing at all cylinders – he will feel right at home.
the thing most people maybe are overlooking is the fact that , Ozil has a very impressive track record -fitness wise, stamina wise (touch wood , long it may continue) …. and also the fact that in him we have finally got our 3 in 1 player that we were so missing after RVP, someone who could take decent corners, free kicks and lift the entire team up with a sheer moment of genius or brilliance on his own.
it’s been one hell of a summer for everyone involved with Arsenal but all is well that ends well – this however , is only just the beginning
i can already see a number of players wanting to join us in the next 2 transfer windows ,who may have been reluctant before to do so, simply because now they know that we mean business.
how many marquee signings did Liverpool and Tottenham manage to attract ? no disrespect to Soldado , he’s very good but not SQ – all the remaining signings are a little bit of this and a lot more for the future.
PS: be nice to JGC or else you know you’re in big trouble.
26. ProudGooner says:
bongo,
that would be good, night.
Fair play for coming on here.
27. TotalArsenal says:
Hi PG – no I reckon he will stick with 4-2-1-3 and therefore he’ll need midfielders to play in the ‘2’. Arteta is very suited for this, and I reckon Wenger might prefer to him and Ramsey together as his first choice again. However, Flamini and Jack – FlamJack or WilMini – would be a good alternative for him. And in the really tight games, against BD, Chavs, Mancs etc, I can see Wenger playing Arteta and Flamini – FlamTeta – to keep it really tight in front of the defence. But I cannot see Arteta playing in the hole or in the box to box role much, if at all.
What do you reckon?
28. ProudGooner says:
Every club needs a star player if you area big club. I feel we have a few. I can not wait to see Cazorla and Ozil link up, those two are amazing players and i can see great thing coming from there partnership. Walcott and Ozil also gets me excited.
29. AFC says:
Bongo, in a few years it could be Spurs, Arsenal, Chelsea and United in the top four. Surely the guys who own City cannot keep pumping so much money into the club with no return. Look what happened to Anzhi. I can see City having to sell all of their stars and having to rebuild again like Anzhi. Night mate. 🙂
30. TotalArsenal says:
Bong0-1 😆
Welcome back. Arsenal were more of a team and had the home crowd behind them, and Giroud was the difference and not just for the goal. Other than that, there was not much in it, but I think we deserved the win.
Did you like your new boys and who impressed you most?
31. James Bond says:
Bongo,
since we all like you here, i’ll be honest and to the point
i honestly thought, you were lucky not to lose 5-0 , you have a worldie in hugo lloris.
we are happy with our transfer business, how about you ? do you feel betrayed ?
32. AB says:
Great post JGC. Agree with most you say, and my thoughts largely covered already. Flam gives us so many options and strengthens all our back and mid positions; if he stays fit whilst others recover then I have no major worries about our defence – quite an improvement. I can’t say the same for our attack though. Giroud has started really well and I have great hopes of him for this season. But he can’t play on all fronts and the back up if he is injured is now terribly thin – as it was 2 seasons ago, when an RVP injury (you know, the usual one after a run of about 10 good games) would have left us looking at mid-table. Sanogo may come on really well – though I haven’t seen much sign of it yet; and I do expect Bendtner to be called upon now, which I never thought I would see again! No blame to Arsene from me for this; Ba as cover would have been the icing on the cake of this TW. I’m not sure where Arsene will turn, but I don’t expect him to buy SQ striker in January, but I’m sure he will look to strengthen then in some way.
Welcome Bongo. My overall feeling at the time was a combination of relief, that we had not piled pressure on ourselves at the critical end to the TW, and pride that the team stood up and fought hard like we should expect in our derby, against a team stuffed with expensive names. No doubt in my mind that we deserved the win based on the performance (best individual performance on the pitch was Loris though), but equally I am under no illusions over how much we can draw from this result. It was important for confidence (for players and fans alike), for keeping us up in the table and not letting a significant points gap grow, and to send the right signals to any potential signing who was wavering over their choice.
I have always loved Wenger, though I can’t pretend to understand some of his decisions and wish he would be less stubborn at times. Whilst I can’t claim total confidence in everything that he does, I can’t see a manager I would swap him for given the option as of today. I think he is building for the future – as he has always done. The signing of Ozil is a landmark one, but does not of itself change how we should view Arsene. The TW as a whole I believe has been really smart business, which has changed how I look at our whole squad; as above, the striker situation still looks a concern though. I don’t think for one moment that Ozil is there to appease the fans though – it would not even occur to Arsene to do such a thing. Ozil is like Wenger’s dream signing, all pace, slick movement, perfect technique, vision and intelligence. And he will make our team a more attractive prospect for future signings as well.
So yes, a derby win and some great signings, and all but the perennial doom merchants are happy at our end. I fully expect a real challenge from Spurs this season however. I don’t think too much of AVB, though he has not been as flaky as I thought, and you have bought well; it will take some time though to see which of your new players adapts to the premiership quickly enough to have a real impact, and to work out what your 1st 11 actually is! From my perspective you may have bought too many players, and I wonder how harmony will be maintained in this new squad. I like our outlook better than I do yours – which is as it should be! Are you feeling equally confident?
33. TotalArsenal says:
It was daft/naive to go for a Chelsea player at the eleventh hour, AFC. But maybe it was a decoy for another transfer target. We missed out and will have to do with what we have got. If Bendtner can pick himself up and focus hard, he could still make a big change in his career, but I am not sure he is capable of this.
34. AFC says:
PG, Santi-Ozil-Walcott could end up being the best ‘3’ in the league. Chelsea may have a better ‘3’ in Hazard, Oscar, Willian/Shurrle though.
35. AFC says:
Reports in Italy said we went in for Di Natale but our bid was rejected because their transfer window was closed already I think.
36. ProudGooner says:
TA,
I like all your formations very much, the possibilities are so great. i feel in the very tight and tough games (BD) I would go Ramteta Ozil and Santi Walcott OG and your all out gunn down i would go Ateta Santi Ozilwith in future Podolski OG Walcott
37. AFC says:
TA, Bendy might actually want to play with the likes of Santi, Ozil and the improved Walcott. Besides he needs to play matches and play them well to get back into the Denmark team and seal a move to a decent club.
38. AB says:
AFC. Can’t see Di Natale’s ego fitting into the Emirates?? He seems set to be the big fish in a small pond
39. ProudGooner says:
Or v Dortmund a bank of Rambo Arteta Flemini and your front 3
40. TotalArsenal says:
Agreed PG – those are good line-ups. When we go to Sunderland next we need metal in midfield, so I would go with Flamini and Ramsey (RamFlam) as Arteta will not be fit yet.
41. AFC says:
AB, maybe that’s why we didn’t sign him. I would have signed Lucina Troare on loan from Anzhi.
42. TotalArsenal says:
He can play with his back towards the goal and do link up footie, AFC….so if his attitude is good, it could work.
43. TotalArsenal says:
Di Natale is one of my favourite players outside Arsenal. A gent and super-talent, but I cannot see him ever leave his club Udinese…
44. AFC says:
Too bad we couldn’t sign him. I think Wenger saw him as a short term option. I doubt he will go back in for him unless things are really bad.
45. Highbury Harmony says:
46. ProudGooner says:
I totally agree Total Arsenal,, you could even play it cleaver in the CL with the gun down midfield to start and score early away goals then close it out with Ramflem and Ateta.
47. Highbury Harmony says:
Not sure if the comment’s been made yet, but Maureen blocked the move for Ba after he found out we had signed Ozil. He believed that we could win the title had we have gotten both Ba and Ozil…
48. TotalArsenal says:
Off to bed now, guys – catch you tomorrow. 🙂
49. AFC says:
I like him as well. I think he still has the pace as well. Klose would have also been a good short term option.
50. ProudGooner says:
Night TA, I will have to get my head down soon as well
51. AFC says:
HH, I beat you to mate. 😉
Maybe Wenger should have went in for someone like Klose. A real legend who could have given us that structure and experienced in attack and he knows Ozil.
52. James Bond says:
hi HH 🙂
do you blame, Jose ? i think he’s one mean son of a gun – love him or hate him, but no one does mind games and tactical battles like he does.
never mind though, then there was January.
53. AFC says:
HH, which line do you think is better?
Santi-Ozil-Walcott
Willian/Shurrle-Oscar-Hazard
54. ProudGooner says:
BA is good, but he is style is very much like OG but OG is better, i am sure the club are working very hard on Sanogo at the moment and i feel he is going to be a fine player. If that comes to be , we are bang in business.we still have walcott anyway but that is dependent on Ryo stepping up and doing the business on the right wing all of which i think can easierly happen
55. AFC says:
PG, that’s probably why Wenger wanted Ba. So we do not have to change our tactics much is Giroud cannot play for some reason.
I’m off now. Speak to everyone soon. 🙂
56. ProudGooner says:
AFC,
True and night, im off to bed too. Goodnight Gooners
57. GhanaGunner says:
Great post JGC!
I don’t think many gunners would’ve been upset if we had been told at the start of the transfer window that we’d sign a CF, AM, DM who can also play across the back four and a GK. That’s exactly what we signed. It’s probably the stature or, if you will, the Presence! of the players involved that may leave some wondering. That plus injuries to the like of Poldi, Ox, old lego hair and the Verminator have left us a bit short. Just wait till they come back! We probably could’ve done better than Sanogo but then again, see what a surprise the Ox was. Flamini is a good signing in my opinion and as far as keeping Szczesny on his toes I think Viviano isn’t a bad bet either.
One of the ideas that really excites me is the influence Oz could have on Zelalem and Eisfeld. Imagine them learning from one of the best in the business! Zelalem already showed he has the potential in preseason and I hope he gets a lot of time on the training ground with Oz and Santi (who couldn’t make the tour due to having competed in the confederations cup).
I liked TA’s suggestion of Wilshere on the right wing with Theo in the center if Giroud can’t play. Allow me to also offer some fantasy formations (the back four just about picks itself so I’ll be leaving them out for now).
………………………………Ramsey/Jack/Arteta…………..Arteta/Flam……………………………………..
Theo/Ox/Ryo/Oz………………………..Oz/Santi/Arteta/Rosicky………………….Santi/Poldi/Gnabry
……………………………………………………Giroud/Poldi/Theo………………………………………………
I think if at least one of Arteta and Flamini play it’ll free up Jack or Ramsey (or Rosicky?) to make more runs into the box. With Arteta and Flamini playing together Arteta would be free to distribute without worrying too much about defense (not that it seems to have slowed him down any 😀 ). We also speak about Oz playing mainly in the AM position but I’d like to see how we fair with him on the right, Santi on the left and Arteta/Rosicky in that AM position. We’d have great creativity and great passing right across the field and I’m sure Arteta would be able to pick out any runs the other two may make into the box. Some mouth-watering prospects we have there!
58. AFC says:
Just heard that Wenger is working hard to keep Mertesacker, Sagna and Rosicky. All three will be offered new contracts. Now I’m gone.
59. GhanaGunner says:
Btw, Lewandowski is a free agent next summer. Any chance of us grabbing him in the January window? I’m sure Dortmund would much prefer him with us than with Bayern!
60. henrychan says:
Top post JGC..
Don’t worry about our CF.. Giroud will do the job greatly.. The Godzilla ( Theo – Giroud – Ozil – Cazolla) will ruin all enemy.. hahaha.. and We still have Bedtner.. Wenger know how to deal with him.. He will become our supersubs..
Bond.. it all because he was injured.. hehe.. if not.. Vermaelen will be at Barca now.. Barca’s fan still upset for the club can’t get a new CB.. hahaha..
Oh happy day.. oh happy day….
61. Milo says:
Anyone wonder why Jack has been playing better for England lately, than Arsenal??? even that one half he played against Scotland, was better than anything he has produced for us this season 😦 I was really hoping this would be his year, and it still could be. IF Ramsey can keep up his work-rate, and improved defensive nous, I would be confident in trying Wilshere in the box to box role next to Ramsey, in most matches, with Ozil ahead of both of them. So it would be 4-2-1-3, with Ramsey and Wilshere in the two and Ozil playing in the hole behind the striker and wingers. What do you think??? I think, if fit, Wenger will do this, as he knows that developing Wilshere in to that all-conquering force, will be the final piece to the puzzle for us, in our starting eleven. What do you guys think???
62. Highbury Harmony says:
AFC, easy Santi-Ozil-Theo. No one in the world can compete with that three. There’s a bit of everything there 🙂
63. Highbury Harmony says:
JB, I do not blame Maureen whatsoever. He was smart in not letting Ba go to us. Who gives away players to rival clubs? Oh wait…
To be honest, if you asked me if I would take back the sales of RVP, Na\$ri, Cole etc. opposed to having Ozil, I would say no. I’d do everything we’ve done the past few years the exact same way every single day of the week and twice on Sunday if the suffering means we are now where we are, with players that genuinely want to play for our club.
64. Highbury Harmony says:
Jgc, absolutely brilliant post mate! I thoroughly enjoyed your entire article and agree with your analysis. What defines a “perfect” transfer window is entirely subjective and you have done a very fine job of explaining and defending why you believe we had a perfect TW.
I’m of the opinion that anytime you can buy a top 10 footballer in the world, for what I believe to be relatively below market value, that you have had a perfect TW. I still can’t believe that Ozil will be playing for us in another week and a half and let it be the start of an even more beautiful future for our club!
65. JM says:
Santi Cazorla, Mesut Oezil, Theo Walcott, Olivier Giroud?
Andres Iniesta, Cesc Fabregas, Neymar, Lionel Messi?
Gareth Bale, Cristiano Ronaldo, Angel di Maria, Karim Benzema?
Franck Ribery, Thomas Mueller, Arjen Robben, Mario Mandzukic?
Marco Reus, Henrikh Mkhitaryan, Pierre-Emerick Aubameyang, Robert Lewandowski?
Ezequiel Lavezzi, Javier Pastore, Edinson Cavani, Zlatan Ibrahimovic?
66. henrychan says:
@JM.. I vote for my The Godzilla.. Theo – Giroud – Ozil – Cazorla.. hehehe..
@HH.. Agree with you.. plus Ramsey and Arteta as our double Pivot.. and Gibbs – Kosc – Merte – Sagna as our fantastic four.. We will win the PL.. hahaha..
If only we sign Cesar.. then we will win the CL also.. hehehehe..
67. jgc says:
All,
OK early bedtime for me last night … now on to replies to some great responses:
TA: Thanks for the kind words, I think the lineups you show are all possible and one could even go very defensive when healthy with a 4-3-1-2 of :
Sagna Per/Kos Gibbs
Arteta Flamini Ramsey
Ozil
OG / Theo
Also useful if resting Santi! Really a 4-3-3 but the top 3 is an inverted triangle..
One could invert that top 3 to be
Ozil-Santi
OG
To rest Theo and so on..
I am very much looking forward to how we respond to Marseilles and BD! That will be the real test..
More later or next reponse
— jgc
68. Prince says:
😆 😆 😆
This got me laughing. “Soldado looks like Almunia on crack”……… 😆 OMG 😆
Great posts in the last few days. Hope your all well 🙂
69. VCC says:
Prince..that tickled me too. I love those videos.
70. VCC says:
71. Prince says:
Morning Vickers,
I had a dream! If we are in all 4 comps in January, Arsene will pay over the odds, and OUTBID Madrid for Suarez. The final piece of the jigsaw puzzle, our plan A, or plan B (if you prefer Giroud) and we will win Big Ears and possibly snatch the EpL flag on the final day……..without the use of lasagne. I know it seems far fetched :roll:, but in my view it his him that could take us to immortality. Arsene knows this, ALL other rivals are in transition and it would be a shame to not strike while the iron is hot. He is a top target of Arsenes and the only top striker who will not be cup tied in the Champions league.. Maybe, just maybe, Arsene takes the dive in his last hurrah and actually achieves the unthinkable. Wishful thinking? I hope not, lets smash the transfer record set for Torres, whilst Madrid are in a financial slide at the minute and all our rivals are yet to gel.
72. VCC says:
BUT, I would prefer Lewanowski. His contract runs out next year, perhaps we can make a cheekie bid in January.
Loving these videos.
Bring it on.
73. jgc says:
TA nd others on ST
Well we do have NB and Theo to fill in.. Pod eventually.. Or Sanogo for league Cup..
One thing that has changed in 2+ days since writingis my thinking on NB. He *will* likely play some…
A motivated, fit Dane, having worked there, is hardworking, tough and impossible to keep away from targets. Unfortunately, as we know, if they arent motivated, just give it up..
If he gets motivated, he could still be become the ST AW likely thought he was and that he actually was when he cared to try…
He *COULD* turn it all around, and one can only hope that all the turndowns he got were finally enough to make him realise that no one valued him like he did, and perhaps he oughta pull finger as it were…
So, if Theo, Pod (already gone) and OG are out… and it isnt League 52 team in the League Cup (Sanogo) I think you will see NB… Hoppe it doesnt come to that because we will have enough trouble as it were
That said, January comes soon, and after we tie up our defenders a bit (one saw your post AFC), we should be good to go work on that, and I think one will likely be avialable..
cheers — jgc
74. Alcide says:
Hahaha that video is hilarious 🙂
Nice post NFC, it’s nice to have a fully optimistic view of things. I thing that like a lot of fellow gooners, We are just starting to fully realize and understand the full extent, meaning, potential and wide ramifications of Ö’s move to Arsenal. Hüge, and as our fellow Germans would say, über.
75. geoffchase says:
AFC and PG
I agree that Bale will sell shirts for RM like, as AFC told me yesterday, Ozil is already doing for Arsenal!
So, yes, financially good enough that way.. especially via image rights and endorsements with whatever deal they worked out. I was really only referring to a player only aspect, but your point is good and I agree
Equally, surprising tho given RMs financial strength in various sales that they still sold Higuain and Ozil. They could have stockpiled like an Oiler… Wonder why not?? Could be some cracks in the foundation??
cheers — jgc
76. geoffchase says:
Dylan,
Per my above, NB will play if he gets motivated enough I think.. He *COULD* be great, really great, which is the frustrating thing about him and makes it all so hateful. On talent, there is no reason his 50k pw wages are anything but a deal, on mental strength and desire hes worth abuot 5k pw..
I think most clubs know that if AW couldnt get it out of him they might very well not either..
time will tell
Regarding Cesc, youve heard me for weeks say that if he was THE guy plunk down 50m and see. Instead, we did 43M and got Ozil (also very good! 🙂 ) .. And, per my post, he will be equally THE GUY to make it all happen.
The hard question now is in January or summer 25-50M on SQ striker or Cesc (should such option be out there at all and Cesc is starting well at Barca it seems)..?? 😈
Unfortunately, if you will, the obtaining of Ozil means we are less needing of a Cesc, tho nice, than DM or ST
cheers — jgc
77. Prince says:
Cup tied in Champions league Vickers!
Its gotta be ‘the toothed one’. If our results and position prove that we can win the EpL and have a favourable tie in the knockout stages of the CL (of course we qualify from the group stages with ease) then i think he might bite (excuse the pun 😉 ) He knows that Stevie Mee is finished and in Ozil they could take their personal games to “ballon d’or heights/levels”. Its not a pipe dream when you think about it. We have proven that we are willing to pay over the odds and break any transfer record, what Arsene is not willing to do is break our wage structure. I believe that both Arsene, Arsenal board and Suarez would be happy with
150-170,000 pounds per week wages for him (if the above ingredients are in place) whilst recognising what he could bring in, and that is:- a double on the pitch, EPL and Champions League.Off the pitch our stocks would only rise. Look at the Ozil deal, the whole world is talking about us. Adding Suarez would get every kid worldwide buying an Arsenal replica again.I’ve got my fingers crossed that Madrid fail and get knocked out early and that come January we are a length and a nose ahead of all our rivals.
Just so you know, i too rate Lewandowski highly, and there could be a sniff of him joining, if it is linked to Klopp joining later down the track…who knows? But, seeing as he will be non-legit, i see that as a summer target if, IF Suarez fails in Jan. The Suarez deal will be dead if it does not materialise in January imo.
78. geoffchase says:
TA
the king of assists … well said, I think my overall philosophy going back this summer to my desire to see Cesc back is that
— Strikers score goals only AFTER they get chances. Chances are created by creators (i.e. assists)…
I think I felt that while we could do better as a team with a SQ striker that a SQ creator would do far more for us with what we have than a Suarez (who is a great scorer all else aside)
This is my overall philosophy in football to an extent which means I prefer what we got, a “nuggety” DM and SQ creator wiht a competitive streak.
cheers — jgc
79. Alcide says:
80. geoffchase says:
Bongo,
thanks for stopping by… my quick thoughts
1. AW never left his best! 🙂 … This is a major strengthening and not a sop to fans, tho some sites make it out that way.. Or so my post would have me believe! 🙂
2. I was *VERY* worried about the derby and your new players, offset slightly that they may not gel as yet
3. I think Lloris kept you in the game, especially in first half where a second goal would have done it… He also saved 3-5 (dependng on your PoV 🙂 ) almost sure bets, versus Scez saving 1-2 for us.. So, 1-0 seems a fair bet and good day for both GKs
Later you note that someday it would be interesting to compette for the league.. I respond:
Why not now?? We both have the players and shot. The real question for Spurs is do they have a lot of solid/very good players and a plan, or just a lot of solid/very good players without a plan. Ie will AVB pull it together right and are they the “right” pieces to fit together??
cheers — jgc
81. geoffchase says:
PG
If AVB wants to play as well, all power to him.. I like a little passion from the coach.. Shows he respected the derby!
cheers — jgc
82. geoffchase says:
JB, AFC and PG:
Actually, I think Ozil will land feet first and running, but hedged my bets! 🙂
As I noted, or tried to, defenders and creators (in that order) bring most of their value via their physical skills with the least reliance on others to succeed in their jobs. Thus, they are the lowest risk to fail.
Strikers are at the other end of the spectrum, Suarez for example, with no service into the final third or all aerial via Stoke or WestHam approach would score far far less..
I agree many will now want to come join our club for the service that willl be on offer.
For AFC and PG: Could be that getting Ozil and that service makes us way more attractive to a top ST than before? they may look and say, “look what he did for CR at RM…” and decide they want that here..
Equally, I think that pursuing the ever more desirable girl at the dance (Jovetic – Higuain – Suarez) left us out of dance partners at the end. Perhaps bad strategy but if we had landed Suarez (and Ozil?) we’d be dancing in the streets (wearing bite proof shoulder pads, which is to say I am sort oof glad we didnnt get Suarez despite what he would have added)
Just a few thoughts.. cheers — jgc
83. geoffchase says:
AB
Per my comments, I think NB will play (despite what I said in my post) and that we do have good options up front if OG isnt around, NB motivated being a very good one,
NB unmotivated will likely get Flamini’s boot stuck up his ass, and word has it that Ozil is not the most patient sort with unmotivated either.. Could be good for the big Dane! 😈
cheers — jgc
84. geoffchase says:
HH and JB, and TA/AFC
Thanks for the kind words.. I think it was as close to perfect or close enough as you know.. Equally I think we were in for Ba earlier and Maureen being himself waited and made a strategic decision.. So, it goes..
The TW is like a big wave, to be ridden, gracefully if possible, but never over powered or mastered. Those who claim it are just taking credit for a very good run (of luck? or money?).. IMO..
cheers — jgc
85. geoffchase says:
JM
Your list of formidable front fours is outstanding and good to see us in that class!
I think we have more experience than several and only think this:
Barca – Neymar is young, else they are BArca
RM: more talent and experience, but more egos, dissension?
BM: I think we equal them
BD: has new pieces so… we can certainly compete
PSG: could be best of the lot but egos and how will they fit together
cheers — jgc
86. henrychan says:
hahahahaha.. Prince.. two thumbs up..
Who make all this video..?? hehehehe..
I love it..
87. geoffchase says:
Prince and VCC
I personally am still unsure about the Biter.. not hs talent but his other talents… But Lewandowski… hmmm 🙂
Think he could be persuaded from his BM dream? We have an increasingly German spine with Per – Ozil – Lewie?
cheers — jgc
88. geoffchase says:
Prince
That Downfall video has been shown about 1m more times than the movie. There is a versionn for almost any job, occupation, event! 😀
Classic that it is out so soon!
cheers — jgc
89. geoffchase says:
Milo
Re: JW: I wonder if he doesnt have far greatr expectatioons on him and within himself at Arsenal then for England.. PErahps that is why he plays better for England (if he does, I am not so informed on that)??
cheers — jgc
90. TotalArsenal says:
Morning chaps 🙂
I am convinced Wenger wanted to fill the hole position with SQ in order for Jack or Ox to have time to develop into a nr10. He considered the Muncher and Granny Lover but ended up with the best pick of the bunch, in terms of a perfect fit nr.10.
So for me there will be no Suarez or Rooney any more, now that Arsene has his toad in the hole (another Glicism 🙂 )
The next key player to sign is another striker who can replace (when required) or improve on Giroud.
91. TotalArsenal says:
I am loving the avatar, jgc – Presence!
92. TotalArsenal says:
hahahahaha ‘don’t cry we have Lasagna for dinner/supper’ 😀
93. VCC says:
Prince…geoffchase.
I hear what you are saying about being champions league tied for Lewanowski, but I would still prefer him to Suarez.
It would definitely be the icing on the cake.
I’m thrilled to bits about Ozil though.
Can’t wait to see him perform in that wonderful Red n White kit of ours.
Bet there isn’t an empty seat in the stadium the next home game.
Bring it on.
94. TotalArsenal says:
JM at 5.10 cheers!
I love it you left the Chavs out of your super-line ups 😆
95. TotalArsenal says:
Excellent comment GhanaG and agreed on Eisfeld, Zelalem (and Gnabry!) learning a lot from Ozil Smozil 🙂
96. TotalArsenal says:
Bring it on VCC! 🙂
97. VCC says:
Hi Ya Totes.
How is Henry? Is he fully grown yet?
You will have to pull your socks up in the UMF, your almost as bad as GLiC. lol
98. TotalArsenal says:
VCC – Henry is not so good. We went to the Animal Health Trust this week to examine his eyes and unfortunately he has cataracts in both eyes which are causing him reduced vision and related problems. His retinas are also not in good shape; basically his eyes are too small… He is too young to operate and we are hoping things might improve/stabilise, but it is not looking very good for the poor chap at the moment… 😦
99. 17highburyterrace says:
Morning boys…Up early today…
Total, very sorry to hear about Henry (pronounce On-Ree, I assume…) Dog health is a biggie…Ours continues to hang in there (in miraculous fashion) but she’s hardly a shadow of her former self…Where’s Gerry on this topic?…
I’m all caught up on my reading (Geoff’s post, comments, other blogs) but I need my coffee before getting into it…In the meantime I’ve got a question…
From the early photos of Ozil (including the one at the top of this post) I must ask: why is (injured) Lukas Poldolski with the German team? Is he healthier than we think? Is he helping do our business? Maybe he was also talking with Schalke? Does anybody know what happened with the younger German (Draxler)? Bond had promised us two Germans and two record breaking signings… Don’t get me wrong, I’m over the moon getting MO11,,,Just curious really, and wondering if there’s a story there. Given our lack of signings up front, Poldi on his feet and smiling is a nice thing in and of itself…
Inquiring minds and all that…
Cheers!
100. James Bond says:
he’s getting checked out by one of the best doctors in the world @ 17HT
he wanted his opinion on it, went with Arsenal’s blessing, if you know what i mean ?…he is suppose to be resting for 2-4 weeks , the wound heals and then he comes back to light training , rehab and so on,
he wasn’t the only player, even schweinsteiger consulted him – it’s normal practice, some players feel more comfortable with certain doctors/consultants
and i don’t blame them for not trusting Arsenal’s own medics.
besides, The German’s look after their assets rather well , considering it’s world cup year and they would need to know what’s going on and take their own assessments and so on – which is normal.
yes – that one is not dead the D, deal.
101. James Bond says:
JGC, wrote “we’d be dancing in the streets”
who is to say that we might not be doing that later on in the season ? the session has only just begun , another 2 transfer windows and we might well be doing that for sure, and not just on the streets either 🙂
102. James Bond says:
ah, and it’s normal for a player to return back home once they have a long injury, Diaby only just returned from France as well – considering the amount of time Poldi likes spending in Germany and Twitter, there is nothing to worry about re- Schalke, not just yet anyway
it’s normal practice really – and even better now since we know that the injury won’t be taking 6-8 weeks and could potentially stretch to 12 weeks.
some fantastic videos posted today, loving them !
103. geoffchase says:
VCC and TA
Actually, I want Lewie, not the Muncher as TA calls him…
It will be very interesting to see how Giroud goes. If he gets more than 20 EPL goals this year and Theo is at or around that number it will be harder than ever to justify SQ at ST, and more likely, IMO, to go for a solid backup (back to Ba or similar)… Then, I’d see the SQ coming at DM… also a good choice! 🙂
cheers — jgc
104. Prince says:
17ht, morning/afternoon?
Now, you enjoy your espresso in the smoky haze 🙂 Im currently on a diet of ‘horse placenta’ (its the latest craze), that and helping my mate MO11 get the low down on all things Arse. Per is also hanging roundn about and we’re all trying to tap up Draxler and Reus to join the Arse.. “Usss Germans arr invading London, und in ze name of Arsenal und ze ‘elp of ze British korrrrr, vee vill rool ze vorld und viktoreee in ze Evropa!!!!”
Vickers, Geoff/Cheers-Jgc,
Each to their own on the striker front i guess. But if Suarez was a green light in Jan and it guaranteed us a major trophy (EpL, CL), as opposed to Lewandowski in the summer on a four yr contract with only 3rd place to show for the patient wait…..which would you choose?
Suarez would justify the sale of Van Judas for me, it would also justify a fair bit of our actions in the transfer window…Oh, another factor is that, by next season i expect every team to improve on where they are now. Maybe we wont get as favourable position next season to strike. “The early bird gets the worm” springs to mind 🙂 Its all hypothetical in the end and depends on where we stand in January, where Real Madrid sit in the Champions League and, do Liverpool have a decent shot at the top 4 at that stage?? Apart from that, its all a matter of opinion i guess eg I dont rate Di Maria as much as others, yet he proves me otherwise. Oh, also, while im ranting…….again 🙄 If not Suarez than a similar player to execute the same play, and that is to chase all of Girouds knock downs and play on the shoulder of the last defender. Chikarito could do a job, but pointless if he is cup tied, Walcott could do it……..ooh i cant wait till Pod an Ox get back. So many combinations. haha
105. geoffchase says:
GhanaG
IMO, if Ozil rubs off on our young’uns (Gnabry, Eisfeld et al) not to mention young starters (Theo, JW et al) then we benefit more..
cheers — jgc
106. geoffchase says:
TA and Henry
IMO, Aaron is achieving his original promise, as well all agree, I think. However, what I think it shows is just how long such a recovery takes. Credit to AW to staying the course and to AR for being so steady about it all…
Equally, if he comes back 100% as it seems he will, AR will actually, IMO, be better for it. The mental strength and confidence gained from that journey will make him *even better* than he might have been. Again, all speculation on my part, but..
cheers — jgc
107. geoffchase says:
JB
I am an optimist! Happy to “dance” at slightest provocations! 🙂
cheers — jgc
108. geoffchase says:
TA
sorry to hear about Henry… tough for the kids too I suspect!
cheers — jgc
109. TERRY MANCINI HAIR TRANSPLANT says:
Fine stuff Professor
You sure get the old brain cells working. Your analysis reminds me of my last year Accountancy exams, bloody hard. hahaha
During one of my papers i was so stressed i had a fit. The table and chair went flying as i ran around the exam hall stripping my clothes off and yelling “Women for Terry, Women for Terry”
As ive said before, i am very pleased with the transfer outcome. I am very much in the Bondy camp, believing this is only the beginning.
Arsenals future is fantastic and i am very excited about it.
The Ghosts of the Thirties are Stirring
110. Prince says:
Can you imagine how long and tedious and depressing this interlull would have been had we failed against the Spudz. The MO signing took a bit of the shining off the win, maybe? Kind of like the suckers who have their birthdays on Christmas….
Still, feels f**king awesome to be a Gooner right now!!!
Enjoy, one of my favourite clips 🙂
111. Prince says:
Hi Mike 🙂
Do you believe Arsene will sign on or does he believe that now we are seeing daylight, his job is done??
112. TERRY MANCINI HAIR TRANSPLANT says:
Very good question Princey, of which i do not know the answer. hahaha
My gut feeling is that he will sign a new one and that it will be his last.
Personaly, i would like him to stay for ever. But i once said that about my ex wife, so who knows.
113. geoffchase says:
Prince,
Re: AW … I think that AW has always been extremely logical, and from that angle the outcomes to your question might be
a. he will re-sign for another term because he likes his job and being logical he understands the fans but truly doesnt let them bother him while trying to keep them happy by winning (and not much else to keep them happy that doesnt involve him trying to win and do as well as he can). I may be one of the only people that likes him for this
b. he will leave the club because he is tired of coaching. I dont see him going to a PSG or such because, being logical, he knows his whole career was made at Arsenal, and everything else will look and feel like an asterisk afterthought. The only change I could see was if he didnt want to coach at the top level anymore he might go to lower Ligue 1 or Ligue 2 “for fun” ??
IMO, either way, like SAF, this is his place and when he leaves it will be for calling it a day..
I would like to see him back myself. I think his competitive drive wants a CL trophy (like most of us, right? 😀 ) … and he appears to be now coming into the players and resources to build just that and have the first serious go in some time.
that’s my call, perhaps I should add it to the predictions page! 🙂
cheers — jgc
114. Prince says:
Terry 🙂
How good has your gut feeling been in the past? I hope Sanogo can impress him enough to sign a 1 yr extension, every year for the next ‘X’ amount of years, so long as their is harmony at board level and in the terraces.
115. geoffchase says:
TA and Terry,
TA, the gr(avatar) was drawn for me by a student. I always tell them to put something on the final exam for every question, so if they have no clue and want at least 1 mark, a highly realistic drawing of my extraordinarily fit and handsome self will do.. I got this in A4! 🙂
Terry and TA, the above story is 100% true, unlike I suspect small parts of Terry’s posts (and Glic’s)… If only because I tried to find Lesbania on a map on line and it kept asking if I meant Lebanon! 🙂
cheers — jgc
116. AFC says:
JGC, just a quick question on presence for you.
Does there come a time where physical presence (in midfield as an example) is no longer needed?
If you have players in the midfield who have excellent technical ability you can surpass the need for physical presence. Using Barca as an example, if you was to take Sergio out of the team and put Pirlo behind Xavi and Iniesta (none of who have physical presence) they would still be able to run the midfield against any team while the team taking on the defensive responsibility collectively which Sergio would normally deal with as a team.
117. 17highburyterrace says:
Haha, thanks Bond… I guess what you’re saying is that we’re still tapping up young Drax (or keeping him “on loan” at Schalke…) Thanks also for the info on German doctors…
Also, very good to see PPP back at it and having fun…That terror window was too much stress and I’m so glad it’s behind us. The 1-nil vs Spuds allowed a little steam to release…The Ozil signing (for me, at least) means each match is not (absolutely) life or death. Finally, we have a measure of relief…
As such, I think our TW business was good. Our situation is soooo pressurized (due to the gulf between reality and expectations) that it’s very difficult for young talents (i.e. Bender, Draxler, etc.) to slot right in. I still can’t believe we scored Messy, but he’s the sort who WILL play from the get-go AND make an immediate impact. I’m positive that AW telling him we’d build our entire offense around him was a huge reason the deal went through. I’m still surprised that it happened given all the consternation in Madrid…Gutsy from Ancelloti and Perez, and they may pay for it, if Barca stays on top…
At the end of last season there was plenty of debate about how many signings were needed, and (no surprise) there were a couple schools of thought. The guys who like competition/quality in depth at every position (too much FIFA playing, I say…) were saying 5-6 signings. The other end of the spectrum wanted only SQ while many settled in the middle, trusting that AW would come up with the right mix of depth and quality. I remember arguing that it was about building upon our gutty (if eye-gouging) run-in, rather than a complete revamp…
Torturous as it was, I believe this is what we’ve gotten. The bottom line is that while Giroud is no RvP and Theo looks best starting out on the touchline a creative player rather than a pure #9 was our biggest need. Nobody wants to say it, but young Jack is not there yet. When fit, the potential is mind-blowing, but there are parts of his game that still need work and fitness is a real bugbear…Ozil solves this conundrum though the two should be able to play side by side. Another left footer cannot hurt Jack…
I have yet to write my “I was wrong about Ramsey” post…and I’m still not ready. Yes, he’s been impressive thus far and in many ways has carried the club (or at least has helped in a very big way) to this point. His running is an inspiration to his teammates, no doubt, but there’s still too much wasted energy and end-product. It’s good to see him already getting on the score sheet but I’d have traded the two vs Fenerbache for the one glorious chance vs Totts that he put into Row Z… With Flamini a rock at the back, Arteta (hopefully) fit soon and Ozil in, AR16 (and Rosicky) may suffer a loss of playing time…With the CL group games (which he helped secure…) we’ve got plenty of matches, however… With everybody fit and in the biggest matches I’m not sure he’d make my team-sheet. Still, what a boon to the team and all our MFs should know that if they don’t give 110%, Ramsey will…
Enough…for the moment… 😆 😯
118. TERRY MANCINI HAIR TRANSPLANT says:
Princey,
I am renowned for my wrongness. I once had a hoard of Gamblers asking me for tips so they could bet on the opponent. I like your 1 year extension idea r.e. Sanogo, Wenger could be around for ages. haha
119. 17highburyterrace says:
AFC, that’s a great question! (And although you asked the professor, I’ll step in, sorry 😆 )
I think in Spain it could happen…In the CL it depends…Sometimes the reffing seems more “continental,” in other years more English…In England, the mania to “keep the game moving” means that contact–serial fouling–is a legitimate tactic and MFs have to get used to it. Players like Pirlo, Xavi, etc. have so much experience that avoiding tackles and knowing when to go down for a whistle is instinctive. They also know all the refs so well… Arteta is almost there and Santi is learning fast. Our younger guys (Ramsey and Wilshere) are learning too. IMO there’s no reason for Ramsey to get his leg broken again (or Ox to get hurt on a middle of the pitch 50-50) We need to control matches through passing (keep-away triangles, tiki taka, call it what you will) rather than running away (with the ball) from the galoots. With Ozil we now have a key piece to the puzzle…
120. 17highburyterrace says:
Prince…I really think the English clubs will not be doing much selling to one another, so no Suarez in January…As always, of course, WTF do I know?…And, of course, if ‘Pool suddenly go south and Suarez is getting red cards (or otherwise protesting) and Madrid don’t need him, you never know…Still, selling your best player to a “rival” is like waving a white flag of surrender. We did it with RvP, but those days (we pray…) are behind us…
Overall, IMO, we’re building but it’s gonna take time. Fingers crossed that our big fella stays fit and that Sanogo starts looking good in 15 minute cameos or in the cups. Likewise about Poldi and Ox coming back soon and strong. Benteke isn’t cup tied in Europe…
121. geoffchase says:
17 and AFC
I will add to 17ht’s response… I think the Euro reffing helps a bit and the fact that more teams run a bit mmore directly in the EPL on attack means a beast can clear space. That physical presence isnt just “hurt” it’s also fear of ball loss. Slows the game down etc..
I think Barca gets away with it for two reasons
a. they are so good at tiki-taka when the hell does the other team actually get the ball. Teams that do get it and run at them found good reason to succeed last year. Witness how easily both they and RM (also a bit lacking there) wennt out to the Germans in the semis of the CL
b. Barca do have Busquets (is it) just behind who is more forward as a defender and has that presence!
cheers — jgc
122. AFC says:
17ht, thanks for the response. Anyone can reply. 🙂
I will continue to use Pirlo, Xavi and Iniesta as an example. All three are not particularly fast (Iniesta has a bit of pace), strong, or have that drive which players like Wilshere or Yaya have but what they do have are countless years of experience and have been playing together for years and have formed a really good partnership in the case of Iniesta and Xavi. They are old and wise (generational talents) who would not be affected by opposing players trying breathing down their neck and tackling them. Pirlo and Xavi and to a lesser extent Iniesta will take the ball if they are marked.
They know how to avoid tackles as you have said and how things work with the refs.
So which midfield would come out on top and which midfield would you prefer to have:
Option 1: Xavi, Iniesta and Pirlo. As you can see there would be no real DMs or Ams. Just all three interchanging positions throughout matches.
Or
Option 2: Sergio, Vidal/Yaya and Ozil. Sergio as the DM. Vidal or Yaya as the box to box midfielder and Ozil as the AM.
123. AFC says:
JGC, my last comment to 17ht is also for you. When deciding which option do not take refs into account.
124. geoffchase says:
AFC
Hate those questions… reason is that when I select teams I do it for the opposition, not the ref anyway… So, if the oppoent parks the bus I want Option 1, all finesse… if I am going against equal and direct opponents (the Germans say! 🙂 ).. then Option 2..
cheers — jgc
125. Prince says:
17…..No Benteke is not. He is currently in form and very strong like Giroud, maybe quicker even. But im looking for something different. Remember when we were playing Arshavin up front and before we got Chamack everybody was calling for a tall striker, some height, a plan B. Then last year with Giroud, he was put into that category B by a few people. Well i dont put him in either A or B. Currently we have him but no other option, no other alternative in style to him. What happens on those days when Giroud is misfiring or in games where he is playing well but more often than not isolated. For me it would be a crying shame if we get to the Champions League semis only to see Giroud have an off with no options on the 68th min. Ive changed my mind on Poldi playing up top, he has lost a yard of pace and i cant see him playing alone…
126. geoffchase says:
AFC part 2,
Hence my excitement about both Ozil and Flamini at opposing spectrum ends. With our existing corps there (and ability to use some to cover ST if needed) we can make a **very wide** range of midfields to suit any opponent that doesnt take us out of shape, BUT, does let us play very different games as they come at us
Thus, depending on opponent, place and opposing players we can look all defensive and counter-attacking (Arteta, Flamini, Ramsey, Ozil, Santi) or all attacking (Arteta, Ramsey/Ox/Pod, Ozil, Santi, Theo)
Hard to get Ramsey out of there with his current form..
cheers — jgc
127. geoffchase says:
AFC
or ultra defennsiely, Gibbs in foor Santi and we could park the bus with Ozil and OG to counter-attack with some B2B running by Ramsey and Gibbs..
I never expect to see that from AW by the way.. he’s a go down swining type! 🙂
heers — jgc
128. AFC says:
JGC, that is why I said do not take refs into account when answering. 🙂
So I’ll put this question to you and everyone else. Let’s suppose there are no refs in this scenario. 😉 Maybe this scenario is taking place in training.
Midfield 1 (of Xavi, Iniesta and Pirlo) comes up against midfield 2 (Sergio, Yaya/Vidal and Ozil.
Which midfield comes out on top to win the battle?
129. geoffchase says:
… go down swinGing type… sigh… jgc
130. AFC says:
It is good that we have so many options and variables.
Another teaser for you.
You can only have one of Lewandowksi or Fabregas.
Would you take Fabregas and play Walcott up top with Ozil, Fabregas and Santi behind or would you take Lewandowski and play him up top with Ozil, Santi and Theo behind?
131. geoffchase says:
AFC
this is one of those Russia vs China cold war things.. the answer is casualties! 🙂
I think midfield 1 could hold well but not defend well if they lost the ball… which always eventually happens.. I myself in coaching have played both styles when necessary.. but, I have to say I always prefer one person who can be counted on to go get the ball if/as required … Right now for us that is Ramsey it seems and maybe Flamini now as well.
Thus, for me midfield 2… but, I dont know if they’d win.. I am also assuming since it is training someone would be upset if someone else’s leg got broken! 🙂 so, not trying to foul either..
cheers — jgc
132. geoffchase says:
AFC
Lewandowski for me, he fits the need we have now better than Cesc.. Sad to say it, but you know for weeks I said, just plunk 50m down for Cesc and see if Barca sold.. Id be just as happy now too.. and asking for Lewandowski over Ozil..
All else equal and both avilable for the same money
cheers — jgc
133. James Bond says:
ah, sorry, missed your earlier comment @ Henrychan
blessing in disguise ? nah, i actually think TV wanted to stay and prove a point – the big hint for me was when AW said, that he would still be our skipper and we value him, that was the confidence he needed really
i believe, any top team must always have at least 3 top notch defenders, which we do
i am hoping a lot of good things from our skipper, especially if he can replicate his earlier promise, bombing forward and having a go at goal e.t.c e.t.c hopefully, he would be more hungry and more organised at the back as well now – less panic and more calm
it’s funny how i was writing this comment and i had a flashback of him gifting 2 goals on his own- first gift was to his pal RVP and the other one to his older pal Suarez – such school boys errors, hopefully are a thing of the past when he comes back (he’s close to a return).
134. James Bond says:
i know i said i won’t be taking part in the transfer speculation and so on,
but sorry to burst everyone’s bubble – Lewandowski is going no where other than BM – why do you think BM, haven’t strengthen up front ? they only have one decent Croatian striker , no ?
i will be very surprised , if he ends up else where – not going to happen in my opinion
futile to even think about it, certain players will always want to be playing for certain clubs – gotta respect that and accept it.
135. 17highburyterrace says:
For the discussion with AFC and JGC (Geoff)…We need HH, but I fear his job actually requires work, these days 😆
I (like HH, I suspect) prefer skilled players (protected by referees) and I think that has always been AW’s view too. In the early days of the new stadium the preferred MF was Cesc, Sicky and Hleb. Pragmatism however meant that (first) Gilberto and (later) Flamini were needed. Who did we miss more when they left? Flamini or Hleb? We probably missed both, but note that we’ve gotten Flamini back. Where is Hleb these days? He more or less was begging for another chance when he did time at Birmingham City…
My point is that Wenger’s dream of a highly skilled technical MF controlling matches through possession (tiki taka) has been replaced with a more pragmatic approach. Ozil will rekindle the dream and, I would assume, kill the dream of Cesc returning. The two together would be overkill and not at all good for (still developing) Wilshere and Ramsey. Or, at least, that’s how I see it…
Agreed with Bond about Lewandoski to Bayern…Our plans up front rely on Giroud improving AND staying fit, Sanogo finding his (size 14) feet and Bendtner turning his attitude and (his entire life) around. Ox and Poldi returning from injury and/Gnabry stepping up would be nice as well. If these planets don’t line up there’s always Theo as CF, part of what he “bargained’ for during his hold-out a year ago… All told, it’s not exactly ideal, but (IMO) it beats the days of relying on Chamakh (is he sold or could we recall him from the other side of the river?…) or little Arsh…
🙄 😯 😀
136. Looks like I killed off the discussion…Luckily I don’t mind talking to myself… 😆
Football is moving forward–even in England…So the new CF (and there’s only one these days–442 is dead…) has to be mobile AND skilled enough to convert the chances when they come. It’s good that Giroud (and Sanogo, as well) is (are) playing in England where size is still an asset up front. Elsewhere, it’s all about the false 9 and finishers having the mobility to fill each others spaces and create chances for one another. At Madrid, it will be Benzema starting up top but clearing and creating for Bale and C-Ron. At Barca, Messi will do likewise for Neymar and Pedro (and Alexis Sanchez, Tello, Cesc, etc.) For the CL champions, Mandzukic can do it whereas Gomez (hair and all…) was more like our own Giroud…Certainly RvP is a false nine…If he and the thick one (Rooney) can work it out, United will contend…City will do fine with Negredo and Little Kun (and even Dzeko, a willing runner, despite his size). Mourinho prefers Torres and Eto’o (formerly mobile…) vs his bigger guys, Lukaku and Demba Ba… Remember, Spain, the greatest of the National squads, has won three big ones (by and large) w/o a striker at all…
The big fella up front still persists in the lower ranks in England. Dalglish and now Fat Sam seem(ed) to think Andy Carroll is (was) the answer. Tony of the Pubes went with Crouch (and Kenwyne Jones)…Di Canio at Sunderland seems to like Conor Wickham…Some of the smaller guys at these clubs are losing out and might work a charm for us (Vaz Te at West Ham, Sessegnon at Sunderland, for example). I hate to bring down the dreamers, but, if our fitness issues worsen by January, these (and their continental equivalents…) are the sorts of guys I would look at AW bringing in during the next round of terror…
137. jgc says:
17 and JB
JB: per my earlier comments (if he wasn’t set on BM…) I agree Lewie is headed to BM. But he’s a good comparator to Suarez as they offer similar potency but different ways. So, in that sense, the discussion is worth having.
I agree with 17 in part, the 4-4-2 could come back, the problem is more finding junior and senior partners. At top clubs it doesn’t pay to be number 2. Witness Ronneys issues with RvJ.. There can be only one sheriff in town and the rest are deputies who get paid less and thrown away sooner. And get less endorsements and a lesser career.
I think the 4-4-2 died from commercial causes leading to a lack of viability, rather than a lack of viability.
Regarding Spain and strikers in general.. Well who needs them? Football is a game of space and movement. Enough good skills and creators will eventually find SOMEONE in front of goal to score.. Why do they have to be some prototypical striker? That imposes rigidity.
What a typical large, but nowadays mobile, striker gives you is the ability to stand and make a defender get a bus pass and transfer to run around them. They thus draw defenders and make life difficult. If they have skills and can finish there is always a room for them as a through ball is not required by law to be run onto, it can apparently also go to feet…
Just a different approach. As always my mantra, get good players and put them together in the best way and all will likely fly.. Put them together stupidly, and….
Cheers — jgc
138. James Bond says:
if, memory serves then we tried the Spain formula by sticking Arshavin there against sunderland many years ago … unfortunately it didn’t work out – and the AW gave up
no reason why we shouldn’t re-visit it with the likes of Ozil running things.
i said it before, no reason why we couldn’t play a 1-4-6
we got the players for it.
139. James Bond says:
indeed @ JGC
i’m just more and more astonished as to why we didn’t make a move for Tevez, at 5 million with 100 k /pw (took a massive pay cut), was an absolute bargain.
in hindsight, it should have been Tevez for me over Higuain –
re- 4-4-2 then many managers are reluctant to deploy that formation these days or from the last few years because it does have some flaws, and a lot of managers are very well versed in exploring those flaws and so on at club level – at least.
140. jgc says:
An JB
That hindsight, always better than 20:20, when you know the price AND that they were really for sale… Agreed he’d have been good, but… Prettier objects were on show with no idea about Ozil…
That’s the real TW problem for many fans. They/we are told its a market and money talks… But, it’s a closed market. It’s a market where the highest or first bidder over s price doesn’t necessarily win. So ManU other factors play, like:
A. You don’t know the player is for sale. Could be not for me and yes for you… Like rascists not selling to those of color, even for more. Money
B. you don’t know the price. Ad if a release clause exists, theoretically you can’t be sure you know that..
C. I don’t have to accept or reject your offer and can instead leave you in limbo while I see who else is out there willing to offer a more attractive package
D. Best yet, all this can change depending on the environment. Like houses, if they rise in my block for some reason, I too want more. If people I don’t like move in, suddenly what was unsalable becomes salable… If I get a second or third house that you don’t know about I become desperate to reduce my mortgage payments by selling or rating one you never expected. It could be my best one as I want the money…
If buying a new car was this hard we’d all be upset… And that’s way harder than almost all other transactions we make in real actual markets..
IMO, there’s a huge mismatch between what is true and what we believe to be true… As fans … It is tus a terror window of uncertainty…
Just some rumblings in the joys of asymmetric, so called, markets! 🙂
Cheers — jgc
141. TERRY MANCINI HAIR TRANSPLANT says:
Some excellent analysis going on here, its like a coaching manual, top stuff.
I will give you an insight watching it close and personal.
I dont think there is a team in our league that can match us for technical football. Chelsea, City and Utd can play some great football, but in my opinion we are the best.
The problem comes when we are not allowed to play it. Teams press hard and sometimes squeeze the life out of pass and move game.
The end result is that the game then hinges on a lot of one on one duels, in which physical power and size tend to come to the fore.
If i am been honest, we lose to many of these duels, and when we do we tend to not get the result.
I dont know what the answer is to this problem but i have a feeling that Arsene is trying to eradicate it not by going like for like, more by aquiring brilliant individual talent up front that can win you games even when your team play does not function
Thats why in the window i always beleived that the search was for attcaking talent. Ozil is great but in the next year we need to add to it with someone like suarez etc.
We are getting closer and very soon we could have the required “effeciency” to our game that will take us to the top
142. Gerry says:
jgc – At least we know what the last two initials stand for, eh Captain Jack?
Sorry I am late coming to this, had a morning and a half trying to get my BTSports 2 channel back, with success too.
Yes,I am fully on board with your post, which speaking as your ‘astro twin’, do I get any credit for inspirational rights, etc? 😀 😀
I am glad you have changed your view on Nicky B in the intervening 48 hours, as I too am harbouring some good thoughts for him. 1, He is in a settled(?) relationship. 2, He is intelligent enough to know that his playing career is nearer the end than the beginning. 3, At 25 he ought to be mature enough to put aside some of his self-mocking behaviour. 4, It is WC year and he has got very little time to earns a place if he does not get his head down, stay out of the headlines(for all the wrong reasons), then he we miss out. 5, And this might just get him more focussed … There is no place for him out on the wing, so he will actually get to play in the best position he is suited for? It is there if he wants it bad enough.
HT17 -The comment you added about Busquets is just what I say we could see Arteta doing occasionaly, eh TA?
On Sanogo I feel we are not looking at the Giroud replacement. Mainly because he is not experienced enough to carry off that role yet. But alongside, different story? There are many possibilities regards formation, and one I would like to see is this:
……………………….Ozil
……..Sanogo …………….Giroud
With Gibbs and Sagna getting crosses in, somebody should profit from knock downs, or one twos? I could also see Bentner/Gnabry in a front pairing to. And while I am on combinatios that might work well together, how about this:
Walcott ………….Ozil………………Eisfeld
……………………Giroud
Well at least until Poldi gets back?
Elsewhere, it is good to see Szcz back in a happy time again. Whatever his blip was last season, i think he will be fine from now on. Apart from injuries to Per, I think we can cope with the short term outs … except to Ozil of course?
Yes, there is so much room for optimism when you put a world class player in the mix. But, it will test our players fully to see how good their football intelligence is. The reason why I put Eisfeld ahead of many is just that. He is very good at being in the right place, and if anybody is going to have a ‘breakout year’, I am willing to bet he will be in the mix.
Theo, on the other hand, may still make poor decisions? Aaron, may still run into blind alleys?
Santi will thrive, Jack should do when he is fully fit, Le Flambeau and leSagna are both very experienced, no problem. Giroud is intelligent, but it might take a few games to know who goes where, but he’ll be sound enough. Gnabry and Akpom(and he is Giro’s true deputy) will both come on whenever they get the chance. We know Per and Kos will inspire at the back, Never mind about Gibbs and Monreal doubling up on occasions, I want to see Hector Bellerin in front of Jenks or Sagna, just to put the frighteners on Walcott, as well as squash the rumour that we need to buy a winger? ha ha
Aargh, the future … what a wonderful place that will be?
Top post, cheers jgc … you’ve got me dreaming too? :;)
143. jgc says:
JB
Refsrding 4-4-2… All patterns have flaws. The best is the o e that fits your players best so that those flaws are minimized! IMO. These flaws are more failures to adapt when the right personnel aren’t available….
When I was coaching super youth in NZ, the parents were perennially pissed I didn’t stick to a formation or positions for their boys.. Well, every game is different and so is every team, each wants us to play OUR game, while acknowledging their strengths in now we adapt it..
To me it was simple and we won heaps including an U19 title … With 15 year olds… And we dominated most teams because they couldn’t adapt…
Analogously, I had one striker and when he was hurt I too went 1-4-6 or really 1-3-4-3 with 3 backs 4 DMs and 3 CAMs …we won 4-0… Parents were pissed because I never named a striker and had way too many defenders on the pitch…
Yet, the other side had a 4-3-3 with three dedicated top STs/CAMs who scored heaps.. I had no ST and made sure their strikers never saw the ball nearer than 3m away… Easy win as they never came back much so we’d push our DMs as holding mids and push a back even and thus always had numbers overloading one or another place… Their coach spent the whole game yelling at his team to “get the damn ball” … I’m still doing a JB ahahahahahahahaahah… But, my teams parents were pissed and complained…
In short, just play the damn game by moving the ball, controlling space and movement by your positioning and running, and from there, adapt as needed.. If your good and adapt, you’ll likely win…it’s a simple game made hard by people with fixed ideas.. Or so goes the philosophy of jgc! 🙂
\end(rant)
Cheers — jgc
144. Gerry says:
TA – That is tough on George. Dogs do cope remarkably well though, so I hope you can stick with him and see him through until the vets know what can be done.
I have one in a similar tricky spot, except she is older, and deaf. She has a ‘fatty’ tumour growing near the lymph gland under her front leg(armpit). It is now so big it is causing her to limp, but it is doubtful if it can be fully removed because of where it is.
My eldest (14) is still going strong though, despite losing some sight in one eye, and getting increasingly deaf. Like I say, they do cope remarkably well?
145. James Bond says:
The Visionary takes a bow to ” The Professor”.
🙂
speaking of 20/20’s , there should be a tri-nations 20-20, Eng/Aus/NZ – would be fantastic to watch, not sure why they only do that with 50 over cricket and not 20-20’s.
The visionary has spoken.
TMHT 🙂
all that talk of Accountancy exams, takes me back to June/December – back in the day, ah, bloody hated them Auditing exams, i often thought of doing the same but unfortunately, unlike you, i couldn’t pull it off, ha
the problem right now is AW signing the contract extension , he needs to bloody sign – ASAP i reckon.
146. jgc says:
Terry
If someone clogs the midfield you’ve two choices, at least .. Both counter intuitive, they start with clog it right back,… Then..
A, if you like pace and space, abandon the high line give ground and draw them in, while holding possesion, and crest numbers and essentially counter attack their pressing . We’ve the team for this as our backs are good with the ball and Gibbs, Kos and TV all like to go forward as the extra player to make numbers.. Equally we are quick with feet and ball…IMO, this is very much what we did to Spurs with and without the ball
Or, B… if they are so completely rude as to not play to your strength and clog the middle but don’t pursue but press defenders.. Then press your backs too and shorten the field hugely and…, put ball to feet of your new exceptional holding midfielder, or the old Santi one who will be less clogged… And let them crest their own space and deliver the clever new thru ball to speedy wings or added defenders (Gibbs, Kos, TV) running forward, and… Admittedly if said mid turns it over at the wrong time you’re a wee touched fire trucked, but that’s why you play the game
Or others, see, simple game!
🙂
Cheers — jgc
147. Gerry says:
Bongo – I never got to welcome you before. So I will now. Hi, and welcome.
I feared the result before the game, because I thought it would only take a couple of your new players to click and you would have been difficult to beat. As it was, for much of the match it was us against Loris, who was everybody’s MOTM?
The biggest shock I had when I saw the game on the ‘Player was how off his game was Vertonghen? I think most of your signings will come good, but I would worry about Soldado?
But yes, overall I think we earned the win.
I presume the return leg will be around Christmas/ New Year, so we will have to see then who has improved the most after this TW?
Cheers for coming on again too.
148. Fozzie B says:
Evening tranny window admirers!! Thanks jgc and afc for your fantastic posts!! Just the tonic needed to settle the tranny window party hangover!! I love the way jgc you use your business acumen to highlight from a risk assessment point of view, just how strong we are now from a relatively limited outlay of funds!! I agree that aw seems focused on getting us our SQ striker and for the other positions. We have a replacement for ageing rosicky and I fully expect a similar SQ for arteta/diary, I’m hoping the foundation is in place for Bender already. I think we will get an amazing SQ st in the next window or the following. I do believe sanogo will adapt quickly because he has the right attitude and fully accepts how big an opportunity it is. He looks green yes, but I’m sure his attitude will be the key and of course Wenger is the key for him too. So really hope AW signs too soon too, perhaps after the other contract extensions are done. 😀
149. James Bond says:
indeed – stick to the basics, a little less of Fifa 2014 or whatever, is hot these days on the ps3 and sorted.
but i’m a firm believer, that most international footballers do train in various different formations and they do come through the ranks as well, so changing formations and adapting should not be a problem – considering that there are times that such changes are enforced by red cards and so on.
not sure if it’s about having the right players anymore , as the more and more football evolves – you get more 2 footed players, players who are flexible / utility players, capable of playing in more than 1 position e.t.c e.t.c
@ JGC.
150. James Bond says:
ah, the JGC and GERRY combo is restored – all is well , all is well, ha
Fozzie with a B in da house !!! 🙂
where’s Glics – should have been back by now from lesbania land.
151. Fozzie B says:
JB I would have loved tevez or David Vila in the last window …
Totes, sorry to hear about Henry fella 😦
Saw this on another blog, lets hope the Ozil oil will make it easier for AW!!
Ozil Ozil Ozil …. Oi oi oi
😆
152. jgc says:
JB 🙂
153. Fozzie B says:
JB -Glic is driving back from orkville with a van load of chloroform and roofys for his tranny window Ozil the Kermit celebration party!! 😀
154. VCC says:
Total…sorry to hear the news about Henry. Must be worrying for you at the moment. As Gerry has said, Dogs do cope remarkably well.
Hopefully he can be treated successfully when the vets see fit.
155. 17highburyterrace says:
Alright, a little less echo and a lot more intelligence here…So much more air space now that the terror is past… 😀
I’ll welcome Bongo too…Welcome! And a piece of good news (from my own athletic experience)…I bet Capoue will be available sooner than later. Ankles can often be super-severe due to swelling but once that’s past they (often) heal pretty quickly…They’ll be weak for a full season but even Spurs probably have a physio who is handy with the white tape… 😆
Professor Geoff, very nice to hear about your successful coaching experiences–This is the benefit of a tighter squad, more complex ideas can be transferred to players AND there’s less pouting out on the touchline from players who don’t get the central spot they (all) grew up playing… My point about the evolution of the game from 442 to 451 or even 4-6-0 is that faster, more skilled, more aware players means that it’s about moving w/o the ball because–if you do–it can get to you quicker. Space is the key, as the professor has said… Funny also that the parents balked at a more fluid set-up–maybe like the agents (or the market forces) as you describe above–“My boy/girl/client isn’t comfortable with your coaching”… 😆
I don’t mean to pile it on the Fantasy/Computer game types (too much…) but, beyond the cost = value fallacy and rigid formations and positions for players, it kills me when people say stuff that is seems blatantly untrue, at least from my observations… These things get repeated and then they become “true”…The latest one that’s bothering me is that Bendtner holds the ball up well. Wrong, unless he’s worked on that part of his game since he played at Arsenal–and I doubt he’s worked on anything beyond his car collection and maybe his tattoos… (For discussion sake)… Bendy is what you guys would call a SS…Tall but not very mobile, and not strong enough to avoid getting pushed around (or off the ball) by strong defenders. Maybe Giroud could give him a tour of the weight room… He’s got decent skills in and around the box but first he needs to get there. Given the quickness–in deed and/or in thought–of players like Theo, Santi, and Messy, Nicklas (and Giroud) look pedestrian. At least Ollie’s got the guns…So, please people, if you’re trying to talk about the upside of NB52, tell me about his finishing skills not his hold-up work…Also, for Bongo…I’ll always love Bendy for that header (to make it 2-1) with his first touch off the bench in a NLD a few years…
But I digress…
Bond… Put Tevez (for me at least) in the same category as Rooney and Suarez…A player with issues on an insane salary who we couldn’t get because City will not sell to a true rival (sorry Bongo, Ade your way is a different matter, sort of like G. Barry to Everton or Kolo to ‘Pool… 😆 ) In the end, to his credit, he took a pay cut to play in Italy. He and Higuain and el Kun (and Pastore and Levezzi at PSG) are all competing for spots (alongside Messi) in Brazil… Maybe after that tournament is over we should try for some Argy-love up front…
156. jgc says:
17
All agreed.. Note, I’ve the other type too! 🙂 two lines I’m known for
A. Me: hey (player) what’s that between your shoulders?
Me: yes… Use it!!
B. me: … Your OTHER right foot!!
Cheers and goodnight!
— jgc
157. Glic says:
Evening Randy Rectum Receivers !. 😆
Very intriguing post Professor, one that could have possibly bamboozled our resident nuclear dictionary, Redders !. hahaha
So basically, all that writing and you could have probably wrote it as an equation !, something like this……Future + ( TQ + R x QR )…..which basically = T !………..Trophies !.
Now give me my Nobellend Peace Prize for inventing a new form of Maths …….Quantumvoetbal ! hahaha
As for Lesbania not being on the map……well its a bit like Narnia without the bestiality …….just wall to wall shaven haven, you still have to through a closet to get there though !, but watch out for VCC coming the other way out of the closet with a limp wrist crying ….”geoff chase me ! “. hahaha
Straight off the press this second !. Anyone seen Rooneys gash on his head ?…..nothing new really….I always thought he was a C**t Head !.
We know Peter Crouch is a Totnumb Spud………..does that make him a Crouch Potato ?.
158. Glic says:
Yes, I too have not yet welcomed Bongo !. I thought I would give him the chance to get used to the new technology of……Colour !. Lucky the comment page is still in Black and White, it makes him feel that little bit at home !. Welcome !.
Hope Henry gets better soon Totes and here`s a message from my Max…….Woof woof ( get better ). 🙂
159. TotalArsenal says:
Evening guys – thanks for the Henry sympathy! 🙂
It came as quite a surprise this week. I knew something was wrong with his vision but did not think it would be so drastic/structural, as he is not even a year old.
Some very fine comments today, and it makes me proud what a quality and diverse blog BK is becoming. 🙂
160. TotalArsenal says:
New Post 🙂
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## Site Tag Cloud
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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJan 27th 2012
had occasion to create dual vector space.
• CommentRowNumber2.
• CommentAuthorzskoda
• CommentTimeJan 30th 2012
$V \mapsto V^*$ extends to a contravariant functor: given a linear map $A: V\to W$, the dual or transpose map $A^* = A^T : W^*\to V^*$ is given by $\langle A^*(w_1), v\rangle = \langle w_1, A(v)\rangle$ $\forall w_1\in W^*$, $\forall v\in V$.
• CommentRowNumber3.
• CommentAuthorzskoda
• CommentTimeSep 5th 2013
• (edited Sep 5th 2013)
New related entry (only a small part of intended material covered so far) dual gebra.
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## Sifnab Group Title Im having a problem Integrating dx/(2+x^(1/2)) When i used U substitution u^2=x and 2udu=dx i got 2udu/(2+u) but i realy dont know what to do now? one year ago one year ago
• This Question is Open
1. adamshai Group Title
Try to substitute: $y = 2 + \sqrt{x} \\ dy = \frac{1}{2\sqrt{x}}dx = \frac{1}{2(y-2)}dx$
2. Sifnab Group Title
yes! I solved it now, thanks! That last step when you changed x^1/2 to (y-2) helpt a lot :D
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So I've been reading through Louis Kaufmann's book Formal Knot Theory, which describes a lattice of "states" on four-regular plane-embedded (multi)graphs, and trying to understand it in different terms, as a structure of spanning trees and local changes from one spanning tree to another.
A four-regular plane multigraph is the same thing as the medial graph of a plane graph without the 4-regularity restriction. To form the medial graph $$M(G)$$ of a plane graph $$G$$, place a vertex of $$M(G)$$ at the midpoint of every edge of $$G$$ and connect pairs of these medial vertices in $$M(G)$$ whenever they belong to adjacent edges around the same face of $$G$$. The faces of $$M(G)$$ can be two-colored (more generally this is true for any plane graph with even degree at every vertex). The faces of one color in $$M(G)$$ lie within the faces of $$G$$, and the faces of the other color in $$M(G)$$ surround the vertices of $$G$$:
Kaufmann's states are formed by placing marks within each face of $$M(G)$$. Two adjacent faces of $$M(G)$$ are marked by stars; the remaining marks are placed near a vertex on each unstarred face of $$M(G)$$, such that each vertex has exactly one mark near it. As Kaufmann shows, these marks correspond to a pair of interdigitating trees. If we return to the underlying graph $$G$$, one of these trees is a spanning tree of $$G$$, and one of these trees is a spanning tree of the planar dual of $$G$$. These two spanning trees are rooted at the vertices corresponding to the starred faces of $$M(G)$$, and the other marks in $$M(G)$$ indicate the parent of each vertex in $$G$$ or its dual. The dual spanning tree is determined once a spanning tree in $$G$$ is selected (the dual spanning tree edges are the edges dual to edges of $$G$$ that are not part of the primal spanning tree) so, less symmetrically, we can view a state as consisting of a choice of outer face of $$G$$, a choice of a vertex on that outer face, and a spanning tree rooted at that vertex.
A rotation consists of finding two marks near the same edge of $$M(G)$$ and replacing them with marks in the other two locations near that edge. In $$G$$, this means: finding a spanning tree edge connecting some vertex $$v$$ to its parent, removing it from the tree, and replacing it with an edge connecting $$v$$ to a different parent, such that the edges to the old and new parents of $$v$$ are adjacent on an interior face of $$G$$ and such that the resulting graph remains a spanning tree. However, such a replacement is not allowed if it would cause a path in the dual tree to reverse its orientation. For instance, in the figures below, the center vertex is not allowed to choose the root as its new parent, even though that would form a valid tree, because it would reorient a dual path.
One can assign a direction to a rotation according to whether the replacement parent for $$v$$ is clockwise or counterclockwise of its old parent. There are two extremal spanning trees for this assignment of directions, both of which can be found by a depth first search that prioritizes the edges at each vertex in the ordering given by the planar embedding, with the cyclic order at each vertex broken into a linear order by the edge connecting it to its DFS tree parent. Thus, these two extrema may be constructed in linear time.
So far, so good. But somewhere around page 50, I'm getting stuck. Kaufmann is claiming that there's a partial order on the set of possible rotations, or equivalently on the set of edges of $$M(G)$$ (one can't rotate a mark clockwise from $$A$$ to $$B$$ until some other move has already put it at $$A$$, and until the corresponding dual mark is in the corresponding position), and therefore that the states can be represented as lower sets of a partial order; by Birkhoff's representation theorem, the states form a distributive lattice in which the rotations from one state to another are the covering relations of the lattice. But there are two problems. First, and less importantly, he doesn't seem to show very carefully that every lower set actually forms a valid marking. But the real flaw is that this proof assumes that, in a sequence of clockwise rotations, the same rotation can happen only once. In Kaufmann's notation, in sequence of consistently-ordered rotations, he assumes that the same edge of $$M(G)$$ can only be rotated once; in our notation of spanning trees in $$G$$, he assumes that a spanning tree edge can only rotate around $$v$$ from an old parent $$u$$ to a new parent $$w$$ once, and then forevermore is barred from repeating the same rotation. But that's not true. By making a more complex graph than the one described above, it is possible to make the two extremal trees spiral around many times before reaching the center, and therefore it's possible for the edge connecting the central vertex to its parent to rotate more than once around in the sequence of rotations connecting the two extremal trees. For instance, even in the five-vertex wheel shown below, the central vertex rotates six times going from one extreme tree to the other; two of the four possible rotations at that vertex are repeated. For larger graphs, the number of repetitions could be larger.
So, at this point, while I still believe Kaufmann's claim that the rooted trees of a plane graph form a lattice, I think his proof is bogus. If they do form a distributive lattice, there is an underlying partial order (by Birkhoff) but it's not as simple as the one he describes. I think the elements of the order are pairs of a vertex in G and an integer, where the integer represents some kind of winding number, but I'm not sure of the details.
More later...
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# zbMATH — the first resource for mathematics
A note on the singular Sturm-Liouville problem with infinitely many solutions. (English) Zbl 1026.34023
Here, the author investigates the nonlinear boundary value problem $-u''(t)= a(t)f\bigl[ u(t)\bigr], \quad 0<t<1,$
$\alpha u(0)-\beta u'(0)=0, \quad \gamma u(1)+ \delta u'(1)=0,$ where $$\alpha,\beta, \gamma, \delta \geq 0$$, $$\alpha\gamma +\alpha\delta +\beta\gamma >0$$ and $$a(t)$$ is in a class of singular functions.
Under certain growth condition imposed on $$f(u)$$, the author obtains infinitely many solutions to the problem.
The main tools used in this paper are the Kramel’skij fixed-point theorem and the Hölder inequality.
##### MSC:
34B16 Singular nonlinear boundary value problems for ordinary differential equations 34B24 Sturm-Liouville theory 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
Full Text:
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Chapter 14.3, Problem 43E
### Algebra and Trigonometry (MindTap ...
4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Chapter
Section
### Algebra and Trigonometry (MindTap ...
4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem
# DISCUSS: Most Likely Outcome for n Tosses of a Coin A balanced coin is tossed n times. In this exercise we investigate the following question: What is the number of heads that has the greatest probability of occurring? Note that for a balanced coin the probability of heads is p = 0.5 .(a) Suppose n = 8 . Draw a probability histogram for the resulting binomial distribution. What number of heads has the greatest probability of occurring? If n = 100 , what number of heads has the greatest probability of occurring?(b) Suppose n = 9 . Draw a probability histogram for the resulting binomial distribution. What number of heads has the greatest probability of occurring? If n = 101 , what number of heads has the greatest probability of occurring?
To determine
(a)
To find:
The number of heads that have the greatest probability of occurring when a coin is tossed n times, draw a probability histogram for n=8 and find the number of heads that have the greatest probability of occurring for n=100.
Explanation
Given:
A balanced coin is tossed n times.
For a balanced coin, the probability of heads is p=0.5.
Approach:
Use excel to draw a probability histogram for n tosses of a coin and the formula for binomial probability P,
Here,
p is the probability of heads,
C(n,r) is a binomial coefficient,
r is the number of successes in n tosses.
Calculation:
Use excel to draw a probability histogram for n=8 as shown in figure (1).
The probability histogram for n=8 is shown in figure (1), the number of heads that have the greatest probability of occurring is 4 and the number of heads that have the greatest probability of occurring are 50 for n=100
To determine
(b)
To draw:
The probability histogram for n=9 and find the number of heads that have the greatest probability of occurring for n=101.
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## Thinking Mathematically (6th Edition)
$\frac{0}{-8}$ = 0 Any number divided by zero is equal to zero.
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# How to assign values using nested Part[ ] expressions?
Why doesn't this work? Can I make it work?
x = Range[10];
x[[4;;7]][[2]]
==> 5
x[[4;;7]][[2]] = 100
==> Set::partd1 : Depth of object x[[4;;7, 2]] is not sufficient for the given part specification
• Why can't you just do x[[4 - 1 + 2]] = 100? – J. M. will be back soon Mar 28 '18 at 16:33
• This comes from passing arguments by reference using Hold[x_]. A function may restrict x to a subrange before calling a nested function, which may do the same thing again leading to a chain of part specifications (e.g. x[[4;;7]][[2;;3]][[1]]). It works for reading, but not for writing. One alternative that I'm not looking forward to is passing x and its part specification separately and somehow collapsing the part spec before accessing x. – user3704499 Mar 28 '18 at 16:39
While I am not sure it is general enough, a first attempt may be to try something like this:
Clear[nestedPartSet];
nestedPartSet // Attributes = {HoldFirst};
nestedPartSet[ sym_ , partspecs__, val_ ] := Module[
{
dimensions = Dimensions@sym,
posArray, positions
},
posArray = Array[ List, dimensions ];
positions = Fold[ Part, posArray, {partspecs} ];
(Part[ sym, #] = val) & @@@ positions;
sym
]
nestedPartSet[ x, 4;;7, 1;;2, 100 ]
(* {1, 2, 3, 100, 100, 6, 7, 8, 9, 10} *)
• Thanks gwr. This helped a lot. I was able to generalize your basic idea to multiple dimensions and arbitrary arguments by wrapping the array and its partial set of indices in a single Unique symbol. You can then further wrap the symbol with more indices to any level. The wrapped symbols can then be passed to functions which can read or write the submatrix. Everything shares the same actual matrix. Its not too fast, but it seems pretty general. I could post the code if you're interested. – user3704499 Mar 29 '18 at 2:00
• @user, you can post the code as an answer to your own question, so people can take a look at it and make suggestions. – J. M. will be back soon Mar 29 '18 at 3:39
Part[] nearly provides composable "views" for read/write operations on lists and arrays, but reading and writing operations are sometimes inconsistent:
x = Range[10]
x[[4 ;; 7]][[2]]
Out[61]=
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Out[62]=
5
In[18]:=
x[[4 ;; 7]][[2]] = 100;
During evaluation of In[18]:= Set::partd1:Depth of object x[[4;;7,2]] is not sufficient for the given part specification. >>
Thanks to gwr's answer, I was motivated to create ArrayRefs for reading/writing pieces of arrays or lists. The basic idea is to wrap a reference to a List or Array with a symbol, and then further wrap the symbol with submatrix expressions ("views") which may be evaluted using set[] and get[] functions. The symbol or submatrix views may be passed to other functions for evaluation, or further wrapped producing sub-sub-matrix views etc. All read/write actions affect the original List or Array.
makeArrayRef[ref_Symbol] := Block[
{obj},
With[{this = Unique[obj]},
set[this, value_] ^:= ref = value; (* Set entire ref to a new value *)
set[this, part__, value_] ^:= ref[[part]] = value; (* Set part of ref *)
get[this] ^:= ref; (* Get entire ref *)
get[this, part__] ^:= ref[[part]]; (* get part of ref *)
this[] := ref; (* shortcuts for get *)
this[part__] := ref[[part]];
this
]
];
SetAttributes[makeArrayRef, HoldAll];
view[p_, parts__] := view$@@ Prepend[substSpan$[List@parts], p];
substSpan$[parts_] := Replace[parts, {s_Span :> span$[s], l_List :> span$[l]}, {1}]; get[view$[p_, parts__]] ^:= get @@ viewEval$[p, parts]; get[view$[p_, parts1__], parts2__] ^:= get[view[view$[p, parts1], parts2]]; set[view$[p_, parts__], value_] ^:= set @@ Append[viewEval$[p, parts], value]; set[view$[p_, parts1__], parts2__, value_] ^:= set[view[view$[p, parts1], parts2], value]; view$[p_, parts1__][parts2___] := get[view$[p, parts1], parts2]; view$[view$[p_, pre___, args1__span$, post___], args2$__] := Module[ {j, args, args2 = List@args2$, n2},
n2 = Length@args2;
j = 1;
args = Replace[List[pre, args1, post], span$[s : (__Span|__List)] :> If[j <= n2, span$[s, args2[[j++]]], span$[s]], {1}]; view$ @@ Join[{p}, args, args2[[j;;]]]
];
view$[view$[p_, args1__], args2__] := view$[p, args1, args2]; (* args1 doesn't contain span$ *)
SetAttributes[span$, Flat]; viewEval$[p_, pre___, parts__span$, post___] := Module[ {i = 1, dim = Dimensions[p[]]}, Prepend[Replace[{pre,parts,post}, {span$[args__] :> Fold[Part, Range[dim[[i++]]], List@args], x_ :> (i++; x)}, {1}], p]
];
viewEval$[p_, parts__] := {p, parts}; (* parts doesn't contain span$ *)
A few motivating examples Make a simple list
x = Range[10];
p = makeArrayRef[x]
Out[20]=
obj$1062 Look at its contents p[] Out[21]= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} Create some references to sub-parts of the list q = view[p, 4 ;; 7] r = view[q, 2 ;; 3] q[] r[] Out[22]= view$[obj$1062, span$[4 ;; 7]]
Out[23]=
view$[obj$1062, span$[4 ;; 7, 2 ;; 3]] Out[24]= {4, 5, 6, 7} Out[25]= {5, 6} Assign values to sub-parts; print the original list set[r, 100] x Out[26]= 100 Out[27]= {1, 2, 3, 4, 100, 100, 7, 8, 9, 10} Further restrict the sub-part set[r, 1, 99] x Out[28]= 99 Out[29]= {1, 2, 3, 4, 99, 100, 7, 8, 9, 10} Construct a matrix m = Array["m", {3, 10}]; p = makeArrayRef[m]; MatrixForm[p[]] Create some sub-matrix references. Use the view[] function. q = view[p, 2 ;; 3, 5 ;; All ;; 2] r = view[q, 1 ;; All, 2] Out[33]= view$[obj$1093, span$[2 ;; 3], span$[5 ;; All ;; 2]] Out[34]= view$[obj$1093, span$[2 ;; 3, 1 ;; All], span$[5 ;; All ;; 2, 2]] Assign values to the sub-matrices. Note that all operations modify the original matrix m set[q, 100] MatrixForm[q[]] set[r, 99] MatrixForm[m] Assign sub-matrices using other sub-matrices set[q, 1 + p[1 ;; 2, 2 ;; 4]]; MatrixForm[m] Indices can be lists too s = view[p, 1, {2, 3, 5, 7}]; set[s, "prime-column"] MatrixForm[m] Works for SparseArrays also {n, nnz} = {15, 50}; n = 15; SeedRandom[1] indices = RandomInteger[{1, n}, {nnz, 2}]; values = RandomReal[{0, 1}, nnz]; spmat = SparseArray[Thread[indices -> values], {n, n}]; MatrixPlot[spmat] p = makeArrayRef[spmat]; q = view[p, 5 ;; 10, 3 ;; 12] set[q, 1] MatrixPlot[spmat] Out[52]= view$[obj$1210, span$[5 ;; 10], span$[3 ;; 12]] Out[53]= 1 Performance kind of sucks when indices involve Spans or Lists Timing[Do[spmat[[5 ;; 10,3 ;; 12]]; , {10000}]] Timing[Do[q[]; , {10000}]] Out[55]= {0.03125, Null} Out[56]= {0.328125, Null} Performance is better without Spans q2 = view[p, 1] Timing[Do[q2[]; , {10000}]] Out[57]= view$[obj\$1210, 1]
Out[58]=
{0.09375, Null}
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# A random sample of 5805 physicians in Colorado showed that 3332 provided at least some charity care (i.e., treated poor people at no cost). a) Let p r
A random sample of 5805 physicians in Colorado showed that 3332 provided at least some charity care (i.e., treated poor people at no cost).
a)
Let p represent the proportion of all Colorado physicians who provide some charity care. Find a point estimate for p. (Round your answer to four decimal places.)
b)
Find a $99\mathrm{%}$ confidence interval for p. (Round your answer to three decimal places.)
lower limit $=?$
upper limit $=?$
c)
Is the normal approximation to the binomial justified in this problem? Explain
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Brighton
Step 1
a)
Here,
The point estimate of the population proportion is calculated as follows:
$\stackrel{^}{p}=\frac{x}{n}$
$=\frac{3332}{5805}$
$=0.573987$
$\approx 0.5740$
Step 2
b)
Since the required confidence interval is $99\mathrm{%}$, the two-tailed z-critical value is 2.5758 using the Excel function $“=NORM.S.INV\left(0.995\right)\text{"}$.
The $99\mathrm{%}$ confidence interval for the population proportion is calculated as follows:
$CI=\stackrel{^}{p}±{z}_{\frac{\alpha }{2}}\sqrt{\frac{\stackrel{^}{p}\left(1-\stackrel{^}{p}\right)}{n}}$
$=0.5740±\left(2.5758\right)\sqrt{0.5740\frac{1-0.5740}{5805}}$
$=0.5740±0.0167$
$=\left(0.5573,0.5907\right)$
$\approx \left(0.557,0.591\right)$
Lower limit $=0.557$
Upper limit $=0.591$
Step 3
c)
The normal approximation to binomial is possible only if,
$np>5$
$nq>5$
Checking the conditions for normality:
$np=5805×\frac{3332}{5805}$
$=3332$
$>5$
$nq=5805×\left(1-\frac{3332}{5805}\right)$
$=2473$
$>5$
Thus, normal approximation to binomial is possible.
Yes,
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# help computing positions of points
This topic is 1806 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
I've been trying to figure out a solution for this math problem. It might be simple, it might be impossible. I don't know because I am still very inexperienced in this domain.
I will be referring to this drawing:
The Problem:
This drawing depicts two rectangles lying on the x-z plane. Think of it like you are looking at them top-down (down the -y axis). The black points (H, I, and J) are given as input. The width of the rectangle is always 4. I need to compute the positions of each green point (A through G).
My Partial Solution:
Computing points D through G is easy:
vec3 forward = normalize(I-J); // direction from J to I
vec3 right = cross(forward, vec3(0,1,0)); // direction from F to G
G = J + (right * 2); // 2 = width/2
F = J - (right * 2);
I can use the same formula to compute D and E.
Where I Need Help:
I don't know how to compute A, B or C!
Any help or advice is greatly appreciated!
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Unless you know the rotation of the rectangle containing the point H, I don't think you can solve it. Or if you had the point opposite of H, the midpoint between D & C, you could solve it, because you could then figure out the rotation from there.
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Unless you know the rotation of the rectangle containing the point H, I don't think you can solve it. Or if you had the point opposite of H, the midpoint between D & C, you could solve it, because you could then figure out the rotation from there.
I thought it might not be possible but I needed another set of eyes to confirm. Thanks for taking the time to respond.
##### Share on other sites
Consider the point K that is the midpoint of DC. HK is a line parallel to BD and AC and perpendicular to DC.
Think of D as being the center of a circle with radius 2. K lies on this circle and is such that HK is a tangent to the circle. Also, lies on the line DC. There's lots of information online about finding tangent lines that pass through a circle and an external point. Pick the tangent line that also intersects the midpoint of DC.
One you find that tangent line, you can trivially find the normal of it along DC. Normalize and scale by 4. That's the location of C. Use this same normal scaled by 2 and -2 relative to H to find A and B.
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Consider the point K that is the midpoint of DC. HK is a line parallel to BD and AC and perpendicular to DC.
Think of D as being the center of a circle with radius 2. K lies on this circle and is such that HK is a tangent to the circle. Also, lies on the line DC. There's lots of information online about finding tangent lines that pass through a circle and an external point. Pick the tangent line that also intersects the midpoint of DC.
One you find that tangent line, you can trivially find the normal of it along DC. Normalize and scale by 4. That's the location of C. Use this same normal scaled by 2 and -2 relative to H to find A and B.
I'm not sure I follow, it sounds like you're using DC (which is undefined, as he doesn't have C) to find C. Am I misinterpreting?
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One alternative I can think of:
- Consider D to be a hinge.
- Place a new rect A'B'C'D' and point H' directly adjacent to DEFG and treat this as being a rotated version of ABCD.
- You now know the positions of both H' and H. Calculate the angle formed between them using D as the common vertex.
- Use that angle to rotate points A' through C' about D, back to their expected positions.
You could probably do this entirely with matrices and never actually measure an angle (I suspect), but I'm not good enough with linear algebra to verify that.
[attachment=19859:4vq7.png]
Edited by Nypyren
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Consider the point K that is the midpoint of DC. HK is a line parallel to BD and AC and perpendicular to DC.
Think of D as being the center of a circle with radius 2. K lies on this circle and is such that HK is a tangent to the circle. Also, lies on the line DC. There's lots of information online about finding tangent lines that pass through a circle and an external point. Pick the tangent line that also intersects the midpoint of DC.
One you find that tangent line, you can trivially find the normal of it along DC. Normalize and scale by 4. That's the location of C. Use this same normal scaled by 2 and -2 relative to H to find A and B.
I understand exactly what you mean. I thought of D being the center of a circle with radius 2 earlier but I have never worked with tangents before so my thought train ended there. I will try to work out a solution with this tomorrow, it looks like a sound solution. Thanks so much!
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One alternative I can think of:
- Consider D to be a hinge.
- Place a new rect A'B'C'D' and point H' directly adjacent to DEFG and treat this as being a rotated version of ABCD.
- You now know the positions of both H' and H. Calculate the angle formed between them using D as the common vertex.
- Use that angle to rotate points A' through C' about D, back to their expected positions.
You could probably do this entirely with matrices and never actually measure an angle (I suspect), but I'm not good enough with linear algebra to verify that.
Not sure I entirely follow. I am going to try to implement SeanMiddleditch's solution tomorrow. Thanks for your response!
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Not sure I entirely follow. I am going to try to implement SeanMiddleditch's solution tomorrow. Thanks for your response!
Sorry. I edited my post with a picture. I only have mspaint so apologies for the low quality.
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Hmm. I just realized my technique only works if the problem guarantees the two rectangles will also have the same length, which your original post didn't specify. Disregard my technique if the rectangles can be different lengths. Edited by Nypyren
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zbMATH — the first resource for mathematics
An elementary study of groups whose order is a product of two primes. (Spanish. English summary) Zbl 1050.20502
Summary: We study the number of finite abstract groups whose order is the product of two primes. We use elementary methods based on the action of the group on itself by conjugation.
MSC:
20D60 Arithmetic and combinatorial problems involving abstract finite groups 20D20 Sylow subgroups, Sylow properties, $$\pi$$-groups, $$\pi$$-structure 20D45 Automorphisms of abstract finite groups
Full Text:
|
# Resource Managing Graph (RMG)
A frame graph and resource manager on top of MarpII
Siebencorgie published on
5 min, 901 words
Categories: Vulkan
Remember this one: The poor man's render graph? The goal was to simplify creating custom renderers using AsyncCompute and other nice buzzwords. It actually worked pretty nice for small renderers, but I was wrong about one part. Specifically this one:
I decided against a blackbox-like graph (where all data is managed by the graph). The main advantage of this more transparent type is, that the developer can choose for instance to write some parts by hand and only let the graph handle common work. Or the other way around: Hand optimize critical paths and let the graph only handle swapchain image submission and async compute.
Turns out this freedom is actually pretty inconvenient. While it's nice* to let something else do the scheduling, you still have to create all the resources, and think about when they are used. This leads to creating manual double buffers through out your code etc. All the time setting the correct usage flags, thinking about vk::ImageLayout etc.
This is the reason why I set out to create the second iteration called Resource Managing Graph or RMG. The idea is to inherit scheduling from the old implementation, but wrap everything into a blackbox that manages all the resources. The user only gets handels to the data without.
To use RMG you have to do two things:
1. Implement the Task trait
I used the occasion to change queue handling a bit. Since you don't have to think about queues anymore, you only specify the type of queue needed for each task. This shrinks down the recording step to the following:
// Recording buffer update, a simulation step, buffer copy (to the forward renderer),
// rendering and finaly swapchain present.
rmg.record(window_extent(&window))
.unwrap()
.unwrap()
.unwrap()
.unwrap()
.unwrap()
.execute()
.unwrap();
Registering data for a task is now done through a Registry which collects all data dependencies for a task. Apart from that scheduling is pretty much the same.
Creating an image now is as easy as this:
let mut depth_desc = ImgDesc::depth_attachment_2d(1, 1, depth_format);
depth_desc.usage |= vk::ImageUsageFlags::SAMPLED;
let depth_image = rmg.new_image_uninitialized(depth_desc, None)?;
The resulting handle behaves similar to a Arc<Image>, meaning that the image is dropped when all handles referencing that image are dropped. This makes managing the lifetime of resources easy. No manual delete calls are needed.
## Enhancements
So far we only discussed the user facing aspect that stayed more or less the same. However, there is one big, opinionated advantage. The whole thing automatically manages a bindless descriptor* setup. Meaning, instead of having to manage descriptor-sets and pools all this is done by the graph. At runtime you can translate a resource handle to a 32bit GPU-resource handle. Push that to the GPU and you are free to access any data.
I used three main resources for the implementation:
1. Vulkan specification
2. TraverseResearch Darius Bouma's posts
3. Vincent Parizet post
This makes writing shaders and passes even easier. For instance there is a small simulation compute shader in the example. The Task implementation looks like this:
impl Task for Simulation {
fn name(&self) -> &'static str {
"Simulation"
}
fn queue_flags(&self) -> vk::QueueFlags {
vk::QueueFlags::COMPUTE
}
fn pre_record(
&mut self,
resources: &mut marpii_rmg::Resources,
_ctx: &marpii_rmg::CtxRmg,
) -> Result<(), marpii_rmg::RecordError> {
self.push.get_content_mut().sim_buffer = resources.get_resource_handle(&self.sim_buffer)?;
self.push.get_content_mut().is_init = self.is_init.into();
if !self.is_init {
self.is_init = true;
}
Ok(())
}
fn register(&self, registry: &mut marpii_rmg::ResourceRegistry) {
registry.request_buffer(&self.sim_buffer);
registry.register_asset(self.pipeline.clone());
}
fn record(
&mut self,
device: &std::sync::Arc<marpii::context::Device>,
command_buffer: &vk::CommandBuffer,
_resources: &marpii_rmg::Resources,
) {
//bind commandbuffer, setup push constant and execute
unsafe {
device.inner.cmd_bind_pipeline(
*command_buffer,
vk::PipelineBindPoint::COMPUTE,
self.pipeline.pipeline,
);
device.inner.cmd_push_constants(
*command_buffer,
self.pipeline.layout.layout,
0,
self.push.content_as_bytes(),
);
device
.inner
.cmd_dispatch(*command_buffer, Self::dispatch_count(), 1, 1);
}
}
}
#version 460
#extension GL_EXT_nonuniform_qualifier : require
#include "shared.glsl"
#define BOUNDS 20.0f
//push constants block
layout( push_constant ) uniform constants{
ResHandle sim;
uint is_init;
uint buf_size;
} Push;
layout(set = 0, binding = 0) buffer SimObjects{
SimObject objects[];
} global_buffers_objects[];
layout(set = 1, binding = 0, rgba8) uniform image2D global_images_2d[];
layout(set = 2, binding = 0) uniform sampler2D global_textures[];
layout(set = 3, binding = 0) uniform sampler samplers[];
//src: https://stackoverflow.com/questions/4200224/random-noise-functions-for-glsl
float rand(vec2 co){
return fract(sin(dot(co, vec2(12.9898, 78.233))) * 43758.5453);
}
layout (local_size_x = 64, local_size_y = 1, local_size_z = 1) in;
void main(){
uint widx = gl_GlobalInvocationID.x;
if (widx >= Push.buf_size){
return;
}
SimObject src;
if (Push.is_init > 0){
src = global_buffers_objects[nonuniformEXT(get_index(Push.sim))].objects[widx];
}else{
vec4 rand = vec4(
rand(vec2(uvec2(widx * 13, widx * 13))),
rand(vec2(uvec2(widx * 17, widx * 17))),
rand(vec2(uvec2(widx * 23, widx * 23))),
rand(vec2(uvec2(widx * 27, widx * 27)))
);
//Init to some random location and velocity
src = SimObject(
rand.xyzw,
rand.wzyx / 100.0
);
}
//"simulation step"
src.location.xyz += src.velocity.xyz;
//flip velocity if we exceed the bounds
if (abs(src.location.x) > BOUNDS){
src.velocity.x *= -1.0;
}
if (abs(src.location.y) > BOUNDS){
src.velocity.y *= -1.0;
}
if (abs(src.location.z) > BOUNDS){
src.velocity.z *= -1.0;
}
global_buffers_objects[nonuniformEXT(get_index(Push.sim))].objects[widx] = src;
}
So far working with the new graph is much more pleasant. I plan on refining the scheduler later based on a more intelligent topological sort.
Have a look at the MarpII repository if you are interested.
|
# Channels¶
Nextflow is based on the Dataflow programming model in which processes communicate through channels.
A channel has two major properties:
1. Sending a message is an asynchronous operation which completes immediately, without having to wait for the receiving process.
2. Receiving data is a blocking operation which stops the receiving process until the message has arrived.
## Channel types¶
Nextflow distinguish two different kinds of channels: queue channels and value channels.
### Queue channel¶
A queue channel is a non-blocking unidirectional FIFO queue which connects two processes or operators.
A queue channel is usually created using a factory method such as a from, fromPath, etc. or chaining it with a channel operator such as map, flatMap, etc.
Queue channels are also created by process output declarations using the into clause.
Note
The definition implies that the same queue channel cannot be used more than one time as process output and more then one time as process input.
In you need to connect a process output channel to more then one process or operator use the into operator to create two (or more) copies of the same channel and use each of them to connect a separate process.
### Value channel¶
A value channel a.k.a. singleton channel by definition is bound to a single value and it can be read unlimited times without consuming its content.
Tip
For this reason a value channel can be used as input by more than one process.
A value channel is created using the value factory method or by operators returning a single value, such us first, last, collect, count, min, max, reduce, sum.
Note
A value channel is implicitly created by a process when an input specifies a simple value in the from clause. Moreover, a value channel is also implicitly created as output for a process whose inputs are only value channels.
For example:
process foo {
input:
val x from 1
output:
file 'x.txt' into result
"""
echo $x > x.txt """ } The process in the above snippet declare a single input which implicitly is a value channel. Therefore also the result output is a value channel that can be read by more than one process. ## Channel factory¶ Channels may be created implicitly by the process output(s) declaration or explicitly using the following channel factory methods. The available factory methods are: ### create¶ Warning This method is deprecated. Creates a new channel by using the create method, as shown below: channelObj = Channel.create() ### of¶ The of method allows you to create a channel emitting any sequence of values that are specified as the method argument, for example: ch = Channel.of( 1, 3, 5, 7 ) ch.view { "value:$it" }
The first line in this example creates a variable ch which holds a channel object. This channel emits the values specified as a parameter in the of method. Thus the second line prints the following:
value: 1
value: 3
value: 5
value: 7
Tip
Range of values are expanded accordingly.
Channel
.of(1..23, 'X', 'Y')
.view()
Prints:
1
2
3
4
:
23
X
Y
### from¶
Warning
This method is deprecated. Use of or fromList instead.
The from method allows you to create a channel emitting any sequence of values that are specified as the method argument, for example:
ch = Channel.from( 1, 3, 5, 7 )
ch.subscribe { println "value: $it" } The first line in this example creates a variable ch which holds a channel object. This channel emits the values specified as a parameter in the from method. Thus the second line will print the following: value: 1 value: 3 value: 5 value: 7 The following example shows how to create a channel from a range of numbers or strings: zeroToNine = Channel.from( 0..9 ) strings = Channel.from( 'A'..'Z' ) Note Note that when the from argument is an object implementing the (Java) Collection interface, the resulting channel emits the collection entries as individual emissions. Thus the following two declarations produce an identical result even tough in the first case the items are specified as multiple arguments while in the second case as a single list object argument: Channel.from( 1, 3, 5, 7, 9 ) Channel.from( [1, 3, 5, 7, 9] ) But when more than one argument is provided, they are always managed as single emissions. Thus, the following example creates a channel emitting three entries each of which is a list containing two elements: Channel.from( [1, 2], [5,6], [7,9] ) ### value¶ The value factory method is used to create a value channel. An optional not null argument can be specified to bind the channel to a specific value. For example: expl1 = Channel.value() expl2 = Channel.value( 'Hello there' ) expl3 = Channel.value( [1,2,3,4,5] ) The first line in the example creates an 'empty' variable. The second line creates a channel and binds a string to it. Finally the last one creates a channel and binds a list object to it that will be emitted as a sole emission. ### fromList¶ The fromList method allows you to create a channel emitting the values provided as a list of elements, for example: Channel .fromList( ['a', 'b', 'c', 'd'] ) .view { "value:$it" }
Prints:
a
b
c
d
### fromPath¶
You can create a channel emitting one or more file paths by using the fromPath method and specifying a path string as an argument. For example:
myFileChannel = Channel.fromPath( '/data/some/bigfile.txt' )
The above line creates a channel and binds to it a Path item referring the specified file.
Note
It does not check the file existence.
Whenever the fromPath argument contains a * or ? wildcard character it is interpreted as a glob path matcher. For example:
myFileChannel = Channel.fromPath( '/data/big/*.txt' )
This example creates a channel and emits as many Path items as there are files with txt extension in the /data/big folder.
Tip
Two asterisks, i.e. **, works like * but crosses directory boundaries. This syntax is generally used for matching complete paths. Curly brackets specify a collection of sub-patterns.
For example:
files = Channel.fromPath( 'data/**.fa' )
moreFiles = Channel.fromPath( 'data/**/*.fa' )
pairFiles = Channel.fromPath( 'data/file_{1,2}.fq' )
The first line returns a channel emitting the files ending with the suffix .fa in the data folder and recursively in all its sub-folders. While the second one only emits the files which have the same suffix in any sub-folder in the data path. Finally the last example emits two files: data/file_1.fq and data/file_2.fq.
Note
As in Linux Bash the * wildcard does not match against hidden files (i.e. files whose name start with a . character).
In order to include hidden files, you need to start your pattern with a period character or specify the hidden: true option. For example:
expl1 = Channel.fromPath( '/path/.*' )
expl2 = Channel.fromPath( '/path/.*.fa' )
expl3 = Channel.fromPath( '/path/*', hidden: true )
The first example returns all hidden files in the specified path. The second one returns all hidden files ending with the .fa suffix. Finally the last example returns all files (hidden and non-hidden) in that path.
By default a glob pattern only looks for regular file paths that match the specified criteria, i.e. it won't return directory paths.
You may use the parameter type specifying the value file, dir or any in order to define what kind of paths you want. For example:
myFileChannel = Channel.fromPath( '/path/*b', type: 'dir' )
myFileChannel = Channel.fromPath( '/path/a*', type: 'any' )
The first example will return all directory paths ending with the b suffix, while the second will return any file and directory starting with a a prefix.
Name Description
glob When true interprets characters *, ?, [] and {} as glob wildcards, otherwise handles them as normal characters (default: true)
type Type of paths returned, either file, dir or any (default: file)
hidden When true includes hidden files in the resulting paths (default: false)
maxDepth Maximum number of directory levels to visit (default: no limit)
followLinks When true it follows symbolic links during directories tree traversal, otherwise they are managed as files (default: true)
relative When true returned paths are relative to the top-most common directory (default: false)
checkIfExists When true throws an exception of the specified path do not exist in the file system (default: false)
Note
More than one path or glob pattern can be specified using a list as argument:
Channel.fromPath( ['/some/path/*.fq', '/other/path/*.fastq'] )
(requires version 0.31.x or later)
### fromFilePairs¶
The fromFilePairs method creates a channel emitting the file pairs matching a glob pattern provided by the user. The matching files are emitted as tuples in which the first element is the grouping key of the matching pair and the second element is the list of files (sorted in lexicographical order). For example:
Channel
.fromFilePairs('/my/data/SRR*_{1,2}.fastq')
.println()
It will produce an output similar to the following:
[SRR493366, [/my/data/SRR493366_1.fastq, /my/data/SRR493366_2.fastq]]
[SRR493367, [/my/data/SRR493367_1.fastq, /my/data/SRR493367_2.fastq]]
[SRR493368, [/my/data/SRR493368_1.fastq, /my/data/SRR493368_2.fastq]]
[SRR493369, [/my/data/SRR493369_1.fastq, /my/data/SRR493369_2.fastq]]
[SRR493370, [/my/data/SRR493370_1.fastq, /my/data/SRR493370_2.fastq]]
[SRR493371, [/my/data/SRR493371_1.fastq, /my/data/SRR493371_2.fastq]]
Note
The glob pattern must contain at least a star wildcard character.
Alternatively it is possible to implement a custom file pair grouping strategy providing a closure which, given the current file as parameter, returns the grouping key. For example:
Channel
.fromFilePairs('/some/data/*', size: -1) { file -> file.extension }
.println { ext, files -> "Files with the extension $ext are$files" }
Table of optional parameters available:
Name Description
type Type of paths returned, either file, dir or any (default: file)
hidden When true includes hidden files in the resulting paths (default: false)
maxDepth Maximum number of directory levels to visit (default: no limit)
followLinks When true it follows symbolic links during directories tree traversal, otherwise they are managed as files (default: true)
size Defines the number of files each emitted item is expected to hold (default: 2). Set to -1 for any.
flat When true the matching files are produced as sole elements in the emitted tuples (default: false).
checkIfExists When true throws an exception of the specified path do not exist in the file system (default: false)
Note
More than one glob pattern can be specified using a list as argument:
Channel.fromFilePairs( ['/some/data/SRR*_{1,2}.fastq', '/other/data/QFF*_{1,2}.fastq'] )
(requires version 0.31.x or later)
### fromSRA¶
The fromSRA method queries the NCBI SRA database and returns a channel emitting the FASTQ files matching the specified criteria i.e project or accession number(s). For example:
Channel
.fromSRA('SRP043510')
.println()
It returns:
[SRR1448794, ftp://ftp.sra.ebi.ac.uk/vol1/fastq/SRR144/004/SRR1448794/SRR1448794.fastq.gz]
[SRR1448795, ftp://ftp.sra.ebi.ac.uk/vol1/fastq/SRR144/005/SRR1448795/SRR1448795.fastq.gz]
[SRR1448792, ftp://ftp.sra.ebi.ac.uk/vol1/fastq/SRR144/002/SRR1448792/SRR1448792.fastq.gz]
[SRR1448793, ftp://ftp.sra.ebi.ac.uk/vol1/fastq/SRR144/003/SRR1448793/SRR1448793.fastq.gz]
[SRR1910483, ftp://ftp.sra.ebi.ac.uk/vol1/fastq/SRR191/003/SRR1910483/SRR1910483.fastq.gz]
[SRR1910482, ftp://ftp.sra.ebi.ac.uk/vol1/fastq/SRR191/002/SRR1910482/SRR1910482.fastq.gz]
(remaining omitted)
Multiple accession IDs can be specified using a list object:
ids = ['ERR908507', 'ERR908506', 'ERR908505']
Channel
.fromSRA(ids)
.println()
[ERR908507, [ftp://ftp.sra.ebi.ac.uk/vol1/fastq/ERR908/ERR908507/ERR908507_1.fastq.gz, ftp://ftp.sra.ebi.ac.uk/vol1/fastq/ERR908/ERR908507/ERR908507_2.fastq.gz]]
[ERR908506, [ftp://ftp.sra.ebi.ac.uk/vol1/fastq/ERR908/ERR908506/ERR908506_1.fastq.gz, ftp://ftp.sra.ebi.ac.uk/vol1/fastq/ERR908/ERR908506/ERR908506_2.fastq.gz]]
[ERR908505, [ftp://ftp.sra.ebi.ac.uk/vol1/fastq/ERR908/ERR908505/ERR908505_1.fastq.gz, ftp://ftp.sra.ebi.ac.uk/vol1/fastq/ERR908/ERR908505/ERR908505_2.fastq.gz]]
Note
Read pairs are implicitly managed are returned as a list of files.
Tip
Behind the scene it's uses the NCBI ESearch API, therefore the fromSRA method allow the usage of any query term supported by this API.
Table of optional parameters available:
Name Description
apiKey NCBI user API key.
cache Enable/disable the caching API requests (default: true).
max Maximum number of entries that can be retried (default: unlimited) .
To access the NCBI search service the NCBI API keys should be provided either:
• Using the apiKey optional parameter e.g. Channel.fromSRA(ids, apiKey:'0123456789abcdef').
• Exporting the NCBI_API_KEY variable in your environment e.g. export NCBI_API_KEY=0123456789abcdef.
Note
This feature requires Nextflow version 19.04.0 or later.
### watchPath¶
The watchPath method watches a folder for one or more files matching a specified pattern. As soon as there is a file that meets the specified condition, it is emitted over the channel that is returned by the watchPath method. The condition on files to watch can be specified by using * or ? wildcard characters i.e. by specifying a glob path matching criteria.
For example:
Channel
.watchPath( '/path/*.fa' )
.subscribe { println "Fasta file: $it" } By default it watches only for new files created in the specified folder. Optionally, it is possible to provide a second argument that specifies what event(s) to watch. The supported events are: Name Description create A new file is created (default) modify A file is modified delete A file is deleted You can specified more than one of these events by using a comma separated string as shown below: Channel .watchPath( '/path/*.fa', 'create,modify' ) .subscribe { println "File created or modified:$it" }
Warning
The watchPath factory waits endlessly for files that match the specified pattern and event(s). Thus, whenever you use it in your script, the resulting pipeline will never finish.
### empty¶
The empty factory method, by definition, creates a channel that doesn't emit any value.
## Binding values¶
Since in Nextflow channels are implemented using dataflow variables or queues. Thus sending a message is equivalent to bind a value to object representing the communication channel.
### bind¶
Channel objects provide a bind( ) method which is the basic operation to send a message over the channel. For example:
myChannel = Channel.create()
myChannel.bind( 'Hello world' )
### operator <<¶
The operator << is just a syntax sugar for the bind method. Thus, the following example produce an identical result as the previous one:
myChannel = Channel.create()
myChannel << 'Hello world'
## Observing events¶
### subscribe¶
The subscribe method permits to execute a user define function each time a new value is emitted by the source channel.
The emitted value is passed implicitly to the specified function. For example:
// define a channel emitting three values
source = Channel.from ( 'alpha', 'beta', 'delta' )
// subscribe a function to the channel printing the emitted values
source.subscribe { println "Got: $it" } Got: alpha Got: beta Got: delta Note Formally the user defined function is a Closure as defined by the Groovy programming language on which the Nextflow scripts are based on. If needed the closure parameter can be defined explicitly, using a name other than it and, optionally, specifying the expected value type, as showed in the following example: Channel .from( 'alpha', 'beta', 'lambda' ) .subscribe { String str -> println "Got:${str}; len: \${str.size()}"
}
Got: alpha; len: 5
Got: beta; len: 4
Got: lambda; len: 6
### onNext, onComplete, and onError¶
The subscribe method may accept one or more of the following event handlers:
• onNext: registers a function that is invoked whenever the channel emits a value. This is the same as using the subscribe with a plain closure as describe in the examples above.
• onComplete: registers a function that is invoked after the last value is emitted by the channel.
• onError: registers a function that it is invoked when an exception is raised while handling the onNext event. It will not make further calls to onNext or onComplete. The onError method takes as its parameter the Throwable that caused the error.
For example:
Channel
.from( 1, 2, 3 )
.subscribe onNext: { println it }, onComplete: { println 'Done' }
1
2
3
Done
|
# Presheaf of groups
This article defines the notion of group object in the category of set-valued presheafs|View other types of group objects
## Definition
### Category-theoretic definition
A presheaf of groups on a topological space, is a contravariant functor from the category of open sets of the topological space (under inclusion) to the category of groups.
### Hands-on definition
Let $X$ be a topological space. A presheaf of groups $F$ on $X$ is the following data:
• For every open subset $U \subset X$, a group $F(U)$
• For every pair of open subsets $U \subset V$, a restriction homomorphism $res_{VU}: F(V) \to F(U)$
such that:
• $res_{UU}$ is the identity map for any $U$
• If $W \subset V \subset U$ then $res_{UW} = res_{VW} \circ res_{UV}$
A particular case of a presheaf of groups is a sheaf of groups.
|
# What is a semiring without commutativity requirement for addition?
A semiring is defined by two operations $+$ and $\times$ on a set $R$, such that:
• $(R, +)$ is a commutative monoid
• $(R, \times)$ is a monoid
• $\times$ left-distributes and right-distributes over $+$
• The identity element for $+$ is an absorbing element for $\times$
What is the name of a structure where $(R, +)$ is only required to be a monoid? I'm interested in this because it may make sense in the study of provenance semirings in relational databases. However, beyond this specific context, I think this is a natural subset of the semiring axioms.
The same question has been asked here for rings (where $(R, +)$ is required to be a commutative group), here and here. In this context, the commutativity requirement can be explained (as in this answer) because commutativity of $+$ is implied by distributivity, the existence of a neutral element for $\times$, associativity of $+$, and cancellativity of $+$. However, in a semiring, $(R, +)$ is only a monoid, so in general it is not cancellative: hence, the same explanation does not work.
A generalization of semirings that removes the commutativity requirement are near-semirings, but they additionally remove the requirement of a neutral element for $\times$ and one of the distributivity requirements (e.g., right-distributivity). Hence, my question is equivalent to asking whether there is a name for near-semirings with multiplicative identity and left- and right-distributivity of $\times$ over $+$.
Another related question here asks about just removing the identity requirement for $\times$. I checked quickly the references from this answer to see whether my concept had a name, but apparently Golan's Semirings and Their Applications and Gondran and Minoux's Graphs, Dioids and Semirings: New Models and Algorithms both assume commutativity of $+$ straight away.
|
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Regular version of the site
## Bokstein homomorphism as a universal object
Advances in Mathematics. 2018. Vol. 324. P. 267-325.
We give a simple construction of the correspondence between
square-zero extensions R of a ring R by an R-bimodule M
and second MacLane cohomology classes of R with coefficients
in M (the simplest non-trivial case of the construction is R =
M = Z/p, R = Z/p^2, thus the Bokstein homomorphism of
the title). Following Jibladze and Pirashvili, we treat MacLane
cohomology as cohomology of non-additive endofunctors of
the category of projective R-modules. We explain how to
describe liftings of R-modules and complexes of R-modules
to R in terms of data purely over R. We show that if
R is commutative, then commutative square-zero extensions
R correspond to multiplicative extensions of endofunctors.
We then explore in detail one particular multiplicative non-
additive endofunctor constructed from cyclic powers of a
module V over a commutative ring R annihilated by a prime p.
In this case, R is the second Witt vectors ring W_2(R)
considered as a square-zero extension of R by the Frobenius
twist R(1).
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# 1-0u-VF capacitorconnecteoDartery How much eneroystoredthe capacitor?Had the capacito Deen connectedOo-V battery nowy much energy woulc havebeen stored?...
## Question
###### 1-0u-VF capacitorconnecteoDartery How much eneroystoredthe capacitor?Had the capacito Deen connectedOo-V battery nowy much energy woulc havebeen stored?
1-0u-VF capacitor connecteo Dartery How much eneroy stored the capacitor? Had the capacito Deen connected Oo-V battery nowy much energy woulc havebeen stored?
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# Tag Info
## Hot answers tagged pressure
4
The pressure at any point is the total weight of everything above an area of a square metre. So for example the atmospheric pressure at Earth's surface, 101325 Pa, means the total weight of atmosphere above a square metre at the surface is 101325 N. So when you ask for the pressure at the centre of the Earth, the way to calculate this is to work out the ...
4
Potential energy has absolutely nothing to do with stress-energy or pressure. The following reference is a good source about the origin of the pressure term in the stress-energy tensor: "Momentum due to pressure: A simple model" by Kannan Jagannathan in American Journal of Physics 77, 432 (2009); http://dx.doi.org/10.1119/1.3081105 Potential energy ...
3
The can is acting as a compact heat pipe. When you grasp the can, the liquified gas inside the can absorbs the heat from your hand and expands, carrying the heat away in convective currents that dissipate the heat to other parts of the surface that are at a lower temperature than your hand. Since it draws heat from your hand it feels cool to the touch.
3
I can't speak to what sources you were reading, but the air under a hovercraft is higher than ambient air pressure, not lower. Wikipedia: Hovercraft use blowers to produce a large volume of air below the hull that is slightly above atmospheric pressure. The pressure difference between the higher pressure air below the hull and lower pressure ...
1
The force would be proportional to the area, so the force on the hole would be 10^(-5) N
1
You have to find out what kind of statistical ensemble you are dealing with. As soon as you know that, you can get the corresponding thermodynamical potential from the knowledge of the partition function. When you know the potential, you know everything! EDIT: Since you don't know to which ensemble this partition function $\mathcal{Z}$ belongs to you ...
1
The required change in pressure for a change in melting point can be found from the phase diagram of water. The typical variations in atmospheric pressure are negligible, just as you neglect the additional water pressure experienced in the lower parts of the ice bath. I will leave it up to you to find the factor involved - it is the slope of the water/ice ...
1
Static pressure in a compressible flow depends on the density but not the speed (not directly). Speed and geometry may affect the density. For isentropic flow (neglecting gravitational potential): $${p \over \rho^\gamma} = constant, \gamma = {c_p \over c_v}$$ which could be turned into this: $${p \over p_0} = ({1 \over 1+{(\gamma-1) \over ... 1 Take an empirical approach; go to a oil-change place. Put the car up on a rack/lift (the kind that supports the frame, not the tires - allows tire rotation during oil change). Have them adjust tire pressure while car is up in the air; have them remeasure when the car is back on the ground (tell them why - give them "scientist for a day" certificate). Because ... 1 If the temperature of the gas is kept constant during the compression then the bulk modulus of an ideal gas is just equal to the pressure. The definition of the bulk modulus is:$$ K = -V\frac{dP}{dV} \tag{1} $$For an ideal gas PV = RT, so P = RT/V. If the temperature is constant this gives:$$ \frac{dP}{dV} = -\frac{RT}{V^2} \tag{2} $$and ... 1 It sounds like you are not asking about Bernoulli's principle, which describes energy conservation in a fluid, but about why fluids move faster in the thin section of a pipe. This is not Bernoulli's principle, it is just something someone might have mentioned when talking about Bernoulli's principle. Suppose the liquid moves the same speed everywhere in the ... 1 Initially, I agreed with Olaf Chujko's answer to this question; however, on further reflection, I think the most accurate answer is 'it depends': Firstly, from the schematic that is given, when switch A is pressed, the cylinder volumes above the two cylinders will be vented to a reservoir at ambient pressure (trust me, I work in Oil & Gas and I look at ... 1 The differential amount of force is given by:$$ dF = \Delta p* dA $$You do need to add up the vertical components, which are given by:$$ dF_\downarrow(\theta) = \Delta p * dA * \sin(\theta) $$This goes from 0 \leq \theta \leq \pi. At each value of \theta the differential area is the same:$$ dA = rd\theta * dx $$This gives that:$$ ...
1
How would you solve this for a single small hole? What happens if you now move that hole down by a small amount? What if you add up the contributions of all these holes? Congratulations, you just integrated the expression for the flow rate over the aperture.
Only top voted, non community-wiki answers of a minimum length are eligible
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• ### LOFAR discovery of radio emission in MACS$\,$J0717.5$+$3745(1805.00473)
We present results from LOFAR and GMRT observations of the galaxy cluster MACS$\,$J0717.5$+$3745. The cluster is undergoing a violent merger involving at least four sub-clusters, and it is known to host a radio halo. LOFAR observations reveal new sources of radio emission in the Intra-Cluster Medium: (i) a radio bridge that connects the cluster to a head-tail radio galaxy located along a filament of galaxies falling into the main cluster, (ii) a 1.9 Mpc radio arc, that is located North West of the main mass component, (iii) radio emission along the X-ray bar, that traces the gas in the X-rays South West of the cluster centre. We use deep GMRT observations at 608 MHz to constrain the spectral indices of these new radio sources, and of the emission that was already studied in the literature at higher frequency. We find that the spectrum of the radio halo and of the relic at LOFAR frequency follows the same power law as observed at higher frequencies. The radio bridge, the radio arc, and the radio bar all have steep spectra, which can be used to constrain the particle acceleration mechanisms. We argue that the radio bridge could be caused by the re-acceleration of electrons by shock waves that are injected along the filament during the cluster mass assembly. Despite the sensitivity reached by our observations, the emission from the radio halo does not trace the emission of the gas revealed by X-ray observations. We argue that this could be due to the difference in the ratio of kinetic over thermal energy of the intra-cluster gas, suggested by X-ray observations.
• ### Radio observations of the double-relic galaxy cluster Abell 1240(1804.11352)
We present LOFAR $120-168$ MHz images of the merging galaxy cluster Abell 1240 that hosts double radio relics. In combination with the GMRT $595-629$ MHz and VLA $2-4$ GHz data, we characterised the spectral and polarimetric properties of the radio emission. The spectral indices for the relics steepen from their outer edges towards the cluster centre and the electric field vectors are approximately perpendicular to the major axes of the relics. The results are consistent with the picture that these relics trace large-scale shocks propagating outwards during the merger. Assuming diffusive shock acceleration (DSA), we obtain shock Mach numbers of $\mathcal{M}=2.4$ and $2.3$ for the northern and southern shocks, respectively. For $\mathcal{M}\lesssim3$ shocks, a pre-existing population of mildly relativistic electrons is required to explain the brightness of the relics due to the high ($>10$ per cent) particle acceleration efficiency required. However, for $\mathcal{M}\gtrsim4$ shocks the required efficiency is $\gtrsim1\%$ and $\gtrsim0.5\%$, respectively, which is low enough for shock acceleration directly from the thermal pool. We used the fractional polarization to constrain the viewing angle to $\geqslant(53\pm3)^\circ$ and $\geqslant(39\pm5)^\circ$ for the northern and southern shocks, respectively. We found no evidence for diffuse emission in the cluster central region. If the halo spans the entire region between the relics ($\sim1.8\,\text{Mpc}$) our upper limit on the power is $P_\text{1.4 GHz}=(1.4\pm0.6)\times10^{23}\,\text{W}\text{Hz}^{-1}$ which is approximately equal to the anticipated flux from a cluster of this mass. However, if the halo is smaller than this, our constraints on the power imply that the halo is underluminous.
• ### LOFAR discovery of a double radio halo system in Abell 1758 and radio/X-ray study of the cluster pair(1804.09187)
Radio halos and radio relics are diffuse synchrotron sources that extend over Mpc-scales and are found in a number of merger galaxy clusters. They are believed to form as a consequence of the energy that is dissipated by turbulence and shocks in the intra-cluster medium (ICM). However, the precise physical processes that generate these steep synchrotron spectrum sources are still poorly constrained. We present a new LOFAR observation of the double galaxy cluster Abell 1758. This system is composed of A1758N, a massive cluster hosting a known giant radio halo, and A1758S, which is a less massive cluster whose diffuse radio emission is confirmed here for the first time. Our observations have revealed a radio halo and a candidate radio relic in A1758S, and a suggestion of emission along the bridge connecting the two systems which deserves confirmation. We combined the LOFAR data with archival VLA and GMRT observations to constrain the spectral properties of the diffuse emission. We also analyzed a deep archival Chandra observation and used this to provide evidence that A1758N and A1758S are in a pre-merger phase. The ICM temperature across the bridge that connects the two systems shows a jump which might indicate the presence of a transversal shock generated in the initial stage of the merger.
• ### Shock location and CME 3D reconstruction of a solar type II radio burst with LOFAR(1804.01025)
April 3, 2018 astro-ph.SR
Type II radio bursts are evidence of shocks in the solar atmosphere and inner heliosphere that emit radio waves ranging from sub-meter to kilometer lengths. These shocks may be associated with CMEs and reach speeds higher than the local magnetosonic speed. Radio imaging of decameter wavelengths (20-90 MHz) is now possible with LOFAR, opening a new radio window in which to study coronal shocks that leave the inner solar corona and enter the interplanetary medium and to understand their association with CMEs. To this end, we study a coronal shock associated with a CME and type II radio burst to determine the locations at which the radio emission is generated, and we investigate the origin of the band-splitting phenomenon.
• ### Discovery of large-scale diffuse radio emission in low-mass galaxy cluster Abell 1931(1804.01099)
April 3, 2018 astro-ph.GA, astro-ph.HE
Extended, steep-spectrum radio synchrotron sources are pre-dominantly found in massive galaxy clusters as opposed to groups. LOFAR Two-Metre Sky Survey images have revealed a diffuse, ultra-steep spectrum radio source in the low-mass cluster Abell 1931. The source has a fairly irregular morphology with a largest linear size of about 550 kpc. The source is only seen in LOFAR observations at 143 MHz and GMRT observations at 325 MHz. The spectral index of the total source between 143 MHz and 325 MHz is $\alpha_{143}^{325} = -2.86 \pm 0.36$. The source remains invisible in Very Large Array (1-2 GHz) observations as expected given the spectral index. Chandra X-ray observations of the cluster revealed a bolometric luminosity of $L_X = (1.65 \pm 0.39) \times 10^{43}$ erg s$^{-1}$ and a temperature of $2.92_{-0.87}^{+1.89}$ keV which implies a mass of around $\sim 10^{14} M_{\odot}$. We conclude that the source is a remnant radio galaxy that has shut off around 200 Myr ago. The brightest cluster galaxy, a radio-loud elliptical galaxy, could be the source for this extinct source. Unlike remnant sources studied in the literature, our source has a steep spectrum at low radio frequencies. Studying such remnant radio galaxies at low radio frequencies is important for understanding the scarcity of such sources and their role in feedback processes.
• ### Deep VLA observations of the cluster 1RXS J0603.3+4214 in the frequency range 1-2 GHz(1712.01327)
Dec. 4, 2017 astro-ph.GA
We report L-band VLA observations of 1RXS J0603.3+4214, a cluster that hosts a bright radio relic, known as the Toothbrush, and an elongated giant radio halo. These new observations allow us to study the surface brightness distribution down to one arcsec resolution with very high sensitivity. Our images provide an unprecedented detailed view of the Toothbrush, revealing enigmatic filamentary structures. To study the spectral index distribution, we complement our analysis with published LOFAR and GMRT observations. The bright brush' of the Toothbrush shows a prominent narrow ridge to its north with a sharp outer edge. The spectral index at the ridge is in the range $-0.70\leq\alpha\leq-0.80$. We suggest that the ridge is caused by projection along the line of sight. With a simple toy model for the smallest region of the ridge, we conclude that the magnetic field is below $5\,\rm\mu G$ and varies significantly across the shock front. Our model indicates that the actual Mach number is higher than that obtained from the injection index and agrees well with the one derived from the overall spectrum, namely ${\cal M}=3.78^{+0.3}_{-0.2}$. The radio halo shows an average spectral index of $\alpha=-1.16\pm0.05$ and a slight gradient from north to south. The southernmost part of the halo is steeper and possibly related to a shock front. Excluding the southernmost part, the halo morphology agrees very well with the X-ray morphology. A power-law correlation is found between the radio and X-ray surface brightness
• ### Mystery solved: discovery of extended radio emission in the merging galaxy cluster Abell 2146(1708.03641)
Dec. 1, 2017 astro-ph.GA, astro-ph.HE
Abell 2146 ($z=0.232$) is a massive galaxy cluster currently undergoing a spectacular merger in the plane of the sky with a bullet-like morphology. It was the first system in which both the bow and upstream shock fronts were detected at X-ray wavelengths (Mach$\sim2$), yet deep GMRT 325 MHz observations failed to detect extended radio emission associated with the cluster as is typically seen in such systems. We present new, multi-configuration $1-2$ GHz Karl G. Jansky Very Large Array (VLA) observations of Abell 2146 totalling 16 hours of observations. These data reveal for the first time the presence of an extended ($\approx850$ kpc), faint radio structure associated with Abell 2146. The structure appears to harbour multiple components, one associated with the upstream shock which we classify as a radio relic and one associated with the subcluster core which is consisted as being a radio halo bounded by the bow shock. The newly detected structures have some of the lowest radio powers detected thus far in any cluster ($P_{\rm 1.4 GHz, halo}=2.4\pm0.2\times10^{23}$ W Hz$^{-1}$ and $P_{\rm 1.4 GHz, relic}=2.2\pm0.2\times10^{23}$ W Hz$^{-1}$). The flux measurement of the halo, as well as its morphology, also suggest that the halo was recently created ($\approx0.3$ Gyr after core passage), consistent with the dynamical state of the cluster. These observations demonstrate the capacity of the upgraded VLA to detect extremely faint and extended radio structures. Based on these observations, we predict that many more radio relics and radio halos in merging clusters should be detected by future radio facilities such as the Square Kilometre Array (SKA).
• ### Gentle re-energisation of electrons in merging galaxy clusters(1710.06796)
Oct. 18, 2017 astro-ph.CO, astro-ph.HE
Galaxy clusters are the most massive constituents of the large-scale structure of the Universe. While the hot thermal gas that pervades galaxy clusters is relatively well understood through observations with X-ray satellites, our understanding of the non-thermal part of the intra-cluster medium remains incomplete. With LOFAR and GMRT observations, we have identified a phenomenon that can be unveiled only at extremely low radio-frequencies and offers new insights into the non-thermal component. We propose that the interplay between radio-emitting plasma and the perturbed intra-cluster medium can gently re-energise relativistic particles initially injected by active galactic nuclei. Sources powered through this mechanism can maintain electrons at higher energies than radiative ageing would allow. If this mechanism is common for aged plasma, a population of mildly relativistic electrons can be accumulated inside galaxy clusters providing the seed population for merger-induced re-acceleration mechanisms on larger scales such as turbulence and shock waves.
• ### LOFAR discovery of an ultra-steep radio halo and giant head-tail radio galaxy in Abell 1132(1708.08928)
Oct. 2, 2017 astro-ph.GA
LOFAR observations at 144 MHz have revealed large-scale radio sources in the unrelaxed galaxy cluster Abell 1132. The cluster hosts diffuse radio emission on scales of $\sim$650 kpc near the cluster center and a head-tail (HT) radio galaxy, extending up to 1 Mpc, South of the cluster center. The central diffuse radio emission is not seen in NVSS, FIRST, WENSS, nor in C & D array VLA observations at 1.4 GHz, but is detected in our follow-up GMRT observations at 325 MHz. Using LOFAR and GMRT data, we determine the spectral index of the central diffuse emission to be $\alpha=-1.75\pm0.19$ ($S\propto\nu^{\alpha}$). We classify this emission as an ultra-steep spectrum radio halo and discuss the possible implications for the physical origin of radio halos. The HT radio galaxy shows narrow, collimated emission extending up to 1 Mpc and another 300 kpc of more diffuse, disturbed emission, giving a full projected linear size of 1.3 Mpc - classifying it as a giant radio galaxy (GRG) and making it the longest HT found to date. The head of the GRG coincides with an elliptical galaxy (SDSS J105851.01$+$564308.5) belonging to Abell 1132. In our LOFAR image, there appears to be a connection between the radio halo and the GRG. The turbulence that may have produced the halo may have also affected the tail of the GRG. In turn, the GRG may have provided seed electrons for the radio halo.
• ### The Association of a J-burst with a Solar Jet(1707.03428)
Aug. 14, 2017 astro-ph.SR
Context. The Sun is an active star that produces large-scale energetic events such as solar flares and coronal mass ejections and numerous smaller-scale events such as solar jets. These events are often associated with accelerated particles that can cause emission at radio wavelengths. The reconfiguration of the solar magnetic field in the corona is believed to be the cause of the majority of solar energetic events and accelerated particles. Aims. Here, we investigate a bright J-burst that was associated with a solar jet and the possible emission mechanism causing these two phenomena. Methods. We used data from the Solar Dynamics Observatory (SDO) to observe a solar jet, and radio data from the Low Frequency Array (LOFAR) and the Nan\c{c}ay Radioheliograph (NRH) to observe a J-burst over a broad frequency range (33-173 MHz) on 9 July 2013 at ~11:06 UT. Results. The J-burst showed fundamental and harmonic components and it was associated with a solar jet observed at extreme ultraviolet wavelengths with SDO. The solar jet occurred at a time and location coincident with the radio burst, in the northern hemisphere, and not inside a group of complex active regions in the southern hemisphere. The jet occurred in the negative polarity region of an area of bipolar plage. Newly emerged positive flux in this region appeared to be the trigger of the jet. Conclusions. Magnetic reconnection between the overlying coronal field lines and the newly emerged positive field lines is most likely the cause of the solar jet. Radio imaging provides a clear association between the jet and the J-burst which shows the path of the accelerated electrons.
• ### VLA Radio Observations of the HST Frontier Fields Cluster Abell 2744: The Discovery of New Radio Relics(1708.03367)
Aug. 10, 2017 astro-ph.CO, astro-ph.GA
Cluster mergers leave distinct signatures in the ICM in the form of shocks and diffuse cluster radio sources that provide evidence for the acceleration of relativistic particles. However, the physics of particle acceleration in the ICM is still not fully understood. Here we present new 1-4 GHz Jansky Very Large Array (VLA) and archival Chandra observations of the HST Frontier Fields Cluster Abell 2744. In our new VLA images, we detect the previously known $\sim2.1$ Mpc radio halo and $\sim1.5$ Mpc radio relic. We carry out a radio spectral analysis from which we determine the relic's injection spectral index to be $\alpha_{\rm{inj}} = -1.12 \pm 0.19$. This corresponds to a shock Mach number of $\mathcal{M}$ = 2.05$^{+0.31}_{-0.19}$ under the assumption of diffusive shock acceleration. We also find evidence for spectral steepening in the post-shock region. We do not find evidence for a significant correlation between the radio halo's spectral index and ICM temperature. In addition, we observe three new polarized diffuse sources and determine two of these to be newly discovered giant radio relics. These two relics are located in the southeastern and northwestern outskirts of the cluster. The corresponding integrated spectral indices measure $-1.81 \pm 0.26$ and $-0.63 \pm 0.21$ for the SE and NW relics, respectively. From an X-ray surface brightness profile we also detect a possible density jump of $R=1.39^{+0.34}_{-0.22}$ co-located with the newly discovered SE relic. This density jump would correspond to a shock front Mach number of $\mathcal{M}=1.26^{+0.25}_{-0.15}$.
• ### Deep LOFAR observations of the merging galaxy cluster CIZA J2242.8+5301(1706.09903)
June 29, 2017 astro-ph.GA, astro-ph.HE
Previous studies have shown that CIZA J2242.8+5301 (the 'Sausage' cluster, $z=0.192$) is a massive merging galaxy cluster that hosts a radio halo and multiple relics. In this paper we present deep, high fidelity, low-frequency images made with the LOw-Frequency Array (LOFAR) between 115.5 and 179 MHz. These images, with a noise of 140 mJy/beam and a resolution of $\theta_{\text{beam}}=7.3"\times5.3"$, are an order of magnitude more sensitive and five times higher resolution than previous low-frequency images of this cluster. We combined the LOFAR data with the existing GMRT (153, 323, 608 MHz) and WSRT (1.2, 1.4, 1.7, 2.3 GHz) data to study the spectral properties of the radio emission from the cluster. Assuming diffusive shock acceleration (DSA), we found Mach numbers of $\mathcal{M}_{n}=2.7{}_{-0.3}^{+0.6}$ and $\mathcal{M}_{s}=1.9_{-0.2}^{+0.3}$ for the northern and southern shocks. The derived Mach number for the northern shock requires an acceleration efficiency of several percent to accelerate electrons from the thermal pool, which is challenging for DSA. Using the radio data, we characterised the eastern relic as a shock wave propagating outwards with a Mach number of $\mathcal{M}_{e}=2.4_{-0.3}^{+0.5}$, which is in agreement with $\mathcal{M}_{e}^{X}=2.5{}_{-0.2}^{+0.6}$ that we derived from Suzaku data. The eastern shock is likely to be associated with the major cluster merger. The radio halo was measured with a flux of $346\pm64\,\text{mJy}$ at $145\,\text{MHz}$. Across the halo, we observed a spectral index that remains approximately constant ($\alpha^{\text{145 MHz-2.3 GHz}}_{\text{across $\sim$1 Mpc}^2}=-1.01\pm0.10$) after the steepening in the post-shock region of the northern relic. This suggests a generation of post-shock turbulence that re-energies aged electrons.
• ### Deep 230-470 MHz VLA Observations of the mini-halo in the Perseus Cluster(1701.03791)
June 13, 2017 astro-ph.CO, astro-ph.GA
We present a low-frequency view of the Perseus cluster with new observations from the Karl G. Jansky Very Large Array (JVLA) at 230-470 MHz. The data reveal a multitude of new structures associated with the mini-halo. The mini-halo seems to be influenced both by the AGN activity as well as by the sloshing motion of the cool core cluster's gas. In addition, it has a filamentary structure similar to that seen in radio relics found in merging clusters. We present a detailed description of the data reduction and imaging process of the dataset. The depth and resolution of the observations allow us to conduct for the first time a detailed comparison of the mini-halo structure with the X-ray structure as seen in the Chandra X-ray images. The resulting image shows very clearly that the mini-halo emission is mostly contained behind the cold fronts, similar to that predicted by simulations of gas sloshing in galaxy clusters. However, due to the proximity of the Perseus cluster, as well as the quality of the data at low radio frequencies and at X-ray wavelengths, we also find evidence of fine structure. This structure includes several radial radio filaments extending in different directions, a concave radio structure associated with the southern X-ray bay and sharp edges that correlate with X-ray edges. Mini-halos are therefore not simply diffuse, uniform radio sources, but are rather filled with a rich variety of complex structures. These results illustrate the high-quality images that can be obtained with the new JVLA at low radio-frequencies, as well as the necessity to obtain deeper, higher-fidelity radio images of mini-halos and halos in clusters to further understand their origin.
• ### LOFAR MSSS: The Scaling Relation between AGN Cavity Power and Radio Luminosity at Low Radio Frequencies(1706.00225)
June 1, 2017 astro-ph.CO, astro-ph.GA
We present a new analysis of the widely used relation between cavity power and radio luminosity in clusters of galaxies with evidence for strong AGN feedback. We study the correlation at low radio frequencies using two new surveys - the First Alternative Data Release of the TIFR GMRT Sky Survey (TGSS ADR1) at 148 MHz and LOFAR's first all-sky survey, the Multifrequency Snapshot Sky Survey (MSSS) at 140 MHz. We find a scaling relation $P_{\rm cav} \propto L_{148}^{\beta}$, with a logarithmic slope of $\beta = 0.51 \pm 0.14$, which is in good agreement with previous results based on data at 327 MHz. The large scatter present in this correlation confirms the conclusion reached at higher frequencies that the total radio luminosity at a single frequency is a poor predictor of the total jet power. We show that including measurements at 148 MHz alone is insufficient to reliably compute the bolometric radio luminosity and reduce the scatter in the correlation. For a subset of four well-resolved sources, we examine the detected extended structures at low frequencies and compare with the morphology known from higher frequency images and Chandra X-ray maps. In Perseus we discuss details in the structures of the radio mini-halo, while in the 2A 0335+096 cluster we observe new diffuse emission associated with multiple X-ray cavities and likely originating from past activity. For A2199 and MS 0735.6+7421, we confirm that the observed low-frequency radio lobes are confined to the extents known from higher frequencies. This new low-frequency analysis highlights the fact that existing cavity power to radio luminosity relations are based on a relatively narrow range of AGN outburst ages. We discuss how the correlation could be extended using low frequency data from the LOFAR Two-metre Sky Survey (LoTSS) in combination with future, complementary deeper X-ray observations.
• ### LOFAR MSSS: Discovery of a 2.56 Mpc giant radio galaxy associated with a disturbed galaxy group(1702.01571)
Feb. 6, 2017 astro-ph.CO, astro-ph.GA
We report on the discovery in the LOFAR Multifrequency Snapshot Sky Survey (MSSS) of a giant radio galaxy (GRG) with a projected size of $2.56 \pm 0.07$ Mpc projected on the sky. It is associated with the galaxy triplet UGC 9555, within which one is identified as a broad-line galaxy in the Sloan Digital Sky Survey (SDSS) at a redshift of $0.05453 \pm 1 \times 10^{-5}$, and with a velocity dispersion of $215.86 \pm 6.34$ km/s. From archival radio observations we see that this galaxy hosts a compact flat-spectrum radio source, and we conclude that it is the active galactic nucleus (AGN) responsible for generating the radio lobes. The radio luminosity distribution of the jets, and the broad-line classification of the host AGN, indicate this GRG is orientated well out of the plane of the sky, making its physical size one of the largest known for any GRG. Analysis of the infrared data suggests that the host is a lenticular type galaxy with a large stellar mass ($\log~\mathrm{M}/\mathrm{M}_\odot = 11.56 \pm 0.12$), and a moderate star formation rate ($1.2 \pm 0.3~\mathrm{M}_\odot/\mathrm{year}$). Spatially smoothing the SDSS images shows the system around UGC 9555 to be significantly disturbed, with a prominent extension to the south-east. Overall, the evidence suggests this host galaxy has undergone one or more recent moderate merger events and is also experiencing tidal interactions with surrounding galaxies, which have caused the star formation and provided the supply of gas to trigger and fuel the Mpc-scale radio lobes.
• ### LOFAR observations of decameter carbon radio recombination lines towards Cassiopeia A(1701.08802)
Jan. 30, 2017 astro-ph.GA
We present a study of carbon radio recombination lines towards Cassiopeia A using LOFAR observations in the frequency range 10-33 MHz. Individual carbon $\alpha$ lines are detected in absorption against the continuum at frequencies as low as 16 MHz. Stacking several C$\alpha$ lines we obtain detections in the 11-16 MHz range. These are the highest signal-to-noise measurements at these frequencies. The peak optical depth of the C$\alpha$ lines changes considerably over the 11-33 MHz range with the peak optical depth decreasing from 4$\times10^{-3}$ at 33 MHz to 2$\times10^{-3}$ at 11 MHz, while the line width increases from 20 km s$^{-1}$ to 150 km s$^{-1}$. The combined change in peak optical depth and line width results in a roughly constant integrated optical depth. We interpret this as carbon atoms close to local thermodynamic equilibrium. In this work we focus on how the 11-33 MHz carbon radio recombination lines can be used to determine the gas physical conditions. We find that the ratio of the carbon radio recombination lines to that of the 158 $\mu$m [CII] fine-structure line is a good thermometer, while the ratio between low frequency carbon radio recombination lines provides a good barometer. By combining the temperature and pressure constraints with those derived from the line width we are able to constrain the gas properties (electron temperature and density) and radiation field intensity. Given the 1$\sigma$ uncertainties in our measurements these are; $T_{e}\approx68$-$98$ K, $n_{e}\approx0.02$-$0.035$ cm$^{-3}$ and $T_{r,100}\approx1500$-$1650$ K. Despite challenging RFI and ionospheric conditions, our work demonstrates that observations of carbon radio recombination lines in the 10-33 MHz range can provide insight into the gas conditions.
• ### Chandra and JVLA observations of HST Frontier Fields cluster MACS J0717.5+3745(1701.04096)
To investigate the relationship between thermal and non-thermal components in merger galaxy clusters, we present deep JVLA and Chandra observations of the HST Frontier Fields cluster MACS J0717.5+3745. The Chandra image shows a complex merger event, with at least four components belonging to different merging subclusters. NW of the cluster, $\sim 0.7$ Mpc from the center, there is a ram-pressure-stripped core that appears to have traversed the densest parts of the cluster after entering the ICM from the direction of a galaxy filament to the SE. We detect a density discontinuity NNE of this core which we speculate is associated with a cold front. Our radio images reveal new details for the complex radio relic and radio halo in this cluster. In addition, we discover several new filamentary radio sources with sizes of 100-300 kpc. A few of these seem to be connected to the main radio relic, while others are either embedded within the radio halo or projected onto it. A narrow-angled-tailed (NAT) radio galaxy, a cluster member, is located at the center of the radio relic. The steep spectrum tails of this AGN leads into the large radio relic where the radio spectrum flattens again. This morphological connection between the NAT radio galaxy and relic provides evidence for re-acceleration (revival) of fossil electrons. The presence of hot $\gtrsim 20$ keV ICM gas detected by Chandra near the relic location provides additional support for this re-acceleration scenario.
• ### Suzaku observations of the merging galaxy cluster Abell2255: The northeast radio relic(1612.03058)
Dec. 8, 2016 astro-ph.CO, astro-ph.HE
We present the results of deep 140 ks Suzaku X-ray observations of the north-east (NE) radio relic of the merging galaxy cluster Abell2255. The temperature structure of Abell2255 is measured out to 0.9 times the virial radius (1.9 Mpc) in the NE direction for the first time. The Suzaku temperature map of the central region suggests a complex temperature distribution, which agrees with previous work. Additionally, on a larger-scale, we confirm that the temperature drops from 6 keV around the cluster center to 3 keV at the outskirts, with two discontinuities at {\it r}$\sim$5\arcmin~(450 kpc) and $\sim$12\arcmin~(1100 kpc) from the cluster center. Their locations coincide with surface brightness discontinuities marginally detected in the XMM-Newton image, which indicates the presence of shock structures. From the temperature drop, we estimate the Mach numbers to be ${\cal M}_{\rm inner}\sim$1.2 and, ${\cal M}_{\rm outer}\sim$1.4. The first structure is most likely related to the large cluster core region ($\sim$350--430 kpc), and its Mach number is consistent with the XMM-Newton observation (${\cal M}\sim$1.24: Sakelliou & Ponman 2006). Our detection of the second temperature jump, based on the Suzaku key project observation, shows the presence of a shock structure across the NE radio relic. This indicates a connection between the shock structure and the relativistic electrons that generate radio emission. Across the NE radio relic, however, we find a significantly lower temperature ratio ($T_1/T_2\sim1.44\pm0.16$ corresponds to~${\cal M}_{\rm X-ray}\sim1.4$) than the value expected from radio wavelengths, based on the standard diffusive shock acceleration mechanism ($T_1/T_2>$ 3.2 or ${\cal M}_{\rm Radio}>$ 2.8).
• ### The LOFAR Two-metre Sky Survey - I. Survey Description and Preliminary Data Release(1611.02700)
Nov. 8, 2016 astro-ph.CO, astro-ph.IM
The LOFAR Two-metre Sky Survey (LoTSS) is a deep 120-168 MHz imaging survey that will eventually cover the entire Northern sky. Each of the 3170 pointings will be observed for 8 hrs, which, at most declinations, is sufficient to produce ~5arcsec resolution images with a sensitivity of ~0.1mJy/beam and accomplish the main scientific aims of the survey which are to explore the formation and evolution of massive black holes, galaxies, clusters of galaxies and large-scale structure. Due to the compact core and long baselines of LOFAR, the images provide excellent sensitivity to both highly extended and compact emission. For legacy value, the data are archived at high spectral and time resolution to facilitate subarcsecond imaging and spectral line studies. In this paper we provide an overview of the LoTSS. We outline the survey strategy, the observational status, the current calibration techniques, a preliminary data release, and the anticipated scientific impact. The preliminary images that we have released were created using a fully-automated but direction-independent calibration strategy and are significantly more sensitive than those produced by any existing large-area low-frequency survey. In excess of 44,000 sources are detected in the images that have a resolution of 25arcsec, typical noise levels of less than 0.5 mJy/beam, and cover an area of over 350 square degrees in the region of the HETDEX Spring Field (right ascension 10h45m00s to 15h30m00s and declination 45d00m00s to 57d00m00s).
• ### Carbon and hydrogen radio recombination lines from the cold clouds towards Cassiopeia A(1609.06857)
Oct. 26, 2016 astro-ph.GA
We use the Low Frequency Array to perform a systematic high spectral resolution investigation of the low-frequency 33-78 MHz spectrum along the line of sight to Cassiopeia A. We complement this with a 304-386 MHz Westerbork Synthesis Radio telescope observation. In this first paper we focus on the carbon radio recombination lines. We detect Cn$\alpha$ lines at -47 and -38 km s$^{-1}$ in absorption for quantum numbers n=438-584 and in emission for n=257-278 with high signal to noise. These lines are associated with cold clouds in the Perseus spiral arm component. Hn$\alpha$ lines are detected in emission for n=257-278. In addition, we also detect Cn$\alpha$ lines at 0 km s$^{-1}$ associated with the Orion arm. We analyze the optical depth of these transitions and their line width. Our models show that the carbon line components in the Perseus arm are best fit with an electron temperature 85 K and an electron density 0.04 cm$^{-3}$ and can be constrained to within 15\%. The electron pressure is constrained to within 20\%. We argue that much of these carbon radio recombination lines arise in the CO-dark surface layers of molecular clouds where most of the carbon is ionized but hydrogen has made the transition from atomic to molecular. The hydrogen lines are clearly associated with the carbon line emitting clouds, but the low-frequency upperlimits indicate that they likely do not trace the same gas. Combining the hydrogen and carbon results we arrive at a firm lower limit to the cosmic ray ionization rate of 2.5$\times$10$^{-18}$ s$^{-1}$, but the actual value is likely much larger.
• ### The Lockman Hole project: LOFAR observations and spectral index properties of low-frequency radio sources(1609.00537)
Sept. 2, 2016 astro-ph.CO, astro-ph.GA
The Lockman Hole is a well-studied extragalactic field with extensive multi-band ancillary data covering a wide range in frequency, essential for characterising the physical and evolutionary properties of the various source populations detected in deep radio fields (mainly star-forming galaxies and AGNs). In this paper we present new 150-MHz observations carried out with the LOw Frequency ARray (LOFAR), allowing us to explore a new spectral window for the faint radio source population. This 150-MHz image covers an area of 34.7 square degrees with a resolution of 18.6$\times$14.7 arcsec and reaches an rms of 160 $\mu$Jy beam$^{-1}$ at the centre of the field. As expected for a low-frequency selected sample, the vast majority of sources exhibit steep spectra, with a median spectral index of $\alpha_{150}^{1400}=-0.78\pm0.015$. The median spectral index becomes slightly flatter (increasing from $\alpha_{150}^{1400}=-0.84$ to $\alpha_{150}^{1400}=-0.75$) with decreasing flux density down to $S_{150} \sim$10 mJy before flattening out and remaining constant below this flux level. For a bright subset of the 150-MHz selected sample we can trace the spectral properties down to lower frequencies using 60-MHz LOFAR observations, finding tentative evidence for sources to become flatter in spectrum between 60 and 150 MHz. Using the deep, multi-frequency data available in the Lockman Hole, we identify a sample of 100 Ultra-steep spectrum (USS) sources and 13 peaked spectrum sources. We estimate that up to 21 percent of these could have $z>4$ and are candidate high-$z$ radio galaxies, but further follow-up observations are required to confirm the physical nature of these objects.
• ### A LOFAR mini-survey for low-frequency radio emission from the nearest brown dwarfs(1608.03852)
Aug. 12, 2016 astro-ph.SR, astro-ph.EP
We have conducted a mini-survey for low-frequency radio emission from some of the closest brown dwarfs to the Sun with rapid rotation rates: SIMP J013656.5+093347, WISEPC J150649.97+702736.0, and WISEPA J174124.26+255319.5. We have placed robust 3-sigma upper limits on the flux density in the 111 - 169 MHz frequency range for these targets: WISE 1506: < 0.72 mJy; WISE 1741: < 0.87 mJy; SIMP 0136: < 0.66 mJy. At 8 hours of integration per target to achieve these limits, we find that systematic and detailed study of this class of object at LOFAR frequencies will require a substantial dedication of resources.
• ### LOFAR/H-ATLAS: A deep low-frequency survey of the Herschel-ATLAS North Galactic Pole field(1606.09437)
June 30, 2016 astro-ph.GA
We present LOFAR High-Band Array (HBA) observations of the Herschel-ATLAS North Galactic Pole survey area. The survey we have carried out, consisting of four pointings covering around 142 square degrees of sky in the frequency range 126--173 MHz, does not provide uniform noise coverage but otherwise is representative of the quality of data to be expected in the planned LOFAR wide-area surveys, and has been reduced using recently developed facet calibration' methods at a resolution approaching the full resolution of the datasets ($\sim 10 \times 6$ arcsec) and an rms off-source noise that ranges from 100 $\mu$Jy beam$^{-1}$ in the centre of the best fields to around 2 mJy beam$^{-1}$ at the furthest extent of our imaging. We describe the imaging, cataloguing and source identification processes, and present some initial science results based on a 5-$\sigma$ source catalogue. These include (i) an initial look at the radio/far-infrared correlation at 150 MHz, showing that many Herschel sources are not yet detected by LOFAR; (ii) number counts at 150 MHz, including, for the first time, observational constraints on the numbers of star-forming galaxies; (iii) the 150-MHz luminosity functions for active and star-forming galaxies, which agree well with determinations at higher frequencies at low redshift, and show strong redshift evolution of the star-forming population; and (iv) some discussion of the implications of our observations for studies of radio galaxy life cycles.
• ### The discovery of lensed radio and X-ray sources behind the Frontier Fields cluster MACS J0717.5+3745 with the JVLA and Chandra(1512.04527)
June 2, 2016 astro-ph.CO, astro-ph.GA
We report on high-resolution JVLA and Chandra observations of the HST Frontier Cluster MACS J0717.5+3745. MACS J0717.5+3745 offers the largest contiguous magnified area of any known cluster, making it a promising target to search for lensed radio and X-ray sources. With the high-resolution 1.0-6.5 GHz JVLA imaging in A and B configuration, we detect a total of 51 compact radio sources within the area covered by the HST imaging. Within this sample we find 7 lensed sources with amplification factors larger than $2$. None of these sources are identified as multiply-lensed. Based on the radio luminosities, the majority of these sources are likely star forming galaxies with star formation rates of 10-50 M$_\odot$ yr$^{-1}$ located at $1 \lesssim z \lesssim 2$. Two of the lensed radio sources are also detected in the Chandra image of the cluster. These two sources are likely AGN, given their $2-10$ keV X-ray luminosities of $\sim 10^{43-44}$ erg s$^{-1}$. From the derived radio luminosity function, we find evidence for an increase in the number density of radio sources at $0.6<z<2.0$, compared to a $z < 0.3$ sample. Our observations indicate that deep radio imaging of lensing clusters can be used to study star forming galaxies, with star formation rates as low as $\sim10$ M$_{\odot}$ yr$^{-1}$, at the peak of cosmic star formation history.
• ### LOFAR 150-MHz observations of the Bo\"otes field: Catalogue and Source Counts(1605.01531)
May 5, 2016 astro-ph.CO, astro-ph.IM
We present the first wide area (19 deg$^2$), deep ($\approx120-150$ {\mu}Jy beam$^{-1}$), high resolution ($5.6 \times 7.4$ arcsec) LOFAR High Band Antenna image of the Bo\"otes field made at 130-169 MHz. This image is at least an order of magnitude deeper and 3-5 times higher in angular resolution than previously achieved for this field at low frequencies. The observations and data reduction, which includes full direction-dependent calibration, are described here. We present a radio source catalogue containing 6276 sources detected over an area of $19$\,deg$^2$, with a peak flux density threshold of $5\sigma$. As the first thorough test of the facet calibration strategy, introduced by van Weeren et al., we investigate the flux and positional accuracy of the catalogue. We present differential source counts that reach an order of magnitude deeper in flux density than previously achieved at these low frequencies, and show flattening at 150 MHz flux densities below 10 mJy associated with the rise of the low flux density star-forming galaxies and radio-quiet AGN.
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How can I interpolate a time series subject to stochastic perturbation?
I have a data set of gas prices. They are not evenly spaced in time, and have quite a few days missing.
Here is a sample of the data
Date Price
2016-05-18 0.9931994220059637
2016-05-19 0.9484317771304708
2016-05-20 0.93686097538978
2016-05-21
2016-05-22
2016-05-23
2016-05-24
2016-05-25
2016-05-26 0.9416552772446175
2016-05-27 0.9312735217012867
Is there a widely used way to interpolate the data? I don't want to do polynomial or linear interpolation since gas prices are subject to perturbation.
Gaussian Process Modeling (GPM) is a non-parametric approach that is excellent at interpolating non-uniformly sampled data which have an expected temporal correlation structure.
There are numerous resources on GPM located here:
http://www.gaussianprocess.org
Including this excellent treatment on GPMs:
http://www.gaussianprocess.org/gpml/
There are GPM capabilities available in Python in SciKitLearn:
http://scikit-learn.org/stable/modules/gaussian_process.html
Using GPM requires you to have some "prior" that describes the correlation (which GPM then fine-tunes from the observed data by solving for kernel hyper-parameters). Arguably the simplest covariance model is the "squared exponential" kernel function which simply says that "things that are close together tend to have similar values", which basically causes GPM to act like a smoothing function. Changing the kernel function based on beliefs concerning temporal correlation can result in different behaviors (for instance, you can add a kernel component that reflects periodic repetition in the data).
An arguably simpler approach would be splines (typically cubic splines), which do smoothing interpolation in a specific way and are also happy to deal with nonuniformly-sampled data. This may suit your needs just fine if you just need some basic smooth interpolation and don't have a strong opinion about the form it should take.
The advantage of GPMs over splines is that they provide a lot more flexibility and control over the behavior of the interpolation based on prior beliefs about its specific temporal covariance structure and are generally more adaptable to the data in terms of inferring underlying structure. Splines are simpler to employ, but always behave in more or less the same fashion and have very limited ability to adapt to underlying structure in the data (apart from the constraint that they always pass through the observed anchor points and interpolate smoothly in a particular fashion).
Additionally, you may not want your interpolation function to always anchor to the observed data exactly (if you believe that the observations are noisy, for instance). In this case, GPMs also have the additional advantage that they can account for noise in the observation data.
(The Kalman filter can do similar things to GPM using "forward and backward smoothing", and has a lot in common with the GPM approach, but GPM is arguably more elegant in its formulation and application in this case, particularly if you don't have a requirement for strictly-causal or incrementally-updating behavior).
There are a number of interpolation capabilities available in Python (including univariate splines, which would be suitable to try with your data).
https://docs.scipy.org/doc/scipy/reference/tutorial/interpolate.html
• The Kalman and GPM approach would provide some idea of the interpolation's variability, while the spline idea is very easy. The Kalman (StructTS) and spline options are available in R as well. – Wayne Oct 24 '16 at 18:21
• Never heard of GPM, but the ability to constrict meaningful confidence intervals is a great part of that procedure. Thanks, great answer. – Demetri Pananos Oct 25 '16 at 14:05
• Definitely true @DemetriPananos, a major advantage of GPMs is that they produce a non-stationary statistical model for the data inclusive of uncertainty which is itself non stationary and data-informed. For certain classes of problems, they're a really powerful tool. – T3am5hark Sep 17 at 18:20
One novel way to interpolate missing values in an EVENLY SPACED TIME SERIES is to simultaneously identify the ARIMA model (just a weighted average without assumptions) and anomalies (unusual values like 1,9,1,9,1,9,5,9 or 1,9,1,9,1,9,1,13 . This is done via Intervention Detection methodology . The coefficients for the newly formed Intervention Series are then the adustments needed to replace the errant values with "what should have been" . In the two cases the adjustment for the errant value is -4 and -4 respectively. Your data set would be insufficient to form the ARIMA model as 5/10 ths (5 out of 10) are errant occluding/masking/hiding the underlying predictive signal/model/equation/weighted average necessary to provide the baseline.
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# Cyclic ADC - Differential non linearity error calculation
Status
Not open for further replies.
#### mvj
Dear All,
I was referred to a paper on Cyclic ADC desing. Can somebody help me understand the deduction of input voltages during the major transitions. Please find the paper attached and I am referring to page 959 - I could not figure out how Vx(n-1) is eliminated while determining Vx.
Best Regards,
M.
#### dgnani
If you are referring to the general formula for Vx(k):
He is simply using induction, you start with a sequence defined by the relation between successive elements and try to generalize to a description of the sequence based only on the index of the sequence
Usually you need to guess the general expression (the one based only on the index) by studying the behavior of the first few elements of the sequence, then you can prove (by induction) that the generalization is correct:
- it is correct for the first element?
- if it is correct for one element is it correct for the following one?
In this case you would start by writing
Vx(0)=Vx
Vx(1)=2(1+eps)Vx(0)-b0 Vref=2(1+eps)Vx-b0 Vref
Vx(2)=2(1+eps)Vx(1)-b1 Vref=2(1+eps)( 2(1+eps)Vx-b0 Vref ) -b1 Vref=
=Vx(2(1+eps))^2 - Vref (b1+2(1+eps)b0)
Vx(3)=...
already at the second element you can estimate the general dependence of the sequence on its index, then you can apply induction to confirm, which is trivial
_________________
If you are referring to the formulas for computing the input signal corresponding to the codes near the MSB transitions:
he is setting
Vx(n-1) ~0
using the first order approximation
(1+eps)^n ~ 1+n eps
and the definition for LSB' as
Vref/(2(1+eps))^(n-1)
since he considering an (n-1)-bit conversion
Last edited:
mvj
Points: 2
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### What are SQLAlchemy Sessions? What does the Session do?
One of the core concepts in SQLAlchemy is the Session. A Session establishes and maintains all conversations between your program and the databases. It represents an intermediary zone for all the Python model objects you have loaded in it. It is one of the entry points to initiate a query against the database, whose results are populated and mapped into unique objects within the Session. A unique object is the only object in the Session with a particular primary key.
A typical lifespan of a Session looks like this:
• Session is constructed, at which point it is not associated with any model objects.
• The Session receives query requests, whose results are persisted / associated with the Session.
• Arbitrary number of model objects are constructed and then added to the Session, after which point the Session starts to maintain and manage those objects.
• Once all the changes are made against the objects in the Session, we may decide to commit the changes from the Session to the database or rollback those changes in the SessionSession.commit() means that the changes made to the objects in the Session so far will be persisted into the database while Session.rollback() means those changes will be discarded.
• Session.close() will close the Session and its corresponding connections, which means we are done with the Session and want to release the connection object associated with it.
### Understanding SQLAlchemy Sessions by Examples
Let’s use a simple example to illustrate how to use Session to insert objects into the databases.
from sqlalchemy import Column, String, Integer, ForeignKey
from sqlalchemy.ext.declarative import declarative_base
Base = declarative_base()
class User(Base):
__tablename__ = 'user'
id = Column(Integer, primary_key=True)
name = Column(String)
from sqlalchemy import create_engine
engine = create_engine('sqlite:///')
from sqlalchemy.orm import sessionmaker
# Construct a sessionmaker object
session = sessionmaker()
# Bind the sessionmaker to engine
session.configure(bind=engine)
# Create all the tables in the database which are
# defined by Base's subclasses such as User
Base.metadata.create_all(engine)
### Create and Persist Session Objects
Once we have a session, we can create objects and add them to the session.
# Make a new Session object
s = session()
john = User(name='John')
# Add User john to the Session object
s.add(john)
# Commit the new User John to the database
s.commit()
Let’s insert another user Mary and inspect the new object’s id at each step during the insertion process.
>>> mary = User(name='Mary')
>>> print(mary.id, mary.name)
(None, 'Mary')
>>> s.add(mary)
>>> print(mary.id, mary.name)
(None, 'Mary')
>>> s.commit()
>>> print(mary.id, mary.name)
(1, u'Mary')
Notice that mary.id is None before s.commit() is called. Why? Because the object mary has not been committed to the database when it’s constructed and added to s, it does not have a primary key assigned by the underlying SQLite database. Once the new object mary is committed by s, then it is assigned a id value by the underlying SQLite database.
### Query Objects
Once we have both John and Mary in the database, we can query them using a Session.
>>> mary = s.query(User).filter(User.name == 'Mary').one()
>>> john = s.query(User).filter(User.name == 'John').one()
>>> mary.id
2
>>> john.id
1
As you can see, the queried objects have valid id values from the database.
### Update Objects
We can change the name of Mary just like changing the attribute of a normal Python object, as long as we remember to call session.commit() at the end.
>>> mary.name = 'Mariana'
>>> s.commit()
>>> mary.name
u'Mariana'
>>> s.query(User).filter(User.name == 'Mariana').one()
>>>
>>> mary.name = 'Mary'
>>> s.commit()
>>> s.query(User).filter(User.name == 'Mariana').one()
Traceback (most recent call last):
......
sqlalchemy.orm.exc.NoResultFound: No row was found for one()
>>> s.query(User).filter(User.name == 'Mary').one()
### Delete Objects
Now we have two User objects persisted in the database, Mary and John. We are going to delete them by calling delete() of the session object.
>>> s.delete(mary)
>>> mary.id
2
>>> s.commit()
>>> mary
>>> mary.id
2
>>> mary._sa_instance_state.persistent
False # Mary is not persistent in the database anymore since she has been deleted by the session
Since Mary has been marked for deletion by the session and the deletion has been committed by the session into the database, we won’t be able to find Mary in the database anymore.
>>> mary = s.query(User).filter(User.name == 'Mary').one()
Traceback (most recent call last):
......
raise orm_exc.NoResultFound("No row was found for one()")
sqlalchemy.orm.exc.NoResultFound: No row was found for one()
### Session Object States
Since we have already seen an Session object in action, it’s important to also know the four different states of session objects:
• Transient: an instance that’s not included in a session and has not been persisted to the database.
• Pending: an instance that has been added to a session but not persisted to a database yet. It will be persisted to the database in the next session.commit().
• Persistent: an instance that has been persisted to the database and also included in a session. You can make a model object persistent by committing it to the database or query it from the database.
• Detached: an instance that has been persisted to the database but not included in any sessions.
Let’s use sqlalchemy.inspect to take a look at the states of a new User object david.
>>> from sqlalchemy import inspect
>>> david = User(name='David')
>>> ins = inspect(david)
>>> print('Transient: {0}; Pending: {1}; Persistent: {2}; Detached: {3}'.format(ins.transient, ins.pending, ins.persistent, ins.detached))
Transient: True; Pending: False; Persistent: False; Detached: False
>>> s.add(david)
>>> print('Transient: {0}; Pending: {1}; Persistent: {2}; Detached: {3}'.format(ins.transient, ins.pending, ins.persistent, ins.detached))
Transient: False; Pending: True; Persistent: False; Detached: False
>>> s.commit()
>>> print('Transient: {0}; Pending: {1}; Persistent: {2}; Detached: {3}'.format(ins.transient, ins.pending, ins.persistent, ins.detached))
Transient: False; Pending: False; Persistent: True; Detached: False
>>> s.close()
>>> print('Transient: {0}; Pending: {1}; Persistent: {2}; Detached: {3}'.format(ins.transient, ins.pending, ins.persistent, ins.detached))
Transient: False; Pending: False; Persistent: False; Detached: True
Notice the change of david‘s state progressing from Transient to Detached at each step of the insertion process. It’s important to become familiar with these states of the objects because a slight misunderstanding may lead to hard-to-find bugs in a program.
### Scoped Session vs. Normal Session
So far, the session object we constructed from the sessionmaker() call and used to communicate with our database is a normal session. If you call sessionmaker() a second time, you will get a new session object whose states are independent of the previous session. For example, suppose we have two session objects constructed in the following way:
from sqlalchemy import Column, String, Integer, ForeignKey
from sqlalchemy.ext.declarative import declarative_base
Base = declarative_base()
class User(Base):
__tablename__ = 'user'
id = Column(Integer, primary_key=True)
name = Column(String)
from sqlalchemy import create_engine
engine = create_engine('sqlite:///')
from sqlalchemy.orm import sessionmaker
session = sessionmaker()
session.configure(bind=engine)
Base.metadata.create_all(engine)
# Construct the first session object
s1 = session()
# Construct the second session object
s2 = session()
Then, we won’t be able to add the same User object to both s1 and s2 at the same time. In other words, an object can only be attached at most one unique session object.
>>> jessica = User(name='Jessica')
>>> s1.add(jessica)
>>> s2.add(jessica)
Traceback (most recent call last):
......
sqlalchemy.exc.InvalidRequestError: Object '' is already attached to session '2' (this is '3')
If the session objects are retrieved from a scoped_session object, however, then we don’t have such an issue since the scoped_session object maintains a registry for the same session object.
>>> session_factory = sessionmaker(bind=engine)
>>> session = scoped_session(session_factory)
>>> s1 = session()
>>> s2 = session()
>>> jessica = User(name='Jessica')
>>> s1.add(jessica)
>>> s2.add(jessica)
>>> s1 is s2
True
>>> s1.commit()
>>> s2.query(User).filter(User.name == 'Jessica').one()
Notice that s1 and s2 are the same session object since they are both retrieved from a scoped_session object who maintains a reference to the same session object.
### Summary and Tips
In this article, we reviewed how to use SQLAlchemy‘s Session and the four different states of a model object. Since unit-of-work is a core concept in SQLAlchemy, it’s crucial to fully understand and be familiar with how to use Session and the four different states of a model object. In the next article, we will show you how to utilize the Session to manage complex model objects and avoid common bugs.
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# Constraining the independent variable in a control system
For an analog closed loop feedback control, I can do the following to model the response of a second-order physical system with an order 1 zeros polynomial to a step disturbance. I have a proportional controller, with no gain on the feedback signal.
physTF = TransferFunctionModel[Kp*(ta*s + 1)/((t1*s + 1) (t2*s + 1)), s];
contTF = TransferFunctionModel[Kc];
backTF = TransferFunctionModel[1];
clTF = SystemsModelFeedbackConnect[
SystemsModelSeriesConnect[physTF, contTF], backTF];
dist = M*UnitStep[t];
params = {ta -> 0.1, t1 -> 0.3, t2 -> 0.6, Kp -> 5, Kc -> 0.1, M -> 1};
resp = OutputResponse[clTF /. params, dist /. params, {t, 0, 10}];
Plot[resp, {t, 0, 2}, PlotRange -> All]
How might I approach the problem for the case where the manipulated variable is subject to a constraint. For example, when the manipulated variable can saturate or only has discrete allowed values?
The simulink solution in MATLAB is to have a quantizer block followed by a saturation block.
• Sorry about readibility, changed to roman letters. Feb 11, 2017 at 23:04
• contTF stands for controller transfer function, which in this instance is just a proportional gain, but generally might have integrating or a semi-proper derivative term in it. I ran my old code, and now edited code, on Mathematica 11 and found it to be functioning. Feb 12, 2017 at 0:10
• so you don't need any answer? I tried to give one, but don't understand what you mean with 'manipulated variable'.
– Phab
Mar 14, 2017 at 7:14
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# Patty Stacey deposits $1200 at the end of each of 5 years in an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end of the 30-year period? Assume an interest rate of 7%, compounded annually. (Round your answer to the nearest cent.)$ (b) Suppose that Patty's husband delays starting an IRA for the first 10 years he works but then makes $1200 deposits at the end of each of the next 15 years. If the interest rate is 7%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? Question (a) Patty Stacey deposits$1200 at the end of each of 5 years in an IRA. If she leaves the money that has accumulated in the IRA account for 25 additional years, how much is in her account at the end of the 30-year period? Assume an interest rate of 7%, compounded annually. (Round your answer to the nearest cent.)
$(b) Suppose that Patty's husband delays starting an IRA for the first 10 years he works but then makes$1200 deposits at the end of each of the next 15 years. If the interest rate is 7%, compounded annually, and if he leaves the money in his account for 5 additional years, how much will be in his account at the end of the 30-year period? (Round your answer to the nearest cent.)
\$
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# The Unapologetic Mathematician
## Multilinear Functionals
Okay, time for a diversion from all this calculus. Don’t worry, there’s tons more ahead.
We’re going to need some geometric concepts tied to linear algebra, and before we get into that we need to revisit an old topic: tensor powers and the subspaces of symmetric and antisymmetric tensors. Specifically, how do all of these interact with duals. Through these post we’ll be working with a vector space $V$ over a field $\mathbb{F}$, which at times will be assumed to be finite-dimensional, but will not always be.
First, we remember that elements of the dual space $V^*=\hom_\mathbb{F}(V,\mathbb{F})$ are called “linear functionals”. These are $\mathbb{F}$-linear functions from the vector space $V$ to the base field $\mathbb{F}$. Similarly, a “$n$-multilinear functional” is a function $f$ that takes $n$ vectors from $V$ and gives back a field element in $\mathbb{F}$ in a way that’s $\mathbb{F}$-linear in each variable. That is,
$\displaystyle f(v_1,\dots,av_i+bw_i,\dots,v_n)=af(v_1,\dots,v_i,\dots,v_n)+bf(v_1,\dots,w_i,\dots,v_n)$
for scalars $a$ and $b$, and for any index $i$. Equivalently, by the defining universal property of tensor products, this is equivalent to a linear function $f:V^{\otimes n}\rightarrow\mathbb{F}$ — a linear functional on $V^{\otimes n}$. That is, the space of $n$-multilinear functionals is the dual space $\left(V^{\otimes n}\right)^*$.
There’s a good way to come up with $n$-multilinear functionals. Just take $n$ linear functionals and sew them together. That is, if we have an $n$-tuple of functionals $(\lambda^1,\dots,\lambda^n)\in\left(V^*\right)^{\times n}$ we can define an $n$-multilinear functional by the formula
$\displaystyle\left[m(\lambda^1,\dots,\lambda^n)\right](v_1\otimes\dots\otimes v_n)=\prod\limits_{i=1}^n\lambda^i(v_i)$
We just feed the $i$th tensorand $v_i$ into the $i$th functional $\lambda^i$ and multiply all the resulting field elements together. Since field multiplication is multilinear, so is this operation. Then the universal property of tensor products tells us that this mapping from $n$-tuples of linear functionals to $n$-multilinear functionals is equivalent to a unique linear map from the $n$th tensor power $\left(V^*\right)^{\otimes n}\rightarrow\left(V^{\otimes n}\right)^*$. It’s also easy to show that this map has a trivial kernel.
This is not to say that dualization and tensor powers commute. Indeed, in general this map is a proper monomorphism. But it turns out that if $V$ is finite-dimensional, then it’s actually an isomorphism. Just count the dimensions — if $V$ has dimension $d$ then each space has dimension $d^n$ — and use the rank-nullity theorem to see that they must be isomorphic. That is, every $n$-multilinear functional is a linear combination of the ones we can construct from $n$-tuples of linear functionals.
Now we can specialize this result. We define a multilinear functional to be symmetric if its value is unchanged when we swap two of its inputs. Equivalently, it commutes with the symmetrizer. That is, it must kill everything that the symmetrizer kills, and so must really define a linear functional on the subspace of symmetric tensors. That is, the space of symmetric $n$-multilinear functionals is the dual space $\left(S^nV\right)^*$. We can construct such symmetric multilinear functionals by taking $n$ linear functionals as before and symmetrizing them. This gives a monomorphism $S^n\left(V^*\right)\rightarrow\left(S^nV\right)^*$, which is an isomorphism if $V$ is finite-dimensional.
Similarly, we define a multilinear functional to be asymmetric or “alternating” if its value changes sign when we swap two of its inputs. Then it commutes with the antisymmetrizer, must kill everything the antisymmetrizer kills, and descends to a linear functional on the subspace of antisymmetric tensors. As before, we can construct just such an antisymmetric $n$-multilinear functional by antisymmetrizing $n$ linear functionals, and get a monomorphism $A^n\left(V^*\right)\rightarrow\left(A^nV\right)^*$. And yet again, this map is an isomorphism if $V$ is finite-dimensional.
October 22, 2009 Posted by | Algebra, Linear Algebra | 8 Comments
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## G = C2×C10×Dic6order 480 = 25·3·5
### Direct product of C2×C10 and Dic6
Series: Derived Chief Lower central Upper central
Derived series C1 — C6 — C2×C10×Dic6
Chief series C1 — C3 — C6 — C30 — C5×Dic3 — C10×Dic3 — Dic3×C2×C10 — C2×C10×Dic6
Lower central C3 — C6 — C2×C10×Dic6
Upper central C1 — C22×C10 — C22×C20
Generators and relations for C2×C10×Dic6
G = < a,b,c,d | a2=b10=c12=1, d2=c6, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 516 in 312 conjugacy classes, 210 normal (18 characteristic)
C1, C2, C2, C3, C4, C4, C22, C5, C6, C6, C2×C4, C2×C4, Q8, C23, C10, C10, Dic3, C12, C2×C6, C15, C22×C4, C22×C4, C2×Q8, C20, C20, C2×C10, Dic6, C2×Dic3, C2×C12, C22×C6, C30, C30, C22×Q8, C2×C20, C2×C20, C5×Q8, C22×C10, C2×Dic6, C22×Dic3, C22×C12, C5×Dic3, C60, C2×C30, C22×C20, C22×C20, Q8×C10, C22×Dic6, C5×Dic6, C10×Dic3, C2×C60, C22×C30, Q8×C2×C10, C10×Dic6, Dic3×C2×C10, C22×C60, C2×C10×Dic6
Quotients: C1, C2, C22, C5, S3, Q8, C23, C10, D6, C2×Q8, C24, C2×C10, Dic6, C22×S3, C5×S3, C22×Q8, C5×Q8, C22×C10, C2×Dic6, S3×C23, S3×C10, Q8×C10, C23×C10, C22×Dic6, C5×Dic6, S3×C2×C10, Q8×C2×C10, C10×Dic6, S3×C22×C10, C2×C10×Dic6
Smallest permutation representation of C2×C10×Dic6
Regular action on 480 points
Generators in S480
(1 428)(2 429)(3 430)(4 431)(5 432)(6 421)(7 422)(8 423)(9 424)(10 425)(11 426)(12 427)(13 113)(14 114)(15 115)(16 116)(17 117)(18 118)(19 119)(20 120)(21 109)(22 110)(23 111)(24 112)(25 271)(26 272)(27 273)(28 274)(29 275)(30 276)(31 265)(32 266)(33 267)(34 268)(35 269)(36 270)(37 466)(38 467)(39 468)(40 457)(41 458)(42 459)(43 460)(44 461)(45 462)(46 463)(47 464)(48 465)(49 287)(50 288)(51 277)(52 278)(53 279)(54 280)(55 281)(56 282)(57 283)(58 284)(59 285)(60 286)(61 83)(62 84)(63 73)(64 74)(65 75)(66 76)(67 77)(68 78)(69 79)(70 80)(71 81)(72 82)(85 375)(86 376)(87 377)(88 378)(89 379)(90 380)(91 381)(92 382)(93 383)(94 384)(95 373)(96 374)(97 478)(98 479)(99 480)(100 469)(101 470)(102 471)(103 472)(104 473)(105 474)(106 475)(107 476)(108 477)(121 188)(122 189)(123 190)(124 191)(125 192)(126 181)(127 182)(128 183)(129 184)(130 185)(131 186)(132 187)(133 316)(134 317)(135 318)(136 319)(137 320)(138 321)(139 322)(140 323)(141 324)(142 313)(143 314)(144 315)(145 331)(146 332)(147 333)(148 334)(149 335)(150 336)(151 325)(152 326)(153 327)(154 328)(155 329)(156 330)(157 310)(158 311)(159 312)(160 301)(161 302)(162 303)(163 304)(164 305)(165 306)(166 307)(167 308)(168 309)(169 291)(170 292)(171 293)(172 294)(173 295)(174 296)(175 297)(176 298)(177 299)(178 300)(179 289)(180 290)(193 260)(194 261)(195 262)(196 263)(197 264)(198 253)(199 254)(200 255)(201 256)(202 257)(203 258)(204 259)(205 339)(206 340)(207 341)(208 342)(209 343)(210 344)(211 345)(212 346)(213 347)(214 348)(215 337)(216 338)(217 392)(218 393)(219 394)(220 395)(221 396)(222 385)(223 386)(224 387)(225 388)(226 389)(227 390)(228 391)(229 406)(230 407)(231 408)(232 397)(233 398)(234 399)(235 400)(236 401)(237 402)(238 403)(239 404)(240 405)(241 442)(242 443)(243 444)(244 433)(245 434)(246 435)(247 436)(248 437)(249 438)(250 439)(251 440)(252 441)(349 445)(350 446)(351 447)(352 448)(353 449)(354 450)(355 451)(356 452)(357 453)(358 454)(359 455)(360 456)(361 414)(362 415)(363 416)(364 417)(365 418)(366 419)(367 420)(368 409)(369 410)(370 411)(371 412)(372 413)
(1 445 195 70 37 287 339 134 176 151)(2 446 196 71 38 288 340 135 177 152)(3 447 197 72 39 277 341 136 178 153)(4 448 198 61 40 278 342 137 179 154)(5 449 199 62 41 279 343 138 180 155)(6 450 200 63 42 280 344 139 169 156)(7 451 201 64 43 281 345 140 170 145)(8 452 202 65 44 282 346 141 171 146)(9 453 203 66 45 283 347 142 172 147)(10 454 204 67 46 284 348 143 173 148)(11 455 193 68 47 285 337 144 174 149)(12 456 194 69 48 286 338 133 175 150)(13 250 98 311 127 409 33 396 231 384)(14 251 99 312 128 410 34 385 232 373)(15 252 100 301 129 411 35 386 233 374)(16 241 101 302 130 412 36 387 234 375)(17 242 102 303 131 413 25 388 235 376)(18 243 103 304 132 414 26 389 236 377)(19 244 104 305 121 415 27 390 237 378)(20 245 105 306 122 416 28 391 238 379)(21 246 106 307 123 417 29 392 239 380)(22 247 107 308 124 418 30 393 240 381)(23 248 108 309 125 419 31 394 229 382)(24 249 97 310 126 420 32 395 230 383)(49 205 317 298 325 428 349 262 80 466)(50 206 318 299 326 429 350 263 81 467)(51 207 319 300 327 430 351 264 82 468)(52 208 320 289 328 431 352 253 83 457)(53 209 321 290 329 432 353 254 84 458)(54 210 322 291 330 421 354 255 73 459)(55 211 323 292 331 422 355 256 74 460)(56 212 324 293 332 423 356 257 75 461)(57 213 313 294 333 424 357 258 76 462)(58 214 314 295 334 425 358 259 77 463)(59 215 315 296 335 426 359 260 78 464)(60 216 316 297 336 427 360 261 79 465)(85 116 442 470 161 185 371 270 224 399)(86 117 443 471 162 186 372 271 225 400)(87 118 444 472 163 187 361 272 226 401)(88 119 433 473 164 188 362 273 227 402)(89 120 434 474 165 189 363 274 228 403)(90 109 435 475 166 190 364 275 217 404)(91 110 436 476 167 191 365 276 218 405)(92 111 437 477 168 192 366 265 219 406)(93 112 438 478 157 181 367 266 220 407)(94 113 439 479 158 182 368 267 221 408)(95 114 440 480 159 183 369 268 222 397)(96 115 441 469 160 184 370 269 223 398)
(1 2 3 4 5 6 7 8 9 10 11 12)(13 14 15 16 17 18 19 20 21 22 23 24)(25 26 27 28 29 30 31 32 33 34 35 36)(37 38 39 40 41 42 43 44 45 46 47 48)(49 50 51 52 53 54 55 56 57 58 59 60)(61 62 63 64 65 66 67 68 69 70 71 72)(73 74 75 76 77 78 79 80 81 82 83 84)(85 86 87 88 89 90 91 92 93 94 95 96)(97 98 99 100 101 102 103 104 105 106 107 108)(109 110 111 112 113 114 115 116 117 118 119 120)(121 122 123 124 125 126 127 128 129 130 131 132)(133 134 135 136 137 138 139 140 141 142 143 144)(145 146 147 148 149 150 151 152 153 154 155 156)(157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180)(181 182 183 184 185 186 187 188 189 190 191 192)(193 194 195 196 197 198 199 200 201 202 203 204)(205 206 207 208 209 210 211 212 213 214 215 216)(217 218 219 220 221 222 223 224 225 226 227 228)(229 230 231 232 233 234 235 236 237 238 239 240)(241 242 243 244 245 246 247 248 249 250 251 252)(253 254 255 256 257 258 259 260 261 262 263 264)(265 266 267 268 269 270 271 272 273 274 275 276)(277 278 279 280 281 282 283 284 285 286 287 288)(289 290 291 292 293 294 295 296 297 298 299 300)(301 302 303 304 305 306 307 308 309 310 311 312)(313 314 315 316 317 318 319 320 321 322 323 324)(325 326 327 328 329 330 331 332 333 334 335 336)(337 338 339 340 341 342 343 344 345 346 347 348)(349 350 351 352 353 354 355 356 357 358 359 360)(361 362 363 364 365 366 367 368 369 370 371 372)(373 374 375 376 377 378 379 380 381 382 383 384)(385 386 387 388 389 390 391 392 393 394 395 396)(397 398 399 400 401 402 403 404 405 406 407 408)(409 410 411 412 413 414 415 416 417 418 419 420)(421 422 423 424 425 426 427 428 429 430 431 432)(433 434 435 436 437 438 439 440 441 442 443 444)(445 446 447 448 449 450 451 452 453 454 455 456)(457 458 459 460 461 462 463 464 465 466 467 468)(469 470 471 472 473 474 475 476 477 478 479 480)
(1 226 7 220)(2 225 8 219)(3 224 9 218)(4 223 10 217)(5 222 11 228)(6 221 12 227)(13 79 19 73)(14 78 20 84)(15 77 21 83)(16 76 22 82)(17 75 23 81)(18 74 24 80)(25 332 31 326)(26 331 32 325)(27 330 33 336)(28 329 34 335)(29 328 35 334)(30 327 36 333)(37 444 43 438)(38 443 44 437)(39 442 45 436)(40 441 46 435)(41 440 47 434)(42 439 48 433)(49 103 55 97)(50 102 56 108)(51 101 57 107)(52 100 58 106)(53 99 59 105)(54 98 60 104)(61 115 67 109)(62 114 68 120)(63 113 69 119)(64 112 70 118)(65 111 71 117)(66 110 72 116)(85 203 91 197)(86 202 92 196)(87 201 93 195)(88 200 94 194)(89 199 95 193)(90 198 96 204)(121 322 127 316)(122 321 128 315)(123 320 129 314)(124 319 130 313)(125 318 131 324)(126 317 132 323)(133 188 139 182)(134 187 140 181)(135 186 141 192)(136 185 142 191)(137 184 143 190)(138 183 144 189)(145 266 151 272)(146 265 152 271)(147 276 153 270)(148 275 154 269)(149 274 155 268)(150 273 156 267)(157 339 163 345)(158 338 164 344)(159 337 165 343)(160 348 166 342)(161 347 167 341)(162 346 168 340)(169 368 175 362)(170 367 176 361)(171 366 177 372)(172 365 178 371)(173 364 179 370)(174 363 180 369)(205 304 211 310)(206 303 212 309)(207 302 213 308)(208 301 214 307)(209 312 215 306)(210 311 216 305)(229 350 235 356)(230 349 236 355)(231 360 237 354)(232 359 238 353)(233 358 239 352)(234 357 240 351)(241 462 247 468)(242 461 248 467)(243 460 249 466)(244 459 250 465)(245 458 251 464)(246 457 252 463)(253 374 259 380)(254 373 260 379)(255 384 261 378)(256 383 262 377)(257 382 263 376)(258 381 264 375)(277 470 283 476)(278 469 284 475)(279 480 285 474)(280 479 286 473)(281 478 287 472)(282 477 288 471)(289 411 295 417)(290 410 296 416)(291 409 297 415)(292 420 298 414)(293 419 299 413)(294 418 300 412)(385 426 391 432)(386 425 392 431)(387 424 393 430)(388 423 394 429)(389 422 395 428)(390 421 396 427)(397 455 403 449)(398 454 404 448)(399 453 405 447)(400 452 406 446)(401 451 407 445)(402 450 408 456)
G:=sub<Sym(480)| (1,428)(2,429)(3,430)(4,431)(5,432)(6,421)(7,422)(8,423)(9,424)(10,425)(11,426)(12,427)(13,113)(14,114)(15,115)(16,116)(17,117)(18,118)(19,119)(20,120)(21,109)(22,110)(23,111)(24,112)(25,271)(26,272)(27,273)(28,274)(29,275)(30,276)(31,265)(32,266)(33,267)(34,268)(35,269)(36,270)(37,466)(38,467)(39,468)(40,457)(41,458)(42,459)(43,460)(44,461)(45,462)(46,463)(47,464)(48,465)(49,287)(50,288)(51,277)(52,278)(53,279)(54,280)(55,281)(56,282)(57,283)(58,284)(59,285)(60,286)(61,83)(62,84)(63,73)(64,74)(65,75)(66,76)(67,77)(68,78)(69,79)(70,80)(71,81)(72,82)(85,375)(86,376)(87,377)(88,378)(89,379)(90,380)(91,381)(92,382)(93,383)(94,384)(95,373)(96,374)(97,478)(98,479)(99,480)(100,469)(101,470)(102,471)(103,472)(104,473)(105,474)(106,475)(107,476)(108,477)(121,188)(122,189)(123,190)(124,191)(125,192)(126,181)(127,182)(128,183)(129,184)(130,185)(131,186)(132,187)(133,316)(134,317)(135,318)(136,319)(137,320)(138,321)(139,322)(140,323)(141,324)(142,313)(143,314)(144,315)(145,331)(146,332)(147,333)(148,334)(149,335)(150,336)(151,325)(152,326)(153,327)(154,328)(155,329)(156,330)(157,310)(158,311)(159,312)(160,301)(161,302)(162,303)(163,304)(164,305)(165,306)(166,307)(167,308)(168,309)(169,291)(170,292)(171,293)(172,294)(173,295)(174,296)(175,297)(176,298)(177,299)(178,300)(179,289)(180,290)(193,260)(194,261)(195,262)(196,263)(197,264)(198,253)(199,254)(200,255)(201,256)(202,257)(203,258)(204,259)(205,339)(206,340)(207,341)(208,342)(209,343)(210,344)(211,345)(212,346)(213,347)(214,348)(215,337)(216,338)(217,392)(218,393)(219,394)(220,395)(221,396)(222,385)(223,386)(224,387)(225,388)(226,389)(227,390)(228,391)(229,406)(230,407)(231,408)(232,397)(233,398)(234,399)(235,400)(236,401)(237,402)(238,403)(239,404)(240,405)(241,442)(242,443)(243,444)(244,433)(245,434)(246,435)(247,436)(248,437)(249,438)(250,439)(251,440)(252,441)(349,445)(350,446)(351,447)(352,448)(353,449)(354,450)(355,451)(356,452)(357,453)(358,454)(359,455)(360,456)(361,414)(362,415)(363,416)(364,417)(365,418)(366,419)(367,420)(368,409)(369,410)(370,411)(371,412)(372,413), (1,445,195,70,37,287,339,134,176,151)(2,446,196,71,38,288,340,135,177,152)(3,447,197,72,39,277,341,136,178,153)(4,448,198,61,40,278,342,137,179,154)(5,449,199,62,41,279,343,138,180,155)(6,450,200,63,42,280,344,139,169,156)(7,451,201,64,43,281,345,140,170,145)(8,452,202,65,44,282,346,141,171,146)(9,453,203,66,45,283,347,142,172,147)(10,454,204,67,46,284,348,143,173,148)(11,455,193,68,47,285,337,144,174,149)(12,456,194,69,48,286,338,133,175,150)(13,250,98,311,127,409,33,396,231,384)(14,251,99,312,128,410,34,385,232,373)(15,252,100,301,129,411,35,386,233,374)(16,241,101,302,130,412,36,387,234,375)(17,242,102,303,131,413,25,388,235,376)(18,243,103,304,132,414,26,389,236,377)(19,244,104,305,121,415,27,390,237,378)(20,245,105,306,122,416,28,391,238,379)(21,246,106,307,123,417,29,392,239,380)(22,247,107,308,124,418,30,393,240,381)(23,248,108,309,125,419,31,394,229,382)(24,249,97,310,126,420,32,395,230,383)(49,205,317,298,325,428,349,262,80,466)(50,206,318,299,326,429,350,263,81,467)(51,207,319,300,327,430,351,264,82,468)(52,208,320,289,328,431,352,253,83,457)(53,209,321,290,329,432,353,254,84,458)(54,210,322,291,330,421,354,255,73,459)(55,211,323,292,331,422,355,256,74,460)(56,212,324,293,332,423,356,257,75,461)(57,213,313,294,333,424,357,258,76,462)(58,214,314,295,334,425,358,259,77,463)(59,215,315,296,335,426,359,260,78,464)(60,216,316,297,336,427,360,261,79,465)(85,116,442,470,161,185,371,270,224,399)(86,117,443,471,162,186,372,271,225,400)(87,118,444,472,163,187,361,272,226,401)(88,119,433,473,164,188,362,273,227,402)(89,120,434,474,165,189,363,274,228,403)(90,109,435,475,166,190,364,275,217,404)(91,110,436,476,167,191,365,276,218,405)(92,111,437,477,168,192,366,265,219,406)(93,112,438,478,157,181,367,266,220,407)(94,113,439,479,158,182,368,267,221,408)(95,114,440,480,159,183,369,268,222,397)(96,115,441,469,160,184,370,269,223,398), (1,2,3,4,5,6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104,105,106,107,108)(109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132)(133,134,135,136,137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152,153,154,155,156)(157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180)(181,182,183,184,185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200,201,202,203,204)(205,206,207,208,209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224,225,226,227,228)(229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252)(253,254,255,256,257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272,273,274,275,276)(277,278,279,280,281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296,297,298,299,300)(301,302,303,304,305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320,321,322,323,324)(325,326,327,328,329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344,345,346,347,348)(349,350,351,352,353,354,355,356,357,358,359,360)(361,362,363,364,365,366,367,368,369,370,371,372)(373,374,375,376,377,378,379,380,381,382,383,384)(385,386,387,388,389,390,391,392,393,394,395,396)(397,398,399,400,401,402,403,404,405,406,407,408)(409,410,411,412,413,414,415,416,417,418,419,420)(421,422,423,424,425,426,427,428,429,430,431,432)(433,434,435,436,437,438,439,440,441,442,443,444)(445,446,447,448,449,450,451,452,453,454,455,456)(457,458,459,460,461,462,463,464,465,466,467,468)(469,470,471,472,473,474,475,476,477,478,479,480), (1,226,7,220)(2,225,8,219)(3,224,9,218)(4,223,10,217)(5,222,11,228)(6,221,12,227)(13,79,19,73)(14,78,20,84)(15,77,21,83)(16,76,22,82)(17,75,23,81)(18,74,24,80)(25,332,31,326)(26,331,32,325)(27,330,33,336)(28,329,34,335)(29,328,35,334)(30,327,36,333)(37,444,43,438)(38,443,44,437)(39,442,45,436)(40,441,46,435)(41,440,47,434)(42,439,48,433)(49,103,55,97)(50,102,56,108)(51,101,57,107)(52,100,58,106)(53,99,59,105)(54,98,60,104)(61,115,67,109)(62,114,68,120)(63,113,69,119)(64,112,70,118)(65,111,71,117)(66,110,72,116)(85,203,91,197)(86,202,92,196)(87,201,93,195)(88,200,94,194)(89,199,95,193)(90,198,96,204)(121,322,127,316)(122,321,128,315)(123,320,129,314)(124,319,130,313)(125,318,131,324)(126,317,132,323)(133,188,139,182)(134,187,140,181)(135,186,141,192)(136,185,142,191)(137,184,143,190)(138,183,144,189)(145,266,151,272)(146,265,152,271)(147,276,153,270)(148,275,154,269)(149,274,155,268)(150,273,156,267)(157,339,163,345)(158,338,164,344)(159,337,165,343)(160,348,166,342)(161,347,167,341)(162,346,168,340)(169,368,175,362)(170,367,176,361)(171,366,177,372)(172,365,178,371)(173,364,179,370)(174,363,180,369)(205,304,211,310)(206,303,212,309)(207,302,213,308)(208,301,214,307)(209,312,215,306)(210,311,216,305)(229,350,235,356)(230,349,236,355)(231,360,237,354)(232,359,238,353)(233,358,239,352)(234,357,240,351)(241,462,247,468)(242,461,248,467)(243,460,249,466)(244,459,250,465)(245,458,251,464)(246,457,252,463)(253,374,259,380)(254,373,260,379)(255,384,261,378)(256,383,262,377)(257,382,263,376)(258,381,264,375)(277,470,283,476)(278,469,284,475)(279,480,285,474)(280,479,286,473)(281,478,287,472)(282,477,288,471)(289,411,295,417)(290,410,296,416)(291,409,297,415)(292,420,298,414)(293,419,299,413)(294,418,300,412)(385,426,391,432)(386,425,392,431)(387,424,393,430)(388,423,394,429)(389,422,395,428)(390,421,396,427)(397,455,403,449)(398,454,404,448)(399,453,405,447)(400,452,406,446)(401,451,407,445)(402,450,408,456)>;
G:=Group( 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(1,2,3,4,5,6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23,24)(25,26,27,28,29,30,31,32,33,34,35,36)(37,38,39,40,41,42,43,44,45,46,47,48)(49,50,51,52,53,54,55,56,57,58,59,60)(61,62,63,64,65,66,67,68,69,70,71,72)(73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96)(97,98,99,100,101,102,103,104,105,106,107,108)(109,110,111,112,113,114,115,116,117,118,119,120)(121,122,123,124,125,126,127,128,129,130,131,132)(133,134,135,136,137,138,139,140,141,142,143,144)(145,146,147,148,149,150,151,152,153,154,155,156)(157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180)(181,182,183,184,185,186,187,188,189,190,191,192)(193,194,195,196,197,198,199,200,201,202,203,204)(205,206,207,208,209,210,211,212,213,214,215,216)(217,218,219,220,221,222,223,224,225,226,227,228)(229,230,231,232,233,234,235,236,237,238,239,240)(241,242,243,244,245,246,247,248,249,250,251,252)(253,254,255,256,257,258,259,260,261,262,263,264)(265,266,267,268,269,270,271,272,273,274,275,276)(277,278,279,280,281,282,283,284,285,286,287,288)(289,290,291,292,293,294,295,296,297,298,299,300)(301,302,303,304,305,306,307,308,309,310,311,312)(313,314,315,316,317,318,319,320,321,322,323,324)(325,326,327,328,329,330,331,332,333,334,335,336)(337,338,339,340,341,342,343,344,345,346,347,348)(349,350,351,352,353,354,355,356,357,358,359,360)(361,362,363,364,365,366,367,368,369,370,371,372)(373,374,375,376,377,378,379,380,381,382,383,384)(385,386,387,388,389,390,391,392,393,394,395,396)(397,398,399,400,401,402,403,404,405,406,407,408)(409,410,411,412,413,414,415,416,417,418,419,420)(421,422,423,424,425,426,427,428,429,430,431,432)(433,434,435,436,437,438,439,440,441,442,443,444)(445,446,447,448,449,450,451,452,453,454,455,456)(457,458,459,460,461,462,463,464,465,466,467,468)(469,470,471,472,473,474,475,476,477,478,479,480), (1,226,7,220)(2,225,8,219)(3,224,9,218)(4,223,10,217)(5,222,11,228)(6,221,12,227)(13,79,19,73)(14,78,20,84)(15,77,21,83)(16,76,22,82)(17,75,23,81)(18,74,24,80)(25,332,31,326)(26,331,32,325)(27,330,33,336)(28,329,34,335)(29,328,35,334)(30,327,36,333)(37,444,43,438)(38,443,44,437)(39,442,45,436)(40,441,46,435)(41,440,47,434)(42,439,48,433)(49,103,55,97)(50,102,56,108)(51,101,57,107)(52,100,58,106)(53,99,59,105)(54,98,60,104)(61,115,67,109)(62,114,68,120)(63,113,69,119)(64,112,70,118)(65,111,71,117)(66,110,72,116)(85,203,91,197)(86,202,92,196)(87,201,93,195)(88,200,94,194)(89,199,95,193)(90,198,96,204)(121,322,127,316)(122,321,128,315)(123,320,129,314)(124,319,130,313)(125,318,131,324)(126,317,132,323)(133,188,139,182)(134,187,140,181)(135,186,141,192)(136,185,142,191)(137,184,143,190)(138,183,144,189)(145,266,151,272)(146,265,152,271)(147,276,153,270)(148,275,154,269)(149,274,155,268)(150,273,156,267)(157,339,163,345)(158,338,164,344)(159,337,165,343)(160,348,166,342)(161,347,167,341)(162,346,168,340)(169,368,175,362)(170,367,176,361)(171,366,177,372)(172,365,178,371)(173,364,179,370)(174,363,180,369)(205,304,211,310)(206,303,212,309)(207,302,213,308)(208,301,214,307)(209,312,215,306)(210,311,216,305)(229,350,235,356)(230,349,236,355)(231,360,237,354)(232,359,238,353)(233,358,239,352)(234,357,240,351)(241,462,247,468)(242,461,248,467)(243,460,249,466)(244,459,250,465)(245,458,251,464)(246,457,252,463)(253,374,259,380)(254,373,260,379)(255,384,261,378)(256,383,262,377)(257,382,263,376)(258,381,264,375)(277,470,283,476)(278,469,284,475)(279,480,285,474)(280,479,286,473)(281,478,287,472)(282,477,288,471)(289,411,295,417)(290,410,296,416)(291,409,297,415)(292,420,298,414)(293,419,299,413)(294,418,300,412)(385,426,391,432)(386,425,392,431)(387,424,393,430)(388,423,394,429)(389,422,395,428)(390,421,396,427)(397,455,403,449)(398,454,404,448)(399,453,405,447)(400,452,406,446)(401,451,407,445)(402,450,408,456) );
G=PermutationGroup([[(1,428),(2,429),(3,430),(4,431),(5,432),(6,421),(7,422),(8,423),(9,424),(10,425),(11,426),(12,427),(13,113),(14,114),(15,115),(16,116),(17,117),(18,118),(19,119),(20,120),(21,109),(22,110),(23,111),(24,112),(25,271),(26,272),(27,273),(28,274),(29,275),(30,276),(31,265),(32,266),(33,267),(34,268),(35,269),(36,270),(37,466),(38,467),(39,468),(40,457),(41,458),(42,459),(43,460),(44,461),(45,462),(46,463),(47,464),(48,465),(49,287),(50,288),(51,277),(52,278),(53,279),(54,280),(55,281),(56,282),(57,283),(58,284),(59,285),(60,286),(61,83),(62,84),(63,73),(64,74),(65,75),(66,76),(67,77),(68,78),(69,79),(70,80),(71,81),(72,82),(85,375),(86,376),(87,377),(88,378),(89,379),(90,380),(91,381),(92,382),(93,383),(94,384),(95,373),(96,374),(97,478),(98,479),(99,480),(100,469),(101,470),(102,471),(103,472),(104,473),(105,474),(106,475),(107,476),(108,477),(121,188),(122,189),(123,190),(124,191),(125,192),(126,181),(127,182),(128,183),(129,184),(130,185),(131,186),(132,187),(133,316),(134,317),(135,318),(136,319),(137,320),(138,321),(139,322),(140,323),(141,324),(142,313),(143,314),(144,315),(145,331),(146,332),(147,333),(148,334),(149,335),(150,336),(151,325),(152,326),(153,327),(154,328),(155,329),(156,330),(157,310),(158,311),(159,312),(160,301),(161,302),(162,303),(163,304),(164,305),(165,306),(166,307),(167,308),(168,309),(169,291),(170,292),(171,293),(172,294),(173,295),(174,296),(175,297),(176,298),(177,299),(178,300),(179,289),(180,290),(193,260),(194,261),(195,262),(196,263),(197,264),(198,253),(199,254),(200,255),(201,256),(202,257),(203,258),(204,259),(205,339),(206,340),(207,341),(208,342),(209,343),(210,344),(211,345),(212,346),(213,347),(214,348),(215,337),(216,338),(217,392),(218,393),(219,394),(220,395),(221,396),(222,385),(223,386),(224,387),(225,388),(226,389),(227,390),(228,391),(229,406),(230,407),(231,408),(232,397),(233,398),(234,399),(235,400),(236,401),(237,402),(238,403),(239,404),(240,405),(241,442),(242,443),(243,444),(244,433),(245,434),(246,435),(247,436),(248,437),(249,438),(250,439),(251,440),(252,441),(349,445),(350,446),(351,447),(352,448),(353,449),(354,450),(355,451),(356,452),(357,453),(358,454),(359,455),(360,456),(361,414),(362,415),(363,416),(364,417),(365,418),(366,419),(367,420),(368,409),(369,410),(370,411),(371,412),(372,413)], [(1,445,195,70,37,287,339,134,176,151),(2,446,196,71,38,288,340,135,177,152),(3,447,197,72,39,277,341,136,178,153),(4,448,198,61,40,278,342,137,179,154),(5,449,199,62,41,279,343,138,180,155),(6,450,200,63,42,280,344,139,169,156),(7,451,201,64,43,281,345,140,170,145),(8,452,202,65,44,282,346,141,171,146),(9,453,203,66,45,283,347,142,172,147),(10,454,204,67,46,284,348,143,173,148),(11,455,193,68,47,285,337,144,174,149),(12,456,194,69,48,286,338,133,175,150),(13,250,98,311,127,409,33,396,231,384),(14,251,99,312,128,410,34,385,232,373),(15,252,100,301,129,411,35,386,233,374),(16,241,101,302,130,412,36,387,234,375),(17,242,102,303,131,413,25,388,235,376),(18,243,103,304,132,414,26,389,236,377),(19,244,104,305,121,415,27,390,237,378),(20,245,105,306,122,416,28,391,238,379),(21,246,106,307,123,417,29,392,239,380),(22,247,107,308,124,418,30,393,240,381),(23,248,108,309,125,419,31,394,229,382),(24,249,97,310,126,420,32,395,230,383),(49,205,317,298,325,428,349,262,80,466),(50,206,318,299,326,429,350,263,81,467),(51,207,319,300,327,430,351,264,82,468),(52,208,320,289,328,431,352,253,83,457),(53,209,321,290,329,432,353,254,84,458),(54,210,322,291,330,421,354,255,73,459),(55,211,323,292,331,422,355,256,74,460),(56,212,324,293,332,423,356,257,75,461),(57,213,313,294,333,424,357,258,76,462),(58,214,314,295,334,425,358,259,77,463),(59,215,315,296,335,426,359,260,78,464),(60,216,316,297,336,427,360,261,79,465),(85,116,442,470,161,185,371,270,224,399),(86,117,443,471,162,186,372,271,225,400),(87,118,444,472,163,187,361,272,226,401),(88,119,433,473,164,188,362,273,227,402),(89,120,434,474,165,189,363,274,228,403),(90,109,435,475,166,190,364,275,217,404),(91,110,436,476,167,191,365,276,218,405),(92,111,437,477,168,192,366,265,219,406),(93,112,438,478,157,181,367,266,220,407),(94,113,439,479,158,182,368,267,221,408),(95,114,440,480,159,183,369,268,222,397),(96,115,441,469,160,184,370,269,223,398)], [(1,2,3,4,5,6,7,8,9,10,11,12),(13,14,15,16,17,18,19,20,21,22,23,24),(25,26,27,28,29,30,31,32,33,34,35,36),(37,38,39,40,41,42,43,44,45,46,47,48),(49,50,51,52,53,54,55,56,57,58,59,60),(61,62,63,64,65,66,67,68,69,70,71,72),(73,74,75,76,77,78,79,80,81,82,83,84),(85,86,87,88,89,90,91,92,93,94,95,96),(97,98,99,100,101,102,103,104,105,106,107,108),(109,110,111,112,113,114,115,116,117,118,119,120),(121,122,123,124,125,126,127,128,129,130,131,132),(133,134,135,136,137,138,139,140,141,142,143,144),(145,146,147,148,149,150,151,152,153,154,155,156),(157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180),(181,182,183,184,185,186,187,188,189,190,191,192),(193,194,195,196,197,198,199,200,201,202,203,204),(205,206,207,208,209,210,211,212,213,214,215,216),(217,218,219,220,221,222,223,224,225,226,227,228),(229,230,231,232,233,234,235,236,237,238,239,240),(241,242,243,244,245,246,247,248,249,250,251,252),(253,254,255,256,257,258,259,260,261,262,263,264),(265,266,267,268,269,270,271,272,273,274,275,276),(277,278,279,280,281,282,283,284,285,286,287,288),(289,290,291,292,293,294,295,296,297,298,299,300),(301,302,303,304,305,306,307,308,309,310,311,312),(313,314,315,316,317,318,319,320,321,322,323,324),(325,326,327,328,329,330,331,332,333,334,335,336),(337,338,339,340,341,342,343,344,345,346,347,348),(349,350,351,352,353,354,355,356,357,358,359,360),(361,362,363,364,365,366,367,368,369,370,371,372),(373,374,375,376,377,378,379,380,381,382,383,384),(385,386,387,388,389,390,391,392,393,394,395,396),(397,398,399,400,401,402,403,404,405,406,407,408),(409,410,411,412,413,414,415,416,417,418,419,420),(421,422,423,424,425,426,427,428,429,430,431,432),(433,434,435,436,437,438,439,440,441,442,443,444),(445,446,447,448,449,450,451,452,453,454,455,456),(457,458,459,460,461,462,463,464,465,466,467,468),(469,470,471,472,473,474,475,476,477,478,479,480)], [(1,226,7,220),(2,225,8,219),(3,224,9,218),(4,223,10,217),(5,222,11,228),(6,221,12,227),(13,79,19,73),(14,78,20,84),(15,77,21,83),(16,76,22,82),(17,75,23,81),(18,74,24,80),(25,332,31,326),(26,331,32,325),(27,330,33,336),(28,329,34,335),(29,328,35,334),(30,327,36,333),(37,444,43,438),(38,443,44,437),(39,442,45,436),(40,441,46,435),(41,440,47,434),(42,439,48,433),(49,103,55,97),(50,102,56,108),(51,101,57,107),(52,100,58,106),(53,99,59,105),(54,98,60,104),(61,115,67,109),(62,114,68,120),(63,113,69,119),(64,112,70,118),(65,111,71,117),(66,110,72,116),(85,203,91,197),(86,202,92,196),(87,201,93,195),(88,200,94,194),(89,199,95,193),(90,198,96,204),(121,322,127,316),(122,321,128,315),(123,320,129,314),(124,319,130,313),(125,318,131,324),(126,317,132,323),(133,188,139,182),(134,187,140,181),(135,186,141,192),(136,185,142,191),(137,184,143,190),(138,183,144,189),(145,266,151,272),(146,265,152,271),(147,276,153,270),(148,275,154,269),(149,274,155,268),(150,273,156,267),(157,339,163,345),(158,338,164,344),(159,337,165,343),(160,348,166,342),(161,347,167,341),(162,346,168,340),(169,368,175,362),(170,367,176,361),(171,366,177,372),(172,365,178,371),(173,364,179,370),(174,363,180,369),(205,304,211,310),(206,303,212,309),(207,302,213,308),(208,301,214,307),(209,312,215,306),(210,311,216,305),(229,350,235,356),(230,349,236,355),(231,360,237,354),(232,359,238,353),(233,358,239,352),(234,357,240,351),(241,462,247,468),(242,461,248,467),(243,460,249,466),(244,459,250,465),(245,458,251,464),(246,457,252,463),(253,374,259,380),(254,373,260,379),(255,384,261,378),(256,383,262,377),(257,382,263,376),(258,381,264,375),(277,470,283,476),(278,469,284,475),(279,480,285,474),(280,479,286,473),(281,478,287,472),(282,477,288,471),(289,411,295,417),(290,410,296,416),(291,409,297,415),(292,420,298,414),(293,419,299,413),(294,418,300,412),(385,426,391,432),(386,425,392,431),(387,424,393,430),(388,423,394,429),(389,422,395,428),(390,421,396,427),(397,455,403,449),(398,454,404,448),(399,453,405,447),(400,452,406,446),(401,451,407,445),(402,450,408,456)]])
180 conjugacy classes
class 1 2A ··· 2G 3 4A 4B 4C 4D 4E ··· 4L 5A 5B 5C 5D 6A ··· 6G 10A ··· 10AB 12A ··· 12H 15A 15B 15C 15D 20A ··· 20P 20Q ··· 20AV 30A ··· 30AB 60A ··· 60AF order 1 2 ··· 2 3 4 4 4 4 4 ··· 4 5 5 5 5 6 ··· 6 10 ··· 10 12 ··· 12 15 15 15 15 20 ··· 20 20 ··· 20 30 ··· 30 60 ··· 60 size 1 1 ··· 1 2 2 2 2 2 6 ··· 6 1 1 1 1 2 ··· 2 1 ··· 1 2 ··· 2 2 2 2 2 2 ··· 2 6 ··· 6 2 ··· 2 2 ··· 2
180 irreducible representations
dim 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 type + + + + + - + + - image C1 C2 C2 C2 C5 C10 C10 C10 S3 Q8 D6 D6 Dic6 C5×S3 C5×Q8 S3×C10 S3×C10 C5×Dic6 kernel C2×C10×Dic6 C10×Dic6 Dic3×C2×C10 C22×C60 C22×Dic6 C2×Dic6 C22×Dic3 C22×C12 C22×C20 C2×C30 C2×C20 C22×C10 C2×C10 C22×C4 C2×C6 C2×C4 C23 C22 # reps 1 12 2 1 4 48 8 4 1 4 6 1 8 4 16 24 4 32
Matrix representation of C2×C10×Dic6 in GL5(𝔽61)
1 0 0 0 0 0 60 0 0 0 0 0 60 0 0 0 0 0 1 0 0 0 0 0 1
,
60 0 0 0 0 0 20 0 0 0 0 0 20 0 0 0 0 0 58 0 0 0 0 0 58
,
1 0 0 0 0 0 0 60 0 0 0 1 1 0 0 0 0 0 46 23 0 0 0 38 23
,
1 0 0 0 0 0 1 1 0 0 0 0 60 0 0 0 0 0 53 41 0 0 0 49 8
G:=sub<GL(5,GF(61))| [1,0,0,0,0,0,60,0,0,0,0,0,60,0,0,0,0,0,1,0,0,0,0,0,1],[60,0,0,0,0,0,20,0,0,0,0,0,20,0,0,0,0,0,58,0,0,0,0,0,58],[1,0,0,0,0,0,0,1,0,0,0,60,1,0,0,0,0,0,46,38,0,0,0,23,23],[1,0,0,0,0,0,1,0,0,0,0,1,60,0,0,0,0,0,53,49,0,0,0,41,8] >;
C2×C10×Dic6 in GAP, Magma, Sage, TeX
C_2\times C_{10}\times {\rm Dic}_6
% in TeX
G:=Group("C2xC10xDic6");
// GroupNames label
G:=SmallGroup(480,1150);
// by ID
G=gap.SmallGroup(480,1150);
# by ID
G:=PCGroup([7,-2,-2,-2,-2,-5,-2,-3,560,2467,304,15686]);
// Polycyclic
G:=Group<a,b,c,d|a^2=b^10=c^12=1,d^2=c^6,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations
×
𝔽
|
Have you ever had this feeling that bus (or tram, or train, etc.) leaves exactly 1 minute before you get to the stop AND the next one is forever away? Or you come to a crossroad which is usually very quiet, but exactly as you are about to cross it, there are like 100 cars going in every direction?
Apparently, both of those phenomenon’s can be explained with what is called “Hitchiker’s paradox”. To save you a bit of clicking, the upshot is that:
… if you take an interval of observation that is big enough, you will observe as many arrivals below 10 minutes and as many arrivals above 10 minutes. And you will see that the average waiting time is 10 minutes.
I’ve learned about long time ago and as soon as I did I started noticing it everywhere. Not that those things didn’t happen with me before, so it is probably some variant of Baader-Meinhof phenomenon.
Anyway, the point of this post is to check it with “real” data that I’ve collected myself (hence “Quantified-self” in the title). The source of the data is my notes every time I came to the tram stop that I take every day to work. Since it happens at around the same time every day, I thought that it should be quite consistent and all variance is explained by the paradox above. Ultimately, I want to find out whether, in general, arrival of tram to my stop follows the Poisson distribution with $$\lambda$$ equal to 4 minutes (official interval at the stop).
That all being said, the data is as follows:
library(ggplot2)
stops <- c(4, 2, 6, 4, 0, 5, 1, 3, 2, 3, 1, 2, 3, 4, 3, 4, 7, 5,
3, 3, 0, 2, 2, 2, 2, 0, 3, 1, 0, 4, 5, 1, 2, 4, 3, 2,
8, 2, 2, 5, 5)
ggplot(tibble::enframe(stops), aes(x = value)) +
geom_bar() +
labs(title = "How long I waited each time",
x = "Minutes",
y = "Frequency")
And $$\lambda$$ is:
parms <- MASS::fitdistr(stops, "poisson")
parms
## lambda
## 2.9268293
## (0.2671817)
So, in fact, whatever feeling I had of trams being too slow to arrive, it looks like they come (on average) even faster than they should. What would I have done without math?
|
Contest Duration: - (local time) (100 minutes) Back to Home
C - Welcome to AtCoder /
Time Limit: 2 sec / Memory Limit: 1024 MB
### 問題文
このコンテストでは、 N 問の問題が出題されます。
i 回目の提出は p_i 番目の問題への提出であり、結果は S_i (AC または WA) でした。
### 制約
• N , M , p_i は整数
• 1 ≤ N ≤ 10^5
• 0 ≤ M ≤ 10^5
• 1 \leq p_i \leq N
• S_iACWA のいずれか
### 入力
N M
p_1 S_1
:
p_M S_M
### 入力例 1
2 5
1 WA
1 AC
2 WA
2 AC
2 WA
### 出力例 1
2 2
### 入力例 2
100000 3
7777 AC
7777 AC
7777 AC
### 出力例 2
1 0
### 入力例 3
6 0
### 出力例 3
0 0
Score : 300 points
### Problem Statement
Takahashi participated in a contest on AtCoder.
Takahashi made M submissions during the contest.
The i-th submission was made for the p_i-th problem and received the verdict S_i (AC or WA).
The number of Takahashi's correct answers is the number of problems on which he received an AC once or more.
The number of Takahashi's penalties is the sum of the following count for the problems on which he received an AC once or more: the number of WAs received before receiving an AC for the first time on that problem.
Find the numbers of Takahashi's correct answers and penalties.
### Constraints
• N, M, and p_i are integers.
• 1 \leq N \leq 10^5
• 0 \leq M \leq 10^5
• 1 \leq p_i \leq N
• S_i is AC or WA.
### Input
Input is given from Standard Input in the following format:
N M
p_1 S_1
:
p_M S_M
### Output
Print the number of Takahashi's correct answers and the number of Takahashi's penalties.
### Sample Input 1
2 5
1 WA
1 AC
2 WA
2 AC
2 WA
### Sample Output 1
2 2
In his second submission, he received an AC on the first problem for the first time. Before this, he received one WA on this problem.
In his fourth submission, he received an AC on the second problem for the first time. Before this, he received one WA on this problem.
Thus, he has two correct answers and two penalties.
### Sample Input 2
100000 3
7777 AC
7777 AC
7777 AC
### Sample Output 2
1 0
Note that it is pointless to get an AC more than once on the same problem.
### Sample Input 3
6 0
### Sample Output 3
0 0
|
# J.-P. Serre: Duality of regular differentials on singular curves
I already asked this on math.stackexchange.com, but didn't get any responses. I hope it is appropriate here.
Let $$X'$$ be an irreducible singular algebraic curve over an algebraically closed field $$k$$, let $$X \to X'$$ be its normalization, and consider a singular point $$Q \in X'$$. Let $$K = Q(X)$$ be the function field of $$X$$ and $$X'$$.
Let $$\mathcal{O}_Q' = \mathcal{O}_{X', Q}$$ be the stalk of the structure sheaf of $$X'$$ at $$Q$$, and let $$\mathcal{O}_Q = \bigcap_{P \mapsto Q} \mathcal{O}_P$$ be its normalization. Here $$\mathcal{O}_P$$ is the stalk of the structure sheaf of $$X$$ at $$P \in X$$, and the intersection is over all points mapping to $$Q$$.
In Algebraic Groups and Class Fields by J.-P. Serre, chapter IV §3, Serre introduces the module $$\underline{\Omega}_Q'$$ of regular differentials at $$Q$$. A differential $$\omega \in D_k(K)$$ is called regular, iff $$$$\sum_{P \mapsto Q} \operatorname{Res}_P(f \omega) = 0 \quad \text{for all} \ f\in \mathcal{O}_Q'.$$$$
Similarly to $$\mathcal{O}_Q$$, Serre defines $$\underline{\Omega}_Q = \bigcap_{P \mapsto Q} \Omega_P.$$ Since every differential $$\omega \in \underline{\Omega}_Q$$ has no poles at any point $$P \mapsto Q$$, clearly $$\operatorname{Res}_P(f \omega) = 0$$ for $$f \in \mathcal{O}_Q'$$, so that $$\underline{\Omega}_Q \subset \underline{\Omega}_Q'$$.
Now to my question: The mapping \begin{align} \mathcal{O}_Q / \mathcal{O}_Q' \times \underline{\Omega}_Q' / \underline{\Omega}_Q & \to k \\ (f, \omega) & \mapsto \sum_{P \mapsto Q} \operatorname{Res}_P(f \omega) \end{align} is clearly bilinear and well-defined. Serre claims, that it is a perfect pairing, but I don't know why. I think we have to show two things:
1. If $$f \in \mathcal{O}_Q$$, with the property that for each $$\omega \in \underline{\Omega}_Q'$$, one has $$\sum_P \operatorname{Res}_P(f \omega) = 0$$, then in fact $$f \in \mathcal{O}_Q'$$.
2. If $$\omega \in \underline{\Omega}_Q'$$, such that for each $$f \in \mathcal{O}_Q$$, one has $$\sum \operatorname{Res}_P(f \omega) = 0$$, then $$\omega \in \underline{\Omega}_Q$$, i.e. $$\omega$$ is regular at every $$P \mapsto Q$$.
Any help would be appreciated :)
• Most of this should be in Tate's paper Residues of differentials on curves''. Oct 21, 2020 at 13:37
• @Meow As far as I can tell from skimming the paper, Tate only considers regular curves. The phenomena discussed here happen exactly when $X'$ is not regular. Oct 21, 2020 at 14:03
• Whoops, sorry! I didn't read the question properly. Oct 22, 2020 at 12:00
Let $$X'_1, \dotsc, X'_r$$ be the irreducible components of $$X'$$ at $$Q$$. Then $$X$$ is the disjoint union of the normalizations $$X_i \to X_i'$$. Since we work in the analytic setting and the question is local in $$X'$$ we can assume that each $$X_i$$ contains exactly one point $$P_i \mapsto Q$$. Algebraically this means $$\mathcal O_Q \cong \prod_i \mathcal O_{P_i}$$. Since the $$\mathcal O_{P_i}$$ are regular rings, we can choose a local coordinate $$\mathcal O_{P_i} \cong \mathbb C\{x_i\}$$.
1. Consider an element $$f \in \mathcal O_Q \setminus \mathcal O_Q'$$. We have to find a differential form $$\omega \in \underline{\Omega}_Q'$$ such that $$\sum_P \operatorname{Res}_P(f \omega) \neq 0$$.
1.1. Suppose $$f(P_i) \neq f(P_j)$$ for some $$i$$ and $$j$$, consider the differential form $$\omega$$ which vanishes at all $$P_k$$ for $$i \neq k \neq j$$, and has simple poles at $$P_i$$ and $$P_j$$ with residues $$\operatorname{Res}_{P_i} = - \operatorname{Res}_{P_j} = 1.$$ Since each $$g \in \mathcal O_Q'$$ can be developed locally at $$P_i$$ in a power series, $$\operatorname{Res}_{P_i}(g \omega) = g(Q)$$, and similarly $$\operatorname{Res}_{P_j}(g \omega) = - g(Q)$$. Hence $$\omega \in \underline{\Omega}_Q'$$, but $$\sum_{P \mapsto Q} \operatorname{Res}_P(f \omega) = f(P_i) - f(P_j) \neq 0.$$
1.2. If $$f(P_i) = f(P_j)$$ for all $$i,j$$, one irreducible component of $$X'$$ has to be singular. It is sufficient to show the existence of $$\omega$$ on the irreducible component, so we might suppose $$X'$$ itself is irreducible. This means we have an inclusion $$\mathcal O_Q' \subset \mathbb C\{x\}$$. Since the quotient $$0 \to \mathcal O_Q' \to \mathbb C\{x\} \to \Bbb C^\delta \to 0$$ is finite-dimensional one has $$x^k \in \mathcal O_Q'$$ for some $$k > \delta$$, and so $$\mathcal O_Q'$$ is given by the vanishing of $$\delta$$ linear equations on the coefficients $$a_1, \dotsc, a_{k-1}$$ of a power series $$\sum_n a_n x^n$$. Let $$l = \gamma_1 a_1 + \dotsb + \gamma_{k-1} a_{k-1}$$ be one of those linear equations with $$l(f) \neq 0$$. Then define $$\omega = \left( \frac{\gamma_1x^{k-2} + \dotsb + \gamma_{k-2} x + \gamma_{k-1}}{x^{k}} \right) dx$$ such that for each power series $$g \in \mathbb C\{x\}$$ we have $$\operatorname{Res}_0(g \omega) = l(g)$$. Thus $$\omega \in \underline{\Omega}_Q'$$ and $$\operatorname{Res}_0(f \omega) \neq 0$$.
2. Suppose $$\omega \in \underline{\Omega}'_Q$$, but $$\omega \notin \underline{\Omega}_Q$$. Then $$\omega$$ has a pole at some $$P_i$$, and we can write $$\omega = h(x_i) dx_i$$ for some Laurentseries $$h(x_i) = \sum_{k \geq -n} h_k x^k_i, \quad h_{-n} \neq 0.$$ Thus $$\operatorname{Res}_{P_i}(x_i^{n-1} \omega) = h_{-n} \neq 0$$. So if we define $$f = (0, \dotsc, 0, x_i^{n-1}, 0, \dotsc, 0) \in \prod_j \mathcal O_{P_j}$$ then $$\sum_j \operatorname{Res}_{P_j}(f \omega) = h_{-n} \neq 0$$.
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unit:V_Ab
Type
Description
A unit of electrical potential equal to one hundred millionth of a volt ($$10^{-8}\,volts$$), used in the centimeter-gram-second (CGS) system of units. One abV is the potential difference that exists between two points when the work done to transfer one abcoulomb of charge between them equals: $$1\,erg\cdot\,1\,abV\,=\,10\,nV$$.
Properties
0.00000001
abV
10.nV
Annotations
A unit of electrical potential equal to one hundred millionth of a volt ($$10^{-8}\,volts$$), used in the centimeter-gram-second (CGS) system of units. One abV is the potential difference that exists between two points when the work done to transfer one abcoulomb of charge between them equals: $$1\,erg\cdot\,1\,abV\,=\,10\,nV$$.
Abvolt(en)
Generated 2022-08-02T09:45:30.201-04:00 by lmdoc version 1.1 with TopBraid SPARQL Web Pages (SWP)
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1. ## [solved]
Tara
2. Originally Posted by MissTara
I’m so sorry to trouble you but I urgently need some maths help. All working must be shown also.
I know this is probably the easiest problem in the review questions, and it’s the only one I can’t solve... I’m feeling a tad stupid right now. Any help would be greatly appreciated.
Tara
well, here are some reviews:
$a^na^m = a^{n+m}$
$(a^n)^m = a^{nm}$
$1 \div a = \dfrac{1}{a}$ and so $1 \div a^n = \dfrac{1}{a^n}$
combine these, you must get the answers..
3. Originally Posted by MissTara
I’m so sorry to trouble you but I urgently need some maths help. All working must be shown also.
I know this is probably the easiest problem in the review questions, and it’s the only one I can’t solve... I’m feeling a tad stupid right now. Any help would be greatly appreciated.
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# Questions tagged [popularity-contest]
A popularity-contest is a competition where the answer with the highest vote tally (upvotes minus downvotes) wins. As these are frequently closed, read the tag info and post your challenge to the sandbox first.
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### Polycops and Robbers (Cops' Thread)
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Signals and Systems - Taking Integral of Unit Step Function
I am a taking signals and systems course and my professor posted the solutions to our latest homework and I am trying to understand one of the steps. Below is the solution. Bracketed in red is what I am trying to understand.
Why does u(t) disappear when you move the bounds of the integral to infinity to zero? I am just trying conceptually understand why instead of just accepting it as fact.
• The unit step function changes from 0 to 1 at x=0. The integral of the unit step from -infinity to 0 is 0. Therefore you move the lower limit up to 0 and remove the unit step function. – A.S. Sep 13 '18 at 16:12
• @A.S. simple and efficient...I wish I could upvote your answer wink wink nudge nudge – Simon Marcoux Sep 13 '18 at 16:24
I suspect $x_1(t) = e^{-2t} u(t)$
Since $u(t) = 0$ for $t<0$, the next step simple changes the boundaries of the integration to reflect that the product shown is zero for all $t<0$. Once you do that, you can just drop the $u(t)$, since multiplying a signal by one just returns the original signal.
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Question
# The median of the following data is xi10131619fi2576
Solution
## There are a total of 20 observations. So the median is the average of the 10th and 11th observation. So the median for this data is 16.
Suggest corrections
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# 31.8: The Langmuir Isotherm Can Be Used to Derive Rate Laws for Surface-Catalyzed Gas-Phase Reactions
It is possible to predict how the kinetics of certain heterogeneously-catalyzed reactions might vary with the partial pressures of the reactant gases above the catalyst surface by using the Langmuir isotherm expression for equilibrium surface coverages.
## Unimolecular Decomposition
Consider the surface decomposition of a molecule A , i.e. the process
$A_{(g)} \rightleftharpoons A_{(ads)} → Products$
Let us assume that :
1. The decomposition reaction occurs uniformly across the surface sites at which molecule A may be adsorbed and is not restricted to a limited number of special sites.
2. The products are very weakly bound to the surface and, once formed, are rapidly desorbed.
3. The rate determining step (rds) is the surface decomposition step.
Under these circumstances, the molecules of A adsorbed on the surface are in equilibrium with those in the gas phase and we may predict the surface concentration of A from the Langmuir isotherm, i.e.
$θ = \dfrac{bP}{1 + bP}$
The rate of the surface decomposition (and hence of the reaction) is given by an expression of the form
$rate = k θ$
This is assuming that the decomposition of A(ads) occurs in a simple unimolecular elementary reaction step and that the kinetics are first order with respect to the surface concentration of this adsorbed intermediate). Substituting for the coverage, θ , gives us the required expression for the rate in terms of the pressure of gas above the surface
$rate = \dfrac{k b P}{1 + b P} \label{rate}$
It is useful to consider two extremes:
### Low Pressure/Binding Limit
This is the low pressure (or weak binding. i.e., small $$b$$) limit : under these conditions the steady state surface coverage, $$θ$$ , of the reactant molecule is very small.
$b P \ll 1$
then
$1 + bP \approx 1$
and Equation $$\ref{rate}$$ can be simplified to
$rate \approx kbP$
Under this limiting case, the kinetics follow a first order reaction (with respect to the partial pressure of $$A$$) with an apparent first order rate constant $$k' = kb$$.
### High Pressure/Binding Limit
This is the high pressure (or strong binding, i.e., large $$b$$) limit: under these conditions the steady state surface coverage, $$θ$$, of the reactant molecule is almost unity and
$bP \gg 1$
then
$1 + bP \approx bP$
and Equation $$\ref{rate}$$ can be simplified to
$rate \approx k$
under this limiting case, the kinetics follow a zero order reaction (with respect to the partial pressure of $$A$$). The rate shows the same pressure variation as does the surface coverage, but this hardly surprising since it is directly proportional to θ.
These two limiting cases can be identified in the general kinetics from Equation $$\ref{rate}$$ in Figure 3.5.1.
Figure 3.5.1:
## Bimolecular Reaction (between molecular adsorbates)
Consider a Langmuir-Hinshelwood reaction of the following type:
$A_{(g)} \rightleftharpoons A_{(ads)} \label{Eq2.1}$
$B_{(g)} \rightleftharpoons B_{(ads)} \label{Eq2.2}$
$A_{(ads)} + B_{(ads)} \overset{slow}{\longrightarrow} AB_{(ads)} \overset{fast}{\longrightarrow} AB_{(g)} \label{Eq2.3}$
We will further assume, as noted in the above scheme, that the surface reaction between the two adsorbed species (left side of Equation $$\ref{Eq2.3}$$ is the rate determining step.
If the two adsorbed molecules are mobile on the surface and freely intermix then the rate of the reaction will be given by the following rate expression for the bimolecular surface combination step
$Rate = k θ_A θ_B$
For a single molecular adsorbate the surface coverage (as given by the standard Langmuir isotherm) is
$θ = \dfrac{bP}{1 + bP}$
Where two molecules ($$A$$ & $$B$$ ) are competing for the same adsorption sites then the relevant expressions are (see derivation):
$\theta_A = \dfrac{b_AP_A}{1+b_AP_A + b_BP_B}$
and
$\theta_B = \dfrac{b_BP_B}{1+b_AP_A + b_BP_B}$
Substituting these into the rate expression gives :
$Rate = k \theta_A \theta_B = \dfrac{k b_AP_A b_BP_B }{( 1+b_AP_A + b_BP_B )^2}$
Once again, it is interesting to look at several extreme limits
### Low Pressure/Binding Limit
$b_A P_A \ll 1$
and
$b_B P_B \ll 1$
In this limit that $$θ_A$$ & $$θ_B$$ are both very low , and
$rate → k b_A P_A b_B P_B = k' P_A P_B$
i.e. first order in both reactants
### Mixed Pressure/Binding Limit
$b_A P_A \ll 1 \ll b_B P_B$
In this limit $$θ_A → 0$$, $$θ_B → 1$$, and
$Rate → \dfrac{k b_A P_A }{b_B P_B } = \dfrac{k' P_A}{P_B}$
i.e. first order in $$A$$, but negative first order in $$B$$
Clearly, depending upon the partial pressure and binding strength of the reactants, a given model for the reaction scheme can give rise to a variety of apparent kinetics: this highlights the dangers inherent in the reverse process - namely trying to use kinetic data to obtain information about the reaction mechanism.
Example 3.5.1: CO Oxidation Reaction
On precious metal surfaces (e.g. Pt), the $$CO$$ oxidation reaction is generally believed to by a Langmuir-Hinshelwood mechanism of the following type :
$CO_{(g)} \rightleftharpoons CO_{(ads)}$
$O_{2 (g)} \rightleftharpoons 2 O_{(ads)}$
$CO_{(ads)} + O_{(ads)} \overset{slow}{\longrightarrow} CO_{2 (ads)} \overset{fast}{\longrightarrow} CO_{2 (g)}$
As CO2 is comparatively weakly-bound to the surface, the desorption of this product molecule is relatively fast and in many circumstances it is the surface reaction between the two adsorbed species that is the rate determining step.
If the two adsorbed molecules are assumed to be mobile on the surface and freely intermix then the rate of the reaction will be given by the following rate expression for the bimolecular surface combination step
$Rate = k \,θ_{CO}\, θ_O$
Where two such species (one of which is molecularly adsorbed, and the other dissociatively adsorbed) are competing for the same adsorption sites then the relevant expressions are (see derivation):
$\theta_{CO} = \dfrac{b_{CO}P_{CO}}{1+ \sqrt{b_OP_{O_2}} + b_{CO}P_{CO}}$
and
$\theta_{O} = \dfrac{ \sqrt{b_OP_{O_2}} }{1+ \sqrt{b_OP_{O_2}} + b_{CO}P_{CO}}$
Substituting these into the rate expression gives:
$rate = k \theta_{CO} \theta_O = \dfrac{ k b_{CO}P_{CO} \sqrt{b_OP_{O_2}} }{(1+ \sqrt{b_OP_{O_2}} + b_{CO}P_{CO})^2} \label{Ex1.1}$
Once again, it is interesting to look at certain limits. If the $$CO$$ is much more strongly bound to the surface such that
$b_{CO}P_{CO} \gg 1 + \sqrt{b_OP_{O_2}}$
then
$1 + \sqrt{b_OP_{O_2}} + b_{CO}P_{CO} \approx b_{CO}P_{CO}$
and the Equation $$\ref{Ex1.1}$$ simplifies to give
$rate \approx \dfrac{k \sqrt{b_OP_{O_2}} } {b_{CO}P_{CO}} = k' \dfrac{P^{1/2}_{O_2}}{P_{CO}}$
In this limit the kinetics are half-order with respect to the gas phase pressure of molecular oxygen, but negative order with respect to the $$CO$$ partial pressure, i.e. $$CO$$ acts as a poison (despite being a reactant) and increasing its pressure slows down the reaction. This is because the CO is so strongly bound to the surface that it blocks oxygen adsorbing, and without sufficient oxygen atoms on the surface the rate of reaction is reduced.
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03 Sep 2012, 05:47
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Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today? (A)$10,350
(B) $10,395 (C)$10,500
(D) $11,500 (E)$12,705
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 03 Sep 2012, 05:47 6 This post received KUDOS Expert's post 2 This post was BOOKMARKED SOLUTION Lucy invested$10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
(A) $10,350 (B)$10,395
(C) $10,500 (D)$11,500
(E) $12,705 The value of the account today would be $$10,000*1.1*1.05*0.9$$. Now, the question is how to calculate this efficiently. $$10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}$$ --> 10,000 will cancel and we'll get: $$11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395$$. Answer: B. _________________ Intern Joined: 28 Aug 2012 Posts: 46 Location: Austria GMAT 1: 770 Q51 V42 Followers: 3 Kudos [?]: 45 [1] , given: 3 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]
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03 Sep 2012, 06:07
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Value after 1 year: 10,000 * 1.1 = 11,000
Value after 2 years: 11,000 * 1.05 = 11,550
Value today: 11,550 * 0.9 = 10,395
Answer B is correct.
The first equation is easy. In the second, first calculate 10% (1,100) and divide that by 2 (550). Add that to 11,000.
In the final equation, calculate 10% again (1,155) and subtract it from 11,550.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 03 Sep 2012, 06:51 2 This post received KUDOS Bunuel wrote: Lucy invested$10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
(A) $10,350 (B)$10,395
(C) $10,500 (D)$11,500
(E) $12,705 This is a question of successive % change. This question ultimately reduces to a multiplication problem. Final value after successive % change on$10,000 = $10,000 X 1.1 X 1.05 X .9 1.1 X 1.05 X .9 = 1.0395 Answer is B) _________________ Regards SD ----------------------------- Press Kudos if you like my post. Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html Manager Joined: 12 Mar 2012 Posts: 167 Location: India Concentration: Technology, General Management GMAT Date: 07-23-2012 WE: Programming (Telecommunications) Followers: 0 Kudos [?]: 57 [0], given: 4 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]
### Show Tags
03 Sep 2012, 07:45
I also followed the same approach and got the answer as B.
But I am wondering if there is any better method of calculating in any problem with successive year interest rates given.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 07 Sep 2012, 03:06 Expert's post 1 This post was BOOKMARKED SOLUTION Lucy invested$10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
(A) $10,350 (B)$10,395
(C) $10,500 (D)$11,500
(E) $12,705 The value of the account today would be $$10,000*1.1*1.05*0.9$$. Now, the question is how to calculate this efficiently. $$10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}$$ --> 10,000 will cancel and we'll get: $$11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395$$. Answer: B. Kudos points given to everyone with correct solution. Let me know if I missed someone. _________________ Manager Joined: 20 Nov 2010 Posts: 221 Followers: 4 Kudos [?]: 32 [1] , given: 38 Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink]
### Show Tags
07 Sep 2012, 21:56
1
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10000 + 1000 = 11000
11000 + 550 = 11550
11550 * 0.9 = 10395
(B)
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### Show Tags
15 Dec 2012, 12:14
Bunuel wrote:
SOLUTION
Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today? (A)$10,350
(B) $10,395 (C)$10,500
(D) $11,500 (E)$12,705
The value of the account today would be $$10,000*1.1*1.05*0.9$$. Now, the question is how to calculate this efficiently.
$$10,000*1.1*1.05*0.9=10,000*\frac{11}{10}*\frac{105}{100}*\frac{9}{10}=10,000*\frac{11*105*9}{10,000}$$ --> 10,000 will cancel and we'll get: $$11*105*9=(9*11)*105=99*105=(100-1)*105=10,500-105=10,395$$.
Answer: B.
Thank you for the answer Bunuel, but i was just wondering. When you chose the denominators for the different fractions, was your goal to get 10 000 in the denominator so we could cancel Lucy's initial investment? Smart move by the way
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### Show Tags
02 May 2013, 11:12
.10x10,000= $1,000 end of y1 = 11,000 .05x11,000=$550.00 end of y2 = 11,550
.10x11,550= 1,150 -1,155
(subtract y2 with the loss of y3) end of y3= 10,395
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06 Aug 2014, 11:49
We can use successive percentage formula : a+b + ab/100
so in the first two years it will increase 10 + 5 + 10*5/100 = 15.5
and in the second and third year it will be : 15.5 - 10 - 15.5*10/100 = 3.95
so finally the investment will increase by 3.95 %
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### Show Tags
10 Sep 2014, 03:43
Bunuel wrote:
Lucy invested $10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today? (A)$10,350
(B) $10,395 (C)$10,500
(D) $11,500 (E)$12,705
Practice Questions
Question: 31
Page: 156
Difficulty: 600
10,000*1.1--> 10% increase in the first year.
11000*1.05 --> 5% increase in second year
10% decrease from 11550 --> 10395
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### Show Tags
20 Nov 2014, 01:50
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Say initial value = 100 (avoiding 2 extra 00)
1st Yr >> 10% increase = 100 + 10 = 110
2nd Yr >> 5% increase = 110 + 5.5 = 115.5
3rd Yr >> 10% decrease = 115.5 - 11.55 = 103.95
Resultant = 103.95 * 100 = 10395
Answer = B
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 19 Dec 2015, 09:19 year 1 Increases 10% 1000 Value became 11000 Year 2 increase 5% 550 value became 11550 Year 3 decrease 10% 1155 value became 11550-1155 =$10395.
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Re: Lucy invested $10,000 in a new mutual fund account exactly [#permalink] ### Show Tags 25 May 2016, 09:01 2 This post received KUDOS Expert's post Bunuel wrote: Lucy invested$10,000 in a new mutual fund account exactly three years ago. The value of the account increased by 10 percent during the first year, increased by 5 percent during the second year, and decreased by 10 percent during the third year. What is the value of the account today?
(A) $10,350 (B)$10,395
(C) $10,500 (D)$11,500
(E) $12,705 To determine the value of the account today we want to set up an expression showing the various percent increases and decreases. Remember we are multiplying each percent increase or decrease against the original value of$10,000.
Also, we must remember that a 10% increase is the same as multiplying by 1.1, a 5% increase is the same as multiplying by 1.05, and a 10% decrease is the same as multiplying by 0.9. That is:
10,000(1.1)(1.05)(0.9)
Because the multiplication may get a bit complicated in the equation above, we should convert each decimal to a fraction, allowing us to reduce before multiplying.
Thus, we have:
10,000(11/10)(105/100)(9/10)
This is equivalent to: 10,000(11 x 105 x 9/10,000)
Thus we see the the two values of 10,000 cancel out, and we are left with:
11 x 105 x 9 = 99 x 105 = 10,395
Note: If you did not want to perform the multiplication of the final step, you could have used a combination of units digits and estimation to come to the correct answer. Keep in mind that the product of 99 and 105 will have a units digit of 5. That leaves us with only B ($10,395) and E ($12,705) as possible answer choices. Next, by rounding up 99 to 100 and multiplying 100 by 105 we get a product of 10,500. Because we rounded up and answer choice E is LARGER than 10,500, it’s not a possible answer choice. Thus, the correct answer is B, $10,395. _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Re: Lucy invested$10,000 in a new mutual fund account exactly [#permalink] 25 May 2016, 09:01
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# pylops.utils.seismicevents.linear3d¶
pylops.utils.seismicevents.linear3d(x, y, t, v, t0, theta, phi, amp, wav)[source]
Linear 3D events
Create 3d linear events given propagation velocity, intercept time, angles, and amplitude of each event.
Parameters: x : numpy.ndarray space axis in x direction y : numpy.ndarray space axis in y direction t : numpy.ndarray time axis v : float propagation velocity t0 : intercept time at $$x=0$$ of each linear event theta : angle in x direction (in degrees) of each linear event phi : angle in y direction (in degrees) of each linear event amp : amplitude of each linear event wav : numpy.ndarray wavelet to be applied to data d : numpy.ndarray data without wavelet of size $$[n_y \times n_x \times n_t]$$ dwav : numpy.ndarray data with wavelet of size $$[n_y \times n_x \times n_t]$$
Notes
Each event is created using the following relation:
$t_i(x, y) = t_{0,i} + p_{x,i} x + p_{y,i} y$
where $$p_{x,i}=sin( \theta_i)cos( \phi_i)/v$$ and $$p_{x,i}=sin( \theta_i)sin( \phi_i)/v$$.
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# Why are my interference patterns completely out of phase?
DIY physics enthusiast here doing a double slit eraser experiment at home with a laser pointer, double slit diaphragm, and few linear polarizers (horizontal at one slit, vertical at the other, +/-45 degrees for the eraser).
When I angle the eraser polarizer at -45 degrees or +45 degrees I get the interference pattern back, however the interference patterns (light/dark bands) are completely out of phase for -45 vs +45. How come that happens?
+45 = | | | | | |
-45 = | | | | | |
P.S. My physics "knowledge" is all from the University of YouTube, so you may have to explain it to me like I'm 5. :)
• What do you mean by "the fringes are completely out of phase"? Do you mean that the pattern is shifted (so bright becomes dark etc.) compared with the pattern without any polarisers? – Philip Wood Jan 19 at 12:16
• @PhilipWood I fixed the terminology and added an example. With the 'erasing' 45 degree polarizer, when it is -45 degrees I get an interference patter, but when it is at +45 degrees I get another interference pattern that is shifted perfectly out of phase compared to the -45 degree interference pattern. – user1165664 Jan 19 at 16:15
• Note that polarizers don't have a direction (like a vector, $\rightarrow$ ), the have an alignment (like a tensor, $\leftrightarrow$), because they are unchanged by a 180 degree rotation. – JEB Jan 20 at 18:36
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1. ## Invertible Matrices
Hello!
This is one problem I've been tackling for a while:
If A, B, and A+B are all invertible matrices of order "n", prove that $A^{-1} + B^{-1}$ is invertible and that:
$(A^{-1}+B^{-1})^{-1} = A(A+B)^{-1}B = B(A+B)^{-1}A$
First, is there a generic formula for $A^{-1} + B^{-1}$? (If so, our instructor never taught us one). I'm also assuming that we can't assume AB is commutable, because that could make everything so much easier. ^_^;
Anyway. Any helpful hints might help. Basically what I've tried to do so far is equate the "middle" and RHS statements by multiplying both sides by inverses to isolate $(A+B)^{-1}$, but I don't really see how that 'proves' anything ...
2. Originally Posted by ginarific
Hello!
This is one problem I've been tackling for a while:
If A, B, and A+B are all invertible matrices of order "n", prove that $A^{-1} + B^{-1}$ is invertible and that:
$(A^{-1}+B^{-1})^{-1} = A(A+B)^{-1}B = B(A+B)^{-1}A$
First, is there a generic formula for $A^{-1} + B^{-1}$? (If so, our instructor never taught us one). I'm also assuming that we can't assume AB is commutable, because that could make everything so much easier. ^_^;
Anyway. Any helpful hints might help. Basically what I've tried to do so far is equate the "middle" and RHS statements by multiplying both sides by inverses to isolate $(A+B)^{-1}$, but I don't really see how that 'proves' anything ...
How do you show a matrix is invertible? Find a matrix that multiplied by the first one gives you the identity one!
Well, let us show that $A^{-1}+B^{-1}$ is the inverse of the matrix $A(A+B)^{-1}B$:
$A(A+B)^{-1}B(A^{-1}+B^{-1})=A\left[(A+B)^{-1}B+(A+B)^{-1}A\right]A^{-1}=$ $A(A+B)^{-1}(B+A)A=I$ and we're done!
Tonio
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# Math Help - Needing help with these problems
1. ## Needing help with these problems
Hello,
I need help with these problems please.
I did the following, please check to ensure they are correct.
Find the distance between A(-3,3) and B(-6,5) using the distance formula.
d= (-6--3)2+(5-3)2
d= (-6+3) 2+(5-3)2
d= (-3)2+(2)2
d= (9) +(4)
d= 14 == 3.741
Find the distance between A (-4,2) and B (-6,4) using the Pythagorean Theorem. Use graph paper.
Also
Find the coordinates of the midpoint of segment QR having the endpoints:
Q (-.4, 2.5) R (3.5, 1.5)
Thank you,
Siobhan
2. well, your distance equation is right.
and to use the pythag. Theorm, you just draw a right triangle with those two points, and solve for the hypotenuse, because you have the 2 legs.
The line that connects the two points is the hypotenuse. Then just make a right triangle with that.
To find the midpoint, you take the average of the 2 x coordinates and the 2 y coordinates, and combine those 2 averages, to make 1 ordered pair.
So:
$-0.4+3.5=3.1$
$3.1/2=1.55$
So the X coordinate of the midpoint will be 1.55
$2.5+1.5=4$
$4/2=2$
So the Y coordinate of the midpoint will be 2
So the midpoint will be: $(1.55,2)$
3. Thanks, you rawk!
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## Thursday, July 2, 2015
### Atomic Lattices and Glowscript
I'm finishing up (read: procrastinating finishing up) a final paper in a material science course that I'm taking this summer. The paper is about cuprous oxide ($Cu_2O$) and its possible use in a homemade diode. That process is outlined here.
HP Friedrichs's homemade diode and holder
I am investigating whether what he has described in terms of process and results jibes with the literature's descriptions of fabrication processes, physical properties, and and electrical properties. All of that's interesting, but one neat part was a look at the crystal structure. It's a combination of two crystals: the copper forms a face-centered cubic sublattice and the oxygen forms a body-centered cubic sublattice.
Specifying crystals, I've learned, is a pretty neat vector operation, and one which lends itself to programming pretty well. There's a basic unit which is repeated at each point of a cube. That unit isn't necessarily as many atoms as you might think: for a body-centered cubic lattice, it's a set of points at (relative coordinates) (0,0,0) and a(.5,.5,.5), where a is the lattice constant, which is the edge length of the cube. hen you replicate this two-atoms basis at each of the corners of a cube of side-length a, you get a body-centered cubic lattice (doing it just once gives some extra atoms; the unit cell consists of just those atoms within the unit cube. Doing it infinitely, though, will give an infinite BCC lattice). It's a little harder to picture the FCC lattice, but its basis consists of (0,0,0), a(0,.5,.5), a(.5,0,.5), and a(.5,.5,0).
So we have a set of atom positions (2 or 4, depending on the lattice) that we want to iterate over all point of the form a(x, y, z), with all coordinates in the integers. That's a perfect setup for VPython/Glowscript. It's easy enough, using some for loops, to iterate over an area of desired dimensions, and then it can all be zoomed and rotated by the user with VPython/Gloscript's native controls. I added a box showing the unit cube for orientation, and.. voila (click image or here to see animation)!
GlowScript 1.1 VPython
scene.background = color.white
# apply basis atoms to each site in cubic lattice
atoms = []
for site in cubic:
for atom in basis:
atoms.append(sphere(color= color, radius = rad, pos = site+atom+offset))
return atoms
# apply basis atoms to each site in cubic lattice
atoms = []
for site in cubic:
for atom in basis:
if 0 <= (site+atom+offset).x <= a and 0 <= (site+atom+offset).y <= a and 0 <= (site+atom+offset).z <= a:
atoms.append(sphere(color= color, radius = rad, pos = site+atom+offset))
return atoms
def cubeDraw(color):
# draw lines around the unit (not primitive) cell
curve(pos = [a*vector(0,0,0),a*vector(1,0,0),a*vector(1,1,0),a*vector(0,1,0),a*vector(0,0,0)], color = color)
curve(pos = [a*vector(0,0,0),a*vector(0,0,1),a*vector(0,1,1),a*vector(0,1,0),a*vector(0,0,0)], color = color)
curve(pos = [a*vector(0,0,1),a*vector(1,0,1),a*vector(1,1,1),a*vector(0,1,1),a*vector(0,0,1)], color = color)
curve(pos = [a*vector(1,0,0),a*vector(1,0,1),a*vector(1,1,1),a*vector(1,1,0),a*vector(1,0,0)], color = color)
a = 1 # lattice constant
# Lattice maker
# basis vectors
bcc = [vector(0,0,0), vector(.5*a,.5*a,.5*a)]
fcc = [vector(0,0,0), vector(0,.5*a,.5*a), vector(.5*a,0,.5*a), vector(.5*a,.5*a,0)]
# Create unit cubic lattice
# horizontal extent (will go from -x to x)
xmin = -1.5
xmax = 1.5
# vertical extent (will go from -y to y)
ymin = -1.5
ymax = 1.5
#in-out extent (will go from -z to z)
zmin = -1.5
zmax = 1.5
cubic = []
for i in arange(xmin,xmax+1,1):
for j in arange(ymin,ymax+1,1):
for k in arange(zmin,zmax+1,1):
cubic.append(a*vector(i,j,k))
# Use this to show a single unit cell
#CuAtoms = makeCellLattice(cubic,bcc,vector(0,0,0),color.red,a/15)
#OAtoms = makeCellLattice(cubic,fcc,(sqrt(3)/8)*a*vector(-1,-1,-1),color.blue,a/20)
#Use this to show a bigger lattice
CuAtoms = makeLattice(cubic,bcc,vector(0,0,0),color.red,a/15)
OAtoms = makeLattice(cubic,fcc,(sqrt(3)/8)*a*vector(-1,-1,-1),color.blue,a/20)
scene.center = a*vector(.5,.5,-.5)
cubeDraw(color.red)
## Saturday, April 25, 2015
### Kinematics Graph Checker
Here's an applet for kinematics (mostly CAPM) practice that I put together this fall. Students have the option to choose what information they are given, from these choices:
• Initial x, v, and a values
• Position graph, initial x values
• Velocity graph, initial x and v values
• Acceleration graph, initial, x, v, and a values
The length of the time interval considered can also be varied. After getting the given information, students can draw their predictions (either sketching the shapes or drawing quantitative graphs), and then press the "Show Solutions" button to reveal the hidden two or three graphs. I finished this one after students were through 1D kinematics this year, so I don't have any info on how effective students find these. Let me know if you like (or don't like) them for your classroom purposes!
## Friday, April 10, 2015
### What Can You Do With This? feat. Phineas and Ferb
I love the "What Can You Do With This?" variety of problem prompts: give the students a situation, photo, video, sound, or piece of equipment and then ask them: "what can you do with this?" That is, "what questions can you ask of this?"
Students have great ownership of these questions, and must really engage with the modeling process - identifying what principles apply, making and justifying assumptions and approximations, determining what information is available, etc., as well as practicing the process of asking interesting but focused and answerable questions. None of these purposes are served well by "textbook problems," not to mention that the process is more enjoyable and engaging for students when they're such a big part of it.
Here's my most recent - a video prompt that I saw while watching Phineas and Ferb with my son:
The students came up with some great questions, made measurements (including scaling) from the video, and did their analyses. It took about 35 minutes, and here are the three whiteboards from this section:
"What's the stiffness constant of the 'trampoline'"?
"What would his maximum acceleration be as he's caught?"
"What's the maximum force exerted on him by the trampoline?"
Also explored by this group, but not pictured: "From how high could he fall and not die?"
"How high does Phineas bounce?"
"How much energy was lost during the bounce?"
## Friday, March 13, 2015
### Counter-factual Animations and Energy
Soon after my students began energy, I presented them with a set of five YouTube videos that I made with VPython of a race between two identical balls, launched by identical springs that had been compressed identical amounts.
The five simulations present five different ways that the race could play out; one is physically accurate and, while the other four have some sort of logic, their results are not physically correct. The students have some time in groups to determine which they think is correct and, more importantly, what specific issues they have with the others. I'm challenging them to figure out the laws of physics in these four alternate universes, in essence.
After they've worked for a while, they vote, and then we go through the unpopular ones first, with students giving their reasons against them, debating as disagreement crops up.
It usually boils down to two or three, and they hone in on the correct answer pretty reliably in a peer-instruction-esque way. The discussion has been lively and productive, and I like it as a way to focus their attention on the kinds of things that energy conservation does and does not allow in the world in general. It also is a good review of some kinematics concepts, including average velocity and the velocity/displacement relationship.
The YouTube format isn't the best - the size is a bit too small, unless you want to switch back and forth between fullscreen and smaller. Additionally, the suggested videos pop-up at the end is distracting and annoying.
To that end, I coded the simulations into GlowScript instead; students can now deal with them in-browser, repeating or switching at will. It would be neat to have two windows to select different simulations to run against each other simultaneously, and I may add that feature in the future. In the meantime, this will be a big improvement for students over the previous incarnation!
## Saturday, February 7, 2015
### Thoughts on Beginning Magnetism
It has been a while since I have been able to get magnetism into the Honors Physics course, but the lack of fourteen million snow days this year has certainly helped. I'm putting it at the end of the second term, which is the term in which we studied gravity and circular motion, so it fits in pretty well - a non-contact, field-based phenomenon which, like gravity, which causes circular motion.
Since it has been several years, I thought that I'd completely revamp my treatment of magnetism. Here are some notes on the first day, and a brief outline of the plan of the rest. It's mostly bullet points, and at least as much for me remembering the thought process as for anything.
My favorite bit is that it's a whole 95-minute day that fleshes out the idea of field relatively well, giving students some concrete experience puzzling them out and creating representations based on their own investigations. Hopefully, this will give them a better mental picture of fields in space.
General ideas:
- Magnetism is similar to gravity, in that it's a non-contact force - it's "invisible.'
- It's all about "fields," and we're going to need to figure out what the heck a field is at some point. That's pretty much the goal for the day.
Operational def’ns: We're going to use an operational def'n of the field (at least the B field direction) today. What’s our op. def. of temperature? It's what a thermometer measures! For B field directions, it’s going to be “where a compass points."
Let’s explore that a little:
- Map of the field in the room. Need better compasses, or maybe use phones? (yes, phones worked much better on the second day) They draw their vectors on board, "complete" them to form field lines.
- Let’s look at another field together: field of wire apparatus (through table), with compasses. Combining little arrows into loops, change i direction to see the opposite direction loop
- They investigate with bar magnet, horseshoe magnet, current loop (?), solenoid - your goal is to draw a good diagram of your object's B field on the WB.
Sharing whiteboards (unfortunately, didn't get any pics here of the boards):
- Bar first - what dir. are the field lines? (N to S) What does that tell us about Earth? (The north geographic pole is near a south magnetic pole!).
- Horseshoe: what’s the orientation of the (unlabeled) poles?
What’s in common so far?
- loops (are they closed? Yes - we couldn't see the part inside the magnet for these, but they're there)
- from N to S
- distance-dependent strength (how can we tell this from the diagram? Density of field lines!)
- opposites/likes
Now the solenoid: puzzling out the shape (if they didn't figure it out - one class did)
RHR - wire current
Current loop, using RHR1 - generates RHR2… let’s check it for the solenoid (go to solenoid)
Looping back around (see what I did there?): what is a field?
- has a value (magnitude, direction) at every point in space
- affects objects that are in it
Which field have we dealt with? Gravitational field, though we haven't called it that, really.
- Planet g field shape; where’s it strongest? same deal; not closed loops, though - that’s a difference.
- What objects create g fields? (masses) what objects does it affect? (masses)
For B fields, what creates them? perm. mag., currents -> moving charges (spin, domains, etc.), and it’ll affect moving charges, too! We'll look at the effects next time!
Future:
- Using this applet to examine the effects of B fields on charges - helps to figure out that the direction of the force on the charge is always perp to v, dependence on q, etc.
- Lorentz force
- Applying that to a current; forces on wires
- Quantifying the fields of wires, solenoids
That's pretty much what we'll have time for before exams!
## Thursday, December 4, 2014
### Independent Friction Labs
At the end of the first term, I give my honors physics students a couple of days to design, implement, and present an independent investigation involving friction. That's about all that I specify, other than the size of the poster and a few details about requiring equations set with software, citations, etc.
This year's crop was great!
This group investigated the "friction" effects of oobleck on a block, dragged through it at constant speed. They determined that the relationship could be modeled in a friction-like way, but only if the "coefficient" was a function of speed.
This group tested the idea that the mass shouldn't affect the acceleration due to friction; three kids wore the same clothes and slid across the floor, using video analysis to determine the acceleration.
This group tested and modeled the friction between interleaved pages of books. They first modeled the friction on a single page, under some number of pages above, and then did a summation to predict the total possible static friction force between the books.
This group tested the classic physics approximation of ice being frictionless. They made pucks out of ice and dry ice, and determined friction coefficients for each.
This group tried to find the optimum pulling angle for breaking the static friction on an object, both experimentally and theoretically.
This group determined the coefficient of static friction between two blocks, then predicted the hanging mass necessary in a half Atwood machine to cause the top block to slip against the bottom block (which is attached to the cart in the half Atwood).
Another half Atwood exploration - they set up a vertical surface on a cart and increased the hanging mass until an eraser would accelerate along with the cart, instead of slipping down.
This group dragged a boat through water at different speeds, trying to determine whether they could model fluid drag as a friction force. They showed that the "coefficient" would be velocity-dependent, so that drag is not really a friction force.
### Circular Motion Simulation Follow-up
I last posted about a new circular motion applet that I was planning on using with my classes as the quantitative part of their UCM paradigm lab. Some reflections:
• When students came up with a list of variables that might affect the size of the centripetal acceleration, the list was: speed, mass, radius (always in that order). The visual accelerometer on a rotating table showed the qualitative effect of speed nicely, and the thought experiment about driving a car around a corner (tight or wide) addressed radius. We couldn't do mass with the given stuff, so I told them to check that out in the applet. A few seconds' work with the slider showed that it's irrelevant.
• The applet is framed in terms of string length (radius) and rotational frequency - instead of speed. This means that students had to confront (and figure out) the relationship between rotational frequency (or period) and speed just to get their data for the acceleration's dependence on speed. I like that.
• The other way that they have to confront it is to control speed while investigating acceleration's dependence on radius - changing the radius but not the frequency would change the speed. The students have the figure out the proper frequency for each new value of the radius in order to keep the speed constant during the second experiment. I like this a lot as well.
• Students still have trouble reconciling their two models ($\bg_black&space;\large&space;a=kv^2$ and $\bg_black&space;\large&space;a=\frac{k}{r}$) to determine the complete function of v and r. Even when they have figured out the units of the two constants, the connection is hard for them to make. I'm very open to suggestions of ways to make this go more easily - I don't have a great handle on what the conceptual difficulty is for them here. In the second section, I framed those two models as "OK, so a is proportional to v-squared, and a is proportional to 1/r," and that may have helped.
• Overall, the quantitative modeling went much more quickly, had some good conceptual things to think about, and was good practice with function modeling, so I'm pretty happy about it, at this point. We'll see how things go over the next couple of weeks; did this begin to build lasting understanding?
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# Tag Info
23
Typically, Mathematica contacts the license server every 2 minutes. If you have a license which supports a very large number of processes, that interval can grow (to help MathLM to scale better). It will never be more than 30 minutes. If three consecutive license checks fail, then Mathematica will instead revalidate the entire license file on what would ...
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Version 10 It is time to start setting up bug fixes and work-arounds for version 10. Fix TableAlignments -> Left not working -- code too long to include; provided in answer there Fix 10.0.2 mapping Association to Dataset warning: Begin["TypeSystemInferencePackagePrivate"]; exprType[e_Association] := If[AssociationQ@Unevaluated@e, ...
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Maybe NotebookDynamicExpression is what you are looking for: SetOptions[EvaluationNotebook[], NotebookDynamicExpression :> Refresh[ SetDirectory[NotebookDirectory[]]; nbs = {"one.nb", "two.nb", "three.nb"}; For[i = 1, i <= Length[nbs], i++, Block[{nb = NotebookOpen[NotebookDirectory[] <> nbs[[i]]]}, FrontEndTokenExecute[nb, ...
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You can use the global AutoOpenNotebooks setting to give a list of notebooks that must be opened on startup. The default path where it looks for these notebooks is $UserBasedirectory/SystemFiles/FrontEnd/TextResources. Now every time you open Mathematica, that notebook will be opened (in my case, tile.nb). 11 I don't know anything about mathStatica, so I can't comment on specifically what it's doing. But I can comment on the various moving parts of the system. The init.m file is created by the paclet manager. It must be that the mathStatica palette is part of a paclet which is under active management by the paclet manager. The paclet manager, as part of its ... 11 There are two typical locations where a user can add an init.m file to be loaded at run-time:$BaseDirectory and $UserBaseDirectory.$BaseDirectory is useful for installation wide customizations that apply to all users while $UserBaseDirectory is used for a specific users customizations. So, anything in$UserBaseDirectory is loaded after the files found in ...
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Here is one that came from a Wolfram employee so it should be safe to add in version 9: FindInstance returns Indeterminate in version 9, but not in 8
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I think I found it but I'd be more than happy to look at other alternatives if any provided: Shift + Ctrl + O to open Options > Notebook options > Evaluation options > Global preferences from the drop down menu at the top Change InitializationCellEvaluation to True and InitializationCellWarning to False The next time the .nb file is launched, the ...
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Cause The problem is due to a bug involving Catch and init.m that occurs in (at least) Mathematica versions 7, 8 and 9. It has been reported to Wolfram Support and they have acknowledged it as a bug. At time of writing, WRI has offered neither diagnosis nor workaround for this problem. Reproduction Steps and Analysis To reproduce the issue, place the ...
8
mathStatica does not alter, nor seek to alter, the MenuSortingValue. In fact, mathStatica does not alter or seek to alter, in any way, how or where the mathStatica palette is listed in the palette menu... this is left entirely to default Mathematica behaviour. The reason the mathStatica palette appears out of alphabetical order in the Palettes menu seems to ...
8
As J.M. pointed out, this can be achieved by using an init.m file. init.m files are loaded on startup. The documentation can be found here. To load the VectorAnalysis package on each startup, you can write the init file using Export. The snippet below will append a Needs["VectorAnalysis"] to the kernel init.m file: initFileName = ...
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Here's a patch from Adam Strzebonski of Wolfram, which fixes a bug in RootReduce in 9.0.1. ToNumberField won't recognize Root as explicit algebraic number
8
I think that Mike has a point: it is always good to start with something simple. Here is a very simple example which shows the main problem you have: the Initialization-code is evaluated only after the body of the DynamicModule has been evaluated. This might be surprising considering its name but I think is in agreement with the documentation, which is ...
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One way to go about this is read in the file names - this way you don't have to explicitly check to see if they exist. path = SystemDialogInput["Directory", NotebookDirectory[]]; fileNames = FileNames["*.txt", path]; allFiles = Table[Import[fileNames[[num]]], {num, 1, Length[fileNames]}]; This reads the names of all files (in the specified path ...
7
I think it is more convenient to use NotebookEvaluate. We can do NotebookEvaluate[filename, EvaluationElements-> "InitializationCell"] Confusing here may be that this has the same result as NotebookEvaluate[filename, EvaluationElements -> Automatic] Even though if we simply do NotebookEvaluate[filename] all the cells get evaluated.
7
This is possible, at least in version 7, but as rcollyer supposed there is a Global security option which cannot be set from within the Notebook (automatically, that is). First change the Global option: SetOptions[$FrontEnd, GlobalInitializationCellWarning -> False ] Then in the Notebook you need: SetOptions[EvaluationNotebook[], ... 6 Take a look at: Programmatically quitting the FrontEnd or running without one? I asked some similar questions and the answers have some good strategies to do this although most of them as workarounds outside of the Mathematica front end. A simple but key thing, adding NotebookSave[] to the end of your initializations cell can avoid some of the ... 6 A bit of an extended comment, but using a package makes all the sense in the world for a situation like you describe. You can see a specific example at this earlier question: What is a good coding style for setting and changing application level constants? In the above answer, a package provides a way to supply constants to any other notebooks. While ... 5 I'm questioning AND answering this because I was looking for a feature like this for a while and now stumbled across FrontEndToken["EvaluateInitialization"] which does exactly what I wanted. Here is the code to make it work: filename = SystemDialogInput["FileOpen"]; nb = NotebookOpen[filename]; FrontEndExecute[FrontEndToken[nb, "EvaluateInitialization"]]; ... 5 According to the documentation, To suppress the loading of kernel initialization files, use the kernel command-line option -noinit. To specify another file to be used for kernel initialization in addition to init.m, use the kernel command-line option -initfile file, where file is the additional initialization file. 4 This has to do with the Notebook's default context setting in the evaluation menu. If it isn't set to Global, the definitions made in init.m are not seen. As rm-rf says, a good way to put custom definitions in the init.m would be to use Begin and End to create an Init context and append that context to the context path so that the definitions are ... 3 This is too long for a comment. I don't really have time to pull this code apart but if the objective is to learn DynamicModule wouldn't a simpler piece of code be a better start? If you look at what variables have been created after the first ENTER this is a small sample of what you get I think it would be best to pull your code apart and figure out why ... 3 It's probably a good idea to look at this question more more information about writing CDF-happy notebooks. In brief, Initialization cells won't function properly in the CDF format. For example if we have the following initialization cell: a = 1; And subsequent cell that is not an initialization cell Manipulate[b + x, {x, 1, 10, 1}] Manipulate[a + x, ... 3 On Mathematica 7 (at least) DeclarePackage doesn't work first time on this Curl example: DeclarePackage["VectorAnalysis", {"Div", "Grad", "Curl"}] v := {3 Xx^2 + 2 Yy + (a - 3 b) Zz, (b - 7 a) Xx - 5 Yy - Zz, 2 Xx + c a Yy + 7 Zz} Curl[v] {0, 0, 0} But strangely when v is defined again and run it works: v := {3 Xx^2 + 2 Yy + (a - 3 b) ... 3 You can run SetDirectory in the kernel initialization file, init.m. You'll find it here: SystemOpen@FileNameJoin[{$UserBaseDirectory, "Kernel"}]
3
2
This question seems to be slightly different from Globally loading packages while using a CellGroup as the default context (which I just posted an answer for). Probably the simplest method would be to define your init.m functions in the System context itself as this is always accessible no matter the CellContext. For example: Systemhex[n_] := ...
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One possibility would be to (programmatically) add dynamic options to all cells. E.g., one cell could look like : Cell["1-1", "Input", Evaluatable->Dynamic[eval], CellOpen->Dynamic[open], Background->Dynamic[bcolor]] Then, if you evaluate in a subsequenc cell (or by Button) this: eval = True; open = True; bcolor = LightGray the Cell becomes ...
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As I understand, three things are needed: Explicitly list the contexts of the functions that are in the package. For example, if you are using the function f in package test call it testf[] instead of just f[]. Call Needs on the package inside the initialization option for the Manipulate that makes up your CDF. I would recommend calling needs with the ...
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for Journals by Title or ISSN for Articles by Keywords help
Subjects -> MATHEMATICS (Total: 864 journals) - APPLIED MATHEMATICS (69 journals) - GEOMETRY AND TOPOLOGY (19 journals) - MATHEMATICS (642 journals) - MATHEMATICS (GENERAL) (40 journals) - NUMERICAL ANALYSIS (19 journals) - PROBABILITIES AND MATH STATISTICS (75 journals) MATHEMATICS (642 journals) 1 2 3 4 | Last
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Computational Optimization and Applications [SJR: 1.481] [H-I: 54] [7 followers] Follow Hybrid journal (It can contain Open Access articles) ISSN (Print) 1573-2894 - ISSN (Online) 0926-6003 Published by Springer-Verlag [2340 journals]
• Second-order orthant-based methods with enriched Hessian information for
sparse $$\ell _1$$ ℓ 1 -optimization
• Authors: J. C. De Los Reyes; E. Loayza; P. Merino
Pages: 225 - 258
Abstract: Abstract We present a second order algorithm, based on orthantwise directions, for solving optimization problems involving the sparsity enhancing $$\ell _1$$ -norm. The main idea of our method consists in modifying the descent orthantwise directions by using second order information both of the regular term and (in weak sense) of the $$\ell _1$$ -norm. The weak second order information behind the $$\ell _1$$ -term is incorporated via a partial Huber regularization. One of the main features of our algorithm consists in a faster identification of the active set. We also prove that a reduced version of our method is equivalent to a semismooth Newton algorithm applied to the optimality condition, under a specific choice of the algorithm parameters. We present several computational experiments to show the efficiency of our approach compared to other state-of-the-art algorithms.
PubDate: 2017-06-01
DOI: 10.1007/s10589-017-9891-z
Issue No: Vol. 67, No. 2 (2017)
• Local and global convergence of a general inertial proximal splitting
scheme for minimizing composite functions
• Authors: Patrick R. Johnstone; Pierre Moulin
Pages: 259 - 292
Abstract: Abstract This paper is concerned with convex composite minimization problems in a Hilbert space. In these problems, the objective is the sum of two closed, proper, and convex functions where one is smooth and the other admits a computationally inexpensive proximal operator. We analyze a family of generalized inertial proximal splitting algorithms (GIPSA) for solving such problems. We establish weak convergence of the generated sequence when the minimum is attained. Our analysis unifies and extends several previous results. We then focus on $$\ell _1$$ -regularized optimization, which is the ubiquitous special case where the nonsmooth term is the $$\ell _1$$ -norm. For certain parameter choices, GIPSA is amenable to a local analysis for this problem. For these choices we show that GIPSA achieves finite “active manifold identification”, i.e. convergence in a finite number of iterations to the optimal support and sign, after which GIPSA reduces to minimizing a local smooth function. We prove local linear convergence under either restricted strong convexity or a strict complementarity condition. We determine the rate in terms of the inertia, stepsize, and local curvature. Our local analysis is applicable to certain recent variants of the Fast Iterative Shrinkage–Thresholding Algorithm (FISTA), for which we establish active manifold identification and local linear convergence. Based on our analysis we propose a momentum restart scheme in these FISTA variants to obtain the optimal local linear convergence rate while maintaining desirable global properties.
PubDate: 2017-06-01
DOI: 10.1007/s10589-017-9896-7
Issue No: Vol. 67, No. 2 (2017)
• Branch-and-price for p -cluster editing
• Authors: Teobaldo Bulhões; Anand Subramanian; Gilberto F. Sousa Filho; Lucídio dos Anjos F. Cabral
Pages: 293 - 316
Abstract: Abstract Given an input graph, the p-cluster editing problem consists of minimizing the number of editions, i.e., additions and/or deletions of edges, so as to create p vertex-disjoint cliques (clusters). In order to solve this $${\mathscr {NP}}$$ -hard problem, we propose a branch-and-price algorithm over a set partitioning based formulation with exponential number of variables. We show that this formulation theoretically dominates the best known formulation for the problem. Moreover, we compare the performance of three mathematical formulations for the pricing subproblem, which is strongly $${\mathscr {NP}}$$ -hard. A heuristic algorithm is also proposed to speedup the column generation procedure. We report improved bounds for benchmark instances available in the literature.
PubDate: 2017-06-01
DOI: 10.1007/s10589-017-9893-x
Issue No: Vol. 67, No. 2 (2017)
• Solving nearly-separable quadratic optimization problems as nonsmooth
equations
• Authors: Frank E. Curtis; Arvind U. Raghunathan
Pages: 317 - 360
Abstract: Abstract An algorithm for solving nearly-separable quadratic optimization problems (QPs) is presented. The approach is based on applying a semismooth Newton method to solve the implicit complementarity problem arising as the first-order stationarity conditions of such a QP. An important feature of the approach is that, as in dual decomposition methods, separability of the dual function of the QP can be exploited in the search direction computation. Global convergence of the method is promoted by enforcing decrease in component(s) of a Fischer–Burmeister formulation of the complementarity conditions, either via a merit function or through a filter mechanism. The results of numerical experiments when solving convex and nonconvex instances are provided to illustrate the efficacy of the method.
PubDate: 2017-06-01
DOI: 10.1007/s10589-017-9895-8
Issue No: Vol. 67, No. 2 (2017)
• An SQP method for mathematical programs with vanishing constraints with
strong convergence properties
• Authors: Matúš Benko; Helmut Gfrerer
Pages: 361 - 399
Abstract: Abstract We propose an SQP algorithm for mathematical programs with vanishing constraints which solves at each iteration a quadratic program with linear vanishing constraints. The algorithm is based on the newly developed concept of $${\mathcal {Q}}$$ -stationarity (Benko and Gfrerer in Optimization 66(1):61–92, 2017). We demonstrate how $${\mathcal {Q}}_M$$ -stationary solutions of the quadratic program can be obtained. We show that all limit points of the sequence of iterates generated by the basic SQP method are at least M-stationary and by some extension of the method we also guarantee the stronger property of $${\mathcal {Q}}_M$$ -stationarity of the limit points.
PubDate: 2017-06-01
DOI: 10.1007/s10589-017-9894-9
Issue No: Vol. 67, No. 2 (2017)
• $$L^1$$ L 1 penalization of volumetric dose objectives in optimal control
of PDEs
• Authors: Richard C. Barnard; Christian Clason
Pages: 401 - 419
Abstract: Abstract This work is concerned with a class of PDE-constrained optimization problems that are motivated by an application in radiotherapy treatment planning. Here the primary design objective is to minimize the volume where a functional of the state violates a prescribed level, but prescribing these levels in the form of pointwise state constraints leads to infeasible problems. We therefore propose an alternative approach based on $$L^1$$ penalization of the violation that is also applicable when state constraints are infeasible. We establish well-posedness of the corresponding optimal control problem, derive first-order optimality conditions, discuss convergence of minimizers as the penalty parameter tends to infinity, and present a semismooth Newton method for their efficient numerical solution. The performance of this method for a model problem is illustrated and contrasted with an alternative approach based on (regularized) state constraints.
PubDate: 2017-06-01
DOI: 10.1007/s10589-017-9897-6
Issue No: Vol. 67, No. 2 (2017)
• Visualization of the $$\varepsilon$$ ε -subdifferential of piecewise
• Authors: Anuj Bajaj; Warren Hare; Yves Lucet
Pages: 421 - 442
Abstract: Abstract Computing explicitly the $$\varepsilon$$ -subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class of (convex univariate) piecewise linear–quadratic functions for which existing numerical libraries allow practical computations. We visualize the results in a primal, dual, and subdifferential views through several numerical examples. We also provide a visualization of the Brøndsted–Rockafellar theorem.
PubDate: 2017-06-01
DOI: 10.1007/s10589-017-9892-y
Issue No: Vol. 67, No. 2 (2017)
• A dual gradient-projection method for large-scale strictly convex
• Authors: Nicholas I. M. Gould; Daniel P. Robinson
Pages: 1 - 38
Abstract: Abstract The details of a solver for minimizing a strictly convex quadratic objective function subject to general linear constraints are presented. The method uses a gradient projection algorithm enhanced with subspace acceleration to solve the bound-constrained dual optimization problem. Such gradient projection methods are well-known, but are typically employed to solve the primal problem when only simple bound-constraints are present. The main contributions of this work are threefold. First, we address the challenges associated with solving the dual problem, which is usually a convex problem even when the primal problem is strictly convex. In particular, for the dual problem, one must efficiently compute directions of infinite descent when they exist, which is precisely when the primal formulation is infeasible. Second, we show how the linear algebra may be arranged to take computational advantage of sparsity that is often present in the second-derivative matrix, mostly by showing how sparse updates may be performed for algorithmic quantities. We consider the case that the second-derivative matrix is explicitly available and sparse, and the case when it is available implicitly via a limited memory BFGS representation. Third, we present the details of our Fortran 2003 software package DQP, which is part of the GALAHAD suite of optimization routines. Numerical tests are performed on quadratic programming problems from the combined CUTEst and Maros and Meszaros test sets.
PubDate: 2017-05-01
DOI: 10.1007/s10589-016-9886-1
Issue No: Vol. 67, No. 1 (2017)
• Error estimates for integral constraint regularization of
state-constrained elliptic control problems
• Authors: B. Jadamba; A. Khan; M. Sama
Pages: 39 - 71
Abstract: In this paper, we study new aspects of the integral contraint regularization of state-constrained elliptic control problems (Jadamba et al. in Syst Control Lett 61(6):707–713, 2012). Besides giving new results on the regularity and the convergence of the regularized controls and associated Lagrange multipliers, the main objective of this paper is to give abstract error estimates for the regularization error. We also consider a discretization of the regularized problems and derive numerical estimates which are uniform with respect to the regularization parameter and the discretization parameter. As an application of these results, we prove that this discretization is indeed a full discretization of the original problem defined in terms of a problem with finitely many integral constraints. Detailed numerical results justifying the theoretical findings as well as a comparison of our work with the existing literature is also given.
PubDate: 2017-05-01
DOI: 10.1007/s10589-016-9885-2
Issue No: Vol. 67, No. 1 (2017)
• A Riemannian conjugate gradient method for optimization on the Stiefel
manifold
• Authors: Xiaojing Zhu
Pages: 73 - 110
Abstract: Abstract In this paper we propose a new Riemannian conjugate gradient method for optimization on the Stiefel manifold. We introduce two novel vector transports associated with the retraction constructed by the Cayley transform. Both of them satisfy the Ring-Wirth nonexpansive condition, which is fundamental for convergence analysis of Riemannian conjugate gradient methods, and one of them is also isometric. It is known that the Ring-Wirth nonexpansive condition does not hold for traditional vector transports as the differentiated retractions of QR and polar decompositions. Practical formulae of the new vector transports for low-rank matrices are obtained. Dai’s nonmonotone conjugate gradient method is generalized to the Riemannian case and global convergence of the new algorithm is established under standard assumptions. Numerical results on a variety of low-rank test problems demonstrate the effectiveness of the new method.
PubDate: 2017-05-01
DOI: 10.1007/s10589-016-9883-4
Issue No: Vol. 67, No. 1 (2017)
• A new approach for finding a basis for the splitting preconditioner for
linear systems from interior point methods
• Authors: Porfirio Suñagua; Aurelio R. L. Oliveira
Pages: 111 - 127
Abstract: Abstract The class of splitting preconditioners for the iterative solution of linear systems arising from Mehrotra’s predictor-corrector method for large scale linear programming problems needs to find a basis through a sophisticated process based on the application of a rectangular LU factorization. This class of splitting preconditioners works better near a solution of the linear programming problem when the matrices are highly ill-conditioned. In this study, we develop and implement a new approach to find a basis for the splitting preconditioner, based on standard rectangular LU factorization with partial permutation of the scaled transpose linear programming constraint matrix. In most cases, this basis is better conditioned than the existing one. In addition, we include a penalty parameter in Mehrotra’s predictor-corrector method in order to reduce ill-conditioning of the normal equations matrix. Computational experiments show a reduction in the average number of iterations of the preconditioned conjugate gradient method. Also, the increased efficiency and robustness of the new approach become evident by the performance profile.
PubDate: 2017-05-01
DOI: 10.1007/s10589-016-9887-0
Issue No: Vol. 67, No. 1 (2017)
• Authors: A. F. Izmailov; E. I. Uskov
Pages: 129 - 154
Abstract: Abstract The stabilized sequential quadratic programming (SQP) method has nice local convergence properties: it possesses local superlinear convergence under very mild assumptions not including any constraint qualifications. However, any attempts to globalize convergence of this method indispensably face some principal difficulties concerned with intrinsic deficiencies of the steps produced by it when relatively far from solutions; specifically, it has a tendency to produce long sequences of short steps before entering the region where its superlinear convergence shows up. In this paper, we propose a modification of the stabilized SQP method, possessing better “semi-local” behavior, and hence, more suitable for the development of practical realizations. The key features of the new method are identification of the so-called degeneracy subspace and dual stabilization along this subspace only; thus the name “subspace-stabilized SQP”. We consider two versions of this method, their local convergence properties, as well as a practical procedure for approximation of the degeneracy subspace. Even though we do not consider here any specific algorithms with theoretically justified global convergence properties, subspace-stabilized SQP can be a relevant substitute for the stabilized SQP in such algorithms using the latter at the “local phase”. Some numerical results demonstrate that stabilization along the degeneracy subspace is indeed crucially important for success of dual stabilization methods.
PubDate: 2017-05-01
DOI: 10.1007/s10589-016-9890-5
Issue No: Vol. 67, No. 1 (2017)
• On merit functions for p -order cone complementarity problem
• Authors: Xin-He Miao; Yu-Lin Chang; Jein-Shan Chen
Pages: 155 - 173
Abstract: Abstract Merit function approach is a popular method to deal with complementarity problems, in which the complementarity problem is recast as an unconstrained minimization via merit function or complementarity function. In this paper, for the complementarity problem associated with p-order cone, which is a type of nonsymmetric cone complementarity problem, we show the readers how to construct merit functions for solving p-order cone complementarity problem. In addition, we study the conditions under which the level sets of the corresponding merit functions are bounded, and we also assert that these merit functions provide an error bound for the p-order cone complementarity problem. These results build up a theoretical basis for the merit method for solving p-order cone complementarity problem.
PubDate: 2017-05-01
DOI: 10.1007/s10589-016-9889-y
Issue No: Vol. 67, No. 1 (2017)
• Analysis on Newton projection method for the split feasibility problem
• Authors: Biao Qu; Changyu Wang; Naihua Xiu
Pages: 175 - 199
Abstract: Abstract In this paper, based on a merit function of the split feasibility problem (SFP), we present a Newton projection method for solving it and analyze the convergence properties of the method. The merit function is differentiable and convex. But its gradient is a linear composite function of the projection operator, so it is nonsmooth in general. We prove that the sequence of iterates converges globally to a solution of the SFP as long as the regularization parameter matrix in the algorithm is chosen properly. Especially, under some local assumptions which are necessary for the case where the projection operator is nonsmooth, we prove that the sequence of iterates generated by the algorithm superlinearly converges to a regular solution of the SFP. Finally, some numerical results are presented.
PubDate: 2017-05-01
DOI: 10.1007/s10589-016-9884-3
Issue No: Vol. 67, No. 1 (2017)
• Penalty and relaxation methods for the optimal placement and operation of
control valves in water supply networks
• Authors: Filippo Pecci; Edo Abraham; Ivan Stoianov
Pages: 201 - 223
Abstract: Abstract In this paper, we investigate the application of penalty and relaxation methods to the problem of optimal placement and operation of control valves in water supply networks, where the minimization of average zone pressure is the objective. The optimization framework considers both the location and settings of control valves as decision variables. Hydraulic conservation laws are enforced as nonlinear constraints and binary variables are used to model the placement of control valves, resulting in a mixed-integer nonlinear program. We review and discuss theoretical and algorithmic properties of two solution approaches. These include penalty and relaxation methods that solve a sequence of nonlinear programs whose stationary points converge to a stationary point of the original mixed-integer program. We implement and evaluate the algorithms using a benchmarking water supply network. In addition, the performance of different update strategies for the penalty and relaxation parameters are investigated under multiple initial conditions. Practical recommendations on the numerical implementation are provided.
PubDate: 2017-05-01
DOI: 10.1007/s10589-016-9888-z
Issue No: Vol. 67, No. 1 (2017)
• An alternating direction and projection algorithm for structure-enforced
matrix factorization
• Authors: Lijun Xu; Bo Yu; Yin Zhang
Abstract: Abstract Structure-enforced matrix factorization (SeMF) represents a large class of mathematical models appearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning techniques useful in many applications including neuroscience and signal processing. In this paper, we present a unified algorithm framework, based on the classic alternating direction method of multipliers (ADMM), for solving a wide range of SeMF problems whose constraint sets permit low-complexity projections. We propose a strategy to adaptively adjust the penalty parameters which is the key to achieving good performance for ADMM. We conduct extensive numerical experiments to compare the proposed algorithm with a number of state-of-the-art special-purpose algorithms on test problems including dictionary learning for sparse representation and sparse nonnegative matrix factorization. Results show that our unified SeMF algorithm can solve different types of factorization problems as reliably and as efficiently as special-purpose algorithms. In particular, our SeMF algorithm provides the ability to explicitly enforce various combinatorial sparsity patterns that, to our knowledge, has not been considered in existing approaches.
PubDate: 2017-04-24
DOI: 10.1007/s10589-017-9913-x
• Approximate ADMM algorithms derived from Lagrangian splitting
• Authors: Jonathan Eckstein; Wang Yao
Abstract: Abstract This paper presents two new approximate versions of the alternating direction method of multipliers (ADMM) derived by modifying of the original “Lagrangian splitting” convergence analysis of Fortin and Glowinski. They require neither strong convexity of the objective function nor any restrictions on the coupling matrix. The first method uses an absolutely summable error criterion and resembles methods that may readily be derived from earlier work on the relationship between the ADMM and the proximal point method, but without any need for restrictive assumptions to make it practically implementable. It permits both subproblems to be solved inexactly. The second method uses a relative error criterion and the same kind of auxiliary iterate sequence that has recently been proposed to enable relative-error approximate implementation of non-decomposition augmented Lagrangian algorithms. It also allows both subproblems to be solved inexactly, although ruling out “jamming” behavior requires a somewhat complicated implementation. The convergence analyses of the two methods share extensive underlying elements.
PubDate: 2017-04-17
DOI: 10.1007/s10589-017-9911-z
• Reliable a posteriori error estimation for state-constrained optimal
control
• Authors: A. Rösch; K. G. Siebert; S. Steinig
Abstract: Abstract We derive a reliable a posteriori error estimator for a state-constrained elliptic optimal control problem taking into account both regularisation and discretisation. The estimator is applicable to finite element discretisations of the problem with both discretised and non-discretised control. The performance of our estimator is illustrated by several numerical examples for which we also introduce an adaptation strategy for the regularisation parameter.
PubDate: 2017-04-10
DOI: 10.1007/s10589-017-9908-7
• Forward–backward quasi-Newton methods for nonsmooth optimization
problems
• Authors: Lorenzo Stella; Andreas Themelis; Panagiotis Patrinos
Abstract: Abstract The forward–backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward–backward envelope (FBE). This allows to extend algorithms for smooth unconstrained optimization and apply them to nonsmooth (possibly constrained) problems. Since the FBE can be computed by simply evaluating forward–backward steps, the resulting methods rely on a similar black-box oracle as FBS. We propose an algorithmic scheme that enjoys the same global convergence properties of FBS when the problem is convex, or when the objective function possesses the Kurdyka–Łojasiewicz property at its critical points. Moreover, when using quasi-Newton directions the proposed method achieves superlinear convergence provided that usual second-order sufficiency conditions on the FBE hold at the limit point of the generated sequence. Such conditions translate into milder requirements on the original function involving generalized second-order differentiability. We show that BFGS fits our framework and that the limited-memory variant L-BFGS is well suited for large-scale problems, greatly outperforming FBS or its accelerated version in practice, as well as ADMM and other problem-specific solvers. The analysis of superlinear convergence is based on an extension of the Dennis and Moré theorem for the proposed algorithmic scheme.
PubDate: 2017-04-10
DOI: 10.1007/s10589-017-9912-y
• Asymmetric forward–backward–adjoint splitting for solving monotone
inclusions involving three operators
• Authors: Puya Latafat; Panagiotis Patrinos
Abstract: Abstract In this work we propose a new splitting technique, namely Asymmetric Forward–Backward–Adjoint splitting, for solving monotone inclusions involving three terms, a maximally monotone, a cocoercive and a bounded linear operator. Our scheme can not be recovered from existing operator splitting methods, while classical methods like Douglas–Rachford and Forward–Backward splitting are special cases of the new algorithm. Asymmetric preconditioning is the main feature of Asymmetric Forward–Backward–Adjoint splitting, that allows us to unify, extend and shed light on the connections between many seemingly unrelated primal-dual algorithms for solving structured convex optimization problems proposed in recent years. One important special case leads to a Douglas–Rachford type scheme that includes a third cocoercive operator.
PubDate: 2017-04-08
DOI: 10.1007/s10589-017-9909-6
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## Baltic OI '09 P5 - Triangulation
View as PDF
Points: 20 (partial)
Time limit: 1.0s
Memory limit: 512M
Problem types
##### Baltic Olympiad in Informatics: 2009 Day 2, Problem 2
A triangulation of a polygon is a set of triangles with vertices at the vertices of a polygon. These triangles must not overlap and must cover the whole polygon.
We define a polygon cut as a straight line separating the polygon into two pieces.
Given a triangulated convex polygon, where each triangle has some color, find the maximal number of cuts one can do so that no two points of the same color end up in two different pieces.
#### Input Specification
The first line of input contains the number of vertices, . Vertices are numbered with unique integers between and . Each of the next lines contains four integer numbers , , and , meaning that the triangle which has its vertices in , and has the color . , , and are three different vertices. The input always contains data about a proper triangulation of a polygon and all triangles are colored.
#### Output Specification
Output one line containing one integer - the maximal number of cuts.
#### Sample Input 1
5
1 2 3 2
4 5 1 1
3 1 4 2
#### Sample Output 1
1
#### Sample Input 2
6
1 4 2 1
2 4 5 2
6 2 5 3
3 6 5 1
#### Sample Output 2
0
#### Constraints
For test cases worth 50% of the total score, .
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# Finding the largest set where a complex function is analytic
I am considering the function $$f(z) = \frac{e^z}{\sin z - \cos z}.$$
So I solved for $\sin z - \cos z = 0$ and got $\pi/4$. But why is it $\pi/4 + k\pi$ and not $\pi/4 + k2\pi$ for the part of the complex plane where this function is not analytic?
Thanks.
-
$$\sin z -\cos z=0\Longleftrightarrow \tan z = 1\Longrightarrow z=\frac{\pi}{4}+k\pi\,\,,\,k\in\Bbb Z$$
as the period of the tangent function is $\,\pi\,$ , not $\,2\pi\,$
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# Derivation of confidence and prediction intervals of predictions for probit and logit (and GLMs in general)
The derivation of the prediction interval for the linear model is quite simple: Obtaining a formula for prediction limits in a linear model .
How to derive the confidence and prediction intervals for the fitted values of the logit and probit regressions (and GLMs in general)?
• Are you defining "predictions" for a binary outcome to be the sampling average, like a proportion or percentage? – AdamO Feb 14 '18 at 23:26
• @AdamO I think he/she is defining predictions of logistic regression as the predicted conditional probability. I.e., the prediction is $\hat{p}(x)$, an estimator for $P(Y|X=x)$, not $\hat{Y}(x)$. – DeltaIV Feb 15 '18 at 18:40
• @AdamO good question, I want an interval that makes my predictions cover the future values of $y$ 95% of the time. That could be done with an interval for $\hat{p}$ that translates into an interval of predictions (which would trivially be either just 0, just 1, or 0 and 1 I guess). – statslearner Feb 16 '18 at 4:16
• @statslearner I don't understand. Do you want a finite interval, which covers the future value of $y$, $100\%$ of times? Here it is: $I=[0,1]$. It doesn't even depend on $x$, what more you could ask for? Seriously, I don't think it makes sense to ask for a prediction interval with a Bernoulli output. On the other hand, if you were using logistic regression for a Binomial variable, then a prediction interval would make sense... – DeltaIV Feb 20 '18 at 19:34
• @statslearner hmmm wait, maybe we're talking about the same thing. Are you fixing $x$, sampling $y|x$ $n$ times, and looking for a prediction interval for the number of successes? The point estimate is obviously $n\hat{p}(x)$, and a trivial $100\%$ PI is $[0,n]$, but you would like a better (shorter) interval. If so, look here: stats.stackexchange.com/questions/255570/… – DeltaIV Feb 21 '18 at 9:36
In GLM, prediction is a non-linear function $f$ of the product of covariates $X$ with estimated coefficient vector $\hat{\beta}$: $$\hat{y} = f(X\hat{\beta})$$ Finite-sample distribution of $\hat{\beta}$ is generally unknown, but as long as $\hat{\beta}$ is a maximum likelihood estimate, it has asymptotic normal distribution $\mathcal{N}(\beta, -H^{-1})$, where $H$ is the Hessian matrix of the likelihood function in its maximum. The p-values of $\beta$ that are shown as an output of a regression are nearly always based on this asymptotics. But if you feel your sample is too small for asymptotics, use numerical distribution (e.g. bootstrapping).
When you use asymptotic normal distribution of $\hat{\beta}$ (and therefore $X\hat{\beta}$), distribution of $\hat{y}$ is still non-normal due to non-linear $f$. You can ignore it - get normal confidence bounds $(z_{lower}, z_{upper})$ for $X\beta$, and plug them into $f$, getting bounds for $y$ as $(y_{lower}, y_{upper}) = (f(z_{lower}), f(z_{upper}))$.
Another strategy (called delta method) is to take a Taylor expansion of $f$ around $X\hat{\beta}$ - it will be linear in $\hat{\beta}$. Therefore, you can approximate distribution of $f(X\hat{\beta})$ as $$f(X\hat{\beta}) \sim \mathcal{N}\left(f(X\beta), -(f^{'}(X\beta))^2 X H^{-1} X^T \right)$$
Then the asymptotic 95% confidence interval for $f(X\beta)$ would look like
$$f(X\hat{\beta}) \pm 1.96 \sqrt{(f^{'}(X\hat{\beta}))^2 X H(\hat{\beta})^{-1} X^T}$$
Now you need only to find expression for Hessian matrices for particular models, like logistic regression in this question. And this question presents practical comparison of bootstrap, transformed normal bounds, and delta method for logistic regression.
• But does that give a confidence interval or a prediction interval of $\hat{y}$. It looks like a confidence interval only, doesn't it? It feels there should be an extra noise considered for a prediction interval. – statslearner Feb 16 '18 at 3:19
• That is only a confidence interval indeed. But for binary responce models (like logit and probit), prediction is already probabilistic - real output is 1 or 0 with some probabilty. That is, "prediction interval" is always either $[0, 1]$, or $[0, 0]$ (if predicted probability is very small), or $[1,1]$ (if predicted probability is very large). But this predicted probability may vary, and confidence interval reflects this. – David Dale Feb 16 '18 at 9:29
When all else fails, you can always construct bootstrapped CIs for any statistic. Here's a simple algorithm:
1. Draw $N$ samples with replacement from $X$ (where $N$ is the number of rows in $X$). You'll find that about 2/3rds of your observations will appear in such a sample.
2. Use these samples to fit a model
3. Use this model to generate predictions for the observations in $X$ that weren't used in training.
4. Repeat this process 100 or so times (the more the merrier) to accumulate a collection of predictions for each observation. This collection is an approximation to the distribution of your predictions. Call these your "bootstrapped predictions".
5. Construct confidence intervals by taking quantiles on the predictions. E.g. for a particular observation, calculate the .025 and .975 quantiles for a 95% confidence interval.
• This is interesting, but under what circumstances can you guarantee me this will cover the true y 95% of the time? – statslearner Feb 16 '18 at 4:24
|
# zbMATH — the first resource for mathematics
A classification of generalised state space reduction methods for linear multivariable systems. (English) Zbl 0859.93024
The aim of this paper is to establish two algorithms which reduce a linear multivariable system $$\Sigma$$, described by a polynomial matrix model of the form: $A(\rho)\beta(t)= B(\rho)u(t), \qquad y(t)= C(\rho)\beta(t)+ D(\rho)u(t), \tag{$$\Sigma$$}$ to an equivalent model in generalized state space form. Here $$\rho=d/dt$$, $$A(\rho)\in\mathbb{R} [\rho]^{r\times r}$$ with $$\text{rank}_\mathbb{R} A(\rho)=r$$, $$B(\rho)\in \mathbb{R}[\rho]^{r\times m}$$, $$C(\rho)\in \mathbb{R}[\rho]^{p\times r}$$, $$D(\rho)\in \mathbb{R}[\rho]^{p\times m}$$, $$\beta(t)$$ is the pseudostate of $$\Sigma$$, $$u(t)$$ the input vector and $$y(t)$$ the output vector.
More precisely, the authors solve the problem of determining a system: $E\dot x(t)= Ax(t)+ Bu(t), \qquad y(t)= Cx(t)+ Du(t) \tag{$${\Sigma_R}$$}$ equivalent to $$\Sigma$$. This equivalence means that they exhibit identical system properties. The first algorithm is based on the realization of $${\mathcal T}(s)$$ defined by: ${\mathcal T}(\rho)=\begin{pmatrix} A(\rho) &B(\rho) &0\\ -C(\rho) &D(\rho) &I_p\\ 0 &-I_m &0\end{pmatrix}\in \mathbb{R}[\rho]^{\bar r\times\bar r}, \qquad \bar r=r+p+m,$ while the second algorithm is based on a realization of $${\mathcal T}(s)^{-1}$$. In fact, all the known reduction algorithms can be classified by these two different theoretical reduction algorithms which are mentioned above.
##### MSC:
93C05 Linear systems in control theory 93C35 Multivariable systems, multidimensional control systems 93B11 System structure simplification
Full Text:
##### References:
[1] B. D. O. Anderson W. A. Coppel, D. J. Cullen: Strong system equivalence (I). J. Austral. Math. Soc. Ser. B 27 (1985), 194-222. · Zbl 0594.93015 [2] O. H. Bosgra, A. J. J. Van Der Weiden: Realisations in generalised state-space form for polynomial system matrices, and the defìnition of poles, zeros and decoupling zeros at infinity. Internat. J. Control 33 (1981), 393-411. · Zbl 0464.93021 [3] G. E. Hayton A. B. Walker, A. C. Pugh: Infinite frequency structure preserving transformations for general polynomial system matrices. Internat. J. Control 52 (1990), 1-14. · Zbl 0702.93021 [4] N. P. Karampetakis, A. I. G. Vardulakis: Matrix fractions and full system equivalence. IMA J. Math. Control Inform. 9 (1992), 147-160. · Zbl 0777.93052 [5] N. P. Karampetakis, A. I. G. Vardulakis: Generalized state-space system matrix equivalents of a Rosenbrock system matrix. IMA J. Math. Control Inform. 10 (1993), 323-344. · Zbl 0807.93009 [6] T. Shaohua, J. Vandewalle: A singular system realisation for arbitrary matrix fraction descriptions. ISCAS’88, pp. 615-618. [7] A. I. G. Vardulakis: Linear Multivariable Control, Algebraic Analysis and Synthesis Methods. Nelson-Wiley, London 1991. · Zbl 0751.93002 [8] A. I. G. Vardulakis: On the transformation of a polynomial matrix model of a linear multivariable system to generalised state space form. Proceedings of the 30th IEEE Conference on Decision and Control, Brighton 1991, U.K., pp. 11-13. [9] G. C. Verghese: Infinite Frequency Behavior in Generalized Dynamical Systems. P\?.D. Dissertation, Stanford Univ., Stanford, CA 1978. [10] W. A. Wolovich: Linear Multivariable Systems. Springer-Verlag, New York 1974. · Zbl 0291.93002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
|
## WeBWorK Problems
### custom answer checker with multiple inputs
by Siman Wong -
Number of replies: 8
I would like to write a custom answer checker that takes in multiple inputs. Here is a simple example to show you what I have in mind (this is strictly for illustration; I know that there are simplier ways to complish this specific example):
-------------------------------
Context()->texStrings;
BEGIN_TEXT
Please enter a 2x2 symmetric matrix with your prescribed value for determinant:
value of a_11: \{ ans_rule(25) \}
value of a_12: \{ ans_rule(25) \}
value of a_21: \{ ans_rule(25) \}
value of a_22: \{ ans_rule(25) \}
value of det: \{ ans_rule(25) \}
END_TEXT
Context()->normalStrings;
$showPartialCorrectAnswers = 1; ANS($ans->cmp( checker=>sub {
my ( $correct,$student, $ansHash ) = @_; return ($a_12==$a21) & ( ($a_11*$a_22 -$a_21*a_11) == $det ); } ) ); ---------------------- The problem here is that I don't know how to pick out from the student's input specific values for each of the variable. I checked the wiki and I couldn't find a similar examples. In case that matters, the problem I'd like to code actually has multiple parts so there are additional inputs, but I'm sure that once I work out this example the rest would follow... Your help and comments are most welcome. THANKS! In reply to Siman Wong ### Re: custom answer checker with multiple inputs by Paul Pearson - Hi Siman, Here's an example from Library/FortLewis/DiffEq/2-Higher-order/01-Linear-2nd-order/Lebl-2-1-01.pg that could serve as a template for what you want. Notice that the correct matrix entries are defined as MathObject Formulas (not using Compute) and that the answer checker uses typeMatch. Also, notice that we use$multians1->ans_rule() instead of ans_rule() for the answer blanks that are graded by the MultiAnswer object. The entries in this matrix problem are functions. If the entries in the matrix are real constants, we could have done all of this using MathObjects.
Have a good evening.
Paul Pearson
##############################
# Initialization
DOCUMENT();
"PGstandard.pl",
"MathObjects.pl",
"PGmatrixmacros.pl",
"parserPopUp.pl",
);
TEXT(beginproblem());
#############################
# Setup
Context("Numeric");
$a = random(2,6,1); do {$b = random(2,6,1); } until ($b !=$a);
$a11 = Formula("e^($a x)");
$a12 = Formula("e^($b x)");
$a21 = Formula("$a e^($a x)");$a22 = Formula("$b e^($b x)");
$wronskian =$a11 * $a22 -$a12 * $a21;$pop = PopUp(["Choose","zero","nonzero"],"nonzero");
$multians1 = MultiAnswer($a11, $a12,$a21, $a22)->with( singleResult => 1, allowBlankAnswers => 1, checkTypes => 0, format => "<table border='0' cellspacing='10'> <tr><td> %s </td><td> %s </td></tr> <tr><td> %s </td><td> %s </td></tr> </table>", tex_format => "\left\lbrack\begin{array}{rr} %s & %s \\ %s & %s \end{array}\right\rbrack", checker => sub { my ($correct, $student,$answerHash ) = @_;
my @c = @{$correct}; my @s = @{$student};
my @score = ();
foreach my $j (0..3) {$score[$j] = 0; if ($c[$j]->typeMatch($s[$j]) &&$c[$j] ==$s[$j]) {$score[$j] = 1; } } return [ @score ]; } ); ###################### # Main text Context()->texStrings; BEGIN_TEXT Use the Wronskian to show that the functions $$y_1 = e^{a x}$$ and $$y_2 = e^{b x}$$ are linearly independent.$PAR
$BCENTER \{ mbox( "Wronskian = $$\mathrm{det}$$", display_matrix([ [$multians1->ans_rule(10),$multians1->ans_rule(10)], [$multians1->ans_rule(10),multians1->ans_rule(10)]], align=>'cc'), " = ".SPACE.ans_rule(20)
);
\}
$ECENTER$PAR
These functions are linearly independent because
the Wronskian is \{ $pop->menu() \} for all $$x$$. END_TEXT Context()->normalStrings; ###################### # Answer evaluation$showPartialCorrectAnswers = 1;
WEIGHTED_ANS( $multians1->cmp(), 50 ); WEIGHTED_ANS($wronskian->cmp(), 40 );
WEIGHTED_ANS( $pop->cmp(), 10 ); COMMENT("MathObject version. Uses parserMultiAnswer.pl to format the matrix nicely."); ENDDOCUMENT(); In reply to Paul Pearson ### Re: custom answer checker with multiple inputs by Paul Pearson - Hi Siman, This example is probably much closer to what you want and uses MathObject Matrix objects instead of MultiAnswer objects. Notice that to produce a matrix of answer blanks, we use$A->ans_array() instead of $A->ans_rule(). Also, in the custom answer checker, we can get individual entries of the student's answer using$student->element(i,j).
Best Regards,
Paul Pearson
##############################
# Initialization
DOCUMENT();
"PGstandard.pl",
"MathObjects.pl",
);
TEXT(beginproblem());
#############################
# Setup
Context("Matrix");
$A = Matrix("[[1,2],[2,1]]");$d = Real("-3");
#############################
# Main text
Context()->texStrings;
BEGIN_TEXT
Enter a symmetric $$2 \times 2$$ matrix
that has determinant $$d$$.
$BR$BR
\{ $A->ans_array(5) \} END_TEXT Context()->normalStrings; ############################## # Answer evaluation$showPartialCorrectAnswers = 1;
ANS( $A->cmp( checker => sub { my ($correct, $student,$answerHash ) = @_;
my $A11stu =$student->element(1,1);
my $A12stu =$student->element(1,2);
my $A21stu =$student->element(2,1);
my $A22stu =$student->element(2,2);
if ( ( $student ==$student->transpose() ) &&
( $A11stu *$A22stu - $A12stu *$A21stu == $d ) ) { return 1; } else { return 0; } })); COMMENT("MathObject version."); ENDDOCUMENT(); In reply to Paul Pearson ### Re: custom answer checker with multiple inputs by Siman Wong - Thanks! Your second example is indeed very close to what I have in mind. Two remaining issues: (1) (For the sake of this example) I would like the student to enter the determinant, as opposed to having it being predetermined. If e.g. I use something like Enter your desired value of det: \{ ans_rule(25) \} then how do I separate this value from the matrix input \{$A->ans_array(5) \} ??
(2) In the actual problem I'd like to code, I need to prescribe values for some of the entries of the matrix (and tell the students what these values are). How can I accomplish that within the framework of your second example?
My original, low-tech approach was to manually layout the matrix, displaying values of the prescribed entries and with answer boxes for entries to be entered. My original question was how to pick up the individual entries of the students' inputs. Your example #2 is clearly a MUCH cleaner way to do this; now if I could figure out how to prescribe values in your setup...
Thanks!
### Re: custom answer checker with multiple inputs
by Paul Pearson -
Hi Siman,
You will need a MultiAnswer object to accomplish what you want because you will need to make the answer blanks in the matrix and the answer blank for the determinant all controlled by the same MutiAnswer object. Here's an example. Note that $s[i] are the student answers in the order in which they appear in the html (so$s[0] is entry A11, $s[1] is entry A12,$s[2] is entry A22, and $s[3] is the determinant). Also, notice that all of the answer blanks are created using$multians1->ans_rule(), so that they're all controlled by the same MultiAnswer object.
Best Regards,
Paul Pearson
##############################
# Initialization
DOCUMENT();
"PGstandard.pl",
"MathObjects.pl",
"PGmatrixmacros.pl",
);
TEXT(beginproblem());
#############################
# Setup
Context("Numeric");
do {
$A11 = random(1,9,1);$A12 = random(1,9,1);
$A21 =$A12; $A22 = random(1,9,1);$d = $A11 *$A22 - $A12**2; } until ($d != 0);
$multians1 = MultiAnswer(Real($A11), Real($A21), Real($A22), Real($d))->with( singleResult => 1, format => " <table border='0' cellspacing='0'> <tr><td> <table border='0' cellspacing='10'> <tr><td> %s </td><td>$A12 </td></tr>
<tr><td> %s </td><td> %s </td></tr>
</table>
</td>
<td> %s </td>
</tr>
</table>",
tex_format =>
"\mathrm{det}
\left\lbrack
\begin{array}{rr}
%s & $A12 \\ %s & %s \end{array} \right\rbrack = %s", checker => sub { my ($correct, $student,$answerHash ) = @_;
my @c = @{$correct}; my @s = @{$student};
my @score = ();
if ( ($s[1] ==$A12) &&
($s[0] *$s[2] - $s[1] *$A12 == $s[3]) && ($s[3] != 0)
)
{ return 1; } else { return 0; }
}
);
######################
# Main text
Context()->texStrings;
BEGIN_TEXT
Enter a symmetric $$2 \times 2$$ matrix
with entry $$A_{1,2} = A12$$ having a
nonzero determinant, and find
its determinant.
$PAR$BCENTER
\{
mbox(
"$$\mathrm{det}$$",
display_matrix([
[$multians1->ans_rule(5),"$$A12$$"], [$multians1->ans_rule(5),multians1->ans_rule(5)]], align=>'cc'), " = ".SPACE.$multians1->ans_rule(10) ); \}$ECENTER
END_TEXT
Context()->normalStrings;
######################
$showPartialCorrectAnswers = 1; ANS($multians1->cmp() );
COMMENT("MathObject version. Uses parserMultiAnswer.pl to format the matrix nicely.");
ENDDOCUMENT();
### Re: custom answer checker with multiple inputs
by Siman Wong -
THANK YOU! This thread (more precisely, Paul's answers) absolutely should be moved to FAQ.
### Re: custom answer checker with multiple inputs
by Christopher Heckman -
The difficulty I am having fits in roughly here.
I am attempting to rewrite a paper test as a WeBWorK test. Two of the problems require a weighted grader, and I got one of them working fine. I'm having trouble with the other one, evidently because it also uses a multi-answer checker. I am getting a strange error (Undefined subroutine &main::50 called).
The code is:
DOCUMENT();
"PGstandard.pl", # Standard macros for PG language
"MathObjects.pl",
"PGchoicemacros.pl",
#"source.pl", # allows code to be displayed on certain sites.
#"PGcourse.pl", # Customization file for the course
);
TEXT(beginproblem());
sub random_perm_matrix { # random_perm_matrix ( n )
my $n = shift; my ($i, $j, @P); my @permutation = NchooseK ($n, $n); push @P, [(0) x$n] for 1 .. $n; for ($i = 0; $i <$n; $i++) {$P[$i][$permutation[$i]] = 1; } Matrix (@P); } sub good_P_matrix { # good_P_matrix (m, (m1, m2, ...)) my$m = shift; my @mult = @_;
my $n = 0; my (@P,$Pm, $d,$i, $j,$k, $s);$n += $_ foreach @mult; push @P, [(0) x$n] for 1 .. n;
do {
$s = -1; foreach$i (@mult) {
$d = random_rref ($i, $n,$i, $m, ()); if ($i == 1) {
for ($k = 1;$k <= $n;$k++) { $P[$s + 1][$n -$k] = $d -> element ($k); }
}
else {
for ($j = 1;$j <= $i;$j++) { for ($k = 1;$k <= $n;$k++) {
$P[$s + $j][$n - $k] = ($d -> element ($j,$k)); } }
}
$s +=$i;
}
$Pm = Matrix (@P); } while ($Pm ->det == 0);
Matrix ($Pm -> transpose); } sub random_rref { # random_rref (m, n, r, M, L) my$m = shift; my $n = shift; my$r = shift; my $M = shift; my @L = @_; my (@Lrest,$i, $indextoremove,$ro, $c, @pivotCols, @R); my$Llength = scalar @L;
for ($i = 0;$i < $n;$i++) { $Lrest[$i] = $i + 1; } for ($i = 0; $i <$Llength; $i++) {$pivotCols[$i] =$L[$i]; for ($j = 0; $j <$n - $i;$j++)
{ if ($L[$i] == $Lrest[$j]) { $indextoremove =$j; } }
splice (@Lrest, $indextoremove, 1); } my @restOfPivots = NchooseK ($n - $Llength,$r - $Llength); for ($i = 0; $i <$r - $Llength;$i++)
{ $pivotCols[$i + $Llength] =$Lrest[$restOfPivots[$i]]; }
@pivotCols = num_sort (@pivotCols);
push @R, [(0) x $n] for 1 ..$m;
for ($i = 0;$i < $r;$i ++) { $R[$i][$pivotCols[$i] - 1] = 1; }
for ($i = 0;$i < $r - 1;$i++) {
for ($c =$pivotCols[$i] + 1;$c < $pivotCols[$i + 1]; $c ++) { for ($ro = 0; $ro <=$i; $ro++) {$R[$ro][$c-1] = random (-$M,$M); }
}
}
for ($c =$pivotCols[$r - 1] + 1;$c <= $n;$c++) {
for ($ro = 0;$ro < $r;$ro++) { $R[$ro][$c - 1] = random (-$M, $M); } } Matrix (@R); }$showPartialCorrectAnswers = 1;
Context("Matrix");
Context() -> texStrings;
Context() -> strings -> add (
Yes => {}, YES => {alias => "Yes"}, Y => {alias => "Yes"}, yes => {alias => "Yes"},
No => {}, NO => {alias => "No"}, N => {alias => "No"}, no => {alias => "No"});
Context() -> noreduce ("(-x)-y");
$e1 = non_zero_random (-3, 3); do {$e2 = non_zero_random (-3, 3); } while ($e1 ==$e2);
$D = Matrix ([$e1, 0], [0, $e2]);$P = good_P_matrix (3, (1, 1));
$v1 = Vector ($P -> column (1));
$v2 = Vector ($P -> column (2));
$A = Matrix ($P * $D * Matrix ($P -> inverse));
$cp = Formula ("x^2 - ($e1 + $e2) * x + ($e1 * $e2)") -> reduce;$isDiag = String ("Yes");
$ma = MultiAnswer ($e1, $v1,$e2, $v2) -> with ( singleResult => 0, allowBlankAnswers => 0, checker => sub { my ($correct, $student,$self) = @_;
my ($stuN1,$stuV1, $stuN2,$stuV2) = @{$student}; # don't need$correct
my ($firstOK,$secondOK) = (0, 0);
if (($stuN1 ==$e1) && ($stuN2 ==$e2)) {
$firstOK =$stuV1 -> isParallel ($v1);$secondOK = $stuV2 -> isParallel ($v2);
}
if (($stuN1 ==$e2) && ($stuN2 ==$e1)) {
$firstOK =$stuV1 -> isParallel ($v2);$secondOK = $stuV2 -> isParallel ($v1);
}
if ($stuV1 -> isZero) {$firstOK = 0; }
if ($stuV2 -> isZero) {$secondOK = 0; }
return [$firstOK,$firstOK, $secondOK,$secondOK];
}
);
BEGIN_TEXT
Let $$A = A.$$ Answer the following questions
$BR$BR
(a) Find the characteristic polynomial of $$A.$$ (Enter $$x$$ instead of $$\lambda.$$)
\{ $cp -> ans_rule (20) \}$BR$BR (b) Find the eigenvalues of $$A.$$ For each eigenvalue of $$A$$, find the corresponding eigenvector(s); put angled brackets $$< >$$ around your answer(s).$BR
$$~ ~ ~ ~ ~ ~ ~$$ Eigenvalue: \{ $ma -> ans_rule (5) \} $$~ ~ ~$$ Eigenvector: \{$ma -> ans_rule (20) \}
$BR $$~ ~ ~ ~ ~ ~ ~$$ Eigenvalue: \{$ma -> ans_rule (5) \} $$~ ~ ~$$
Eigenvector: \{ $ma -> ans_rule (20) \}$BR$BR (c) Is $$A$$ diagonalizable, yes or no? \{$isDiag -> ans_rule (10) \}
END_TEXT
Context() -> normalStrings;
WEIGHTED_ANS ($cp -> cmp, 25); WEIGHTED_ANS ($ma -> cmp, 50);
WEIGHTED_ANS ($isDiag -> cmp, 25); COMMENT ('MathObject version.'); ENDDOCUMENT(); The error message is: • Error in Translator.pm::process_answers: Answer AnSwEr0004: |1| • Undefined subroutine &main::50 called at line 208 of (eval 9176) • Error in Translator.pm::process_answers: Answer AnSwEr0004: • Answer evaluators must return a hash or an AnswerHash type, not type || at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1232 • There is no answer evaluator for the question labeled AnSwEr0006 at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1203 • Error in Translator.pm::process_answers: Answer AnSwEr0006: • Unrecognized evaluator type || at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1227 • Error in Translator.pm::process_answers: Answer AnSwEr0006: • Answer evaluators must return a hash or an AnswerHash type, not type || at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1232 • Use of uninitialized value$credit{"AnSwEr0004"} in numeric eq (==) at (eval 9176) line 287.
• Use of uninitialized value $credit{"AnSwEr0006"} in numeric eq (==) at (eval 9176) line 287. • Use of uninitialized value$credit{"AnSwEr0004"} in multiplication (*) at (eval 9176) line 303.
• Use of uninitialized value $credit{"AnSwEr0006"} in multiplication (*) at (eval 9176) line 303. • Use of uninitialized value in numeric ge (>=) at /opt/webwork/webwork2/lib/WeBWorK/ContentGenerator/ProblemUtil/ProblemUtil.pm line 92. • Use of uninitialized value in numeric ge (>=) at /opt/webwork/webwork2/lib/WeBWorK/ContentGenerator/ProblemUtil/ProblemUtil.pm line 92. In reply to Christopher Heckman ### Re: custom answer checker with multiple inputs by Davide Cervone - The issue is not one that you would be able to identify without looking very carefully at the MultiAnswer code. It turns out that when singleResult is 0, $ma->cmp produces an array of answer checkers (one for each answer in the multi-answer), rather than just a single one. But the WEIGHTED_ANS() expects answer checkers interspersed with their weights. That is, the odd arguments are treated as answer checkers and the even ones are the weights. Since here are 4 answers, that means the 50 (intended as a weight) is in the 5th position, and treated as an answer checker, which causes the error you are seeing.
One way to avoid this is to use singleResult => 1 (and use the format and tex_format attributes to format the student answers better). But you may not like that since the coloring for correct/incorrect isn't processed properly for single results.
To work when singleResult => 0, you could intersperse the weights with the answer checkers using map but there is another problem. It turns out that the checkers that the MultiAnswer object produces don't propagate the weight properly, and so even if you do this, you don't get the right result.
I've attached a corrected version of parserMultiAnswer.pl that fixes the problem. If you put this in your course's templates/macros folder, you can then use
map {WEIGHTED_ANS($_,50/4)} ($ma->cmp);
in place of
WEIGHTED_ANS(\$ma->cmp,50);
Here, the 50/4 puts a quarter of the total weight on each part. That means that partial credit will be handled proportionately (so if the first two are correct, you will get 25%.
See if that does what you need.
|
#### Effects of empathy on the evolution of fairness in group-structured populations
##### Yanling Zhang, Jian Liu, Aming Li
The ultimatum game has been a prominent paradigm in studying the evolution of fairness. It predicts that responders should accept any nonzero offer and proposers should offer the smallest possible amount according to orthodox game theory. However, the prediction strongly contradicts with experimental findings where responders usually reject low offers below $20\%$ and proposers usually make higher offers than expected. To explain the evolution of such fair behaviors, we here introduce empathy in group-structured populations by allowing a proportion $\alpha$ of the population to play empathetic strategies. Interestingly, we find that for high mutation probabilities, the mean offer decreases with $\alpha$ and the mean demand increases, implying empathy inhibits the evolution of fairness. For low mutation probabilities, the mean offer and demand approach to the fair ones with increasing $\alpha$, implying empathy promotes the evolution of fairness. Furthermore, under both weak and strong intensities of natural selection, we analytically calculate the mean offer and demand for different levels of $\alpha$. Counterintuitively, we demonstrate that although a higher mutation probability leads to a higher level of fairness under weak selection, an intermediate mutation probability corresponds to the lowest level of fairness under strong selection. Our study provides systematic insights into the evolutionary origin of fairness in group-structured populations with empathetic strategies.
arrow_drop_up
|
## Believing that the Earth is Round When it Matters
A world map. Canada seems much bigger than Israel. Note, however, that in the map countries near the equator looks smaller than they are. Update: The round-earth hypothesis is clearer to the people of New Zealand; see the comments section.
One difficult aspect of the academic life is the requirement to fly to conferences and other academic activities all over the world. Strangely, speaking about this hardship to non- academic friends does not always elicit the sympathy we deserve.
Last month, I had to be on duty in two places outside Jerusalem. The first was a conference in Beijing and the second was a conference and a visit in the the Los Angeles area. My solution was to make a round trip to Beijing and another round trip to LA. (I am simplifying matters since there was some interference due to additional travels, visa matters, etc..)
I discovered the following flaws I make in planning my trips:
1) I am (somewhat) biased toward round trips.
More seriously…
2) I dont take into account that the earth is round.
The book solution to this travel was to go from Jerusalem to Beijing and then from Beijing to Los Angeles and from LA to Jerusalem. I completely ignored this possibility. When I realized it, it made me wonder what this reveals about my true beliefs regarding the round earth hypothesis.
Believing that this coffee cup is a realistic model of the world suffices to prefer the Beijing-LA solution over two round-trips solution!
Remark: As a matter of fact in order to think of the possibility to fly from Beijing to LA one does not have to be as advanced as to believe in the “round earth hypothesis”. It is enough to believe that the world is either round or a cylinder so that the right and left boundaries of the world map are glued together.
This entry was posted in Mathematics to the rescue and tagged , , , . Bookmark the permalink.
### 16 Responses to Believing that the Earth is Round When it Matters
1. Kea says:
Hmmm. Where I am from (NZ) a round-the-world ticket is standard. And it is also clear that the world is round: if you go from Sydney to Copenhagen via Japan, there is a flight from Tokyo to Copenhagen over the north pole via Anchorage. It is difficult to understand why other people make this all so complicated, but I have actually met many northerners who don’t even know that our seasons are out of phase with yours. This is truly a Dark Age.
• Gil Kalai says:
Dear Kea, it is certainly easier to believe in and take comfort from the round-earth hypothesis if you are so close to the boundary of the earth like in NZ.
• Pravesh says:
Very interesting! I couldnt understand at first why Sydney to Copenhagen via Japan and Anchorage will be a shorter trip.!
2. Kea says:
LOL, yeah. I wouldn’t want to fall off the edge. But then, my friends in Antarctica update their Facebook pages regularly, so it can’t be all that bad.
3. shmuel says:
It would be nice to have an app that would produce a steroeographic projection of the Earth with any given point as origin (and oriented at any angle). I am still stuck on the North is Up issue.
• Gil Kalai says:
Thats a good idea. Maybe such an application already exist somewhere on the web? We can prepare a map like the one in the post by prescribing two places one (Chicago, say) to center of the map and one (Jerusalem, say) for the up direction.
4. Gabriel says:
This Dilbert cartoon has more on the topic of flat-earth theories ;-)
http://dilbert.com/2011-02-07/
(…and also ordinal numbers?)
5. Gaurav says:
Ohh.. This is why Greenland $Area=2175000 {km}^2$ look 2 or more times bigger than India $Area=3287263 {km}^2$.
6. Niz says:
What about Archimedes hat-box theorem? Is it not actually saying that the surface measure on a shpere equals the measure on a cylinder, and a map is it not a flattened cylinder? Then countries near poles should look proportionally to the scale as big as they are (only distorted in shape) if presumably the map gives the correct projection.
• was says:
Niz, one could produce maps that preserve the area (using a suitable projection). But, the projections most frequently used for maps do not. (As the area-preserving maps, do not preserve other things one cares about, and it is impossible to preserve ‘everything.’)
7. Alfredo Hubard says:
this is a classic: “Canada seems much bigger than Israel.”
8. soak says:
Sarah Palin already knew that.. russia is her neighbor – the world is round – and she knows bearing strait – u ignored the possibility of meeting her in JC Land
?
canada is not bigger than isarel canada ais in detroit or i guess suburb of detroit
cheers
soak
9. sesli sohbet says:
I agree round the world. but people do it? I think every human being in this world do not have the same rights
10. LOL, yeah. I wouldn’t want to fall off the edge. But then, my friends in Antarctica update their Facebook pages regularly, so it can’t be all that bad.
11. Kelley says:
Today, I went to the beach front with my children. I found a sea shell and
gave it to my 4 year old daughter and said “You can hear the ocean if you put this to your ear.” She placed the shell to her ear
and screamed. There was a hermit crab inside and it
pinched her ear. She never wants to go back! LoL I know this is entirely off
topic but I had to tell someone!
|
# Need Help Solving a problem for work
• November 2nd 2012, 08:09 AM
macleodjb
Need Help Solving a problem for work
Hi All,
I've been tasked at work for create an excel based product library for my company which will product parts. I'm working on a product that needs to be parametric. Please see the attached image
Attachment 25525
If the lengths of the angled lines were a fixed length i would know how to calculate all of this. But since they lengths are relative to the front radius I'm kinda at a loss on how to generate the x and y points for each line. Any help would be appreciated. I'm sure this is a snap for most of you but I suck at math especially trig.
Joe
• November 2nd 2012, 11:09 PM
chiro
Re: Need Help Solving a problem for work
Hey macleodjb.
How much calculus do you know?
The reason is that you will know the tangent for the start and ends of the circle since you know the angles and you you have a formula regarding what the derivatives are for a given circle with an equation x^2 + y^2 = r^2 and the dy/dx will correspond to the gradient as a function of the angle.
So you have two gradients so you will essentially get a relation to where the (x,y) points are for the circle part (you get two solutions and discard one for each tangent) and this will give you the relative points for that circle which gives the (x,y) points at the two positions.
• November 3rd 2012, 05:02 AM
macleodjb
Re: Need Help Solving a problem for work
Sorry I don't know any calculus. I googled derivatives but the math jargon is just way over my head. Would you mind breaking it down in laymens terms for me. Like Step 1 Angle1/Radius+Whatever.
• November 3rd 2012, 09:23 AM
Soroban
Re: Need Help Solving a problem for work
Hello, Joe!
This takes a lot of work.
I have a start on it.
Maybe you or someone else can finish it.
(I assume the lower-left corner is a right angle.)
Code:
| | o P | * * | * * | * * | * * B| * β * (0,b)o - - - - - * | * b | * | * α - - * - - - - - - o - - - - - - - O a (a,0) A
The line $AP$ has slope $\tan\alpha.$
Its equation is: . $y \:=\:\tan\alpha(x-a) \quad\Rightarrow\quad y \:=\:x\tan\alpha - a\tan\alpha$ .[1]
The line $BP$ has slope $\tan\beta.$
Its equation is: . $y \:=\:x\tan\beta + b$ .[2]
Equate [1] and [2]:
. . $\begin{array}{c}x\tan\alpha - a\tan\alpha \:=\:x\tan\beta + b \\ x\tan\alpha - x\tan\beta \:=\: a\tan\alpha + b \\ x(\tan\alpha - \tan\beta) \:=\:a\tan\alpha + b \\ x \:=\:\dfrac{a\tan\alpha + b}{\tan\alpha - \tan\beta} \end{array}$
Substitute into [2]:
. . $y \:=\:\left(\frac{a\tan\alpha + b}{\tan\alpha - \tan\beta}\right)\tan\beta + b \quad\Rightarrow\quad y \:=\:\frac{\tan\alpha(a\tan\beta + b)}{\tan\alpha - \tan\beta}$
We know the coordinates of point $P\left(\frac{a\tan\alpha + b}{\tan\alpha - \tan\beta},\;\frac{\tan\alpha(a\tan\beta + b)}{\tan\alpha - \tan\beta}\right)$
We are given $r$, the radius of the circle.
Find the equation of the line parallel to $AP$ (to the left of $AP$)
. . and at a distance $r$ from $AP.$
Find the equation of the line parallel to $BP$ (and below $BP$)
. . and at a distance $r$ from $BP.$
The intersection of these lines is the center of the circle.
|
## polygons – Question about error executing RegionResize of map
I want to resize the map of the country as below.
``````region = EntityValue[Entity["Country", "SouthKorea"], "Polygon"] /. g_GeoPosition :> g["LongitudeLatitude"]
newregion = RegionResize[region, 10]
``````
Also, all previously executed information will be erased.
``````mf = RegionMember[newregion]; mf[{125, 35}]
``````
I want to discriminate the inside and outside of the data with a resized map.
Could the error be caused by the map being disconnected? How can I solve this?
## geometry – What is the sum of angles of polygons on a sphere (and other Riemann surface)
The sum of the angles of a triangle on a sphere is $$pi (1+4f)$$, where $$f$$ is the fraction of the area enclosed by the triangle. Then is it true that the sum of the angles of an $$n$$-polygon is $$pi(n-2+4f)$$? By induction, we can divide an $$n$$-polygon into a $$n-1$$-polygon and a triangle so the area is $$pi (n-3+4f_{n-1}) + pi (1+4f_1) = pi (n-2 +4f_{n-1}+4f_1) = pi(n-2+4f)$$. The only issue is that we have to prove there exists such a geodesic contained in the polygons that divides it as desired. I think this holds in sphere but I’m not sure about other surfaces.
Also I’m curious about the results in other Riemann surface. For sphere we only need to consider the fraction of area because the curvature is constant. What if it’s not and how can we express the sum of the angles of triangle in terms of the curvature at the edges?
## Different colors (shadows) when using Graphics3D to plot polygons
I am trying to plot a list of polygons. I would like the color to be uniform, i.e yellow is strictly yellow. However, when I rotate it, the sides of the structure seem to have a shadow or just a different color i.e orange-ish instead of yellow. Here is the picture:
I think I can add something to the code to avoid this, but I am not sure what. I tried playing with the lighting and the MeshShading with no good results. Any help would be immensely appreciated.
## Bounding box of polygons intersection via boost geometry
I am trying to calculate the bounding box of the polygon which is result of intersection of 2 polygons. In my case, poly1 lies completely inside poly2 and I am aiming to get bounding box which just encapsulates poly1.
I am hoping to get code which works for the case when poly1 and poly2 overlap partially and not just completely within each other
`````` boost::geometry::Polygon poly1;
// Additional code to populate poly1
//
boost::geometry::Polygon poly2;
// Additional code to populate poly2
//
boost::geometry::correct(poly1);
boost::geometry::correct(poly2);
std::deque<boost::geometry::Polygon> output;
// Check poly1 inside poly2
// This check is TRUE with the data I have
bool completely_inside = boost::geometry::within(poly1.outer(), poly2.outer());
if (completely_inside)
{
output.push_back(poly1);
boost::geometry::model::box<boost::geometry::Point> box;
boost::geometry::envelope(output(0).outer(), box);
}
``````
Issue is that bounding box above is much bigger than the bounding box of the intersection of the 2 polygons. I am not sure what is wrong in above code as i am following right process.
## Is a point inside a graphics group composed of multiple Polygons and FilledCurves, not all overlapping?
I have many thousands of points, and I want to check if they are inside a GraphicsGroup that is composed of many Polygons and FilledCurves, similar to GeoWithin but without having to make tedious cloud inquiries.
I get RegionMember Errors and besides I suspect RegionMember is too smart to do a simple 2D numerical True/False test efficiently.
I’ve done this once many years ago by counting if a line from the point to infinity crossed all of the polygon segments an even or odd number of times, but would expect Mathematica to have an function already.
## discrete geometry – Convex Polyhedrons that can be Folded from Convex Polygons
This question is based on http://www.science.smith.edu/~jorourke/Papers/FoldingPP.pdf.
Therein is stated the theorem: Every convex polygon folds to an infinite number (a continuum) of noncongruent convex polyhedra.
Question: What could one say in the reverse direction: given any convex polyhedron, what could one say about the polygon(s) that could fold into it? If there are convex polyhedrons that cannot be folded from convex polygons, then, how does one characterize convex polyhedrons (such as for example, the regular tetrahedron) that can be folded out of convex polygons?
## discrete geometry – Folding Polygons into ‘Vessels’
This question is based on http://www.science.smith.edu/~jorourke/Papers/FoldingPP.pdf
Define an vessel as a convex polyhedron with one face removed – in other words, a vessel can be converted into a convex polyhedron by attaching to it exactly one convex polygonal face (the ‘lid’). The capacity of a vessel is the volume of this convex polyhedron
Note: in a gravitational field, the vessel will have to be suitably oriented/mounted for it to be filled to its capacity; insisting on the stability of the filled vessel will give a variant to this question.
Question: Given a polygonal region, how does one fold/wrap it into a vessel of maximum capacity?
Remarks: For example, starting with a unit square, we can form (not sure of optimality) a ‘tub’ with dimensions (2/3 X 2/3 X 1/6 which is not uniformly thick but has more capacity than the volume of the (closed) largest polyhedron (of uniform thickness) that can be folded from the unit square (‘Geometric Folding Algorithms’ by Demaine and O’Rourke, page 418-19).
It seems that starting with a convex polygonal sheet, to achieve maximum capacity, one necessarily will have to allow for some overlap/ folding over of the material (thus leading to a vessel of non-uniform thickness) – a Greek cross can be folded into a cubical vessel without any overlap but it is not convex.
## algorithms – How to find simple polygons in a complex polygon created by two lines
Given the image attached, I am looking for a way/strategy/pseudocode to iteratively find each polygon created either by two blue-dotted lines, a blue-dotted line and an intersection, or two intersections.
I have an ordered list of line segments for each line, an ordered list of blue-dotted lines (also stored as line segments), and an ordered list of intersections. Segments are stored as a list of two (x,y) tuples, intersections are stored as one (x,y) tuple. By ordered in this case I mean the shape has been processed from left to right, so everything is stored as if you were to follow the paths in an S shape from the bottom left to the top right.
At the moment I am processing each section of the polygon based on what is contained within two projections, although I don’t think this is a good way of going about it. I feel as though any attempt at an algorithm so far has overfit to this specific example. I’m fairly new to computational geometry so any help is appreciated.
## graphics – On the geometric transformations of polygons
Each starry set has the following property:
``````pts0 = {{1, 0}, {2, 2.5}, {3, 0}, {2.5, 3.5}, {4, 5}, {2.5, 4.5},
{2, 7}, {1.5, 4.5}, {0, 5}, {1.5, 3.5}, {1, 0}};
centroid = Mean(Drop(pts0, -1));
pts = Table(k pts0 + ConstantArray((1 - k) centroid, Length(pts0)), {k, 0, 1, 0.2});
plots = Table(Graphics({Red, Point(pts((k))), Blue, Line(pts((k)))}), {k, Length(pts)});
Show(plots)
``````
while if a set isn’t starry, this geometric transformation doesn’t work:
``````pts0 = {{1, 0}, {2, 0}, {2, 3}, {3, 3}, {3, 4}, {0, 4}, {0, 3}, {1, 3}, {1, 0}};
centroid = Mean(Drop(pts0, -1));
pts = Table(k pts0 + ConstantArray((1 - k) centroid, Length(pts0)), {k, 0, 1, 0.2});
plots = Table(Graphics({Red, Point(pts((k))), Blue, Line(pts((k)))}), {k, Length(pts)});
Show(plots)
``````
In the latter case, to get what you want, you can proceed manually:
``````pts0 = {{1, 0}, {2, 0}, {2, 3}, {3, 3}, {3, 4}, {0, 4}, {0, 3}, {1, 3}, {1, 0}};
offset = {{1, 1}, {-1, 1}, {-1, 1}, {-1, 1}, {-1, -1}, {1, -1}, {1, 1}, {1, 1}, {1, 1}};
pts = Table(pts0 + k offset, {k, 0, 0.5, 0.1});
plots = Table(Graphics({Red, Point(pts((k))), Blue, Line(pts((k)))}), {k, Length(pts)});
Show(plots)
``````
but I honestly can’t see a way to generalize it.
So, I’m here to ask if there’s a way to get the first and last graphic result via a single code, thanks!
## 2d – What does Polygon2D’s polygons property do?
If we venture down to the Godot source code, on `Polygon_2d.cpp` we find how `polygons` is used (here).
Godot expects the array to contain arrays of integers. Reading the code we can also figure out that they are indexes (0 based) for the points.
So, let us try that. We create a `Polygon2D` on the editor, give it a set of points, and then in the `polygons` property we add `PoolIntArray` elements (Using a regular `Array` and adding `int` values also works). On each we add the indexes for the points.
Here I placed points in a grid, and created a couple polygons using the `polygons` property:
I placed the odd rows are left to right, and even rows are right to left, just because it was easy.
As we can see the single `Polygon2D` node is capable of representing multiple polygons created from the same set of points. The `polygons` property of `Polygon2D` specifies the lists of indexes that make up those polygons. That’s what the `Polygon2D`‘s `polygons` property does.
When we set something to it, the `Polygon2D` disappears because it will not longer create a single polygon loopings the points in the `polygon` property. Instead the `polygons` property specifies the indexes for the points to create multiple polygons. And, of course, setting anything invalid results in nothing visible.
It is worth noting that the property is just specified as “Array”. The type system does not tell an array of what (it is `Variant`, actually). And the editor will let you add elements to the `Array` that are not valid for this property. Which fails silently (there is no warning or error message).
However, if I add valid arrays of integers, and in them I set negative number, I get an error.
Also worth noting is that they are actually drawn as separate polygons. Here I have made some overlapping polygons and gave them some alpha transparency:
I used alpha on the `Polygon2D` color for that screenshot. However, using alpha on modulate has the same result.
As you can see the overlapping area appears more opaque.
|
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Use of PSpice with OrCAD Capture PSpice with OrCAD Capture (release 9. = Some electronic components such diodes and transistors do not obey Ohm’s law and have a non-linear current-voltage relationship. LTspice Tutorials. For instance, suppose we wanted to make the voltage source above model: v2 = 3 v1, where v1 is the independent variable (across resistor R2 in figure above). Check your result using PSpice or MultiSim. The following sources are available in SPICE simulation. INPUT_VARIABLE voltage or current source. Show The Voltage And Current Values. Capacitors: Configuration #2: an admittance sC in series with an independent voltage source V 0 /s 𝑖𝑅 𝑉 𝑅. A reference voltage source V ref to normalize the input. PARAM (parameter) 63. RSC Contact resistance on the source. Change the schematic diagram of the project to look like this: V V1 FREQ = 10. Symbol Library - pspice Description: Legacy pspice symbol library Description: Voltage source symbol for simulation only Keys: simulation: Last updated on 30. Consider the pulse voltage source in the above image, with the following characteristics: Pin1 (positive) is connected to net CP. Note Down The Value Of Voltage Across R6. The paper presents and discusses an algorithm for average modeling of the PWM modulator in switch-mode power systems by general purpose electronic circuit simulators such as PSPICE. Cgdmax and Cgdmin are. As you know for all type of software’s there exist a type of input format and a type of output format to a file used for this software. OrCAD PSpice® Quick Reference PSpice shortcut keys PSpice toolbars PSpice Model Editor shortcut keys and toolbar PSpice Stimulus Editor shortcut keys and toolbar Technical support (503) 671-9400 Corporate offices (503) 671-9500 OrCAD Japan K. That is, a current flowing from the positive terminal of a battery (or other power source) will be shown as a negative value in the Spice output. Note that in PSpice, there are two ways to represent a source with a negative sign. Notes for ORCAD PSpice. Historically this was a separate application but it is now integrated with PSpice. 2) source voltage is a pulse signal with a period of 0s, width of 5ms, rise and fall times of 1µs, amplitude of 20V and an initial value of 0V and all initial conditions set equal to zero. The behavior of an enhancement n-channel metal-oxide field-effect transistor (nMOSFET) is largely controlled by the voltage at the gate (usually a positive voltage). Circuit Solver strives to verify Ohm's law, Kirchhoff's current and voltage laws by creating models that are both stable and efficient. Performing Initialization and Analysis DC Initialization and Point Analysis 6-4 Star-Hspice Manual, Release 1998. The LM134/LM234/LM334 are true floating. Select Voltage to measure the voltage across the terminals of the AC Voltage Source block. The circuit of a ramp generator using timer 555 is shown in figure. Some versions of PSpice allow you to ask for a current through a resistor without using a voltage source (EX: I(R1) gives the current in the resistor R1). LM334 is a 3 terminal current source component. We will generate the voltage VCC with a current-controlled voltage source (H part), for which the control current comes from a fixed 12 V source in series with a 1-ohm nominal Rbreak part. Jeffrey Tomich, E&E News reporter. ppt), PDF File (. voltage source peak-to-peak voltage? What is its frequency? What is its internal source resistance? (or is it "ideal")? What are the attributes of the diode? (or is it "ideal"? Here it is with a 3vpp 50Hz ideal source with an ideal Silicon diode. When we change voltage source, the current that flow through the LED will also changes, causes LED not stable brightness. The inductances. EDIT: Don`t forget to use an appropriate voltage source Vsin (NOT Vac). In this context, we are speaking about an electrical equivalent. In Lecture 1 we introduced the idea of a current source, and mentioned that these were slightly more difficult to implement than the perhaps more familiar voltage source. A circuit that could provide an output voltage of 3v can be designed by using resistors and Ohm’s law to figure out what resistance is needed to create an output of 3V from 10V source. After the + sign, the statement can continue in any column. How can I step it's voltage parameter. See the description of V(BR)DSS in Static Electrical. Newbie needs help seting up ramp function as voltage source Posted Oct 16, 2012, 11:11 AM EDT AC/DC & Electromagnetics Version 4. Mesh analysis depends on the available voltage source whereas nodal analysis depends on the current source. Change the start and end frequency in the property window according the portion of the graph you want to see. Then, current from the 5V power supply through VR1 and R2. For example, if you have three AC sources in the circuit and are running a simulation from 10 Hz to 100 MHz, then all three sources are set at 10Hz at the same time and 100MHz. Pulse period is 30ns with 50% duty cycle. The Working Voltage is rated at one third (1/3) of the DWV test voltage. You should now see values on your circuit representing current and/or voltage. This limitation is overcome with a voltage controlled current source ABM expression (Figure 4). From the simulation, you will see that for the first couple of cycles, v L and v C. The project is an 8-bit digital-to-analog converter that utilizes a resister ladder network to divide current with equal current sources, and an operational amplifier to sum these currents and convert them into an output voltage. Build the circuit As described in the “pspice_DC” tutorial, launch the PSPICE program and start a new, blank “Analog or Mixed A/D” project. ramp voltage Negative Voltage Regulator w/ LM317 PUBLIC. Current is established with one external resistor and no other parts are required. MOSFET Self-Turn-On Phenomenon. 0V to 36V input voltage range, and provi des up to 4A of continuous output current. Create a new schematic and enter your Thevenin equivalent. PSPICE VERSION: PSPICE : This popular version of SPICE, available from Orcad (now Cadence) runs under the PC platforms. Simulate it with PSpice using specific models for your devices. Tech in Computer Science and Engineering has twenty-six+ years of academic teaching experience in different universities, colleges and thirteen+ years of corporate training experiences for 170+ companies and trained 50,000+ professionals. PSpice Square/Tiangulare wave form - Duration: 5:42. Click on to close the window. Notice I didn't use extreme values like 1ps for the timings, or so, but simply a more relaxed 0. V1 1 0 AC=10V,90 VIN 1 0 AC 10V 90 The above two examples specify an AC voltage source with a magnitude of 10 V and a phase of 90 degrees. standard 60 Hz electrical supply. Product Code: RA1768. The ground can be obtained by clicking on the right side bar menu, and then select "0/SOURCE" in the "Place Ground" window as shown in Figure 13 below. An independent current source delivers a constant current. 7 board to the RPi. For instance, suppose we wanted to make the voltage source above model: v2 = 3 v1, where v1 is the independent variable (across resistor R2 in figure above). For voltage sources, current is measured from the positive terminal to the negative terminal; this is opposite to the positive current flow convention and. We can gain a lot of additional insight by simulating our buffer via PSpice, as depicted in Figure 4. · Simulate the circuit using Pspice. A Thévenin or Norton equivalent circuit is valuable for analyzing the source and load parts of a circuit. be connected to a voltage source which represents the ambient temperature. The op-amp chip: Study the chip layout of the 741 op-amp shown in Figure A-4. ramp voltage Negative Voltage Regulator w/ LM317 PUBLIC. ppt), PDF File (. VOUT2 LOUT LOUT RT REF FB COMP 0 0 0 0 0 0 0 0 R9 {6m/3} DMBR2045CTP/ON D1 R16 5. In this part, we will investigate the usefulness of a voltage follower using PSpice. Apply a current source and use DC sweep to obtain the V-I graph for the Thevenin circuit and compare with the original. Use this voltage source component for your input signals. A common circuit-topology is a voltage-source inverter which is shown in Fig. This is the minor concession that must be made to accommodate. The same controller causes the LED current to gradually ramp down to zero if the EN pin is pulsed while the output channel is ON. PSpice => Bias Points, and check Enable, Enable Bias Current Display, and/or Enable Bias Voltage Display. No power-up sequencing is required for normal operation. Heatbed MK2B is currently the best construction of its kind in the market. as with standard b-sources (note: power is sourced when f is negative). An ideal op-amp integrator uses a capacitor C1, connected between the output and the op-amp inverting input terminal, as shown in the figure below. The LM317 / LM338 / LM350 family of adjustable 3-terminal positive voltage regulators can take a input of 3 to 40 Volts DC and provide a regulated voltage over a 1. Note that a phase shift of 90 degree is what we expect between the current and voltage signals across a capacitor. The maximum temperature which can be reached is 120°C and the device heats up from 0°C to 100°C in 5 minutes at a low voltage of 12V. For voltage sources, just put in the basic DC value if you are doing DC analysis. In this session of Logic Noise, we’ll be playing around with the voltage-controlled oscillator from a 4046 phase-locked loop chip, and using it to make “musical” pitches. The ramp will vary from -10 volts to +10 volts over 20 seconds. Clamp Meters. Figure 3 shows the equivalent circuit diagram on a Level 3 model of an Infineon MOSFET. Please note. PSpice is a free open source software, download it here. The type of simulation performed by PSpice depends on the source specifications and control statements. Consider the sinusoidal voltage source in the above image, with the following characteristics: Pin1 (positive) is connected to net INPUT. 02)\$I know to use the VPULSE source but it has only two voltages as parameters but I need 3. A voltage amplifier with supply limits can be built with the voltage controlled voltage source. Select Analysis/Setup to setup analysis. For transient analysis, click advanced, go to the left side, click Sine (usually) and enter the amplitude (peak value) and frequency. Voltage controlled current source: Gname N1 N2 NC1 NC2 Value. Another approach would be to use a VCO and a comparator. Figure 1: Power System with AC source and electrical load. LTspice Guide. The inductances. The LM317 voltage regulators can provide up to 1. When the supply is put under load and switches into current limit mode the output drops in around 2mS. CMOS offers low power dissipation, relatively high speed, high noise margins in both states, and will operate over a wide range of source and input voltages (provided the source voltage is fixed). Select Analysis/Setup to setup analysis. The fade ramp can be interrupted mid-cycle before completion of the ramp cycle. PSpice modifies the standard calls for dependent voltage controlled sources (E and G elements). The method that I used was based on the equation for the output voltage: Vout= integral[ (1/(RC)) * Vin dt] I wanted a 5kHz triangle wave, so I drew it out and determined the slope I would need. [email protected] Begin by starting the program Capture from ORCAD. An evaluation (student) version, which can handle small circuits with up to 10 transistors, is freely available. In fact, it explains the features of different model versions both in terms of static and dynamic characteristics. After working the math out, it turned out that the slope was equal to 1. Use PSpice and AC Analysis for a single point 60 Hz to obtain the node voltages V1 and V2, and current in R3. Apply a current source and use DC sweep to obtain the V-I graph for the Thevenin circuit and compare with the original. In order to avoid large currents at voltages near zero, the arbitrary power sink/sources foldbacks to resistive behavior when the. Dependent Sources Voltage controlled voltage source: Ename N1 N2 NC1 NC2 Value. Example Spectre Command Line: v1 (p 0 c1 0) pvcvs coeffs=[0 0 0 0. Here the pSpice simulator has been used to predict the performance of the circuit as the supply voltage is varied over a range. In this circuit, the humble resistor R acts as a voltage-to-current converter; the whole combination of the constant voltage source and the voltage-to-current converter acts as a constant current source:. = Some electronic components such diodes and transistors do not obey Ohm’s law and have a non-linear current-voltage relationship. Configure a new simulation profile with name AC. Please try again later. In this context, we are speaking about an electrical equivalent. TEMP VAL1 VAL2 VAL3. While NSF’s move was a major challenge, it also became a source of opportunity. The symbol for a polynomial or nonlinear source is POLY (n), where n is the number of dimensions of the polynomial. The voltage source connected to the input of the operational amplifier is a new type which you will use extensively in later assignments. VOLTAGE and POWER Ratings final 101207. I found that many examples for Pspice cannot be used properly. The turns-ratio may be set in the behavioral functions, but I chose to. After the + sign, the statement can continue in any column. 1W Power Dissipation TA=+25°C (D Package). Linear current ramp generator are extensively used in television deflection systems. A simple PSPICE model that can generate open-loop-gain Bode plots and predict load transient response for MAX8546 designs is presented. This allows you to make a plot of a voltage or current in the circuit as a function of the DC source voltage. 15mm2 layer, 35um copperRed Soldermask - both sidesWhite Silkscreen. Each dependent source also has two input terminals, thought these are not always explicitly shown. Specifications:High rate PWMLow resistanceSixteen cells Max (with BEC disabled)User programmable brakeLow voltage auto setting based on batteryThrottle range self-adjustingSoft start ramp upAuto motor cutoff with resetRuns motor in forward or. standard 60 Hz electrical supply. The voltage source VSIN is a transient signal that is a sinusoid rather than a square wave pulse. The step-down transformer that I have is a 120V primary 24V secondary transformer. Don't start Frequency sweeps at 0! Set the points/Decade to be at least 20. New Models. - Ramp-up Rate 5°C/second max Reflow - Temperature (T L) (Liquidus) 217°C. A comparator to perform the function s(x i − x) by comparing the DAC's voltage with the input voltage. marker, you need to create the netlist first (PSpice Create Netlist). The Thevenin equivalent circuit. (c)Print out the output file for your submission. Since microcontrollers. Coupled to an Arduino Mega, it represents a basic and flexible control package that is highly suitable for most 3D printing needs. The voltage on the capacitor is time averaged, and the square-root is taken (the resistor is a dummy load that satisfies the SPICE algorithms). Khandker Akif Aabrar 1,658 views. (ii) When you use PSpice to simulate your circuit, make sure to use fourth or fifth cycle of your voltage waveforms to measure peak voltage and phase angle, i. com 12 The PWM Switch Concept 1 4 2 Q1 5 Rb_upper 1Meg Rb_lower 100k Vg Vout 8 3 7 h11 Beta. Last modified Friday, 26th June, 2015 @ 06:24pmUnknown MySQL server host 'webdb. In the beginning, by increasing the voltage the current change very slowly but when the voltage reaches 0. steady-state DC sources). A linear ramp would at least make it easier to adjust the subcircuit to get the correct value of rise/fall times. Back to E&E News index page. How can I step it's voltage parameter. Abstract: The MAX8546 is a low-cost, wide-input-voltage range, step-down controller with foldback current limit. UCC3895 Bicmos Advanced Phase Shift PWM Controller. Quick Links. Since microcontrollers. Thévenin’s and Norton’s theorem allow you to replace a complicated array of independent sources and resistors, turning the source circuit into a single independent source connected with a single resistor. Another way to get a modulated waveform is to use a behavioral voltage source with a function such as "V=sin(2*pi*50*time)*sin(2*pi*1k*time)" My circuit designs should be regarded as experimental. Ib Rc 10k Re 150 Ce 1nF Req Rb_upper//Rb_lower b c e ib ic ie Rc Vin 10k Re. Change the schematic diagram of the project to look like this: V V1 FREQ = 10. Specify the magnitude and phase of the impulse with the AC keyword. TF I(V1) VS Finds the small-signal transconductance using the current through the source V1 as the output variable and VS as the input variable. The half-bridge driver chip is able to supply this high voltage by using a bootstrapping circuit. Perform a DC sweep analysis using a DC source (VDC). PSPICE Schematic Student 9. The dimensions depend on the number of controlling sources. The AOZ1284 integrates an N-channel high-side power MOSFET. In our example this means that when the high mosfet is turned on the voltage at the source pin (the high side of the motor) is 24V so the voltage at the gate must be about 34V. However, when broken down into the basic definitions of harmonics and distortion, it becomes much easier to understand. 02% + 600 µV 50 µV. During the time that the supplies ramp up some circuits may latch up or have unpredictable. In this part, we will investigate the usefulness of a voltage follower using PSpice. The MAX8546 is a low-cost, wide-input-voltage range, step-down controller with foldback current limit. Place a V DC source from the source library and set its value to 10V. steady-state DC sources). Design Problems 112. amp can be modeled by placing limits on the output voltage of the voltage-controlled voltage source E b. Because of the presence of virtual ground. The voltage source V1 is used as a current reference for the behavioral current source B1. · Proficiency in electrical system simulation software such as Pspice, Multisim and ETAP · Capable of independently verifying electrical designs through calculations and simulations · Design experience with cable sizing, creepage and clearance and protection device sizing and selection. 0V using external resistors (R. A times VN. The symbol of the op-amp with the associated terminals and ports is shown on Figure 1(a) and (b). output is multiplied by a gain equal to the input DC voltage (12V), and the resulting AC voltage drives the output L-C filter and load. The same ohms' law as discussed in the previous tutorial applies on the AC. He developed and taught courses at Motorola University and has written many articles on power circuit modeling for PCIM, PEIN, and Intusoft Online. 3) Sweep Variable: Voltage Source. 6), Switching period, ⁄ =100μs Switch ON. Inverters are used for many applications, as in situations where low voltage DC sources such as batteries, solar panels or fuel cells must be converted so that devices can run off of AC power. Rectangular pulses of voltage into an inductor result in a triangular current waveform. This uses a constant amplitude AC source whose frequency can be varied over some range. Another approach would be to use a VCO and a comparator. voltage source peak-to-peak voltage? What is its frequency? What is its internal source resistance? (or is it "ideal")? What are the attributes of the diode? (or is it "ideal"? Here it is with a 3vpp 50Hz ideal source with an ideal Silicon diode. They act as a sawtooth wave generator circuit, by C1 to charge and discharge. Consider the pulse voltage source in the above image, with the following characteristics: Pin1 (positive) is connected to net CP. Spice model tutorial for Power MOSFETs Introduction This document describes ST’s Spice model versions available for Power MOSFETs. Fluke 772 and 773. To set the squarewave source, right-click the body of the voltage source, leave both textboxes blank and choose the advanced button. Active 4 =1. Pspice Simulation Tip #1 Managing Power Supply Voltages One problem when using Pspice for simulation of Transient (Time Domain) Analysis is that at time = 0 the Power Supplies are stable. OrCAD PSpice® Quick Reference PSpice shortcut keys PSpice toolbars PSpice Model Editor shortcut keys and toolbar PSpice Stimulus Editor shortcut keys and toolbar Technical support (503) 671-9400 Corporate offices (503) 671-9500 OrCAD Japan K. AC calls the source by its _reference_name_!. 7V (for silicon) the current start to change rapidly for a small change. 1 ns rise time. LTspice Tutorial: Part 6. capacitance can be viewed in PSpice as the expression: - I(V1)/D(V(V1:+)), which is derived from equation (2b). 1 depicts a PSpice con-figuration and the waveform. LTspice Tutorial: Part 6. LTspice - 3 ways how to get an AM - amplitude modulated signal. The arbitrary sources in LTspice are incredibly versatile and useful. With this purpose, let's connect a resistor between the voltage source and the capacitor. The voltage across the latter is given by the voltage drop across Because the two MOSFETs are matched, and have precisely the same gate-source and threshold voltages (vGSA = vGSB), their drain currents will be equal. The first op amp is an inverting integrator. This value is varied through the DEV, therefore it should be different from the nominal. Download PSpice for free and get all the Cadence PSpice models. A series inductance was also added to model the switch. This Is Problem 4. This is the idea behind the circuit. However, because SPICE is a rich language, it is not always possible to perform a full conversion without some manual intervention. V1 1 0 AC=10V,90 VIN 1 0 AC 10V 90 The above two examples specify an AC voltage source with a magnitude of 10 V and a phase of 90 degrees. Now let's run pspice simulation. constant-current-source Constant current regulator PUBLIC. 2410 and 2410-C SourceMeter® Specifications SOURCE SPECIFICATIONS1 VOLTAGE PROGRAMMING ACCURACY (LOCAL OR REMOTE SENSE) RANGE PROGRAMMING RESOLUTION ACCURACY (1 Year) 23°C ±5°C ±(% rdg. Since PWL functions are useful in creating custom waveforms, they are typically used in defining voltage or current sources. Type in V1 as the name of the source. 2 Principle of Space Vector PWM The circuit model of a typical three-phase voltage source PWM inverter is shown in Fig. The PSPICE version available at The University of Mississippi can be used on a personal computer for sophisticated analysis of electric circuits of. Voltage sources, in addition to being used for circuit excitation, are the 'ammeters' for SPICE, that is, zero valued voltage sources may be inserted into the circuit for the purpose of measuring current. vbs Initial bulk-source voltage. For example, it is used to simulate and design electronics circuits, digital circuits and you will see the example of all of these in this complete list of tutorials. I don't think the IBIS spec defines how PULLUP or PULLDOWN turn on. Transforming the voltage source to the current source and writing the node-voltage equation results in. for your voltage source instead of VAC (VOFF is the DC offset, VAMPL is the amplitude, and FREQ is the frequency of the sine wave). Some examples of energy sources applied are DC capacitors, batteries and that drawn from the line through a rectifier. Select Open to install these libraries. 0 0 T1 R2 25 R1 25 V1 1. For transient analysis, click advanced, go to the left side, click Sine (usually) and enter the amplitude (peak value) and frequency. Use of PSpice with OrCAD Capture PSpice with OrCAD Capture (release 9. This source is similar to the function generators you will use in the lab and can supply a voltage of the form VSIN(t) = VDC + VAMPL*SIN(2*π*F*t). For any current-controlled dependent source, a dummy voltage is needed in series with the source so PSPICE can determine the current through the source. It is likely that the old URL for this PSpice tutorial will disappear on August 31, 2015. AC sweep is analysis from V3. Quick Links. 93 using source transformation. The first stage of this cascade provides the necessary voltage gain. The arbitrary sources in LTspice are incredibly versatile and useful. The positive terminal is connected to node 23 while. Often this conversion is automatic. Go to PSpice => Edit Simulation Profile. Use PSpice and AC Analysis for a single point 60 Hz to obtain the node voltages V1 and V2, and current in R3. 2 vgs = 0v, f = 1mhz 2000 1500 500 0 0 5 10 15 20 25 c, capacitance (pf) vds, drain-to-source voltage (v) crss 1000 coss ciss 60 45 30 15 0 5. PSpice to measure this "shift" in time: ts = 1. A triangle wave source can be created using the Voltage Source component available in the Waveform Sources group of the Analog Primitives section in the Component menu. AC Analysis Close the simulation and modify the circuit, replacing the VSIN source with a VAC source. · Simulate the circuit using Pspice. Energywire: Friday, May 8, 2020. But it is always a simple matter to insert a 0-V voltage source. Following Ohm's law for the conversion of volts to amperes, oil-filled coils generally require 3 to 5 amperes of primary current to produce 20,000-30,000 volts of secondary current. ] N+ is the positive node, and N- is the negative node as shown in the above fig(a),. PSpice A/D digital simulation condition messages 61. If you use only one extruder, you can connect the fan to the 2 pins in the middle of the 6 blue output pins. This feature is not available right now. Op amps are extremely versatile and have become the amplifier of choice for very many applications. LABORATORY EXPERIMENTS In the lab, repeat all of the experiments you did in PSpice in the prelab (that is, 1 through 7 above). Similarly, to create a white current noise source, we can use a voltage dependent current source (G source). The Simulation Settings are shown in Figure 2. Enjoy a classic solo career progression system: after 3 trails you move onto the next stage. VOFF (Offset Voltage). Current-controlled voltage source (CCVS) This is a voltage source whose value is controlled by a current elsewhere in the circuit. PSPICE to look for the sources. V1 DC = 9V R1 1k R2 1k R3 1k 0 Figure 1: Simple circuit to illustrate node naming procedure. Quick Links. tex Page 5 Passive Elements The that begins an element instance denotes the circuit element. Place resistor RL and set its value to {rvariable}. LTspice linearly ramps the low voltage to the high voltage during that time, then back. By using a rise and fall time equal to 1/2 of your period of your pulse function, you are creating a triangle wave. 2V to 37V output range. If one takes that same 9 volts again but now for a 1 Amp RED LED with a forward Voltage of 2 Volts, you will need a resistor capable of handling (9-2)x1x1=7 Watt, while the resistor in an average constant current source only needs to be 0. Process Milliamp Clampmeter. It's a plug-in replacement for the Arduino Mega in your RAMPS setup for a quick and easy upgrade to 32-bit goodness. A current source is the dual of a voltage source. Approach: As illustrated in figure 1, an effective solution for such an amplifier is a cascade of a CE and a CC amplifier. The half-bridge driver chip is able to supply this high voltage by using a bootstrapping circuit. People often refer to the whole suite as 'Spice'. IC statement. 33amps) = 13. step command and set z=0. 30 in Eletric Circuits 10th edition by nilsson only the initial values are different. The open circuit voltage. 2 x 50µs open-circuit voltage waveform and the 8 x 20µs short-circuit current waveform (Figures 2 and 3 respectively) [4]. The type of simulation performed by PSpice depends on the source specifications and control statements. They act as a sawtooth wave generator circuit, by C1 to charge and discharge. Double click on the dependent source Click on gain and change the value to 8. A triangle wave source can be created using the Voltage Source component available in the Waveform Sources group of the Analog Primitives section in the Component menu. An ideal op-amp integrator uses a capacitor C1, connected between the output and the op-amp inverting input terminal, as shown in the figure below. A common design of the electromagnetic relay is shown below: Manually operated relay is not common these days. A times VN. 6) Apr 21, 2008 2 Source SimCode model definitions are stored in an ASCII text file (*. An Ideal current source is a two-terminal circuit element which supplies the same current to any load resistance connected across its terminals. Please try again later. 001 AC 1 sin (0 1 1meg) 5. There are several circuit topologies and control methods used to convert a dc input into a 3-phase ac output. Alternatively, you can just press the "Esc" key in your keyboard, then the red part in dotted rectangle will disappear. Use this voltage source component for your input signals. The parameters needed to define a MOSFET in LTspice are as follows: Lambda is the change in drain current with drain source voltage and is used with Kp to determine the RDSon. Show The Voltage And Current Values. Current controlled voltage source:. According to compensation theorem, this resistor can be replaced by a voltage source that’s generated voltage will be V (= IR) and will be directed against the direction of network voltage or direction of current I. Power Transformer; AC Voltage Source; In this circuit, we will use a step-down transformer. doc 8 OF 13 10/18/2007 D-SCOPE-TECH, INC. 5 - Typical Capacitance vs. an examination of the output file shows that PSpice has assigned the node names shown in Figure 2. The polarities in both the half cycles will be different from each other. for your voltage source instead of VAC (VOFF is the DC offset, VAMPL is the amplitude, and FREQ is the frequency of the sine wave). VOLTAGE MODE CONTROL OF BUCK CONVERTER Department of Electrical & Electronics Engineering, NMAMIT, NITTE 10 2. For another thing, you have added AC = 0 to your AC source, which forces the RMS value to zero, and this apparently overrides the peak specification VAMPL = 100V. For a passive RC integrator circuit, the input is connected to a resistance while the output voltage is taken from across a capacitor being the exact opposite to the RC Differentiator Circuit. Place resistor RL and set its value to {rvariable}. A useful reference node is one which is connected to the maximum number of voltage sources. The maximum temperature which can be reached is 120°C and the device heats up from 0°C to 100°C in 5 minutes at a low voltage of 12V. en Pspice con marcadores y valores rms - Duration: 8:15 Circuit tutorial: sawtooth generator w/ current sources, diode switches, hysteresis. Also some simulations are done for resistive-inductive load in the output of the inverter. For example, it is used to simulate and design electronics circuits, digital circuits and you will see the example of all of these in this complete list of tutorials. The sizing of a battery charging solar system was based on a Voltage Source Photovoltaic Model (VSPVM) that was implemented using PSpice software environment. 1 ns rise time. Easily generate HTML reports from your simulation results. Linear Voltage Regulators Depletion type MOSFETs in source-follower configuration are used in linear voltage regulator circuits as pass transistors (Figure 5). Find The Contribution Of The Voltage Source V2 Alone. pdf), Text File (. This is compatible with SPICE. If you had used the search feature, and typed in DC voltage source, the search would have returned no result. output is multiplied by a gain equal to the input DC voltage (12V), and the resulting AC voltage drives the output L-C filter and load. Figure A-3. Xiong This tutorial will guide you through the creation and analysis of a simple MOSFET circuit in PSPICE Schematic. Click on the Voltage/Level Marker button to add a marker to the Vout node by clicking on it as shown below. Build the circuit As described in the “pspice_DC” tutorial, launch the PSPICE program and start a new, blank “Analog or Mixed A/D” project. 01V for the start value, end value and increment, respectively. Using LM317 to create a negative voltage power supply. Ramp - For a ramp waveform, set V1 and V2 to the initial and final voltages of the waveform. Pulse amp is 2v. DC Simulation: To solve the circuits, a matrix is defined based on all the components inside the circuit. (c)Print out the output file for your submission. 0 SPICE ‘Quick’ Reference Sheet THE GENERAL ANATOMY OF A SPICE DECK SPECIFYING CIRCUIT TOPOLOGY: DATA STATEMENTS Basic Components Resistors Capacitors and Inductors Voltage and Current Sources Independent DC Sources Independent AC Sources Transient Sources Sinusoidal Sources Piecewise Linear Source (PWL) Pulse. The same ohms' law as discussed in the previous tutorial applies on the AC. PRINT (print) 66 Independent voltage source & stimulus 230 Current-controlled switch 231 Capture parts 232 Ideal switches 232 Current-controlled switch model parameters 233. little feedback, and the source voltage would ramp all the way to the Vth(1) threshold of the IRIS4009, but in this case the input voltage is 230VAC, so the feedback has generated an offset voltage to reduce the peak current in the transformer, and hence the source voltage ramps to about 0. According to compensation theorem, this resistor can be replaced by a voltage source that’s generated voltage will be V (= IR) and will be directed against the direction of network voltage or direction of current I. The ramp input source applies a ramp or a step voltage to the input of the circuit under test. We know that if a capacitor is charged from a voltage source through a resistor, an exponential waveform is produced while charging of a capacitor from a constant current source produces a ramp. In some cases you may need a negative sense on the voltage source if you use an inverting summer. Make sure the sweep type is linear and use 0V, 2V and 0. 9 ns to 5 V at 100 ns, then from 5 V at 200 ns to 0 V at 200. Set TD to 0. Therefore, the output voltage Vout is a constant -Rƒ*C times the derivative of the input voltage Vin with respect to time. For any current-controlled dependent source, a dummy voltage is needed in series with the source so PSPICE can determine the current through the source. 416 Peak-Peak ripple current is limited to 30% of load current, Using equation (2. Use PSpice and AC Analysis for a single point 60 Hz to obtain the node voltages V1 and V2, and current in R3. sch) The voltage source and the current source frequency are 60 Hz. Also Pspice is a simulation program that models the behavior of a circuit. Arbitrary Power Sink or Source where function f is a constant or is an arbitrary function of any valid node voltage, branch current, etc. Active 4 =1. LTspice linearly ramps the low voltage to the high voltage during that time, then back. 7V (for silicon) the current start to change rapidly for a small change. voltage source peak-to-peak voltage? What is its frequency? What is its internal source resistance? (or is it "ideal")? What are the attributes of the diode? (or is it "ideal"? Here it is with a 3vpp 50Hz ideal source with an ideal Silicon diode. Note Down The Value Of Voltage Across R6. Simulation of Power Electronic Systems Using PSpice - Free download as Powerpoint Presentation (. The PSpice schematics editor provides a very powerful and easy to use interface to generate digital circuits. Figure B-2. Use of PSpice with OrCAD Capture PSpice with OrCAD Capture (release 9. Notes for ORCAD PSpice. WORKING VOLTAGE The Working Voltage of a connector is just that; it is the amount of voltage that a connector can withstand all the time. An evaluation (student) version, which can handle small circuits with up to 10 transistors, is freely available. select Place Part (P for shortcut), 2. Current source ISRC has a 1/3 amp RMS AC response with a 45 degree phase Offset. This determines the drain current that flows for a given gate source voltage. GRBL for RAMPS 1. You will learn how to do the following: Start a Project Æ Draw a schematic Æ Simulate circuit Æ Graph data. 1) Analysis type: DC Sweep. LTSpice Voltage Controlled Voltage Source (VCVS) We have a divide-by-2 voltage divider followed by the VCVS which multiplies the input voltage, Vg with a gain factor of 10$\$\ V_g = {1 \over 2} * V1 = {1 \over 2} * 1 = 0. RE-ARM is a 100Mhz, 32-bit ARM controller with the popular Arduino MEGA footprint. 81-45-621-1911 OrCAD UK Ltd. The source VAC is a 440 Hz. Ask Question Asked 7 years ago. Click on File, New, Project. Tension of displacement, continuous voltage that represents the zero for the sine. Following Ohm's law for the conversion of volts to amperes, oil-filled coils generally require 3 to 5 amperes of primary current to produce 20,000-30,000 volts of secondary current. Page 79 Configuring PSpice Schematics When Autosave is enabled, PSpice Schematics creates a temporary file with the same name as the active working file, and a file name extension ending in ' ' (for example, ". It also protects the input from undesired shorts and transients coming from the source. This circuit uses a current source to generate a voltage ramp whenever the switch is closed. Place a V DC source from the source library and set its value to 10V. Check your result using PSpice or MultiSim. ] N+ is the positive node, and N- is the negative node as shown in the above fig(a),. Create a PSpice simulation profile called transient and select Analysis type: to Time Domain (Transient) and enter a Run to time of 10ms, which will display 10 cycles of the sinewave (Figure 7. Current source ISRC has a 1/3 amp RMS AC response with a 45 degree phase Offset. A circuit that could provide an output voltage of 3v can be designed by using resistors and Ohm’s law to figure out what resistance is needed to create an output of 3V from 10V source. Vpulse triangle signal EE234 Lab. ) How? One way is to replace the -15 VDC supply with a voltage source that varies. The rapid change in the current shows that the resistance decrease as we. PSpice Simulation of Step Response. LTspice has a built in triangle wave function, although it may not seem that way. 220-spice-notes. Set the analysis. draw the circuit (in the example, a Band Pass) V DD is a ramp voltage generator that creates a voltage ramp in V DS. Milliamp Process. 1 Tutorial --X. Since we want to plot the voltage and current versus time, the Transient analysis is used. How do I read the sample, and what does it mean? For example R9 5 2 15K means that Resistor R9 lies between Node 5 and Node 2, and has a value of 15000 Ohms. One final point to mention, the Op-amp Differentiator circuit in its basic form has two main disadvantages compared to. By using the nodes of the current source for voltage control, resistor behaviour may be expressed as I = V/R(Tj). 2), Duty Ratio, D =0. Simulation with HSPICE. The current sources are further categorised as Ideal and Practical current source. The role of the ignition coil is to multiply battery voltage into high voltage. Polynomial source - pspice The symbol for a polynomial or nonlinear source is POLY (n), where n is the number of dimensions of the polynomial. LTspice - 3 ways how to get an AM - amplitude modulated signal. Milliamp Process. Some of the main features that are being explored in the examples are hierarchical structures and busses, and bias voltage display. As expected, if v(2)>v(1) the output voltage v(3, 5) is 30V. This uses a constant amplitude AC source whose frequency can be varied over some range. source the frequency in Hz is 2/(2π) = 1/π = 0. DC Simulation: To solve the circuits, a matrix is defined based on all the components inside the circuit. The PSpice Ground has symbol , which is different from ordinary ground with symbol. Although models can be a useful tool in evaluating device performance, they cannot model exact device performance under all. The voltage across the latter is given by the voltage drop across Because the two MOSFETs are matched, and have precisely the same gate-source and threshold voltages (vGSA = vGSB), their drain currents will be equal. The sizing of a battery charging solar system was based on a Voltage Source Photovoltaic Model (VSPVM) that was implemented using PSpice software environment. 30 PSpice|Multisim. If the design is working correctly, we expect to find the current to be independent of V1. Place a V DC source from the source library and set its value to 10V. Application uptime without the balancing act. 7 board to the RPi. PSpice to measure this "shift" in time: ts = 1. Pspice voltage sources. in Physics Hons Gold medalist, B. Simulation of Power Electronic Systems Using PSpice - Free download as Powerpoint Presentation (. It is a voltage source of type VSIN. By varying the voltage supplied by the source, the circuit will be DC. Some versions of PSpice allow you to ask for a current through a resistor without using a voltage source (EX: I(R1) gives the current in the resistor R1). However, the voltage ramp rate can be adjusted by placing an external capacitor between the gate of the MOSFET and ground. Click OK, and go to PSpice => Run to run the simulation. Voltage across the capacitor in the inverting terminal is also same as the ramp function. The TISP4xxxM3BJ range consists of nineteen voltage variants to meet various maximum system voltage levels (58 V to 320 V). Don't start Frequency sweeps at 0! Set the points/Decade to be at least 20. PSpice => Bias Points, and check Enable, Enable Bias Current Display, and/or Enable Bias Voltage Display. steady-state DC sources). Voltage Ramp Hot Swap Controller (TPS2301-EVM) Inrush Currents Most of the Texas Instruments voltage ramp controllers have a fixed ramp. 5 Where VIN is the source's name (you make that up), 3 and 7 are the node numbers where the source is connected (which you. 100mA Analog inputs (EAP, EAN, EAOUT, RAMP, SYNC, ADS, CS, SS/DISB). Build the circuit As described in the “pspice_DC” tutorial, launch the PSPICE program and start a new, blank “Analog or Mixed A/D” project. Here the source voltage, V L follows the gate voltage, V G minus the gate-to-source voltage, V GS. Close • Posted by 5 minutes ago. 4 is an inexpensive, well-supported hardware controller for your 3D printer. Pspice Simulation Tip #1 Managing Power Supply Voltages One problem when using Pspice for simulation of Transient (Time Domain) Analysis is that at time = 0 the Power Supplies are stable. These are. X device - Subcircuit Call. An evaluation (student) version, which can handle small circuits with up to 10 transistors, is freely available. Pspice voltage sources. 19 in Hambley (RC transient analysis). FREQ (Frequency). PSpice Tutorials 4th Tutorial: Transient Analysis Linear Inductors Linear Capacitors Transient Analysis Use of the. For z=1, only the voltage injection source Vz is active, for z=0, only the input source Vi (or Ii) is active, and for z=-1, only the current injection source Iz is active. Figure 4 A DC power source in MultiSim. 3) Sweep Variable: Voltage Source. little feedback, and the source voltage would ramp all the way to the Vth(1) threshold of the IRIS4009, but in this case the input voltage is 230VAC, so the feedback has generated an offset voltage to reduce the peak current in the transformer, and hence the source voltage ramps to about 0. It may be damaged, it must be a constant current flowing through it. V1 DC = 9V R1 1k R2 1k R3 1k 0 Figure 1: Simple circuit to illustrate node naming procedure. g: voltage controlled current source. Give the junction between the Source and the R the alias Vin. Thus, the current Io becomes a replica, or "mirror image" of the reference current. Modelling photovoltaic systems using pspice. The current sources are further categorised as Ideal and Practical current source. Download PSpice for free and get all the Cadence PSpice models. AC calls the source by its _reference_name_!. A single voltage source and a single resistance in series with the source serves as the electrical equivalent to networks of voltage sources, current sources, and resistors. 065 VAMPL = 1 VOFF = 0 L1 10H 1 2 0 V C1. In previous tutorials we have described the DC voltage source, VDC, and the sinusoidal voltage source, VSIN. Scope parameters are assumed to be 1Meg input resistance plus 50p input cap. View attachment 117706. However, inverting amplifiers are "cheap" in a simulation, so keep the voltage sense +ve and use an inverter with a gain of one where necessary, I have appended a file of at a quick glance what I think the system should look like, cheers, Richard. We will generate the voltage VCC with a current-controlled voltage source (H part), for which the control current comes from a fixed 12 V source in series with a 1-ohm nominal Rbreak part. S is the diode’s reverse saturation current, is the applied voltage bias, V V t is the thermal voltage (equal to kT/q which is about 25mV at room temperature) and I D is the current through the device. ) How? One way is to replace the -15 VDC supply with a voltage source that varies. The stair signal can be generated with a counter and a multiplexer (16 stairs) or with a DAC if you need. The first quadrant of the V-I characteristics curves shows the forward operation of the diode. Just draw the schematic, then assign names for the resistor, capacitor, voltage source (R1, C1, VS) and node numbers (1 and 2). PSpice in simulating power electronics circuits, induction machines and induction motor drives. 1) source voltage is 40V DC with all initial conditions set equal to zero. Bode Plots. Show The Voltage And Current Values. Polynomial source - pspice The symbol for a polynomial or nonlinear source is POLY (n), where n is the number of dimensions of the polynomial. After working the math out, it turned out that the slope was equal to 1. However, the voltage ramp rate can be adjusted by placing an external capacitor between the gate of the MOSFET and ground. To allow us to set the transconductance factor of the source to the noise density in fA/√Hz, we need a resistor with a noise density of 1 fV/√Hz, which means that the resistor shall have the very small value of 60. Most of the Texas Instruments voltage ramp controllers have a fixed ramp. V1: 신호의 최소전압 (Minimum voltage) V2: 신호의 최대전압 (Maximum Voltage) PW : V2 전압의 폭 (Pulse Width time) TR: V1 에서 V2 로 상승하는. We present PSpice simulations of voltage source inverters with two levels, induction machine fed by three-phase voltage source inverter and of vector control of induction machine when exact motor parameters are known. A buck-boost converter is used for this application. AC Sources AC current and voltage sources are impulse functions used for an AC analysis. Then you can continue to insert other parts or perform other. Go to PSpice => Edit Simulation Profile. Project Help. As an example, we'll create a netlist for a simple low-pass RC filter. Voltage Buffer Simulation. Define a finer step size i. 2 Lite edition) Before one can simulate a circuit one needs to specify the circuit configuration. Figure 3 shows the equivalent circuit diagram on a Level 3 model of an Infineon MOSFET. This current and voltage that increase and reduce, cause Q1 to generate a signal. doc 8 OF 13 10/18/2007 D-SCOPE-TECH, INC. A comparator to perform the function s(x i − x) by comparing the DAC's voltage with the input voltage. The following sources are available in SPICE simulation. On the basis of the Pspice program various simulations have been undertaken. CMOS offers low power dissipation, relatively high speed, high noise margins in both states, and will operate over a wide range of source and input voltages (provided the source voltage is fixed). Define a finer step size i. Simulated open-loop gain and phase for step-down converter. For a passive RC integrator circuit, the input is connected to a resistance while the output voltage is taken from across a capacitor being the exact opposite to the RC Differentiator Circuit. Here's the converter schematic in TINA-TI: I changed the initial load to 11. No ideal voltage source in closed inductor loop. Here the source voltage, V L follows the gate voltage, V G minus the gate-to-source voltage, V GS. The voltage at the iavg node 238 ramps up at a rate set by the iavg voltage to current function 134 which provides charging current for the iavg ramp capacitor 140. Consider the pulse voltage source in the above image, with the following characteristics: Pin1 (positive) is connected to net CP. Often this conversion is automatic. Primary voltage ramp properties. Using Cursors to Measure Slopes in PSpice. 1u and your signal reaches 5V. Performing Initialization and Analysis DC Initialization and Point Analysis 6-4 Star-Hspice Manual, Release 1998. Voltage controlled current source: Gname N1 N2 NC1 NC2 Value. Pspice voltage sources. Dependent Source Setup Place all the elements including current-controlled-voltage-source, H. Allegro PSpice Simulator advanced analysis - Smoke analysis - Sensitivity analysis - Optimizer - Monte Carlo analysis BSIM1, BSIM3, EKV models Datasheet specifications Vendor models Part table file MRP/ERP/PDM system PCB layout Fabrication, assembly and test Custom semiconductor models Part Manager Purchasing/ inventory Figure 1: Allegro PSpice. DC Sweep Analysis. The ground can be obtained by clicking on the right side bar menu, and then select "0/SOURCE" in the "Place Ground" window as shown in Figure 13 below. Setting up DC sweep. PSPICE Schematic Student 9. The power dissipated by a given circuit component is the product of voltage and current, PIV= The unit of power is the Joule per second (J/s), which is also known as a Watt (W). 2 Lite edition) Before one can simulate a circuit one needs to specify the circuit configuration. The flat spot in the middle is where there's no data for the BV to use, but it catches up again at the end. A voltage doubler application is a DC power supply capable of using either a 240 VAC or 120 VAC source. Configuration #2: an impedance sL in parallel with an independent current source I 0 /s If the initial current is zero the s-domain circuit for both representations simplifies to just the impedance sL. Current-controlled voltage source (CCVS) This is a voltage source whose value is controlled by a current elsewhere in the circuit. For a passive RC integrator circuit, the input is connected to a resistance while the output voltage is taken from across a capacitor being the exact opposite to the RC Differentiator Circuit. The issue is that when you click the "Add Ground" button on the toolbar (a couple of buttons beneath the "Add Part" button), the dialog box does not automatically include the proper library. The open circuit voltage. No stacked current sources (i. The is a phase shift PWM controller that implements control of a full-bridge power stage by phase shifting the switching of one half-bridge Adaptive Delay Set with respect to the other. This current and voltage that increase and reduce, cause Q1 to generate a signal. Build The Circuit Above On PSPICE And Simulate It. ] N+ is the positive node, and N- is the negative node as shown in the above fig(a),. Then the node on the left is the positive node and the node on the right is the negative node. Thévenin’s and Norton’s theorem allow you to replace a complicated array of independent sources and resistors, turning the source circuit into a single independent source connected with a single resistor. 30 In Eletric Circuits 10th Edition By Nilsson Only The Initial Values Are Different Use The Node-voltage Method To Find The Power Developed By The 30 V Source. SPICE allows users to specify input that varies in form. 25 milliseconds. I have an AC voltage source(V1) SINE(0 34 50). In previous tutorials we have described the DC voltage source, VDC, and the sinusoidal voltage source, VSIN. V1 is set to 0 V so that it has no effect on the circuit. VPULSE (Set delay time, TD = 0, for simulations in. , normalized drain-to-source breakdown voltage tj, junction temperature (oc) t c, case temperature (oc) 0 25 50 75 100 125 150 175 power dissipation multiplier 0. The AOZ1284 is a high voltage, high efficiency, simple to use, 4A buck regulator optimized for a variety of applications. behavioral-source constant-current-source lm317 newbie test CB Current Source PUBLIC. It calculates all nodal voltages and branch currents over a range of values. The Coal Creek Station near Underwood, N. An independent current source delivers a constant current. How can I step it's voltage parameter. Thus, the current Io becomes a replica, or "mirror image" of the reference current. It is likely that the old URL for this PSpice tutorial will disappear on August 31, 2015. A simple switch model was incorporated for the MOSFET switch array. Editing The Value of A DC Voltage Source Figure 6 and Figure 7 show the specification of a -15 volt voltage source labeled Vee. A window comes up giving the coordinates of the points where you clicked and the differences between the points. This unique package is adapted to complex PCB designs and interfaces directly with your circuit schematic data. Some questions - 1) Do you want a ramp symmetrical about ground or from gnd to some + value ? 2) You stuck on this circuit ? 3) Do you care about rise/fall time of ramp reset ? 4) Single supply or split supply preferable ? 5) Voltage controlled frequency ? If so range of V and F. tex Page 5 Passive Elements The that begins an element instance denotes the circuit element. The voltage buffer utilized in the previous article. Actually, it looks like the final ramp value needs to be 1002 in order for the output to be 2V, but this also varies with different ramps, so the attenuation can be considered ~1000x. To allow us to set the transconductance factor of the source to the noise density in fA/√Hz, we need a resistor with a noise density of 1 fV/√Hz, which means that the resistor shall have the very small value of 60. 00 mV 5 µV 0. A PSpice independent-voltage source can produce an approx-imate sawtooth waveform if the source is represented by a periodic pulse voltage. The TISP4xxxM3BJ range consists of nineteen voltage variants to meet various maximum system voltage levels (58 V to 320 V). PSPICE to look for the sources. PSpice is a free open source software, download it here. The supply uses a switch selected full-wave bridge to produce about 300 VDC from a 240 VAC source. The same controller causes the LED current to gradually ramp down to zero if the EN pin is pulsed while the output channel is ON. standard 60 Hz electrical supply. They were used earlier, in manually operated relay the. 3) Sweep Variable: Voltage Source. 3) Sweep Variable: Voltage Source. Arnab Chakraborty is a Calcutta University alumnus with B. How do I create one? A triangle waveform, along with sawtooth, ramp, step, and impulse waveforms, can all be created through the Pulse capability of the Voltage Source component. Since PWL functions are useful in creating custom waveforms, they are typically used in defining voltage or current sources. Products/Services for Pspice Voltage Regulators. DESCRIPTION. What is the A. capacitance can be viewed in PSpice as the expression: - I(V1)/D(V(V1:+)), which is derived from equation (2b).
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Calculus
# Taylor Series Approximation
Let $f(x)$ be a function such that $f(0)=3, f'(0)=1,$ and $f(3)=1.$ Using a quadratic Taylor polynomial of $f(x),$ we can approximate the value of $f''(0)$ as $f''(0) \approx -\frac{A}{B},$ where $A$ and $B$ are coprime integers. Find the value of $AB.$
Using the quadratic Taylor polynomial of $f(x) = \frac{1}{x}$ at $x=5,$ find the approximate value of $\frac{1}{7}$ multiplied by $5^3.$
For the linear Taylor polynomial $g(x)=ax+b$ of $f(x)=-\frac{1}{x-1}$ at $x=2,$ find the error $e$ defined by $e=\int_{2}^{3}{(g(x)-f(x))^2 dx}.$
Using the quadratic Taylor polynomial of $f(x) = \ln{x}$ at $x=4,$ we can approximate the value of $\ln{9}$ in the form $\ln{A}+B,$ where $A$ and $B$ are rational numbers. Find the value of $2A^2B.$
Let $f(x)$ be a function such that $f(0)=1, f'(0)=2,$ and $f(3)=1.$ Using a quadratic Taylor polynomial of $f(x),$ we can approximate the value of $f''(0)$ as $f''(0) \approx -\frac{A}{B},$ where $A$ and $B$ are coprime integers. Find the value of $AB.$
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## Home Runs Per Game: A bit more in-depthDecember 23, 2011
Posted by tomflesher in Baseball, Economics.
Tags: , , , , , ,
I know I’ve done this one before, but in my defense, it was a really bad model.
I made some odd choices in modeling run production in that post. The first big questionable choice was to detrend according to raw time. That might make sense starting with a brand-new league, where we’d expect players to be of low quality and asymptotically approach a true level of production – a quadratic trend would be an acceptable model of dynamics in that case. That’s not a sensible way to model the major leagues, though; even though there’s a case to be made that players being in better physical condition will lead to better production, there’s no theoretical reason to believe that home run production will grow year over year.
So, let’s cut to the chase: I’m trying to capture a few different effects, and so I want to start by running a linear regression of home runs on a couple of controlling factors. Things I want to capture in the model:
• The DH. This should have a positive effect on home runs per game.
• Talent pool dilution. There are competing effects – more batters should mean that the best batters are getting fewer plate appearances, as a percentage of the total, but at the same time, more pitchers should mean that the best pitchers are facing fewer batters as a percentage of the total. I’m including three variables: one for the number of batters and one for the number of pitchers, to capture those effects individually, and one for the number of teams in the league. (All those variables are in natural logarithm form, so the interpretation will be that a 1% change in the number of batters, pitchers, or teams will have an effect on home runs.) The batting effect should be negative (more batters lead to fewer home runs); the pitching effect should be positive (more pitchers mean worse pitchers, leading to more home runs); the team effect could go either way, depending on the relative strengths of the effects.
• Trends in strategy and technology. I can’t theoretically justify a pure time trend, but I also can’t leave out trends entirely. Training has improved. Different training regimens become popular or fade away, and some strategies are much different than in previous years. I’ll use an autoregressive process to model these.
My dependent variable is going to be home runs per plate appearance. I chose HR/PA for two reasons:
1. I’m using Baseball Reference’s AL and NL Batting Encyclopedias, which give per-game averages; HR per game/PA per game will wash out the per-game adjustments.
2. League HR/PA should show talent pool dilution as noted above – the best hitters get the same plate appearances but their plate appearances will make up a smaller proportion of the total. I’m using the period from 1955 to 2010.
After dividing home runs per game by plate appearances per game, I used R to estimate an autoregressive model of home runs per plate appearance. That measures whether a year with lots of home runs is followed by a year with lots of home runs, whether it’s the reverse, or whether there’s no real connection between two consecutive years. My model took the last three years into account:
$\hat{HR}_t = .0234 + .5452HR_{t-1} + .1383HR_{t-2} + .1620HR_{t-3} + \varepsilon_t$
Since the model doesn’t fit perfectly, there will be an “error” term, $\varepsilon$ , that’s usually thought of as representing a shock or an innovation. My hypothesis is that the shocks will be a function of the DH and talent pool dilution, as mentioned above. To test that, I’ll run a regression:
$\varepsilon_t = DH_t + logbat_t + logpitch_t + logtm_t$
The results:
$\begin{tabular}{c|ccc} Variable & Sign Predicted & Estimate & P \\ Intercept&0&-0.011070&0.1152 \\ DH&+&-0.000063&0.9564 \\ logbat&-&-0.000245&0.9335 \\ logpitch&+&\bf{0.005550}&0.0489 \\ logtm&?&\bf{-0.006854}&0.0237 \\ \end{tabular}$
The DH and batter effects aren’t statistically different from zero, surprisingly; the pitching effect and the team effect are both significant at the 95% level. Interestingly, the team effect and the pitching effect have opposite signs, meaning that there’s some factor in increasing the number of teams that doesn’t relate purely to pitching or batting talent pool dilution.
For the record, fitted values of innovations correlate fairly highly with HR/PA: the correlation is about .70, despite a pretty pathetic R-squared of .08.
Posted by tomflesher in Baseball, Economics.
Tags: , , , , , , , , ,
1 comment so far
I was all set to fire up the Choke Index again this year. Unfortunately, Derek Jeter foiled my plan by making his 3000th hit right on time, so I can’t get any mileage out of that. Perhaps Jim Thome will start choking around #600 – but, frankly, I hope not. Since Jeter had such a callous disregard for the World’s Worst Sports Blog’s material, I’m forced to make up a new statistic.
This actually plays into an earlier post I made, which was about home field advantage for the Giants. It started off as a very simple regression for National League teams to see if the Giants’ pattern – a negative effect on runs scored at home, no real effect from the DH – held across the league. Those results are interesting and hold with the pattern that we’ll see below – I’ll probably slice them into a later entry.
The first thing I wanted to do, though, was find team effects on runs scored. Basically, I want to know how many runs an average team of Greys will score, how many more runs they’ll score at home, how many more runs they’ll score on the road if they have a DH, and then how many more runs the Phillies, the Mets, or any other team will score above their total. I’m doing this by converting Baseball Reference’s schedules and results for each team through their last game on July 10 to a data file, adding dummy variables for each team, and then running a linear regression of runs scored by each team against dummy variables for playing at home, playing with a DH, and the team dummies. In equation form,
$\hat{R} = \beta_0 + \beta_1 Home + \beta_2 DH + \delta_{PHI} + \delta_{ATL} + ... + \delta_{COL}$
For technical reasons, I needed to leave a team out, and so I chose the team that had the most negative coefficient: the Padres. Basically, then, the $\delta$ terms represent how many runs the team scores above what the Padres would score. I call this “RAP,” for Runs Above Padres. I then ran the same equation, but rather than runs scored by the team, I estimated runs allowed by the team’s defense. That, logically enough, was called “ARAP,” for Allowed Runs Above Padres. A positive RAP means that a team scores more runs than the Padres, while a negative ARAP means the team doesn’t allow as many runs as the Padres. Finally, to pull it all together, one handy number shows how many more runs better off a team is than the Padres:
$Padre Differential = RAP - ARAP$
That is, the Padre Differential shows whether a team’s per-game run differential is higher or lower than the Padres’.
The table below shows each team in the National League, sorted by Padre Differential. By definition, San Diego’s Padre Differential is zero. ‘Sig95’ represents whether or not the value is statistically significant at the 95% level.
$\begin{tabular}{|r||r|r|r|r|r|} \hline \textbf{Team}&\textbf{RAP}&\textbf{Sig95}&\textbf{ARAP}&\textbf{Sig95}&\textbf{Padre Differential}\\ \hline PHI&0.915521&1&\textbf{-0.41136}&0&\textbf{1.326881}\\ \hline ATL&0.662871&0&-0.26506&0&0.927931\\ \hline CIN&\textbf{1.44507}&1&0.75882&0&0.68625\\ \hline STL&1.402174&1&0.75&0&0.652174\\ \hline NYM&1.079943&1&0.58458&0&0.495363\\ \hline ARI&1.217101&1&0.74589&0&0.471211\\ \hline SFG&0.304031&0&-0.15842&0&0.462451\\ \hline PIT&0.628821&0&0.1873&0&0.441521\\ \hline MIL&1.097899&1&0.74016&0&0.357739\\ \hline WSN&0.521739&0&0.17391&0&0.347829\\ \hline COL&1.036033&0&0.81422&0&0.221813\\ \hline LAD&0.391595&0&0.38454&0&0.007055\\ \hline FLA&0.564074&0&0.66097&0&-0.0969\\ \hline CHC&0.771739&0&1.31522&1&-0.54348\\ \hline HOU&0.586857&0&1.38814&1&-0.80128\\ \hline \end{tabular}$
Unsurprisingly, the Phillies – the best team in baseball – have the highest Padre Differential in the league, with over 1.3 runs on average better than the Padres. Houston, in the cellar of the NL Central, is the worst team in the league and is .8 runs worse than the Padres per game. Florida and Chicago are both worse than the Padres and are both close to (Florida, 43) or below (Chicago, 37) the Padres’ 40-win total.
## June Wins Above ExpectationJuly 1, 2011
Posted by tomflesher in Baseball, Economics.
Tags: , , ,
Even though I’ve conjectured that team-level wins above expectation are more or less random, I’ve seen a few searches coming in over the past few days looking for them. With that in mind, I constructed a table (with ample help from Baseball-Reference.com) of team wins, losses, Pythagorean expectations, wins above expectation, and Alpha.
Quick definitions:
• The Pythagorean Expectation (pyth%) is a tool that estimates what percentage of games a team should have won based on that team’s runs scored and runs allowed. Since it generates a percentage, Pythagorean Wins (pythW) are estimated by multiplying the Pythagorean expectation by the number of games a team has played.
• Wins Above Expectation (WAE) are wins in excess of the Pythagorean expected wins. It’s hypothesized by some (including, occasionally, me) that WAE represents an efficiency factor – that is, they represent wins in games that the team “shouldn’t” have won, earned through shrewd management or clutch play. It’s hypothesized by others (including, occasionally, me) that WAE represent luck.
• Alpha is a nearly useless statistic representing the percentage of wins that are wins above expectation. Basically, W-L% = pyth% + Alpha. It’s an accounting artifact that will be useful in a long time series to test persistence of wins above expectation.
The results are not at all interesting. The top teams in baseball – the Yankees, Red Sox, Phillies, and Braves – have either negative WAE (that is, wins below expectation) or positive WAE so small that they may as well be zero (about 2 wins in the Phillies’ case and half a win in the Braves’). The Phillies’ extra two wins are probably a mathematical distortion due to Roy Halladay‘s two tough losses and two no-decisions in quality starts compared with only two cheap wins (and both of those were in the high 40s for game score). In fact, Phildaelphia’s 66-run differential, compared with the Yankees’ 115, shows the difference between the two teams’ scoring habits. The Phillies have the luxury of relying on low run production (they’ve produced about 78% of the Yankees’ production) due to their fantastic pitching. On the other hand, the Yankees are struggling with a 3.53 starters’ ERA including Ivan Nova and AJ Burnett, both over 4.00, as full-time starters. The Phillies have three pitchers with 17 starts and an ERA under 3.00 (Halladay, Cliff Lee, and Cole Hamels) and Joe Blanton, who has an ERA of 5.50, has only started 6 games. Even with Blanton bloating it, the Phillies’ starer ERA is only 2.88.
That doesn’t, though, make the Yankees a badly-managed team. In fact, there’s an argument that the Yankees are MORE efficient because they’re leading their league, just as the Phillies are, with a much worse starting rotation, through constructing a team that can balance itself out.
That’s the problem with wins above expectation – they lend themselves to multiple interpretations that all seem equally valid.
Tables are behind the cut. (more…)
## Is scoring different in the AL and the NL?May 31, 2011
Posted by tomflesher in Baseball, Economics.
Tags: , , , , , , , ,
1 comment so far
The American League and the National League have one important difference. Specifically, the AL allows the use of a player known as the Designated Hitter, who does not play a position in the field, hits every time the pitcher would bat, and cannot be moved to a defensive position without forfeiting the right to use the DH. As a result, there are a couple of notable differences between the AL and the NL – in theory, there should be slightly more home runs and slightly fewer sacrifice bunts in the AL, since pitchers have to bat in the NL and they tend to be pretty poor hitters. How much can we quantify that difference? To answer that question, I decided to sample a ten-year period (2000 until 2009) from each league and run a linear regression of the form
$\hat{R} = \beta_0 + \beta_1 H + \beta_2 2B + \beta_3 3B + \beta_4 HR + \beta_5 SB + \beta_6 CS + \\ \beta_7 BB + \beta_8 K + \beta_9 HBP + \beta_{10} Bunt + \beta_{11} SF$
Where runs are presumed to be a function of hits, doubles, triples, home runs, stolen bases, times caught stealing, walks, strikeouts, hit batsmen, bunts, and sacrifice flies. My expectations are:
• The sacrifice bunt coefficient should be smaller in the NL than in the AL – in the American League, bunting is used strategically, whereas NL teams are more likely to bunt whenever a pitcher appears, so in any randomly-chosen string of plate appearances, the chance that a bunt is the optimal strategy given an average hitter is much lower. (That is, pitchers bunt a lot, even when a normal hitter would swing away.) A smaller coefficient means each bunt produces fewer runs, on average.
• The strategy from league to league should be different, as measured by different coefficients for different factors from league to league. That is, the designated hitter rule causes different strategies to be used. I’ll use a technique called the Chow test to test that. That means I’ll run the linear model on all of MLB, then separately on the AL and the NL, and look at the size of the errors generated.
The results:
• In the AL, a sac bunt produces about .43 runs, on average, and that number is significant at the 95% level. In the NL, a bunt produces about .02 runs, and the number is not significantly different from saying that a bunt has no effect on run production.
• The Chow Test tells us at about a 90% confidence level that the process of producing runs in the AL is different than the process of producing runs in the NL. That is, in Major League Baseball, the designated hitter has a statistically significant effect on strategy. There’s structural break.
R code is behind the cut.
## Weird Pitching Decisions Almanac in 2010December 24, 2010
Posted by tomflesher in Baseball.
Tags: , , , , , , , , , , , , , , , , , , , , ,
1 comment so far
I’m a big fan of weird pitching decisions. A pitcher with a lot of tough losses pitches effectively but stands behind a team with crappy run support. A pitcher with a high proportion of cheap wins gets lucky more often than not. A reliever with a lot of vulture wins might as well be taking the loss.
In an earlier post, I defined a tough loss two ways. The official definition is a loss in which the starting pitcher made a quality start – that is, six or more innings with three or fewer runs. The Bill James definition is the same, except that James defines a quality start as having a game score of 50 or higher. In either case, tough losses result from solid pitching combined with anemic run support.
This year’s Tough Loss leaderboard had 457 games spread around 183 pitchers across both leagues. The Dodgers’ Hiroki Kuroda led the league with a whopping eight starts with game scores of 50 or more. He was followed by eight players with six tough losses, including Justin Verlander, Carl Pavano, Roy Oswalt, Rodrigo Lopez, Colby Lewis, Clayton Kershaw, Felix Hernandez, and Tommy Hanson. Kuroda’s Dodgers led the league with 23 tough losses, followed by the Mariners and the Cubs with 22 each.
There were fewer cheap wins, in which a pitcher does not make a quality start but does earn the win. The Cheap Win leaderboard had 248 games and 136 pitchers, led by John Lackey with six and Phil Hughes with 5. Hughes pitched to 18 wins, but Lackey’s six cheap wins were almost half of his 14-win total this year. That really shows what kind of run support he had. The Royals and the Red Sox were tied for first place with 15 team cheap wins each.
Finally, a vulture win is one for the relievers. I define a vulture win as a blown save and a win in the same game, so I searched Baseball Reference for players with blown saves and then looked for the largest number of wins. Tyler Clippard was the clear winner here. In six blown saves, he got 5 vulture wins. Francisco Rodriguez and Jeremy Affeldt each deserve credit, though – each had three blown saves and converted all three for vulture wins. (When I say “converted,” I mean “waited it out for their team to score more runs.”)
## Pitchers Hit This Year (or, Two Guys Named Buchholz)December 23, 2010
Posted by tomflesher in Baseball.
Tags: , , , , , , , , , , , , , , ,
Okay, I admit it. This post was originally conceived as a way to talk about the supremely weird line put up by Gustavo Chacin, who in his only plate appearance for Houston hit a home run to leave him with the maximum season OPS of 5.0. Unfortunately, Raphy at Baseball Reference beat me to it. Instead, I noticed while I was browsing the NL’s home run log to prepare to run some diagnostics on it that Kenley Jansen had two plate appearances comprising one hit and one walk. (Seriously, is there anything this kid can’t do?)
In Kenley’s case, that’s not entirely surprising, since he was a catcher until this season. His numbers weren’t great, but he was competent. What surprised me was that 75 pitchers since 2000 have finished the season with a perfect batting average. 9 were from this year, including Clay Buchholz and his distant cousing Taylor Buchholz. Evan Meek and Bruce Chen matched Jansen’s two plate appearances without an out. None of the perfect batting average crowd had an extra-base hit except for Chacin.
Since 2000, the most plate appearances by a pitcher to keep the perfect batting average was 4 by Manny Aybar in 2000.
At the other end of the spectrum, this year only three pitchers managed a perfect 1.000 on-base percentage without getting any hits at all. George Sherrill and Matt Reynolds both walked in their only plate appearances; Jack Taschner went them one better by recording a sacrifice hit in a second plate appearance.
Finally, to round things out, this year saw Joe Blanton and Heureusement, ici, c’est le Blog‘s favorite pitcher, Yovani Gallardo, each get hit by two pitches. Gallardo had clearly angered other pitchers by being so much more awesome than they were.
## Diagnosing the ALDecember 22, 2010
Posted by tomflesher in Baseball, Economics.
Tags: , , , , , ,
In the previous post, I crunched some numbers on a previous forecast I’d made and figured out that it was a pretty crappy forecast. (That’s the fun of forecasting, of course – sometimes you’re right and sometimes you’re wrong.) The funny part of it, though, is that the predicted home runs per game for the American League was so far off – 3.4 standard errors below the predicted value – that it’s highly unlikely that the regression model I used controls for all relevant variables. That’s not surprising, since it was only a time trend with a dummy variable for the designated hitter.
There are a couple of things to check for immediately. The first is the most common explanation thrown around when home runs drop – steroids. It seems to me that if the drop in home runs were due to better control of performance-enhancing drugs, then it should mostly be home runs that are affected. For example, intentional walks should probably be below expectation, since intentional walks are used to protect against a home run hitter. Unintentional walks should probably be about as expected, since walks are a function of plate discipline and pitcher control, not of strength. On-base percentage should probably drop at a lower magnitude than home runs, since some hits that would have been home runs will stay in the park as singles, doubles, or triples rather than all being fly-outs. There will be a drop but it won’t be as big. Finally, slugging average should drop because a loss in power without a corresponding increase in speed will lower total bases.
I’ll analyze these with pretty new R code behind the cut.
## What Happened to Home Runs This Year?December 22, 2010
Posted by tomflesher in Baseball, Economics.
Tags: , , , , , , , ,
1 comment so far
I was talking to Jim, the writer behind Apparently, I’m An Angels Fan, who’s gamely trying to learn baseball because he wants to be just like me. Jim wondered aloud how much the vaunted “Year of the Pitcher” has affected home run production. Sure enough, on checking the AL Batting Encyclopedia at Baseball-Reference.com, production dropped by about .15 home runs per game (from 1.13 to .97). Is that normal statistical variation or does it show that this year was really different?
In two previous posts, I looked at the trend of home runs per game to examine Stuff Keith Hernandez Says and then examined Japanese baseball’s data for evidence of structural break. I used the Batting Encyclopedia to run a time-series regression for a quadratic trend and added a dummy variable for the Designated Hitter. I found that the time trend and DH control account for approximately 56% of the variation in home runs per year, and that the functional form is
$\hat{HR} = .957 - .0188 \times t + .0004 \times t^2 + .0911 \times DH$
with t=1 in 1955, t=2 in 1956, and so on. That means t=56 in 2010. Consequently, we’d expect home run production per game in 2010 in the American League to be approximately
$\hat{HR} = .957 - .0188 \times 56 + .0004 \times 3136 + .0911 \approx 1.25$
That means we expected production to increase this year and it dropped precipitously, for a residual of -.28. The residual standard error on the original regression was .1092, so on 106 degrees of freedom, so the t-value using Texas A&M’s table is 1.984 (approximating using 100 df). That means we can be 95% confident that the actual number of home runs should fall within .1092*1.984, or about .2041, of the expected value. The lower bound would be about 1.05, meaning we’re still significantly below what we’d expect. In fact, the observed number is about 3.4 standard errors below the expected number. In other words, we’d expect that to happen by chance less than .1% (that is, less than one tenth of one percent) of the time.
Clearly, something else is in play.
## Home Run Derby: Does it ruin swings?December 15, 2010
Posted by tomflesher in Baseball, Economics.
Tags: , , , , , , , , , , ,
Earlier this year, there was a lot of discussion about the alleged home run derby curse. This post by Andy on Baseball-Reference.com asked if the Home Run Derby is bad for baseball, and this Hardball Times piece agrees with him that it is not. The standard explanation involves selection bias – sure, players tend to hit fewer home runs in the second half after they hit in the Derby, but that’s because the people who hit in the Derby get invited to do so because they had an abnormally high number of home runs in the first half.
Though this deserves a much more thorough macro-level treatment, let’s just take a look at the density of home runs in either half of the season for each player who participated in the Home Run Derby. Those players include David Ortiz, Hanley Ramirez, Chris Young, Nick Swisher, Corey Hart, Miguel Cabrera, Matt Holliday, and Vernon Wells.
For each player, plus Robinson Cano (who was of interest to Andy in the Baseball-Reference.com post), I took the percentage of games before the Derby and compared it with the percentage of home runs before the Derby. If the Ruined Swing theory holds, then we’d expect
$g(HR) \equiv HR_{before}/HR_{Season} > g(Games) \equiv Games_{before}/162$
The table below shows that in almost every case, including Cano (who did not participate), the density of home runs in the pre-Derby games was much higher than the post-Derby games.
Player HR Before HR Total g(Games) g(HR) Diff Ortiz 18 32 0.54321 0.5625 0.01929 Hanley 13 21 0.54321 0.619048 0.075838 Swisher 15 29 0.537037 0.517241 -0.0198 Wells 19 31 0.549383 0.612903 0.063521 Holliday 16 28 0.54321 0.571429 0.028219 Hart 21 31 0.549383 0.677419 0.128037 Cabrera 22 38 0.530864 0.578947 0.048083 Young 15 27 0.549383 0.555556 0.006173 Cano 16 29 0.537037 0.551724 0.014687
Is this evidence that the Derby causes home run percentages to drop off? Certainly not. There are some caveats:
• This should be normalized based on games the player played, instead of team games.
• It would probably even be better to look at a home run per plate appearance rate instead.
• It could stand to be corrected for deviation from the mean to explain selection bias.
• Cano’s numbers are almost identical to Swisher’s. They play for the same team. If there was an effect to be seen, it would probably show up here, and it doesn’t.
Once finals are up, I’ll dig into this a little more deeply.
## Quickie: Ryan Howard’s Choke IndexOctober 25, 2010
Posted by tomflesher in Baseball.
Tags: , , , , ,
1 comment so far
The Choke Index is alive and well.
Previous to 2010, Ryan Howard of the Philadelphia Phillies hit home runs in three consecutive postseasons. He managed 7 in his 140 plate appearances, averaging out to .05 home runs per plate appearance. Not too shabby. It’s a bit below his regular season rate of about .067, but there are a bunch of things that could account for that.
This year, Ryan made 38 plate appearances and hit a grand total of 0 home runs in the postseason. What’s the likelihood of that happening? I use the Choke Index (one minus the probability of hitting 0 home runs in a given number of plate appearances) to measure that. As always, the closer a player gets to 1, the more unlikely his homer-free streak is.
The binomial probability can be calculated using the formula
$f(k;n,p) = \Pr(K = k) = {n\choose k}p^k(1-p)^{n-k}$
Or, since we’re looking for the probability of an event NOT occurring,
$(1-p)^k$
or $.95^{38}= .142$
using his career postseason numbers. That means that Ryan Howard’s 2010 postseason Choke Index is .858. Pretty impressive!
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Can Someone help me with this?
2. Originally Posted by lilwayne
Can Someone help me with this?
If the half life is 3.3 days and you have m = 880 mg at t = 0 then you will obviously have 440 mg when t = 3.3 ....
3. Originally Posted by mr fantastic
If the half life is 3.3 days and you have m = 880 mg at t = 0 then you will obviously have 440 mg when t = 3.3 ....
yeah i know that but i dont get what to fill in the blanks..
4. $440 = 880e^{3.3k}$
solve for $k$ and finish the problem.
5. Originally Posted by skeeter
$440 = 880e^{3.3k}$
solve for $k$ and finish the problem.
yeah i ended up doing that and what i got was 1/2 and 3.3 for the first 2 blanks.
2 and 3.3 for the second 2 blanks.
880, 2 and 3.3 for the last 3 blanks.
but it was wrong, what did i do wrong?
6. Originally Posted by lilwayne
yeah i ended up doing that and what i got was 1/2 and 3.3 for the first 2 blanks.
2 and 3.3 for the second 2 blanks.
880, 2 and 3.3 for the last 3 blanks.
but it was wrong, what did i do wrong?
you forgot to divide the right side by 880 ...
$440 = 880e^{3.3k}$
divide both sides by 880 ...
$\displaystyle \frac{1}{2} = e^{3.3k}
$
continue ...
7. yeah i did that, then i did ln1/2 = lne^3.3k
which is ln1/2 = 3.3k
and i was told that ln(1/2) = -ln(2)
so i had k = -ln(2)/3.3
is that right so far?
8. Nvm got it.
9. Originally Posted by lilwayne
Nvm got it.
you're welcome.
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# If $G$ is a compact Lie group acting effectively on $X$ then it is a subspace of Homeo$(X)$?
Let $G$ be a compact Lie group acting effectively on a simply connected space $X$. Let Homeo$(X)$ be the group of all homeomorphisms of $X$ with itself given the compact open topology.
Is the topology on $G$ the same as the subspace topology it inherits from Homeo$(X)$? If not then is one topology finer than the other?
I'm not quite sure where to begin here. If I can somehow show that $G$ is closed in Homeo$(X)$ then I will be done. But I am unsure how to proceed (or even if it is true).
My ultimate goal is to see if $G$ is compact as a subspace of Homeo$(X)$. So even if I can show that the subspace topology on $G$ is contained in the topology of $G$ then it is enough (I'm not sure how to prove this either). However I was wondering if the two topologies are equal?
The two topologies agree if $X$ is locally compact and Hausdorff.
If $X$ is locally compact then by the proposition A.14 here we have that $G\hookrightarrow\operatorname{Homeo}(X)$ is continuous. Now since a continuous, injective map from a compact space to a Hausdorff space is a homeomorphism onto its image, we are done.
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# Apply the conditional Hamiltonian evolution (HHL)
I have a problem with the conditional Hamiltonian. In the original article on HHL (p.3) they wrote that applying the conditional Hamiltonian correspond to: $$\sum_{\tau=0}^{T-1}|\tau\rangle\langle\tau|\otimes e^{2i\pi A\frac{\tau}{T}}$$
Where $$T=2^t$$ the number of qubits in the clock register.
And I saw an implementation in this article (p.50), for a 2 qubits register they apply 2 gates $$e^{i\pi A}$$ and $$e^{i\pi A/2}$$.
What I don't understand, is that it doesn't correspond to the sum above which have 4 terms, but to this one (I change the index of the sum): $$\sum_{\tau=1}^{2^{t-1}}|\tau\rangle\langle\tau|\otimes e^{2i\pi A\frac{\tau}{2^t}}$$.
Did I miss something ?
• Could you say what page number it is in the review article? – AHusain Jul 19 '19 at 1:10
• @AHusain I added it. – lufydad Jul 19 '19 at 9:13
Be careful! They don't apply $$e^{i\pi A}$$ and $$e^{i\pi A/2}$$. They apply $$|0\rangle\langle 0|\otimes I\otimes I+|1\rangle\langle 1| \otimes I\otimes e^{i\pi A}$$ and $$I\otimes |0\rangle\langle 0|\otimes I+I\otimes |1\rangle\langle 1|\otimes e^{i\pi A/2},$$ i.e. controlled versions of the gates, controlled off two different qubits.
So, consider the 4 possible values of the first two registers: $$|00\rangle, |01\rangle, |10\rangle$$ and $$|11\rangle$$. On the third register, these give you respectively, $$I,e^{i\pi A/2},e^{i\pi A},e^{i3\pi A/2}$$, as required.
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# zbMATH — the first resource for mathematics
## Zhang, Xiangsun
Compute Distance To:
Author ID: zhang.xiangsun Published as: Zhang, X; Zhang, X.; Zhang, X. S.; Zhang, X.-S.; Zhang, Xiang-Sun; Zhang, Xiang-sun; Zhang, Xiangsun
Documents Indexed: 146 Publications since 1981, including 3 Books
all top 5
#### Co-Authors
7 single-authored 17 Zhang, Juliang 10 Wu, Lingyun 8 Li, Zhenping 7 Wang, Ruisheng 6 Chen, Luonan 6 Du, Ding-Zhu 4 Zhang, Jihong 4 Zhang, Shihua 3 Chen, Zhongwen 3 Liu, Degang 3 Qiu, Yuqing 3 Zhao, Yuying 3 Zhuo, Xinjian 2 Chen, Jian 2 Liu, Hongwei 2 Ren, Xianwen 2 Wang, Jiguang 2 Wang, Mingjie 2 Wang, Yong 2 Xu, Zongben 1 Chen, Jie 1 Chen, Zhiping 1 Deng, Naiyang 1 Jing, Zhujun 1 Li, Jinshan 1 Liao, Li-Zhi 1 Lu, Delin 1 Ning, Xuemei 1 Shen, Jie 1 Shi, Zhenjun 1 Su, Yongmei 1 Wang, Lin 1 Wang, Yiju 1 Wang, Yong 1 Wang, Yongcui 1 Wei, Quanling 1 Wu, Fangtao 1 Xiu, Naihua 1 Yan, Guiying 1 Zhan, Zhongwei 1 Zhang, Chunhua 1 Zhang, Jianzhong 1 Zhang, Junhua 1 Zhang, Liping 1 Zhang, Zhongyuan 1 Zhou, Wenfeng 1 Zhu, Hui-can
all top 5
#### Serials
10 Acta Mathematicae Applicatae Sinica. English Series 9 Journal of Systems Science and Complexity 7 Journal of Systems Science and Mathematical Sciences 4 Acta Mathematicae Applicatae Sinica 3 Journal of Global Optimization 2 Computers & Mathematics with Applications 2 Mathematica Applicata 2 Science in China. Series A 2 European Journal of Operational Research 2 Mathematical Programming. Series A. Series B 2 Computational Biology and Chemistry 1 Applied Mathematics and Computation 1 Applied Mathematics and Optimization 1 Information Sciences 1 Journal of Computational and Applied Mathematics 1 Mathematics and Computers in Simulation 1 Mathematical Programming 1 Advances in Mathematics 1 Journal of Computational Mathematics 1 Computers & Operations Research 1 Journal of Qufu Normal University. Natural Science 1 Annals of Operations Research 1 Systems Science and Mathematical Sciences 1 Computational Statistics and Data Analysis 1 Applied Mathematics. Series B (English Edition) 1 Journal of Combinatorial Optimization 1 RAIRO. Operations Research 1 Lecture Notes in Computer Science 1 Nonconvex Optimization and Its Applications 1 OR Transactions 1 Journal of Chongqing Normal University. Natural Science 1 Journal of Theoretical Biology
all top 5
#### Fields
52 Operations research, mathematical programming (90-XX) 18 Numerical analysis (65-XX) 10 Biology and other natural sciences (92-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 8 Computer science (68-XX) 5 Combinatorics (05-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 General and overarching topics; collections (00-XX) 2 Statistics (62-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Operator theory (47-XX) 1 Systems theory; control (93-XX)
#### Citations contained in zbMATH
80 Publications have been cited 441 times in 397 Documents Cited by Year
An adaptive trust region method and its convergence. Zbl 1105.90361
Zhang, Xiangsun; Zhang, Juliang; Liao, Lizhi
2002
Inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems. Zbl 1119.74334
Zhang, X.; Sharma, P.
2005
A nonmonotone adaptive trust region method and its convergence. Zbl 1065.90071
Zhang, Ju-Liang; Zhang, Xiang-Sun
2003
Nonlinear deformation and breakup of stretching liquid bridges. Zbl 0899.76133
Zhang, X.; Padgett, R. S.; Basaran, O. A.
1996
An inverse DEA model for inputs/outputs estimate. Zbl 0948.91019
Wei, Quanling; Zhang, Jianzhong; Zhang, Xiangsun
2000
A simulated annealing and hill-climbing algorithm for the traveling tournament problem. Zbl 1103.90042
Lim, A.; Rodrigues, B.; Zhang, X.
2006
Capacitated facility location problem with general setup cost. Zbl 1126.90042
Wu, Ling-Yun; Zhang, Xiang-Sun; Zhang, Ju-Liang
2006
An atomistic and non-classical continuum field theoretic perspective of elastic interactions between defects (force dipoles) of various symmetries and application to graphene. Zbl 1120.74315
Zhang, X.; Jiao, K.; Sharma, P.; Yakobson, B. I.
2006
Global stabilization of a class of time-delay nonlinear systems. Zbl 1121.93065
Zhang, X.; Cheng, Z.
2005
Global asymptotic stabilization of feedforward nonlinear systems with a delay in the input. Zbl 1120.93048
Zhang, X.; Gao, Hongyan; Zhang, C.
2006
A modified SQP method with nonmonotone linesearch technique. Zbl 1068.90616
Zhang, Ju-Liang; Zhang, Xiang-Sun
2001
A meshless, compositional approach to shape optimal design. Zbl 1173.74371
Zhang, X.; Rayasam, M.; Subbarayan, G.
2007
A smoothing Levenberg-Marquardt method for NCP. Zbl 1104.65061
Zhang, Ju-Liang; Zhang, Xiangsun
2006
Meshless Galerkin least-squares method. Zbl 1143.74390
Pan, X. F.; Zhang, X.; Lu, M. W.
2005
Neural networks in optimization. Zbl 1017.90109
Zhang, Xiang-Sun
2000
Haplotype assembly from aligned weighted SNP fragments. Zbl 1102.92031
Zhao, Yuying; Wu, Lingyun; Zhang, Jihong; Wang, Ruisheng; Zhang, Xiangsun
2005
A nonmonotone trust-region algorithm with nonmonotone penalty parameters for constrained optimization. Zbl 1059.65053
Chen, Zhongwen; Zhang, Xiangsun
2004
A robust SQP method for optimization with inequality constraints. Zbl 1034.65048
Zhang, Juliang; Zhang, Xiangsun
2003
Experimental NMR realization of a generalized quantum search algorithm. Zbl 0969.81513
Long, G. L.; Yan, H. Y.; Li, Y. S.; Tu, C. C.; Tao, J. X.; Chen, H. M.; Liu, M. L.; Zhang, X.; Luo, J.; Xiao, L.; Zeng, X. Z.
2001
A note on the continuity of solutions of parametric linear programs. Zbl 0704.90090
Zhang, Xiangsun; Liu, Degang
1990
A convergence theorem of Rosen’s gradient projection method. Zbl 0626.90077
Du, Dingzhu; Zhang, Xiangsun
1986
Global convergence of Rosen’s gradient projection method. Zbl 0683.90081
Du, Dingzhu; Zhang, Xiangsun
1989
Portfolio selection under DEA-based relative financial strength indicators: Case of US industries. Zbl 1153.90454
Edirisinghe, N. C. P.; Zhang, X.
2008
Scheduling sports competitions at multiple venues – revisited. Zbl 1137.90504
Lim, A.; Rodrigues, B.; Zhang, X.
2006
Modified fixed-point equations and related iterative methods for variational inequalities. Zbl 1057.49013
Xiu, Naihua; Wang, Yiju; Zhang, Xiangsun
2004
Bound-preserving high-order schemes. Zbl 1368.65149
Xu, Z.; Zhang, X.
2017
Unsteady simulations of the flow around a short surface-mounted cylinder. Zbl 1235.76085
Pattenden, R. J.; Bressloff, N. W.; Turnock, S. R.; Zhang, X.
2007
Global linear and quadratic one-step smoothing Newton method for $$P_0$$-LCP. Zbl 1046.90092
Zhang, Liping; Zhang, Xiangsun
2003
A SQP method for inequality constrained optimization. Zbl 1114.90480
Zhang, Juliang; Zhang, Xiangsun
2002
Coarse grain parallel finite element simulations for incompressible flows. Zbl 0923.76113
Grant, P. W.; Webster, M. F.; Zhang, X.
1998
Discussion on Polak’s algorithm of nonlinear programming. Zbl 0485.90077
Zhang, Xiangsun
1981
Improved coupling of finite element method with material point method based on a particle-to-surface contact algorithm. Zbl 1423.74870
Chen, Z. P.; Qiu, X. M.; Zhang, X.; Lian, Y. P.
2015
A mesh-grading material point method and its parallelization for problems with localized extreme deformation. Zbl 1423.74901
Lian, Y. P.; Yang, P. F.; Zhang, X.; Zhang, F.; Liu, Y.; Huang, P.
2015
A combinatorial model and algorithm for globally searching community structure in complex networks. Zbl 1245.90013
Zhang, Xiang-Sun; Li, Zhenping; Wang, Rui-Sheng; Wang, Yong
2012
3-D numerical analysis of natural convective liquid cooling of a $$3\times 3$$ heater array in rectangular enclosures. Zbl 0973.76610
Tou, S. K. W.; Tso, C. P.; Zhang, X.
1999
Some advances in the analysis of fluid flows. Zbl 0918.76035
Bathe, K. J.; Zhang, H.; Zhang, X.
1997
Mathematical analysis of some neural networks for solving linear and quadratic programming. Zbl 0856.90079
Zhang, Xiangsun
1996
A neural network model for quadratic programming with simple upper and lower bounds and its application to linear programming. Zbl 0953.90562
Zhang, Xiang-sun; Zhu, Hui-can
1994
On a new gradient projection method. Zbl 0727.90076
Du, Dingzhu; Zhang, Xiangsun
1989
Quasi-finite-time control for high-order nonlinear systems with mismatched disturbances via mapping filtered forwarding technique. Zbl 1358.93142
Zhang, X.; Huang, X. L.; Lu, H. Q.
2017
A coupled finite difference material point method and its application in explosion simulation. Zbl 1356.80062
Cui, X. X.; Zhang, X.; Zhou, X.; Liu, Y.; Zhang, F.
2014
Detecting community structure: from parsimony to weighted parsimony. Zbl 1208.91121
Zhang, Junhua; Qiu, Yuqing; Zhang, Xiang-Sun
2010
Input/output selection in DEA under expert information, with application to financial markets. Zbl 1206.91019
Edirisinghe, N. C. P.; Zhang, X.
2010
Convergence analysis of adaptive trust region methods. Zbl 1377.90090
Shi, Zhen-Jun; Zhang, Xiang-Sun; Shen, Jie
2007
An optimization approach to the reconstruction of positional DNA sequencing by hybridization with errors. Zbl 1128.90032
Zhang, Ji-Hong; Wu, Ling-Yun; Zhao, Yu-Ying; Zhang, Xiang-Sun
2007
Identification of functional modules in a PPI network by clique percolation clustering. Zbl 1112.92028
Zhang, Shihua; Ning, Xuemei; Zhang, Xiangsun
2006
Time accurate numerical study of turbulent supersonic jets. Zbl 1236.76048
Rona, A.; Zhang, X.
2004
On fractional $$(g,f)$$-deleted graphs. Zbl 1032.05113
Li, Zhenping; Yan, Guiying; Zhang, Xiangsun
2003
A trust-region and affine scaling algorithm for linearly constrained optimization. Zbl 1105.90354
Chen, Zhongwen; Zhang, Xiangsun
2002
Geometry effects on flow transition in multilouvered fins – onset, propagation, and characteristic frequencies. Zbl 1091.76508
Tafti, D. K.; Zhang, X.
2001
Classification and effects of thermal wakes on heat transfer in multilouvered fins. Zbl 0983.76500
Zhang, X.; Tafti, D. K.
2001
A smoothing approximation to the exact penalty function for optimization with inequality constraints. Zbl 0991.90124
Zhang, Juliang; Zhang, Xiangsun
2000
Test problem generator by neural network for algorithms that try solving nonlinear programming problems globally. Zbl 0962.90037
Liu, Degang; Zhang, Xiangsun
2000
On Rosen’s gradient projection methods. Zbl 0704.90081
Du, Dingzhu; Wu, F.; Zhang, Xiangsun
1990
On the convergence of Rosen’s gradient projection method. Zbl 0566.90077
Zhang, Xiangsun
1985
Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift. Zbl 07285692
Menozzi, S.; Pesce, A.; Zhang, X.
2021
Constructing likelihood functions for interval-valued random variables. Zbl 1444.62139
Zhang, X.; Beranger, B.; Sisson, S. A.
2020
On natural modes in moonpools and gaps in finite depth. Zbl 1419.76346
Molin, Bernard; Zhang, X.; Huang, H.; Remy, F.
2018
A delay-range-partition approach to analyse stability of linear systems with time-varying delays. Zbl 1346.93305
Xue, Y.; Zhang, X.; Han, Y. Y.; Shi, M.
2016
Dynamical Casimir-polder force in a cavity comprising a dielectric with output coupling. Zbl 1295.81123
Yang, H.; Zheng, T. Y.; Shao, X. Q.; Zhang, X.; Pan, S. M.
2013
Self-organizing map of complex networks for community detection. Zbl 1208.91119
Li, Zhenping; Wang, Ruisheng; Zhang, Xiang-Sun; Chen, Luonan
2010
Improved modification direction methods. Zbl 1198.94029
Kim, H. J.; Kim, C.; Choi, Y.; Wang, S.; Zhang, X.
2010
Equipment scheduling problem under disruptions in mail processing and distribution centres. Zbl 1171.90413
Zhang, X.; Chakravarthy, A.; Gu, Q.
2009
Self-organizing map approaches for the haplotype assembly problem. Zbl 1172.92016
Wu, Ling-Yun; Li, Zhenping; Wang, Rui-Sheng; Zhang, Xiang-Sun; Chen, Luonan
2009
Quantum dot-DNA interaction: Computational issues and preliminary insights on use of quantum dots as biosensors. Zbl 1162.92007
Anandampillai, S.; Zhang, X.; Sharma, P.; Lynch, Gillian C.; Franchek, M. A.; Larin, K. V.
2008
A trust region method for optimization problem with singular solutions. Zbl 1144.90020
Zhang, Juliang; Wu, Lingyun; Zhang, Xiangsun
2007
Superlinearly convergent trust-region method without the assumption of positive-definite Hessian. Zbl 1139.90032
Zhang, J. L.; Wang, Y.; Zhang, X. S.
2006
A dynamic programming algorithm for the $$k$$-haplotyping problem. Zbl 1130.90412
Li, Zhenping; Wu, Lingyun; Zhao, Yuying; Zhang, Xiangsun
2006
Impact of weak localization on wave dynamics: crossover from quasi-1D to slab geometry. Zbl 1092.81028
Zhang, Z. Q.; Cheung, S. K.; Zhang, X.; Chabanov, A. A.; Genack, A. Z.
2004
Predictor-corrector smoothing methods for monotone LCP. Zbl 1138.90486
Zhang, Juliang; Zhang, Xiangsun; Su, Yongmei
2004
Sequential penalty algorithm for nonlinear constrained optimization. Zbl 1061.90108
Zhang, J. L.; Zhang, X. S.
2003
An adaptive neural network model for nonlinear programming problems. Zbl 1022.90032
Zhang, Xiang-sun; Zhuo, Xin-jian; Jing, Zhu-jun
2002
An exact method for penny-shaped cracked homogeneous and composite cylinders. Zbl 1005.74056
Xie, Y. J.; Zhang, X.; Wang, X. H.
2001
An SQP method based on smoothing penalty function fo nonlinear optimization with inequality constraint. Zbl 1062.90521
Zhang, Juliang; Zhang, Xiangsun
2001
A SQP method for equality constrained optimization and its convergence. Zbl 0964.90054
Zhang, Juliang; Zhang, Xiangsun
2001
Trust region method in neural network. Zbl 0885.68127
Zhang, Xiangsun
1997
Nonlinear control of a planar multiaxis servohydraulic test facility using exact linearization techniques. Zbl 0829.70019
Hahn, H.; Zhang, X.; Leimbach, K.-D.; Sommer, H.-J.
1994
An appraisal of different stochastic linearization techniques. Zbl 0925.70298
Elishakoff, I.; Zhang, X.
1992
The solution of stress intensity factor for mode II cracking in orthotropic cracked plate by complex variable-variational method. Zbl 0731.73063
Cui, D.; Zhang, X.
1991
Discussion on the convergence of Rosen’s gradient projection method. Zbl 0624.65052
Zhang, Xiangsun
1987
Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift. Zbl 07285692
Menozzi, S.; Pesce, A.; Zhang, X.
2021
Constructing likelihood functions for interval-valued random variables. Zbl 1444.62139
Zhang, X.; Beranger, B.; Sisson, S. A.
2020
On natural modes in moonpools and gaps in finite depth. Zbl 1419.76346
Molin, Bernard; Zhang, X.; Huang, H.; Remy, F.
2018
Bound-preserving high-order schemes. Zbl 1368.65149
Xu, Z.; Zhang, X.
2017
Quasi-finite-time control for high-order nonlinear systems with mismatched disturbances via mapping filtered forwarding technique. Zbl 1358.93142
Zhang, X.; Huang, X. L.; Lu, H. Q.
2017
A delay-range-partition approach to analyse stability of linear systems with time-varying delays. Zbl 1346.93305
Xue, Y.; Zhang, X.; Han, Y. Y.; Shi, M.
2016
Improved coupling of finite element method with material point method based on a particle-to-surface contact algorithm. Zbl 1423.74870
Chen, Z. P.; Qiu, X. M.; Zhang, X.; Lian, Y. P.
2015
A mesh-grading material point method and its parallelization for problems with localized extreme deformation. Zbl 1423.74901
Lian, Y. P.; Yang, P. F.; Zhang, X.; Zhang, F.; Liu, Y.; Huang, P.
2015
A coupled finite difference material point method and its application in explosion simulation. Zbl 1356.80062
Cui, X. X.; Zhang, X.; Zhou, X.; Liu, Y.; Zhang, F.
2014
Dynamical Casimir-polder force in a cavity comprising a dielectric with output coupling. Zbl 1295.81123
Yang, H.; Zheng, T. Y.; Shao, X. Q.; Zhang, X.; Pan, S. M.
2013
A combinatorial model and algorithm for globally searching community structure in complex networks. Zbl 1245.90013
Zhang, Xiang-Sun; Li, Zhenping; Wang, Rui-Sheng; Wang, Yong
2012
Detecting community structure: from parsimony to weighted parsimony. Zbl 1208.91121
Zhang, Junhua; Qiu, Yuqing; Zhang, Xiang-Sun
2010
Input/output selection in DEA under expert information, with application to financial markets. Zbl 1206.91019
Edirisinghe, N. C. P.; Zhang, X.
2010
Self-organizing map of complex networks for community detection. Zbl 1208.91119
Li, Zhenping; Wang, Ruisheng; Zhang, Xiang-Sun; Chen, Luonan
2010
Improved modification direction methods. Zbl 1198.94029
Kim, H. J.; Kim, C.; Choi, Y.; Wang, S.; Zhang, X.
2010
Equipment scheduling problem under disruptions in mail processing and distribution centres. Zbl 1171.90413
Zhang, X.; Chakravarthy, A.; Gu, Q.
2009
Self-organizing map approaches for the haplotype assembly problem. Zbl 1172.92016
Wu, Ling-Yun; Li, Zhenping; Wang, Rui-Sheng; Zhang, Xiang-Sun; Chen, Luonan
2009
Portfolio selection under DEA-based relative financial strength indicators: Case of US industries. Zbl 1153.90454
Edirisinghe, N. C. P.; Zhang, X.
2008
Quantum dot-DNA interaction: Computational issues and preliminary insights on use of quantum dots as biosensors. Zbl 1162.92007
Anandampillai, S.; Zhang, X.; Sharma, P.; Lynch, Gillian C.; Franchek, M. A.; Larin, K. V.
2008
A meshless, compositional approach to shape optimal design. Zbl 1173.74371
Zhang, X.; Rayasam, M.; Subbarayan, G.
2007
Unsteady simulations of the flow around a short surface-mounted cylinder. Zbl 1235.76085
Pattenden, R. J.; Bressloff, N. W.; Turnock, S. R.; Zhang, X.
2007
Convergence analysis of adaptive trust region methods. Zbl 1377.90090
Shi, Zhen-Jun; Zhang, Xiang-Sun; Shen, Jie
2007
An optimization approach to the reconstruction of positional DNA sequencing by hybridization with errors. Zbl 1128.90032
Zhang, Ji-Hong; Wu, Ling-Yun; Zhao, Yu-Ying; Zhang, Xiang-Sun
2007
A trust region method for optimization problem with singular solutions. Zbl 1144.90020
Zhang, Juliang; Wu, Lingyun; Zhang, Xiangsun
2007
A simulated annealing and hill-climbing algorithm for the traveling tournament problem. Zbl 1103.90042
Lim, A.; Rodrigues, B.; Zhang, X.
2006
Capacitated facility location problem with general setup cost. Zbl 1126.90042
Wu, Ling-Yun; Zhang, Xiang-Sun; Zhang, Ju-Liang
2006
An atomistic and non-classical continuum field theoretic perspective of elastic interactions between defects (force dipoles) of various symmetries and application to graphene. Zbl 1120.74315
Zhang, X.; Jiao, K.; Sharma, P.; Yakobson, B. I.
2006
Global asymptotic stabilization of feedforward nonlinear systems with a delay in the input. Zbl 1120.93048
Zhang, X.; Gao, Hongyan; Zhang, C.
2006
A smoothing Levenberg-Marquardt method for NCP. Zbl 1104.65061
Zhang, Ju-Liang; Zhang, Xiangsun
2006
Scheduling sports competitions at multiple venues – revisited. Zbl 1137.90504
Lim, A.; Rodrigues, B.; Zhang, X.
2006
Identification of functional modules in a PPI network by clique percolation clustering. Zbl 1112.92028
Zhang, Shihua; Ning, Xuemei; Zhang, Xiangsun
2006
Superlinearly convergent trust-region method without the assumption of positive-definite Hessian. Zbl 1139.90032
Zhang, J. L.; Wang, Y.; Zhang, X. S.
2006
A dynamic programming algorithm for the $$k$$-haplotyping problem. Zbl 1130.90412
Li, Zhenping; Wu, Lingyun; Zhao, Yuying; Zhang, Xiangsun
2006
Inclusions and inhomogeneities in strain gradient elasticity with couple stresses and related problems. Zbl 1119.74334
Zhang, X.; Sharma, P.
2005
Global stabilization of a class of time-delay nonlinear systems. Zbl 1121.93065
Zhang, X.; Cheng, Z.
2005
Meshless Galerkin least-squares method. Zbl 1143.74390
Pan, X. F.; Zhang, X.; Lu, M. W.
2005
Haplotype assembly from aligned weighted SNP fragments. Zbl 1102.92031
Zhao, Yuying; Wu, Lingyun; Zhang, Jihong; Wang, Ruisheng; Zhang, Xiangsun
2005
A nonmonotone trust-region algorithm with nonmonotone penalty parameters for constrained optimization. Zbl 1059.65053
Chen, Zhongwen; Zhang, Xiangsun
2004
Modified fixed-point equations and related iterative methods for variational inequalities. Zbl 1057.49013
Xiu, Naihua; Wang, Yiju; Zhang, Xiangsun
2004
Time accurate numerical study of turbulent supersonic jets. Zbl 1236.76048
Rona, A.; Zhang, X.
2004
Impact of weak localization on wave dynamics: crossover from quasi-1D to slab geometry. Zbl 1092.81028
Zhang, Z. Q.; Cheung, S. K.; Zhang, X.; Chabanov, A. A.; Genack, A. Z.
2004
Predictor-corrector smoothing methods for monotone LCP. Zbl 1138.90486
Zhang, Juliang; Zhang, Xiangsun; Su, Yongmei
2004
A nonmonotone adaptive trust region method and its convergence. Zbl 1065.90071
Zhang, Ju-Liang; Zhang, Xiang-Sun
2003
A robust SQP method for optimization with inequality constraints. Zbl 1034.65048
Zhang, Juliang; Zhang, Xiangsun
2003
Global linear and quadratic one-step smoothing Newton method for $$P_0$$-LCP. Zbl 1046.90092
Zhang, Liping; Zhang, Xiangsun
2003
On fractional $$(g,f)$$-deleted graphs. Zbl 1032.05113
Li, Zhenping; Yan, Guiying; Zhang, Xiangsun
2003
Sequential penalty algorithm for nonlinear constrained optimization. Zbl 1061.90108
Zhang, J. L.; Zhang, X. S.
2003
An adaptive trust region method and its convergence. Zbl 1105.90361
Zhang, Xiangsun; Zhang, Juliang; Liao, Lizhi
2002
A SQP method for inequality constrained optimization. Zbl 1114.90480
Zhang, Juliang; Zhang, Xiangsun
2002
A trust-region and affine scaling algorithm for linearly constrained optimization. Zbl 1105.90354
Chen, Zhongwen; Zhang, Xiangsun
2002
An adaptive neural network model for nonlinear programming problems. Zbl 1022.90032
Zhang, Xiang-sun; Zhuo, Xin-jian; Jing, Zhu-jun
2002
A modified SQP method with nonmonotone linesearch technique. Zbl 1068.90616
Zhang, Ju-Liang; Zhang, Xiang-Sun
2001
Experimental NMR realization of a generalized quantum search algorithm. Zbl 0969.81513
Long, G. L.; Yan, H. Y.; Li, Y. S.; Tu, C. C.; Tao, J. X.; Chen, H. M.; Liu, M. L.; Zhang, X.; Luo, J.; Xiao, L.; Zeng, X. Z.
2001
Geometry effects on flow transition in multilouvered fins – onset, propagation, and characteristic frequencies. Zbl 1091.76508
Tafti, D. K.; Zhang, X.
2001
Classification and effects of thermal wakes on heat transfer in multilouvered fins. Zbl 0983.76500
Zhang, X.; Tafti, D. K.
2001
An exact method for penny-shaped cracked homogeneous and composite cylinders. Zbl 1005.74056
Xie, Y. J.; Zhang, X.; Wang, X. H.
2001
An SQP method based on smoothing penalty function fo nonlinear optimization with inequality constraint. Zbl 1062.90521
Zhang, Juliang; Zhang, Xiangsun
2001
A SQP method for equality constrained optimization and its convergence. Zbl 0964.90054
Zhang, Juliang; Zhang, Xiangsun
2001
An inverse DEA model for inputs/outputs estimate. Zbl 0948.91019
Wei, Quanling; Zhang, Jianzhong; Zhang, Xiangsun
2000
Neural networks in optimization. Zbl 1017.90109
Zhang, Xiang-Sun
2000
A smoothing approximation to the exact penalty function for optimization with inequality constraints. Zbl 0991.90124
Zhang, Juliang; Zhang, Xiangsun
2000
Test problem generator by neural network for algorithms that try solving nonlinear programming problems globally. Zbl 0962.90037
Liu, Degang; Zhang, Xiangsun
2000
3-D numerical analysis of natural convective liquid cooling of a $$3\times 3$$ heater array in rectangular enclosures. Zbl 0973.76610
Tou, S. K. W.; Tso, C. P.; Zhang, X.
1999
Coarse grain parallel finite element simulations for incompressible flows. Zbl 0923.76113
Grant, P. W.; Webster, M. F.; Zhang, X.
1998
Some advances in the analysis of fluid flows. Zbl 0918.76035
Bathe, K. J.; Zhang, H.; Zhang, X.
1997
Trust region method in neural network. Zbl 0885.68127
Zhang, Xiangsun
1997
Nonlinear deformation and breakup of stretching liquid bridges. Zbl 0899.76133
Zhang, X.; Padgett, R. S.; Basaran, O. A.
1996
Mathematical analysis of some neural networks for solving linear and quadratic programming. Zbl 0856.90079
Zhang, Xiangsun
1996
A neural network model for quadratic programming with simple upper and lower bounds and its application to linear programming. Zbl 0953.90562
Zhang, Xiang-sun; Zhu, Hui-can
1994
Nonlinear control of a planar multiaxis servohydraulic test facility using exact linearization techniques. Zbl 0829.70019
Hahn, H.; Zhang, X.; Leimbach, K.-D.; Sommer, H.-J.
1994
An appraisal of different stochastic linearization techniques. Zbl 0925.70298
Elishakoff, I.; Zhang, X.
1992
The solution of stress intensity factor for mode II cracking in orthotropic cracked plate by complex variable-variational method. Zbl 0731.73063
Cui, D.; Zhang, X.
1991
A note on the continuity of solutions of parametric linear programs. Zbl 0704.90090
Zhang, Xiangsun; Liu, Degang
1990
On Rosen’s gradient projection methods. Zbl 0704.90081
Du, Dingzhu; Wu, F.; Zhang, Xiangsun
1990
Global convergence of Rosen’s gradient projection method. Zbl 0683.90081
Du, Dingzhu; Zhang, Xiangsun
1989
On a new gradient projection method. Zbl 0727.90076
Du, Dingzhu; Zhang, Xiangsun
1989
Discussion on the convergence of Rosen’s gradient projection method. Zbl 0624.65052
Zhang, Xiangsun
1987
A convergence theorem of Rosen’s gradient projection method. Zbl 0626.90077
Du, Dingzhu; Zhang, Xiangsun
1986
On the convergence of Rosen’s gradient projection method. Zbl 0566.90077
Zhang, Xiangsun
1985
Discussion on Polak’s algorithm of nonlinear programming. Zbl 0485.90077
Zhang, Xiangsun
1981
all top 5
#### Cited by 812 Authors
11 Zhang, Xiangsun 8 Basaran, Osman A. 7 Kimiaei, Morteza 7 Zhang, Xianfu 6 Amini, Keyvan 6 Su, Ke 5 Jahanshahloo, Gholam Reza 5 Peyghami, Mohammad Reza 5 Shi, Zhenjun 5 Zhang, Kecun 4 Ahookhosh, Masoud 4 Du, Ding-Zhu 4 Lin, Shih-Wei 4 Liu, Qingrong 4 Pepe, Pierdomenico 4 Pu, Dingguo 4 Qu, Shaojian 4 Subbarayan, Ganesh 4 Tarzanagh, D. Ataee 4 Zhang, Juliang 3 Afraimovich, L. G. 3 Ambravaneswaran, Balasubramanian 3 Babaie-Kafaki, Saman 3 Choi, Ho-Lim 3 Cui, Zhaocheng 3 Delfani, M. R. 3 Esmaeili, Hamid 3 Hosseinzadeh Lotfi, Farhad 3 Kim, Hyun Jung 3 Ma, Changfeng 3 Ma, Huimin 3 Mo, Jiangtao 3 Razavyan, Shabnam 3 Rezaee, Saeed 3 Seo, Yu-Deok 3 Shoja, Naghi 3 Sun, Wenyu 3 Tohidi, Ghasem 3 Wang, Shouyang 3 Wei, Zengxin 3 Yang, Yueting 3 Youn, Sung-Kie 3 Yu, Haodong 3 Yu, Vincent F. 3 Yu, Zhensheng 3 Yuan, Gonglin 3 Zhang, Chenghui 3 Zhang, Jianzhong 3 Zhou, Qunyan 2 Augarde, Charles Edward 2 Baloch, A. 2 Baron, Luc 2 Benabdallah, Amel 2 Bhat, Pradeep P. 2 Boukas, El-Kébir 2 Charlton, Tim J. 2 Che, Jianren 2 Chen, Luonan 2 Chen, Xiandong 2 Cheung, Kevin K. H. 2 Chou, Shuo-Yan 2 Coombs, William M. 2 Cordeau, Jean-François 2 Cui, Jinchuan 2 de Sampaio, Raimundo J. B. 2 Dodds, Shawn 2 Echi, Nadhem 2 Espino, José L. 2 Fan, Bin 2 Foroughi, Ali Asghar 2 Fu, Jinhua 2 Ganghoffer, Jean-François 2 Gendron, Bernard 2 Guo, Jinhua 2 Han, Jiye 2 Huang, Juntao 2 Iesan, Dorin 2 Jena, Sanjay Dominik 2 Jin, Wenliang 2 Jing, Yuanwei 2 Kumar, Satish 2 Laverón-Simavilla, Ana 2 Li, Wenyu 2 Li, Zhenping 2 Lian, Yanping 2 Lim, Jong-Tae 2 Liu, Liang 2 Liu, Taowen 2 Liu, Zhenhong 2 Long, Guilu 2 Lu, Yunlong 2 Maranganti, R. 2 Maurice, Gérard 2 Meseguer, José 2 Mesgarani, Hamid 2 Pasquali, Matteo 2 Perić, Djordje 2 Qin, Xinqiang 2 Rahali, Yosra 2 Rasmussen, Rasmus V. ...and 712 more Authors
all top 5
#### Cited in 136 Serials
26 European Journal of Operational Research 22 Applied Mathematics and Computation 19 Computer Methods in Applied Mechanics and Engineering 18 Journal of Computational and Applied Mathematics 9 Computers & Operations Research 9 Computational Optimization and Applications 9 Physics of Fluids 8 Acta Mechanica 8 Computers & Mathematics with Applications 8 Acta Mathematicae Applicatae Sinica. English Series 8 European Journal of Mechanics. A. Solids 8 Journal of Systems Science and Complexity 8 Journal of Applied Mathematics and Computing 7 International Journal of Solids and Structures 7 Annals of Operations Research 7 Applied Mathematical Modelling 6 International Journal of Heat and Mass Transfer 6 Journal of Fluid Mechanics 6 Engineering Analysis with Boundary Elements 6 Optimization Letters 5 Journal of the Mechanics and Physics of Solids 5 Journal of Optimization Theory and Applications 4 Journal of Computational Physics 4 Automatica 4 Systems & Control Letters 4 Computational and Applied Mathematics 4 Mathematics and Mechanics of Solids 4 Quantum Information Processing 3 International Journal of Control 3 Optimization 3 Numerical Algorithms 3 Automation and Remote Control 3 International Journal of Robust and Nonlinear Control 3 Nonlinear Dynamics 3 Optimization Methods & Software 3 RAIRO. Operations Research 3 Discrete Optimization 3 International Journal of Systems Science. Principles and Applications of Systems and Integration 2 Computers and Fluids 2 International Journal of Engineering Science 2 International Journal of Systems Science 2 Journal of the Franklin Institute 2 Journal of Mathematical Analysis and Applications 2 International Journal for Numerical Methods in Engineering 2 Mathematics and Computers in Simulation 2 Numerical Functional Analysis and Optimization 2 Mathematical and Computer Modelling 2 Journal of Global Optimization 2 Journal of Elasticity 2 Journal of Non-Newtonian Fluid Mechanics 2 Mathematical Programming. Series A. Series B 2 Mathematical Problems in Engineering 2 Abstract and Applied Analysis 2 Soft Computing 2 European Journal of Mechanics. B. Fluids 2 Acta Mathematica Sinica. English Series 2 Journal of Applied Mathematics 2 Sādhanā 2 Journal of Theoretical Biology 2 Journal of the Operations Research Society of China 2 Journal of Mathematical Modelling and Algorithms in Operations Research 2 Journal of Optimization 1 Modern Physics Letters B 1 International Journal of Theoretical Physics 1 Information Processing Letters 1 Mathematical Methods in the Applied Sciences 1 Periodica Mathematica Hungarica 1 Reviews of Modern Physics 1 Ukrainian Mathematical Journal 1 Wave Motion 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematics of Computation 1 Shock Waves 1 Applied Mathematics and Optimization 1 Information Sciences 1 International Journal of Circuit Theory and Applications 1 Journal of Differential Equations 1 Kybernetika 1 Mathematical Programming 1 Meccanica 1 Opsearch 1 Pacific Journal of Mathematics 1 Proceedings of the Japan Academy. Series A 1 Theoretical Computer Science 1 Optimal Control Applications & Methods 1 Operations Research Letters 1 Bulletin of the Iranian Mathematical Society 1 Journal of Classification 1 Applied Numerical Mathematics 1 Computational Mechanics 1 Asia-Pacific Journal of Operational Research 1 Journal of Scientific Computing 1 Neural Networks 1 International Journal of Adaptive Control and Signal Processing 1 MSCS. Mathematical Structures in Computer Science 1 Applications of Mathematics 1 Annals of Physics 1 Communications in Statistics. Theory and Methods 1 Chinese Science Bulletin 1 Archive of Applied Mechanics ...and 36 more Serials
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#### Cited in 26 Fields
204 Operations research, mathematical programming (90-XX) 102 Numerical analysis (65-XX) 69 Mechanics of deformable solids (74-XX) 48 Fluid mechanics (76-XX) 42 Systems theory; control (93-XX) 19 Calculus of variations and optimal control; optimization (49-XX) 16 Computer science (68-XX) 15 Biology and other natural sciences (92-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 Classical thermodynamics, heat transfer (80-XX) 9 Combinatorics (05-XX) 9 Statistics (62-XX) 8 Partial differential equations (35-XX) 7 Quantum theory (81-XX) 6 Ordinary differential equations (34-XX) 4 Number theory (11-XX) 3 Mechanics of particles and systems (70-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Information and communication theory, circuits (94-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Operator theory (47-XX) 2 Convex and discrete geometry (52-XX) 2 Probability theory and stochastic processes (60-XX) 2 Geophysics (86-XX) 1 Optics, electromagnetic theory (78-XX) 1 Relativity and gravitational theory (83-XX)
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Coronal hard X-ray sources revisited
This paper reports on the re-analysis of solar flares in which the hard X-rays (HXRs) come predominantly from the corona rather than from the more usual chromospheric footpoints. All of the 26 previously analyzed event time intervals, over 13 flares, are re-examined for consistency with a flare model in which electrons are accelerated near the top of a magnetic loop that has a sufficiently high density to stop most of the electrons by Coulomb collisions before they can reach the footpoints. Of particular importance in the previous analysis was the finding that the length of the coronal HXR source increased with energy in the 20 – 30 keV range. However, after allowing for the possibility that footpoint emission at the higher energies affects the inferred length of the coronal HXR source, and using analysis techniques that suppress the possible influence of such footpoint emission, we conclude that there is no longer evidence that the length of the HXR coronal sources increase with increasing energy. In fact, for the 6 flares and 12 time intervals that satisfied our selection criteria, the loop lengths decreased on average by 1.0 +/- 0.2 arcsec between 20 and 30 keV, with a standard deviation of 3.5 arcsec. We find strong evidence that the peak of the coronal HXR source increases in altitude with increasing energy. For the thermal component of the emission, this is consistent with the standard CHSKP flare model in which magnetic reconnection in a coronal current sheet results in new hot loops being formed at progressively higher altitudes. The explanation for the nonthermal emission is not so clear.
Original Article: http://arxiv.org/abs/1809.04631
The coronal volume of energetic particles in solar flares as revealed by microwave imaging
The spectrum of gyrosynchrotron emission from solar flares generally peaks in the microwave range. Its optically-thin, high-frequency component, above the spectral peak, is often used for diagnostics of the nonthermal electrons and the magnetic field in the radio source. Under favorable conditions, its low-frequency counterpart brings additional, complementary information about these parameters as well as thermal plasma diagnostics, either through gyrosynchrotron self-absorption, free-free absorption by the thermal plasma, or the suppression of emission through the so-called Razin effect. However, their effects on the low-frequency spectrum are often masked by spatial nonuniformity. To disentangle the various contributions to low-frequency gyrosynchrotron emission, a combination of spectral and imaging data is needed. To this end, we have investigated Owens Valley Solar Array (OVSA) multi-frequency images for 26 solar bursts observed jointly with Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) during the first half of 2002. For each, we examined dynamic spectra, time- and frequency-synthesis maps, RHESSI images with overlaid OVSA contours, and a few representative single-frequency snapshot OVSA images. We focus on the frequency dependence of microwave source sizes derived from the OVSA images and their effect on the low-frequency microwave spectral slope. We succeed in categorizing 18 analyzed events into several groups. Four events demonstrate clear evidence of being dominated by gyrosynchrotron self-absorption, with an inferred brightness temperature of $\geq10^8$~K. The low-frequency spectra in the remaining events are affected to varying degree by Razin suppression. We find that many radio sources are rather large at low frequencies, which can have important implications for solar energetic particle production and escape.
Original Article: http://arxiv.org/abs/1809.04753
Evolution of the solar Ly-$\alpha$ line profile during the solar cycle. II. How accurate is the present radiation pressure paradigm for interstellar neutral H in the heliosphere?
Following the derivation of a more accurate model of the evolution of the solar Lyman-$\alpha$ line with the changing solar activity by Kowalska-leszczynska et al. 2018 (IKL18) than the formerly used model by Tarnopolski et al. 2009 (ST09), we investigate potential consequences that adoption of the resulting refined model of radiation pressure has for the model distribution of interstellar neutral (ISN) H in the inner heliosphere and on the interpretation of selected observations. We simulated the ISN H densities using the two alternative radiation pressure models and identical models of all other factors affecting the ISN H distribution. We found that during most of the solar cycle, the IKL18 model predicts larger densities of ISN H and PUIs than ST09 in the inner heliosphere, especially in the downwind hemisphere. However, the density of ISN H at the termination shock estimated by Bzowski et al. 2008 obtained using ST09 does not need revision, and the detection of ISN D by IBEX is supported. However, we point out the existence of a considerable absorption of a portion of the solar Lyman-$\alpha$ spectral flux inside the heliosphere. Therefore, the model of radiation pressure for ISN H is still likely needs revision, and hence the available models of ISN H are not self-consistent.
Original Article: http://arxiv.org/abs/1809.04929
Casting the Coronal Magnetic Field Reconstruction Tools in 3D Using MHD Bifrost Model
Quantifying coronal magnetic field remains a central problem in solar physics. Nowadays the coronal magnetic field is often modelled using nonlinear force-free field (NLFFF) reconstructions, whose accuracy has not yet been comprehensively assessed. Here we perform a detailed casting of the NLFFF reconstruction tools, such as pi-disambiguation, photospheric field preprocessing, and volume reconstruction methods using a 3D snapshot of the publicly available full-fledged radiative MHD model. Specifically, from the MHD model we know the magnetic field vector in the entire 3D domain, which enables us to perform "voxel-by-voxel" comparison of the restored and the true magnetic field in the 3D model volume. Our tests show that the available pi-disambiguation methods often fail at the quiet sun areas dominated by small-scale magnetic elements, while they work well at the AR photosphere and (even better) chromosphere. The preprocessing of the photospheric magnetic field, although does produce a more force-free boundary condition, also results in some effective elevation’ of the magnetic field components. This elevation’ height is different for the longitudinal and transverse components, which results in a systematic error in absolute heights in the reconstructed magnetic data cube. The extrapolations performed starting from actual AR photospheric magnetogram are free from this systematic error, while have other metrics comparable with those for extrapolations from the preprocessed magnetograms. This finding favors the use of extrapolations from the original photospheric magnetogram without preprocessing. Our tests further suggest that extrapolations from a force-free chromospheric boundary produce measurably better results, than those from the photospheric boundary.
Original Article: http://arxiv.org/abs/1703.06360
The dynamic chromosphere: pushing the boundaries of observations and models
Tiago M. D. Pereira
The interface between the bright solar surface and the million-degree corona continues to hold the key to many unsolved problems in solar physics. Advances in instrumentation now allow us to observe the dynamic structures of the solar chromosphere down to less than 0.1" with cadences of just a few seconds and in multiple polarisation states. Such observational progress has been matched by the ever-increasing sophistication of numerical models, which have become necessary to interpret the complex observations. With an emphasis on the quiet Sun, I will review recent progress in the observation and modelling of the chromosphere. Models have come a long way from 1D static atmospheres, but their predictions still fail to reproduce several key observed features. Nevertheless, they have given us invaluable insight into the physical processes that energise the atmosphere. With more physics being added to models, the gap between predictions and observations is narrowing. With the next generation of solar observatories just around the corner, the big question is: will they close the gap?
Original Article: http://arxiv.org/abs/1809.04077
Disparity among low first ionization potential elements
The elemental composition of the solar wind differs from the solar photospheric composition. Elements with low first ionization potential (FIP) appear enhanced compared to O in the solar wind relative to the respective photospheric abundances. This so-called FIP effect is different in the slow solar wind and the coronal hole wind. However, under the same plasma conditions, for elements with similar FIPs such as Mg, Si, and Fe, comparable enhancements are expected. We scrutinize the assumption that the FIP effect is always similar for different low FIP elements, namely Mg, Si, and Fe. We investigate the dependency of the FIP effect of low FIP elements on the O7+/O6+ charge state ratio depending on time and solar wind type. We order the observed FIP ratios with respect to the O7+/O6+ charge state ratio into bins and analyze separately the respective distributions of the FIP ratio of Mg, Si, and Fe for each O7+/O6+ charge state ratio bin. We observe that the FIP effect shows the same qualitative yearly behavior for Mg and Si, while Fe shows significant differences during the solar activity maximum and its declining phase. In each year, the FIP effect for Mg and Si always increases with increasing O7+/O6+ charge state ratio, but for high O7+/O6+ charge state ratios the FIP effect for Fe shows a qualitatively different behavior. During the years 2001-2006, instead of increasing with the O7+/O6+ charge state ratio, the Fe FIP ratio exhibits a broad peak. Also, the FIP distribution per O7+/O6+ charge state bin is significantly broader for Fe than for Mg and Si. These observations support the conclusion that the elemental fractionation is only partly determined by FIP. In particular, the qualitative difference behavior with increasing O7+/O6+ charge state ratio between Fe on the one hand and Mg and Si on the other hand is not yet well explained by models of fractionation.
Original Article: http://arxiv.org/abs/1809.04345
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Re: [HACKERS] On-disk bitmap index patch
On 7/26/06 11:50 PM, "Tom Lane" <[EMAIL PROTECTED]> wrote:
> "Jie Zhang" <[EMAIL PROTECTED]> writes:
>> On 7/26/06 10:14 PM, "Tom Lane" <[EMAIL PROTECTED]> wrote:
>>> ... A nonuniform distribution would probably mean that some
>>> of the bitmaps compress better-than-expected and others worse. I have
>>> no idea how to model that and guess what the overall result is ...
>
>> The paper "Optimizing Bitmap Indices With Efficient Compression" by Kesheng
>> Wu et al gave an approximate answer for this question. Assume that there are
>> c distinct values. Let the i-th value has a probability of p_i, the number
>> of rows r, and the word size w. then the total size of the compressed bitmap
>> index is about (N/(w-1))(c- \sum(1-p_i)^(2w-2) - \sum(p_i)^(2w-2)), where in
>> both \sum's, i is from 1 to c.
>
> Hm, but that's still begging the question no? It's still assuming that
> any one value is uniformly distributed. ISTM the cases that would break
> my simplistic calculation involve clustering of particular values, such
> that some areas of the bitmap are all-zero while other areas have lots
> of ones.
Yes, you are right -- each value is still uniformly distributed. But this
will be the worst case in terms of the size of a bitmap vector. As for how
to model the size of a bitmap vector for an non-uniformly distributed value,
that's a good question. I don't really know. But we do know the best case
and the worse case.
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heat transfer coefficient on air side = h A = 0. J/mol Enthalpy of vaporization 2257 J/g 40660 J/mol Specific heat of solid H 2 O (ice) The values given in this table are a compromise among the accepted averages from several top-selling general chemistry textbooks. 2 ∙𝐾 Heat Rate: 𝑞= ℎ𝐴. The thesis consists of three different parts comprising description of procedures for thermal design of LNG heat exchangers, description of a test facility for measurements of heat transfer and pressure drop in a coil-wound heat exchanger, and presentation of measured data and models for calculation of heat transfer and pressure drop. Double pipe heat exchanger 8. Unlike convection or conduction, where energy from gases, liquids, and solids is transferred by the molecules with or without their physical movement, radiation does not need any medium (molecules or atoms). Heat Transfer MCQ question is the important chapter for a Chemical Engineering and GATE students. Heat is a form of energy, but it is energy in transit. Electrical analogue4. the convection heat transfer coefficient for cross flow over a circular cylinder. K), A is the heat exchange area (m2), F is the correction factor for the deviation from cocurrent or countercurrent flow, dTavg is the. Our community brings together students, educators, and subject enthusiasts in an online study community. Propylene Glycol Based. 2020 00:57, MayFlowers. Conjugate heat transfer • “Conjugate heat transfer” refers to the ability to compute conduction of heat through solids, coupled with convective heat transfer in a fluid. When a catalyst is used the reaction proceeds faster because it lowers the amount of activation energy required, so more collisions will be successful. All of this occurs at the melting point of the substance. For a gas, the heat transfer is related to a change in temperature. 203 ratings • 16 reviews. Given the gas and the liquid are at a certain pressure, but the temperature of the gas and the liquid differ. This could be used for free convection between a fluid and a vertical plate, horizontal plate, inclined plate, horizontal cylinder, or sphere. When objects transfer heat, they cool down to a lower temperature unless the heat energy they lose is constantly replaced. Enter all the known values in their proper units and click solve to calculate the remaining values. Here are some of the ways that you will see Energy and Power represented: Modify the value in any box and see what happens. Q = m x c x ΔT = 100 x 4·2 x 20 = 8400 J. Heat Transfer The heat transfer equation contains both diffusion and convection components, and a source term: V(Cp I( T) = V*(KVT)+S where C, is the heat capacity of the flowing gas and K is the thermal conductivity of the material. 8 ft)-cube/kg is compressed reversibly according to the law PV RAISE TO POWER 1. Heat transfer through the process of conduction occurs in substances which are in direct contact with each other. The outlet temperature of the water is 36°C. For more details, we suggest you to read this article on Conduction Heat Transfer. Umang Goswami. If two objects having different temperatures are in contact, heat transfer starts between them. • Calculate the rotameter setting for the desired water-side flow rate; write in your lab notebook. Ray Sinnott, Gavin Towler, in Chemical Engineering Design (Sixth Edition), 2020. Laminar boundary layer flow For flow over the flat plate, the following correlation can be used for the estimation of local heat transfer coefficient The equation expresses the local values of the heat transfer coefficient. The equation for the overall heat transfer coefficient of a shell and tube heat exchanger is: 1/U = 1/hi + Rfi + Rfo + Rw + 1/ho Where U= overall heat transfer coefficient hi= inside convective. It consists of the pipe, insulation, a weather barrier and gaps between. Often determined with the aid of correlations and empirical relations, the heat transfer coefficient provides information about heat transfer between solids and fluids. m Total heat transfer area of the reactor = Area of cylinder + Area of torispherical dish. Temperature calculation inside the sample was performed using the macroscopic heat transfer balance. Pharma Engineering An Engineer's Choice. It was submitted to the Department of Aerospace. The author provides the reader with a very thorough account of the fundamental principles and their applications to engineering practice, including a. ΔT: Temperature change, in K. It depends on how much water you have, and to what temperature you want to raise it to. Measurements of Heat Transfer in Physical and Chemical Processes Using Computer-Interfaced Calorimetry Abbas Cliff Arami INTRODUCTION This unit is designed for students taking first year high school chemistry, but it also intends to improve students' knowledge in physics and mathematics. Chemical Engineering and Processing: Process Intensification 1984, 18 (3) , 157-169. Can object transfer heat between each other without even touching? How? 7. Phase Changes and Heat Transfer. 58pv where p is in KN/METERSQUARE and v is in meter-cube. Heat exchanger design and structure of heat transfer equipment varies a lot depending on the application where they are used and the heat transfer media involved. Steam systems are a part of almost every major industrial process today. It includes the internal energy, which is the energy required to create a system, and the amount of energy required to make room for. The equation equates the energy absorbed by ice and energy released by liquid water. Here are some of the ways that you will see Energy and Power represented: Modify the value in any box and see what happens. or W/m 2-K - S. We now define the local heat transfer about the chosen area by the general convection heat transfer equation:. In thermodynamics. ) Dimensionless Numbers for a Forced Convection Heat Transfer Coefficient Calculator. The calculator is generic and can be used for both metric and imperial units as long as the use of units is consistent. Therefore, the amount of heat in a substance depends on the mass of the object. When it's hot in my house and cold outside the the heat flow to the outside of my house Q will have a positive value, ie, heat flows from hot insides to cold outsides. Heat transfer by free convection7. Since the unit of the specific heat capacity of liquid water is given as 4. In thermodynamics we are only interested with the amount of heat transfer. 2020 00:57, MayFlowers. The FE chemical exam consists of 16 chemical engineering topics: mathematics, engineering probability & statistics, engineering sciences, computational tools, materials science, chemistry, fluid mechanics/dynamics, thermodynamics, material/energy balances, heat transfer, mass transfer and separation, chemical reaction engineering, process design and economics, process control, safety, health. Calculations of Heat Transfer Conservation of energy theorem is also applied to heat transfer. Theoretical Chemistry Thermophysical Properties of Air & Fluid Systems Viscosity, Gas Viscosity, Kinematic Viscosity, Liquid Viscosity, etc. But in engineering we extend the thermodynamics analysis through the study of modes of heat transfer and through the development of relations to calculate heat transfer rates. Theory and Calculation of Heat Transfer in Furnaces chemistry book Theory and Calculation of Heat Transfer in Furnaces chemistry book Written by : Yanguo Zhang Qinghai Li Hui Zhou Join Link Chemist FB Group Click Here to Download Want more chemistry e-books…. Overall Heat Transfer Co-efficient Calulation based on Trials. ? 📚📙📘Comment below which book you want ,we will try our best to give you for free. q = n × C n × ΔT. Like thermodynamic work, heat transfer is a process involving more than one system, not a property of any one system. The Heat Transfer Module contains features for modeling conjugate heat transfer and nonisothermal flow effects. CHE 370 - HEAT AND MASS TRANSFER (4 credits). Free Excel/VBA Spreadsheets for Heat Transfer the user is urged to verify the accuracy of these property functions before using them. Jan 23, 2019 by Paul Mueller Company Engineering Staff in Heat Transfer, Chemical Processing, Heat Exchangers 0 Comments Effective and efficient heat exchange is a crucial part of plating and anodizing processes whether you are in the automotive, industrial electronics, or construction industries. Heat transfer between gas fluidized beds of solid particles and the surfaces of immersed heat exchanger elements, part I. Carlson Heat Exchanger Fluid to Fluid Sizing Calculator. For example, the number of passes, number of baffles and baffle spacing etc. convention ASHRAE convention IIR convention. The temperature change will most likely differ in the two, even if the bodies are made of the same material (but are different size). Though chemical equations usually list only the matter components of a reaction, you can also consider heat energy as a reactant or product. We will be using Kantahl resistance heating wire. This formula will show you how to calculate the total heat transfer from a cooling coil. Heat Press Packages Bundle and save while getting everything you need to start heat pressing. The article, “Calculation of Forced Convection Heat Transfer Coefficients with Excel Spreadsheets,” provides information about correlations and Excel spreadsheets to calculate heat transfer coefficients for several forced convection heat transfer configurations. Heat Capacity The heat capacity of an object is the energy transfer by heating per unit tem-perature change. The calculator includes 3 tools in 1 application: Product comparison calculator – Make side-by-side comparisons of up to six fluids for physical and performance properties, and heat transfer coefficients. Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy between physical systems. I suggest attend at least two years of engineering. Heat transfer through plates instead of tubes offers many advantages. Calculation of individual heat transfer coefficient of the boiling liquid: The. Enter the value to convert from into the input box on the left. The reasoning is that energy and species equations are strongly impacted by user defined sources (i. % Volume Glycol % Weight Glycol. Calculations of Heat Transfer. NOTES: Heat energy is the sum of the kinetic energy of the particles of a substance, whereas temperature is the average kinetic energy of the particles of a substance. Calculate overall heat transfer inclusive convection ; k - thermal conductivity (W/(mK), Btu/(hr o F ft 2 /ft)). Pharma Engineering An Engineer's Choice. Standard convention is that the addition of heat to an object is positive. Graham is a leading designer and builder of vacuum and heat transfer equipment for process industries world-wide, Markets for vacuum technology are chemical, petrochemical, petroleum refining, electric power generating industries like cogeneration and geothermal plants. RE: Heat Transfer Coefficient Calculation georgeverghese (Chemical) 12 Jun 18 01:08 By definition, to get the total surface area of the tubes, L is the total tube length. It may also be necessary to define the stable operating region or acceptable reagent addition. This is a rearrangement of Q = U A ΔT. thermal conductivity - a measure of the ability of a material to transfer heat. g, in kmol/h), Hi is the specific enthalpy of stream i (kJ/kmol), U is the overall heat transfer coefficient (kJ/m2. Sublimation powder coating is also called Heat Transfer Powder Coating because of the process of heat transfer printing. Internal energy. Convective Heat Transfer Calculator. Electrical analogue 4. We service customers in the Process Industries, both locally and internationally. Heat is not a property of a system. A heat exchanger is a device used for the process of heat exchange between two fluids that are at different temperatures. X-ray Interactions with Matter. Chemistry 301. If you don't know the air velocity over your tank, select "1 foot/second". Heat transfer is a branch of engineering science which seeks to determine the rate of energy transfer between bodies as a result of temperature differences. This is the currently selected item. Heat can move, transfer, through material by conduction. Specific heat refers to the amount of heat required to raise unit mass of a substance's temperature by 1 degree. If you don't know the air velocity over your tank, select "1 foot/second". Chemistry, 09. The process of heat transfer between a surface and a fluid flowing in contact with it is called convective heat transfer. The form might be a moving mass, light, heat, an elevated mass, particular chemical combinations, or electricity in a wire. The Heat Load Exchanger And Steam Relationship. EU Glycol Calculator. Ramco Computer Supplies is your online source for Heat Transfer Paper,Inkjet Cartridges, Printer Ribbons, Typewriter Ribbons, Toner, Drums, OPC, Calculator Ribbons,time clock ribbons, InkJet Paper, security paper. Very easy to use and user friendly. Calculations of Heat Transfer Conservation of energy theorem is also applied to heat transfer. It is to be noted that the heat capacity at constant pressure must remain constant during the change of temperature. This Heat Transfer Calculator is intended to be used to approximate a heat transfer system and is not intended to provide engineering recommendations. This would include viscous effects and heat conduction/convection effects. The general equation for calculating heat energy to change a solid to a liquid is: Heat = Mass x Heat of Fusion Q = m Lf Calculate the heat necessary to change 10 g of ice(s) at 0°C to 10 g of water(l) at 0°C. Where T is temperature. The temperature change will most likely differ in the two, even if the bodies are made of the same material (but are different size). Maintenance burdens are reduced. International Association for the Properties of Water and Steam. Electrical analogue4. Heat transfer coefficient correlation for external flow. Achievements air compressor capacity air compressor online calculator air dryer calculation Boil-off gas Boiler centrifugal compressor Chemical Engineer Chemical engineering City gas Cooling tower design of shell and tube heat exchanger domestic wastewater energy audit energy audit in indonesia energy conservation energy management energy. Align or stagger the tubes with buttons. An understanding of the heat transfer efficiency is important for heat exchanger design optimization and their integration into larger systems. average air temperature inside the enclosure average enclosure internal wall surface temperature. The FE chemical exam consists of 16 chemical engineering topics: mathematics, engineering probability & statistics, engineering sciences, computational tools, materials science, chemistry, fluid mechanics/dynamics, thermodynamics, material/energy balances, heat transfer, mass transfer and separation, chemical reaction engineering, process design and economics, process control, safety, health. Overall Heat Transfer Co-Efficient Calculation. Determination of thermal conductivity2. It using to estimate the needed heat transfer area, based on an estimate of the overall heat transfer coefficient. A 50g sample of an unknown metal is heated with 800 joules. heat transfer coefficient on air side = h A = 0. A single tracer utilizing Thermon’s heat transfer compound has the equivalent performance of three. Though chemical equations usually list only the matter components of a reaction, you can also consider heat energy as a reactant or product. Our primary focus is to show you how Nickzom Calculator solves Logarithmic Mean Radius. Calculate overall heat transfer inclusive convection ; k - thermal conductivity (W/(mK), Btu/(hr o F ft 2 /ft)). Heat Exchanger Design And Transfer. The heat transfer area is determined from the overall heat transfer coefficient (U). From this perspective, it is. Electrical analogue4. Are solids better heat conductors than liquids or gases? Why / Why not? 6. Build Your Understanding - This is how to measure the specific heat capacity of a metal. In addition to providing heat-transfer coefficients, the. All chemical changes are accompanied by the absorption or release of heat. - enter two of the three shaded portions for Hot. $\begingroup$ You would have to treat the surroundings as a separate system and you would have to solve the transient partial differential momentum balance and heat transfer equations for the entire process for both the system and surroundings. The iterative heat exchanger design process requires an initial rough estimate in order to be able to calculate an initial estimate of the needed heat transfer area. Department of Chemical and Biomolecular Engineering. com Calculator. The rate at which energy is transferred is called power and the amount of energy that is usefully transferred is called efficiency. An overall heat transfer coefficient can be calculated for heat exchanger design using Excel spreadsheets that can be downloaded (U. Correct answers: 2 question: Which type of heat transfer does the situation below model? Several dominoes are standing close together on edge. Calculation of time to heat or cool a fixed amount of liquid inside a batch reactor usually assume the process and utility heat capacity and the overall heat transfer coefficient to be constant throughout the calculations. The model is written in the state space and uses some dimensionless values, including a "heat transfer coefficient" β. value is correct. The above 3 formulas are used for solving problems involving energy calculations. conductivity 'k' of steel = 60 W/mK (at given temperature range) Overall heat transfer coefficient for a heat exchanger is a proportionality constant used to calculate overall heat transfer rate between two bodies, arising from the temperature difference between those two bodies. 67 should be in the numerator or denominator. 67 suggests to me that this is a calculation in Imperial / US Customary units. This can occur in heat exchangers, boilers, condensers, evaporators, and a host of other process. LMTD Correction Factor Charts Calculate Log Mean Temperature. This allows choice of a preliminary heat exchanger. In the analysis of a heat transfer system, as in all engineering systems, our first step should be to write out the appropriate balance equations. Phase Changes and Heat Transfer. the flowrate of the hot stream, the heat transfer rate ; and the heat transfer area. Equations for laminar [1] and turbulent [2] flow are combined to form a single equation that is suitable for calculating the convection coefficient for laminar, transition to turbulent and turbulent flows through the heat sink. Convection is usually the dominant form of heat transfer in liquids and gases. Conductive Heat Transfer Calculator. The convective heat transfer coefficient for the air is 18 Btu/hr-ft 2 - o F. Calculating internal energy and work example. ΔT: Temperature change, in K. Heat Transfer MCQ question is the important chapter for a Chemical Engineering and GATE students. It consists of the pipe, insulation, a weather barrier and gaps between. Finned tube heat exchanger9. Energy changes in chemical reactions. h in is heat transfer coefficient for fluid flowing in pipe and h air is heat transfer coefficient due to air. In many engineering applications involving conjugate heat transfer, such as designing heat exchangers and heat sinks, it's important to calculate the heat transfer coefficient. Heat duty calculator is a free software to help with computing the sensible heat duty and the latent heat transfer rate, the calculator uses the equations stated in website. Select the unit to convert to in the output units list. Ethylene Glycol Based. Boiling Heat Transfer (3) Condensation (5) Convection (2) Heat Transfer Coefficients (2) Heat Transfer Correlations (8) Mass Transfer (26) Diffusion (5) Mass Transfer Coefficients (9) Physical Chemistry (6). Thanks for contributing an answer to Chemistry Stack Exchange! Please be sure to answer the question. The process of heat transfer between a surface and a fluid flowing in contact with it is called convective heat transfer. Our extremely versatile heat transfer surface can change the temperature of any volume or type of liquid you need - quickly. This equation can be rearranged to calculate the amount of heat energy gained or lost by a substance given its molar heat capacity (C n), the amount of the substance in moles (n), and the temperature change (ΔT):. Copper’s accepted. Thermon Heat Transfer Compounds (cement) provide an efficient thermal connection between the tracer and the process equipment. The rate of flow of oil is 1 kg/s. Learn heat transfer chemistry with free interactive flashcards. This definition may be used to calculate the entropy of a system at a temperature T 2 from a knowledge of its entropy at a temperature T 1 and the heat supplied to change the temperature from T 1 to T 2: If we consider the situation where the system is subjected to a constant pressure. Types of Baffles. (Use $$\displaystyle c_p$$ and assume it is constant over the temperature range. The heat transfer coefficient has the SI units W/(m 2 K) and is calculated in the following way:. The enthalpy of freezing for benzene is 127J/g. The concluding chapter covers an application where each of these processes is occurring simultaneously - water cooling and humidification. The overall heat transfer of heat exchangers is the ability of transferring heat through different resistances, It depends upon, the properties of the process fluids, temperatures, flow rates and geometrical arrangement of the heat exchanger. 8 kJ Calculate the amount of heat transferred when 27. Evaluated heat transfer-related plant issues including heat losses, accuracy of temperature measurements, tracing systems. The principles of heat and mass transfer in chemical engineering systems are covered. H i = A x V x 0. If the temperature of the. The LMDT is the logarithmic average of the temperature differences at each end of the heat exchanger. 6703 x 10-8 (W/m 2 K 4)] T Hot = Higher temperature [o C] T Cold = Cold temperature [o C] A = Cross sectional area [m 2] Enter the given values in the below online radiation heat transfer calculator and click. It utilizes laboratory. Engineering Connection. Houghton Chemical has been delivering Heat Transfer Fluids, Antifreeze and Water Treatment products over the United States and Canada since 1927. We now introduce two concepts useful in describing heat flow and temperature change. Radiation is transfer of heat through electromagnetic waves through space. Tell the energy story for real-life systems. Heat Transfer (Q = m * C * dT) Equation Solver Solve for any variable (Q, m, C, dT) in the Heat Transfer equation (Q = m * C * dT). To calculate heat rate deviation cost, it is important to understand that several factors need to be known and understood. Heat transfer can also cause a change in the state of matter. 5 Heat Exchangers The general function of a heat exchanger is to transfer heat from one fluid to another. Specific heat of a substance of unit mass is the amount of heat that is needed to raise it's temperature by 1 o C (or 1K). We get the same answer with more effort by saying it is 353 - 293 = 60 K. , chemical reaction rates). The value of the constant is different for different materials. We are a distributor of the following products:. 6 of volume fraction)? It is also saturated liquid and vapour in gas cylinder. Enthalpy and Gibbs Free Energy Calculator Introduction : the purpose of this calculator is to calculate the value of the enthalphy of a reaction (delta H) or the Gibbs free energy of a reaction (delta G). Through facilitated deliberation, students will design the procedure for conducting the lab and data collection. Transfer of heat is occurred without any material medium or through a perfect vacuum. A heat exchanger transfers thermal energy from a hot-flowing substance to a cold-flowing substance. Evaporate the water C. The software can accept input in SI kg/s, kg/h, kg/day, lb/s, lb/h, lb/day The output heat rate (Duty) is calculated in kW, Btu/h, hp. Heat transfer compounds are used where high temperature maintenance or high exposure temperatures are prevalent. Thermodynamics is defined as the branch of science that deals with the relationship between heat and other forms of energy, such as work. Department of Chemical and Biomolecular Engineering. On the basis of size, cost requirement and ability to support tube bundle are categorized as : Longitudinal Flow Baffles : Mainly used in two shell pass heat exchanger. In addition to providing heat-transfer coefficients, the. Turbulent flow at low velocity produces high heat transfer efficiency and low fouling. com sales. Lienhard IV and John H. The blue. The spreadsheet will calculate initial values of the heat transfer coefficients, the rate of heat transfer across both fluids, and the length of the heat exchanger. Overall heat transfer coefficient of an insulated pipe is defined as following. The Heat Sink Calculator uses a combination of semi-empirically derived equations to calculate the heat transfer and pressure drop due to forced convection. Mechanics). Heat Exchangers. This book contains experiments in Heat Transfer(under graduate Chemical Engineering)1. conductivity 'k' of steel = 60 W/mK (at given temperature range) Overall heat transfer coefficient for a heat exchanger is a proportionality constant used to calculate overall heat transfer rate between two bodies, arising from the temperature difference between those two bodies. Simply put, heat is a form of kinetic energy due to molecular vibration. Some of the worksheets for this concept are Work methods of heat transfer conduction, Name date class measuring heat transfer work answers, Work methods of heat transfer conduction, Thermal energy temperature and heat work, Lesson 5 conduction convection radiation, Heat transfer conduction convection and. LMTD Correction Factor Charts Calculate Log Mean Temperature. This article titled 'How to calculate the heat duty'. of the liquid in the calorimeter. Insulation thickness3. Calculation with Heat Transfer with Examples. The source of this temperature difference is called the heat capacity ( C) of the material. The outlet temperature of the water is 36°C. HEAT TRANSFER EQUATION SHEET Heat Conduction Rate Equations (Fourier's Law) is the conversion of internal energy (chemical, nuclear, electrical) to thermal or mechanical energy, and. It is frequently summarized as three laws that describe restrictions on how different forms of energy can be interconverted. Tell the energy story for real-life systems. Shankar Subramanian. In many engineering applications involving conjugate heat transfer, such as designing heat exchangers and heat sinks, it's important to calculate the heat transfer coefficient. Some Related Articles. Radiation Radiation is the transfer of heat through space or matter by means other than conduction or convection. Lienhard IV and John H. Forced Convection:- Heat transfer is caused by use of external means of agency ; 3. Flat Plate Heat Transfer Convected Equation And Calculator. The thesis consists of three different parts comprising description of procedures for thermal design of LNG heat exchangers, description of a test facility for measurements of heat transfer and pressure drop in a coil-wound heat exchanger, and presentation of measured data and models for calculation of heat transfer and pressure drop. I Chemical Engineer-Heat Transfer Library Home. As the substance gets heated, the molecules move apart and the substance becomes less dense than the liquid in the lamp. Where U - overall heat transfer coeff 1/U = 1/hi + 1/ho + R. Enter all the known values in their proper units and click solve to calculate the remaining values. Very easy to use and user friendly. In the analysis of heat exchangers, it is often convenient to work with an overall heat transfer coefficient, known as a U-factor. Thanks a lot Heat Transfer Coefficient. Our community brings together students, educators, and subject enthusiasts in an online study community. Heat Exchangers. In the limit for any temperature difference ∆T across a length ∆x as both L, T A - T B → 0, we can say dx dT kA L T T. Using the Heat Transfer Coefficient Converter Converter. Unsteady state heat transfer5. For example, the number of passes, number of baffles and baffle spacing etc. However, the developer accepts no responsibility for the accuracy, use of or calculation results derived from herein. • The student will explain specific heat and describe how it differs from substance to substance. As we know heat is a kinetic energy parameter, included by the particles in the given system. Download Link: Heat Transfer (A Practical Approach) by Yunus A. Efforts have been made to confirm the accurracy of all calculations. The amount of heat given is equal to the amount of heat taken. The right heat transfer can make a huge impact on the efficiency and sustainability of your processes. Determining the value for the heat transfer coefficient is the major part of convective heat transfer calculations. 0 h and sleep for the other 8. Heat transfer methods finds a variety of applications in the chemical process This application will allow the user to calculate the time it takes to heat up and then cool a batch vessel or tank. Heat transfer in fluids generally takes place via convection. States of matter. The heat loss can be calculated from the equation Q= UA o (T s? T a), where Q is heat loss, U is overall heat-transfer coefficient, A o is area of the outside surface of the insulation (= 2 ?. First, heat transfer causes a difference in temperature when heat flows from one body to another. Heat tracing may be used in place of jacketed equipment, often at lower cost and with lowered risk of cross-contact. Both laminar and turbulent flow are supported and can be modeled with natural and forced convection. #N#Overview of sim controls, model simplifications, and insights into student thinking ( PDF ). Mineral oil is filled in between the narrow gap of 2 horizontal smooth plates which are maintained at constant temperature. Thermo; FAQs; Links. Heat is a type of energy transfer that is caused by a temperature difference, and it can change the temperature of an object. Weight and footprint are smaller. Heat "flows" from high to low temperature. Our community brings together students, educators, and subject enthusiasts in an online study community. The increase in rate would break intermolecular forces and cause the solid to change phase into a liquid, where the. Heat is always transferred from the object at the higher temperature to the object with the lower temperature. Engineering Connection. Heat Transfer: Chemical Engineering. Pipe Heat Loss; Packed Bed Flow; Gas Orifice Meter; Vapor Control Valve. Given the gas and the liquid are at a certain pressure, but the temperature of the gas and the liquid differ. Heat transfer in rubber is likely to be significant from the first processing steps to the end use of the product. The venue of the Workshop is the Terrace Hall, West End Hotel, 45 New Marine Lines, Near Bombay Hospital, Mumbai - 400 020. Radiation Heat Transfer. The rate of heat transfer depends on the following: ΔQΔt ∝ A(T1-T2)x. Overall Heat Transfer Co-efficient Calulation based on Trials. Abdallah Samad,. In the analysis of heat exchangers, it is often convenient to work with an overall heat transfer coefficient, known as a U-factor. sic physical and chemical laws represented below as conservation equations. HEAT TRANSFER Mechanisms of Heat Transfer: (1) Conduction where Q is the amount of heat, Btu, transferred in time t, h k is the thermal conductivity, Btu/[h ft2 (oF/ft)] A is the area of heat transfer normal to heat flow, ft2 T is the temperature, oF x is the thickness of the conduction path, ft. The model is written in the state space and uses some dimensionless values, including a "heat transfer coefficient" β. Fluid Mechanics Heat Transfer and Mass Transfer Chemical Engineering by K. The temperature profile should satisfy. Typically live steam is introduced to the jacket on the vessel to heat the vessel. The aligned configuration has flow lanes for the air whereas the staggered configuration disrupts these flow lanes. Since heat transfer is impacted by the reaction mass, the heat removal system, and the reactor design, the overall heat transfer coefficient [U] consists of three individual resistances: the reactor film [hr], the reactor wall [dw/λ] and the process-side film. Chemical reactions transform both matter and energy. Objective Experimentally determine the amount of heat transferred from an aluminum block Determine the convective heat transfer coefficient Select a piece of aluminum Heat to 55°C Remove from oven Place on three points to minimize conduction Take temperature readings every 300 seconds Calculate the heat transfer coefficient from data Radiation. When scaling a stirred tank reactor from lab to plant, heat transfer is critical. Characteristic thickness of stationary fluid layer for estimating heat transfer coeffients 95 17. Clarkson University. Heat Sink Performance Calculation : in the last few columns, i described methods to calculate pressure drop and heat transfer in rectangular channels, as well as spreading resistance. Heat Capacity, Speciflc Heat, and Enthalpy Stephen R. Chemistry 301. The use of liquids reduces many of the costs associated with pressurized steam-handling systems and simplifies operation. Lecture 2 Play Video: Introduction to Heat Transfer - Potato Example An experiment is discussed with a student to demonstrate the main concepts of heat transfer. The reasoning is that energy and species equations are strongly impacted by user defined sources (i. This equation was first developed and solved by Joseph Fourier in 1822. Calculate free convection by entering surface area, heat transfer coefficient and surface and fluid temperatures. It falls onto the next one, which falls onto its neighbor, and so on. Our engineering process equipment team is committed to providing precise heat transfer calculations to maximize your process and minimize waste. Thermal conductivities of air and water 94 16. The heat capacity is a constant that tells how much heat is added per unit temperature rise. This definition may be used to calculate the entropy of a system at a temperature T 2 from a knowledge of its entropy at a temperature T 1 and the heat supplied to change the temperature from T 1 to T 2: If we consider the situation where the system is subjected to a constant pressure. However, the transfer of energy as heat occurs at the. 5 gram piece of ice at 0oC is placed into a styrofoam cup with 119. #N#Overview of sim controls, model simplifications, and insights into student thinking ( PDF ). Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy between physical systems. Mathematically specific heat is simply the ratio of the heat with the product of the temperature change and the mass of the substance. Shell and Tube Heat Exchanger Design software (S&THex). Heat exchangers are commonly used in industry, and proper design of a heat exchanger depends on many variables. Correct answers: 2 question: Which type of heat transfer does the situation below model? Several dominoes are standing close together on edge. Overall Heat Transfer Co-efficient Calulation based on Trials. Heat Exchanger Rating (Bell Delaware) Heat Exchanger Analysis (ε - NTU) Double Pipe Heat Exchanger Air Cooled Heat Exchanger Sizing Shortcut Heat Exchanger Sizing. Heat transfer takes place from one molecule to another molecule as a result of the vibratory motion of the molecules. The heat transfer coefficient is the calculated amount of heat that passes between the thermal fluid to or from any given surface it comes in contact with by way of convection - with the driving force behind the transfer of heat being the temperature differential between the two. The model is written in the state space and uses some dimensionless values, including a "heat transfer coefficient" β. The extensive use of heat transfer has spurred a wide variety of types of heat exchangers and a broad choice of heat transfer fluids. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. This low specific heat capacity indicates that copper is a good conductor of heat. Enthalphy Calculation. This would include viscous effects and heat conduction/convection effects. Evaluated heat transfer-related plant issues including heat losses, accuracy of temperature measurements, tracing systems. Thanks for contributing an answer to Chemistry Stack Exchange! Please be sure to answer the question. emissive power: 𝐸. There are various sections of heat transfer but for the purpose of this post. Above equations have been programmed by Ankur , a experience Chemical Engineer, share with readers of Chemical and Process Technology. When it's hot in my house and cold outside the the heat flow to the outside of my house Q will have a positive value, ie, heat flows from hot insides to cold outsides. Enthalpy and Gibbs Free Energy Calculator Introduction : the purpose of this calculator is to calculate the value of the enthalphy of a reaction (delta H) or the Gibbs free energy of a reaction (delta G). Double pipe heat exchanger8. Formula to calculate heat transfer is given by: where, Q = Heat Transfer [joules] m = Mass [kg] c = Specific Heat [kj/kg K] ΔT = Temperature difference [k]. Unsteady state heat transfer. $\begingroup$ You would have to treat the surroundings as a separate system and you would have to solve the transient partial differential momentum balance and heat transfer equations for the entire process for both the system and surroundings. a high thermal conductivity) the potato is not heating up uniformly. s, Check followed table for common material Thermal Conductivity Constant. By eliminating the air voids, heat is directed into the pipe or tank wall through conduction rather than convection. Chilling water problem. Ramco Computer Supplies is your online source for Heat Transfer Paper,Inkjet Cartridges, Printer Ribbons, Typewriter Ribbons, Toner, Drums, OPC, Calculator Ribbons,time clock ribbons, InkJet Paper, security paper. Clarkson University. It generally takes place in solids. Teacher-Submitted Activities. This definition may be used to calculate the entropy of a system at a temperature T 2 from a knowledge of its entropy at a temperature T 1 and the heat supplied to change the temperature from T 1 to T 2: If we consider the situation where the system is subjected to a constant pressure. Although often discussed as a distinct method of heat transfer, convective heat transfer involves the combined processes of conduction (heat diffusion) and advection (heat. We constructed a unit plan using AACT resources that is designed to teach the Phase Changes and Heat Transfer to your students. Heating and cooling are essential in many unit operations, to bring materials to an appropriate temperature for processing or subsequent handling. Lab instructors: Dr. A single tracer utilizing Thermon’s heat transfer compound has the equivalent performance of three. Learn heat transfer chemistry with free interactive flashcards. Heat Transfer Operations 1 - Dec 2015. Heat Transfer in a System Heat, q: Transfer of energy due to temperature difference Exothermic Reaction: System gives off heat (Exiting) Ex: Methane Burning: CH 4 + O 2 → CO 2 + H 2O Bonds stronger in CO 2 and H 2O molecules than in CH 4 + O 2 Heat goes from system to surroundings Endothermic Reaction: System gains heat (Entering) Ex: Ice. However, the transfer of energy as heat occurs at the molecular level as a result of. Problem 300 grams of ethanol at 10 °C is heated with 14640 Joules of energy. Fill in the following and click on the Calculate button Heat transferred is BTU per hour from side to side. where, k PIPE , k INSULATION are thermal conductivity of pipe and insulation. North America : +1 312 9405070 Europe : +44 12 120 03453 Asia Pacific : +65 23 121 89102. ΔT: Temperature change, in K. All of this occurs at the melting point of the substance. help with chemistry heat transfer question? how much will the temperature of a cup (130 g) of water at 87 degrees celsius be reduced when a 34-g silver spoon (with a specific heat of 0. 0 Inhibitors & Water 4. Fundamentals; 1. So if your object gains heat (gets hotter), then q is positive. This equation was first developed and solved by Joseph Fourier in 1822. Specific heat refers to the amount of heat required to raise unit mass of a substance's temperature by 1 degree. Applications include HVAC, Refrigeration, Food, Beverage, Pharma & Chemical Processing. It using to estimate the needed heat transfer area, based on an estimate of the overall heat transfer coefficient. Excel calculator for LMTD LMTD, Log mean temperature difference is the temperature driving force for heat transfer in flow systems. Cengel Download Link: Heat Transfer by Jack P. However, the “front end” is solely the responsibility of the user. R Sekulib University of Kentucky INTRODUCTION A heat exchanger is a device that is used for transfer of thermal energy (enthalpy) between two or more fluids, between a solid surface and a fluid, or between solid particulates and a. Example: Calculation of Heat Exchanger. CHAPTER 17 HEAT EXCHANGERS R. Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy between physical systems. It features the following equipment: a shell and tube heat exchanger, a plate heat exchanger, a double pipe heat exchanger, a jacketed vessel heat exchanger, a thermal conductivity measuring apparatus for solids, a. Insulation thickness3. Problem 300 grams of ethanol at 10 °C is heated with 14640 Joules of energy. Calculate the heat transfer when 1. Temperature is a measure of the average kinetic energy of the particles in a substance. Heat transfer methods finds a variety of applications in the chemical process This application will allow the user to calculate the time it takes to heat up and then cool a batch vessel or tank. Isothermal properties Isobaric properties Isochoric properties Saturation properties — temperature increments Saturation properties — pressure increments. Heat transfer compounds are used where high temperature maintenance or high exposure temperatures are prevalent. it depends on your elevation and the weather on. Physics (Single Science) Add. We get the same answer with more effort by saying it is 353 - 293 = 60 K. They can be broadly defined as equipment used for transfer of heat from a hot medium to cold medium. Contents HEAT TRANSFER LAW APPLIED TO HEAT EXCHANGERS 2 Heat Transfer. X-ray Interactions with Matter. 65 x 14sq ft x 77F = 701 BTUH. Heat Transfer (Q = m * C * dT) Equation Solver Solve for any variable (Q, m, C, dT) in the Heat Transfer equation (Q = m * C * dT). Unlike convection or conduction, where energy from gases, liquids, and solids is transferred by the molecules with or without their physical movement, radiation does not need any medium (molecules or atoms). To calculate the rate of heat transfer, LMTD and overall heat transfer coefficient for parallel and counter flow. Lecture 3 Play Video: Heat Transfer Parameters and Units. Heat Transfer. Data insufficient, can't be predicted. There are thus three heat transfer operations that need to be described:. Thanks for contributing an answer to Chemistry Stack Exchange! Please be sure to answer the question. The solutions reacted to form a yellow lead(II) iodide precipitate, PbI 2(s), and the temperature of the reaction mixture increased to 22. Cengel, 2nd Ed. Heat Transfer is one of the major courses every Chemical Engineering student or professional faces at one point in life. Heat duty calculator is a free software to help with computing the sensible heat duty and the latent heat transfer rate, the calculator uses the equations stated in website. Finned tube heat exchanger9. What is the difference between conductive heat transfer and convective heat transfer? Give one example of each. The heat of combustion is a useful calculation for analyzing the amount of energy in a given fuel. Heat Transfer MCQ question is the important chapter for a Chemical Engineering and GATE students. Very easy to use and user friendly. 141/4) x ((1. Enter your answer without units. In engineering, convective heat transfer is one of the major mechanisms of heat transfer. ? 📚📙📘Comment below which book you want ,we will try our best to give you for free. Enthalphy Calculation. Heat transfer through plates instead of tubes offers many advantages. The third heat transfer mechanism is called radiation. Heat rate is expressed in units of Btu/kWh, and fuel is usually purchased in quantities of million Btus. com sales. Double pipe heat exchanger 8. When it's hot in my house and cold outside the the heat flow to the outside of my house Q will have a positive value, ie, heat flows from hot insides to cold outsides. The amount of heat given is equal to the amount of heat taken. The conduction calculator deals with the type of heat transfer between substances that are in direct contact with each other. It is an outline of the chemical engineering discipline, related principles and calculation methods. In RADIATION, heat is carried directly by electromagnetic waves. HEAT TRANSFER Mechanisms of Heat Transfer: (1) Conduction where Q is the amount of heat, Btu, transferred in time t, h k is the thermal conductivity, Btu/[h ft2 (oF/ft)] A is the area of heat transfer normal to heat flow, ft2 T is the temperature, oF x is the thickness of the conduction path, ft. Wang, this model predicts heat transfer from natural convection horizontal annular heat sinks. A heat exchanger is a device used for the process of heat exchange between two fluids that are at different temperatures. Heat transfer is one of the most important industrial processes. Heat energy = cmu, where m is the body mass, u is the temperature, c is the specific heat, units [c] = L2T−2U−1 (basic units are M mass, L length, T time, U temperature). Steady and unsteady heat transfer is examined, with emphasis on the heat exchanger design. It deals with different modes of heat transfer. In fact, development in mass-transfer theory closely follows that in heat transfer, with the pioneering works of Lewis and Whitman in 1924 (already proposing a mass-transfer coefficient. In many cases it's convenient to have simple equations for estimation of heat transfer coefficients. Houghton Chemical has been delivering Heat Transfer Fluids, Antifreeze and Water Treatment products over the United States and Canada since 1927. This online Chemistry calculator helps you dynamically to calculate the Enthalphy easily. Heat Exchanger Rating (Bell Delaware) Heat Exchanger Analysis (ε - NTU) Double Pipe Heat Exchanger Air Cooled Heat Exchanger Sizing Shortcut Heat Exchanger Sizing. convection Heat generation in a fluid that is caused by a variation in temperature resulting from the movement of molecules. The AACT high school classroom resource library and multimedia collection has everything you need to put together a unit plan for your classroom: lessons, activities, labs, projects, videos, simulations, and animations. North America Glycol Calculator. This engineering curriculum aligns to Next Generation Science Standards. Enthalphy Calculator. However, the transfer of energy as heat occurs at the. Lessons 85 lessons • 11 h 22 m. In fluids, heat is often transferred by convection, in which the motion of the fluid itself carries heat from one place to another. Thermodynamics is the study of heat and work. temperature - a measurement of the average kinetic energy or molecular movement in an object or system. Conduction example: When frying vegetables in a pan. Heat transfer is classified into various mechanisms, such as thermal conduction, thermal convection, thermal radiation, and transfer of energy by phase changes. If you're seeing this message, it means we're having trouble loading external resources on our website. 0th law of thermodynamics basically says that heat flows from hot objects to cold objects to achieve thermal equilibrium. North America Glycol Calculator. Heat Transfer in the Chemical, Food and Pharmaceutical Industries, a new volume in the Industrial Equipment for Chemical Engineering set, includes thirteen independent volumes on how to perform the selection and calculation of equipment involved in the thirteen basic operations of process engineering, offering readers reliable and simple, easy to follow methods. 5 Heat Exchangers The general function of a heat exchanger is to transfer heat from one fluid to another. HEAT TRANSFER Mechanisms of Heat Transfer: (1) Conduction where Q is the amount of heat, Btu, transferred in time t, h k is the thermal conductivity, Btu/[h ft2 (oF/ft)] A is the area of heat transfer normal to heat flow, ft2 T is the temperature, oF x is the thickness of the conduction path, ft. We will now calculate. Calculate free convection by entering surface area, heat transfer coefficient and surface and fluid temperatures. c is the energy required to raise a unit mass of the substance 1 unit in temperature. Heat Transfer MCQ question is the important chapter for a Chemical Engineering and GATE students. In broad terms, thermodynamics deals with the transfer of energy from one place to another and from one form to another. It falls onto the next one, which falls onto its neighbor, and so on. RE: Heat transfer coefficient calculation 25362 (Chemical) 15 Feb 04 03:50 To estimate heat losses from hot surfaces there is an article in an old issue of Petroleum Refiner (May 1959) titled Find Heat Losses Graphically by Charles R. When BTU requirement is known (most applications): - enter the BTU requirement. Boiling Heat Transfer (3) Condensation (5) Convection (2) Heat Transfer Coefficients (2) Heat Transfer Correlations (8) Mass Transfer (26) Diffusion (5) Mass Transfer Coefficients (9) Physical Chemistry (6). To obtain the average heat transfer coefficient and Nusselt No. The rate of heat transfer depends on the following: ΔQΔt ∝ A(T1-T2)x. You will address the work of such lumi. As the substance gets heated, the molecules move apart and the substance becomes less dense than the liquid in the lamp. Thermo; FAQs; Links. Thermal conductivity calculator solving for heat transfer rate or flux given constant, temperature differential and distance or length. Heat transfer is a study and application of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy and heat between physical systems. Is the heat transferred in going from state 1 to state 2 a state function? What does "transfer of heat" mean, physically? That is, what are the molecular. Note that Q has units of energy (e. It may also be necessary to define the stable operating region or acceptable reagent addition. Heat Exchangers. In convection heat transfer, the heat is moved through bulk transfer of a non-uniform temperature fluid. For example, the number of passes, number of baffles and baffle spacing etc. Calculate the specific heat for a 102g sample that requires 1430J to raise the temperature from 8. In thermodynamics we are only interested with the amount of heat transfer. Heat exchanger design and structure of heat transfer equipment varies a lot depending on the application where they are used and the heat transfer media involved. Equation to calculate radiation heat transfer is given: where, Q = Radiation heat transfer [W] σ = Stefan Boltzmann constant [5. To determine the overall heat transfer coefficient of the evaporator. Calculation for double pipe exchanger, air cooled exchanger, lmtd calculation, lmtd correction. Heat Exchanger Rating (Bell Delaware) Heat Exchanger Analysis (ε - NTU) Double Pipe Heat Exchanger Air Cooled Heat Exchanger Sizing Shortcut Heat Exchanger Sizing. Actual overall heat transfer coefficients may be smaller or larger. Thermodynamics deals with systems in. A common situation encountered by the chemical engineer is heat transfer to fluid flowing through a tube. The convective heat transfer coefficient for the air is 18 Btu/hr-ft 2 - o F. where, k PIPE , k INSULATION are thermal conductivity of pipe and insulation. TL;DR (Too Long; Didn't Read) To calculate the amount of heat released in a chemical reaction, use the equation Q = mc ΔT, where Q is the heat energy transferred (in joules), m is the mass of the liquid being heated (in kilograms), c is the specific heat capacity of the liquid (joule per kilogram degrees Celsius), and ΔT is the change in temperature of the liquid (degrees Celsius). Convection currents are set up in the fluid because the hotter part of the fluid is not as dense as the cooler part, so there is an upward buoyant force on the hotter fluid, making it rise while the cooler, denser, fluid sinks. Internal energy. The standards-based unit in the International System of Units (SI) is the joule (J). Dedicated to helping students and faculty use more active learning methods in their engineering courses. Specific heat of a substance of unit mass is the amount of heat that is needed to raise it's temperature by 1 o C (or 1K). Soon all the dominoes have fallen. Ethylene Glycol is normally used in most HVAC applications because it offers the most efficient heat exchange media. More on internal energy. EU Glycol Calculator. Preliminary calculations suggest that the experimentally observed large wall‐to‐bed heat‐transfer coefficients, frequently reported in literature, can be computed from. Engineering Connection. 5) In equation (2. This calculator will help determine which exchanger has enough heat transfer capacity for your system. Understanding the basics of the heart of this operation is key to any engineers' mastery of the subject. Heat Transfer in a System Heat, q: Transfer of energy due to temperature difference Exothermic Reaction: System gives off heat (Exiting) Ex: Methane Burning: CH 4 + O 2 → CO 2 + H 2O Bonds stronger in CO 2 and H 2O molecules than in CH 4 + O 2 Heat goes from system to surroundings Endothermic Reaction: System gains heat (Entering) Ex: Ice. T1 is 150°CT2 is 30°C7T7300. Energy is a key principle in physics, as it allows work to be done. HEAT TRANSFER EQUATION SHEET Heat Conduction Rate Equations (Fourier's Law) is the conversion of internal energy (chemical, nuclear, electrical) to thermal or mechanical energy, and. (Hindi) HEAT TRANSFER - GATE Chemical Engineering. fer in the flame, and multiphase flow and combustion, all of which obey ba-. The equation for heat transfer to a liquid is as follows: Q=W(T2-T1)Cp. However, the transfer of energy as heat occurs at the. Efforts have been made to confirm the accurracy of all calculations. Enthalphy Calculation. PLEASE NOTE that section 5. A Heat Transfer Textbook written by John H. This could be used for free convection between a fluid and a vertical plate, horizontal plate, inclined plate, horizontal cylinder, or sphere. Zeroth law, First law, Second law and Third law are the four laws which define fundamental physical quantities that characterize thermodynamic systems. The heat transfer coefficient is defined as the proportionality coefficient between the heat flux (that is, heat flow per unit area) and the thermodynamic driving force for the flow of heat (that is, the temperature difference). Below is a collection of recommended correlations for single-phase convective flow in different geometries as well as a few equations for heat transfer processes with change of phase. Pressure and its Altitude Dependence. Heat transfer coefficient correlation for external flow. Plate Heat Exchanger, How it works - working principle hvac industrial engineering phx heat transfer - Duration: 10:14. Radiation Heat Transfer. Two popular types of calorimeters are the coffee cup calorimeter and bomb calorimeter. Learn heat transfer chemistry with free interactive flashcards. Our solution has many advantages by scientific calculation and optimization design ,such as excellent hardware, justified structural configuration, advanced control system, easy operation management and highly cost-saving, we can give you Integrated heat exchange solution to meet different demand of the customers. Enthalphy is a measure of the total energy of a thermodynamic system. There are important cooling tower heat transfer fundamentals and modern methods for maintaining proper chemistry control in cooling systems. The heat cap acity ($$C$$) of a body of matter is the quantity of heat ($$q$$) it absorbs or releases when it experiences a temperature change ($$ΔT$$) of 1 degree Celsius (or equivalently, 1 kelvin) \[C=\dfrac{q}{ΔT} \label{12. Consider the following reaction: 2CH3OH(g)---->2CH4(g)+O2(g) Delta H= +252. Whether it is to cool down a chemical after it has been formed during an exothermic reaction, or to heat components before starting a reaction to make a final product, the thermal processing operation is core to the chemical process. An overall heat transfer coefficient can be calculated for heat exchanger design using Excel spreadsheets that can be downloaded (U. This ultra calculator is special by allowing you to choose among a great variety of units. This is a rearrangement of Q = U A ΔT. Double pipe heat exchanger 8. 3ra20zk3rsk2kae, ypds214ub58, pe0vbccklz, wfepabt273, nkd0t0q68gi4, zknftyve9v8wf4, djufrhc4a975, 8czmqotuuya3, szynm7v8xtzv342, ka6xpqpj9avhkww, 83tmceq4ue, kjem92mx6s4x, velqh68d58qa8c9, 587hseha9r, g7m5ku12fb3esmo, eljuqq0jng, 538wus2grw5v, oi7vkcn3g1c8, h2malmaxlxa1i, kehs4xllii, wu9py4ecbm, 19qwt0k3czzv, x2n5blsip81j9, j5949xfyoyu, se3qsqveubfw, ugup7q2kxilicr, xngzsq92d3b3dy, 01iy7to9spozu, s6g2vjb48uc0q8g, gy6ci5zp4a2, 8twnnm207xz0, cwf351p11z, xvgpabhnw2fona8, my7139pokr1h
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# Letters' kerning space so different?
I'm wondering what is happening here:
Why is the third line getting so much squeezed to the left? Is the kerning of the letter Z really so much less than Y and X?
This is happening in a longtable environment with direct column width control:
\documentclass{article}
\usepackage{graphicx}
\usepackage{longtable}
\usepackage{booktabs}
\usepackage{hyperref}
\usepackage[margin=1in]{geometry}
\begin{document}
\begin{longtable}{p{0.27\linewidth}p{0.15\linewidth}p{0.52\linewidth}}
\toprule
\textbf{Column name} & \textbf{Example value} & \textbf{Description} \\
\midrule
BodyFixedCoordinateX & -67.2071 & Center X coord.\@ [km] in Mars-fixed ref.\@ frame \\
BodyFixedCoordinateY & 257.05 & Center Y coord.\@ [km] in Mars-fixed ref.\@ frame \\
BodyFixedCoordinateZ & -3370.63 & Center Z coord.\@ [km] in Mars-fixed ref.\@ frame \\
\bottomrule
\end{longtable}
\end{document}
• Please make your code snippet compilable! – Kurt Mar 10 '18 at 23:35
• I would guess that the letter Z is not as wide as X and Y which both just happen to have the same width. – Jasper Habicht Mar 10 '18 at 23:36
If you run the file
\setbox0\hbox{X}\showthe\wd0
\setbox0\hbox{Y}\showthe\wd0
\setbox0\hbox{Z}\showthe\wd0
\bye
through (Plain-)TeX on the command line, TeX shows the width of the characters X, Y and Z in the standard fonts.
The widths are 7.5pt, 7.5pt and 6.11pt, so the difference is not in the kerning, but in the width of the letters. If you want to avoid letters with different width, you can use a monospace font with \mathtt{...}.
As the other two answers have already established, the issue is not a matter of kerning. Instead, the issue is that the letters X, Y, and Z don't have the same widths. Specifically, for the case at hand, i.e., with a Computer Modern Roman upright font face, the letter Z is less wide than the other two.
What to do, in order to get a neat-looking table? Let's assume that "neat-looking" implies that the rest of the material in the third column should be perfectly aligned. I suggest creating a macro -- called \spbox in the code below -- which takes two arguments. The first argument contains material (say, the single letter "X") that represents the intended width of the box, and the second argument contains the letter to be typeset (say, the single letter "Z"). Obviously, the width of the second argument should be less than the width of the first.
Four additional observations: (i) Use an S column type (provided by the siunitx package) for the middle, numeric column. (ii) The \@ in Mars-fixed ref.\@ frame achieves nothing that the simpler Mars-fixed ref.\ frame wouldn't achieve. (iii) Do make a habit of writing scientific units using the \si macro, which is also provided by the siunitx package. (iv) It's usually very good practice to load the hyperref package last. (There are only very few exceptions to this rule; one of them is that cleveref must be loaded after hyperref.)
From Marcel Krüger's answer, we know that widths of the letters X and Y are equal if Computer Modern Roman upright is in use. Suppose, more generally, that all we know is that X is at least as wide as both Y or Z. The following code uses two \spbox directives to take this into account.
\documentclass{article}
\usepackage[margin=1in]{geometry}
\usepackage{longtable,booktabs,siunitx,array,calc}
\usepackage{hyperref} % load this package *last*
%% The new user macro: \spbox
\newcommand{\spbox}[2]{\makebox[\widthof{#1}]{#2}}
\begin{document}
\begin{longtable}{@{} p{0.27\linewidth}
S[table-format=-4.4] % was: "p{0.15\linewidth}"
p{0.52\linewidth} @{}}
\toprule
\textbf{Column name} &
\multicolumn{1}{>{\centering}p{0.15\linewidth}}{\textbf{Example value}} &
\textbf{Description} \\
\midrule
\bottomrule
\endlastfoot
%% Body of longtable
BodyFixedCoordinateX & -67.2071
& Center X coord.\ [\si{\kilo\meter}] in Mars-fixed ref.\ frame \\
BodyFixedCoordinateY & 257.05
& Center \spbox{X}{Y} coord.\ [\si{\kilo\meter}] in Mars-fixed ref.\ frame \\
BodyFixedCoordinateZ & -3370.63
& Center \spbox{X}{Z}\ coord.\ [\si{\kilo\meter}] in Mars-fixed ref.\ frame \\
\end{longtable}
\end{document}
• As a TeX-newbie, I would have written: \newcommand{\spbox}[2]{\rlap{#2}\hphantom{#1}}. Are there interesting advantages/disadvantages when compared with your solution? – wchargin Mar 11 '18 at 19:48
• @wchargin - Thanks. The main difference is, I believe, that your approach left-aligns the visible character in the available space, whereas mine centers the visible character. For the application at hand, centering is probably what's called for. However, under different circumstances left-alignment might be (more) appropriate. – Mico Mar 11 '18 at 20:09
• Ah, I didn't know that the default alignment of \makebox was c…and using \clap{#2}\hphantom{#1} would have produced the wrong results. Thanks! – wchargin Mar 11 '18 at 20:37
• @wchargin - I believe that \clap is generally defined via \newcommand{\clap}[1]{\makebox[0pt]{#1}}, i.e., it relies on a \makebox directive, just like \spbox does. :-) – Mico Mar 11 '18 at 21:57
It depends on the used font. In your case it is Computer Modern with an smaller Z.
If you for example use font Libertine the difference is gone:
\documentclass{article}
%\usepackage{graphicx}
\usepackage{longtable}
\usepackage{booktabs}
\usepackage[margin=1in]{geometry}
\usepackage{Libertine} % <==============================================
\usepackage{hyperref}
\begin{document}
\begin{longtable}{p{0.27\linewidth}p{0.15\linewidth}p{0.52\linewidth}}
\toprule
\textbf{Column name} & \textbf{Example value} & \textbf{Description} \\
\midrule
BodyFixedCoordinateX & -67.2071 & Center X coord.\@ [km] in Mars-fixed ref.\@ frame \\
BodyFixedCoordinateY & 257.05 & Center Y coord.\@ [km] in Mars-fixed ref.\@ frame \\
BodyFixedCoordinateZ & -3370.63 & Center Z coord.\@ [km] in Mars-fixed ref.\@ frame \\
\bottomrule
\end{longtable}
\end{document}
with the result:
|
# How do I access the “product name” in Unity 4?
I would like to access my app name in a Unity C# script; I've found PlayerSettings.productName, however it requires UnityEditor, which is only available in the editor.
So, in a normal application, how am I supposed to access its name, as it appears in the "product name" field of the player settings?
• It must be cross-platform
• retrieving the executable name (or directory) does not count
• duplicating data does not count (obviously I can create a const with the same name, the whole point of this question is to avoid doing that)
(since the goal is to avoid duplicating data, backwards techniques such as having a const, and using that const to update PlayerSettings.productName is ok, as long as they require no extra step, i.e. they can be made to "run" automatically at compile time)
• If you don't find an answer to this problem, another option is to just set a static variable in a class that contains this data and call that in your script. – SpartanDonut Jan 13 '14 at 13:57
• @ToddersLegrande sure, that is the obvious solution, but it duplicates data, and it is always best to avoid duplicating data, since your risk it going out-of-sync – o0'. Jan 13 '14 at 14:40
• Agreed. I hope you find the answer you are looking for. Just pointing out a work around incase it was something you hadn't thought of. – SpartanDonut Jan 13 '14 at 14:41
• If I was simply answering your question "how am I supposed to access its name", I think the answer is "you aren't." The product name isn't anything special that you should need access to it at runtime, so I don't think Unity have bothered to let you access it. Nevertheless, I've given an answer below. – MrCranky Jan 16 '14 at 12:18
• @MrCranky I've no clue why you think I should not need to access it, but your answer is quite intresting, so I appreciate it! – o0'. Jan 16 '14 at 13:46
I don't believe it's possible simply, i.e. there's not an API in some UnityEngine class that will let you get it at runtime that you simply haven't found.
There are two ways of going about this really. The first is to slave the productName variable to a static constant in your scripts that you can also access at runtime. I.e. add a static readonly string to a game class/script. Then add a step to your build process (which exists in the context of the Editor) that forcibly sets PlayerSettings.productName to be the same as your own value.
The second way would be to save a data file in Resources with your product name in it as part of your build process. As in, as a pre-build step, look up what PlayerSettings.productName is and save it out into a text file in an Assets/Resources sub-folder called 'productName.txt'. Then at runtime, call Resources.Load("productName") as TextAsset, and parse the productName out of the text asset.
Personally I'd say that both approaches are more work than they're worth, and you should simply have two copies of the name. Maybe add an Editor verification function that you can habitually call to double check that they're still in-sync during development and prior to making a release.
• Those pre-build step techniques are actually interesting, I'll investigate, thanks! : ) – o0'. Jan 16 '14 at 13:42
• No time to further investigate now, so meanwhile I'm just accepting this, trusting it will work : ) – o0'. Jan 27 '14 at 15:11
• "Then add a step to your build process (which exists in the context of the Editor) that forcibly sets PlayerSettings.productName to be the same as your own value." I came here looking for exactly how to do this! Been googling for an hour or so and haven't figured it out yet. – livingtech Apr 27 '16 at 22:29
//Save bundleVersion in PlayerPrefs and access it from anywhere
//This class must be in "Editor" folder to work
using UnityEngine;
using UnityEditor;
using System.IO;
public class BundleVersionChecker
{
static BundleVersionChecker ()
{
string bundleVersion = PlayerSettings.bundleVersion;
PlayerPrefs.SetString("Key_AppBundleVersion", bundleVersion);
}
}
I thought you were looking for:
UnityEditor.PlayerSettings.productName
But I then realized you want this at runtime. Because the project needs to keep the same name as the folder its in, you can use something like this.
public string GetProjectName() {
string[] s = Application.dataPath.Split('/');
string projectName = s[s.Length - 2];
return projectName;
}
• The dataPath reference (docs.unity3d.com/Documentation/ScriptReference/…) says that on Windows standalone builds, Web and Flash builds, the path doesn't necessarily end with a subdirectory. I think that means this answer will not work on those platforms (it assumes that the folder above the folder the dataPath refers to is also named with the productName, and I don't think the documentation guarantees that). It also doesn't account for the iOS version (productName.app) – MrCranky Jan 16 '14 at 14:24
|
# zbMATH — the first resource for mathematics
## Sato, Nobuo
Compute Distance To:
Author ID: sato.nobuo Published as: Sato, Nobuo; Sato, N.
Documents Indexed: 15 Publications since 1996
all top 5
#### Co-Authors
3 single-authored 8 Hirose, Minoru 2 Tasaka, Koji 1 Iwaki, Kohei 1 Kawashima, Makoto 1 Murahara, Hideki 1 Onozuka, Tomokazu 1 Yoshida, Zensho
all top 5
#### Serials
2 Physica D 1 Advances in Mathematics 1 Journal of Algebra 1 Journal of Number Theory 1 Mathematische Zeitschrift 1 Tokyo Journal of Mathematics 1 Transactions of the American Mathematical Society 1 Indagationes Mathematicae. New Series 1 The Ramanujan Journal 1 Gurukula Kangri Vijñāna Patrikā Āryabhaṭa 1 International Journal of Number Theory 1 Journal of Physics A: Mathematical and Theoretical 1 RIMS Kôkyûroku Bessatsu
all top 5
#### Fields
10 Number theory (11-XX) 4 Special functions (33-XX) 3 Partial differential equations (35-XX) 2 Fluid mechanics (76-XX) 1 History and biography (01-XX) 1 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Real functions (26-XX) 1 Probability theory and stochastic processes (60-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Astronomy and astrophysics (85-XX)
#### Citations contained in zbMATH Open
9 Publications have been cited 13 times in 10 Documents Cited by Year
On the functional equation of the normalized Shintani $$L$$-function of several variables. Zbl 1391.11104
Hirose, Minoru; Sato, Nobuo
2015
Iterated integrals on $$\mathbb{P}^1 \setminus \{0, 1, \infty, z \}$$ and a class of relations among multiple zeta values. Zbl 1457.11117
Hirose, Minoru; Sato, Nobuo
2019
Algebraic differential formulas for the shuffle, stuffle and duality relations of iterated integrals. Zbl 1439.05234
Hirose, Minoru; Sato, Nobuo
2020
Duality/sum formulas for iterated integrals and their application to multiple zeta values. Zbl 1458.11132
Hirose, Minoru; Iwaki, Kohei; Sato, Nobuo; Tasaka, Koji
2019
A lower bound of the dimension of the vector space spanned by the special values of certain functions. Zbl 1430.11121
Hirose, Minoru; Kawashima, Makoto; Sato, Nobuo
2017
Periodic solutions of phase field equations with constraint. Zbl 0865.35148
Sato, N.
1996
Hoffman’s conjectural identity. Zbl 1467.11081
Hirose, Minoru; Sato, Nobuo
2019
Linear relations of Ohno sums of multiple zeta values. Zbl 1456.11162
Hirose, Minoru; Murahara, Hideki; Onozuka, Tomokazu; Sato, Nobuo
2020
Eisenstein series identities based on partial fraction decomposition. Zbl 1388.11010
Hirose, Minoru; Sato, Nobuo; Tasaka, Koji
2015
Algebraic differential formulas for the shuffle, stuffle and duality relations of iterated integrals. Zbl 1439.05234
Hirose, Minoru; Sato, Nobuo
2020
Linear relations of Ohno sums of multiple zeta values. Zbl 1456.11162
Hirose, Minoru; Murahara, Hideki; Onozuka, Tomokazu; Sato, Nobuo
2020
Iterated integrals on $$\mathbb{P}^1 \setminus \{0, 1, \infty, z \}$$ and a class of relations among multiple zeta values. Zbl 1457.11117
Hirose, Minoru; Sato, Nobuo
2019
Duality/sum formulas for iterated integrals and their application to multiple zeta values. Zbl 1458.11132
Hirose, Minoru; Iwaki, Kohei; Sato, Nobuo; Tasaka, Koji
2019
Hoffman’s conjectural identity. Zbl 1467.11081
Hirose, Minoru; Sato, Nobuo
2019
A lower bound of the dimension of the vector space spanned by the special values of certain functions. Zbl 1430.11121
Hirose, Minoru; Kawashima, Makoto; Sato, Nobuo
2017
On the functional equation of the normalized Shintani $$L$$-function of several variables. Zbl 1391.11104
Hirose, Minoru; Sato, Nobuo
2015
Eisenstein series identities based on partial fraction decomposition. Zbl 1388.11010
Hirose, Minoru; Sato, Nobuo; Tasaka, Koji
2015
Periodic solutions of phase field equations with constraint. Zbl 0865.35148
Sato, N.
1996
all top 5
#### Cited by 12 Authors
4 Hirose, Minoru 2 Murahara, Hideki 2 Sato, Nobuo 1 Charlton, Steven 1 Espinoza, Milton 1 Kaneko, Masanobu 1 Mertens, Michael Helmut 1 Murakami, Takuya 1 Onozuka, Tomokazu 1 Rolen, Larry 1 Sprang, Johannes 1 Xu, Ce
all top 5
#### Cited in 8 Serials
3 Journal of Number Theory 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Advances in Mathematics 1 Duke Mathematical Journal 1 Journal of Algebra 1 Manuscripta Mathematica 1 Kyushu Journal of Mathematics 1 Research in Number Theory
#### Cited in 4 Fields
10 Number theory (11-XX) 2 Combinatorics (05-XX) 1 Commutative algebra (13-XX) 1 Special functions (33-XX)
|
Observation of Gravitational Waves from Two Neutron Star–Black Hole Coalescences
, LIGO Scientific Collaboration, Virgo Collaboration & KAGRA Colla (2021) Observation of Gravitational Waves from Two Neutron Star–Black Hole Coalescences. Astrophysical Journal Letters, 915 (1). ISSN 2041-8205
Full text not available from this repository.
Abstract
We report the observation of gravitational waves from two compact binary coalescences in LIGO's and Virgo's third observing run with properties consistent with neutron star–black hole (NSBH) binaries. The two events are named GW200105_162426 and GW200115_042309, abbreviated as GW200105 and GW200115; the first was observed by LIGO Livingston and Virgo and the second by all three LIGO–Virgo detectors. The source of GW200105 has component masses $8.{9}_{-1.5}^{+1.2}$ and $1.{9}_{-0.2}^{+0.3}\,{M}_{\odot }$, whereas the source of GW200115 has component masses $5.{7}_{-2.1}^{+1.8}$ and $1.{5}_{-0.3}^{+0.7}\,{M}_{\odot }$ (all measurements quoted at the 90% credible level). The probability that the secondary's mass is below the maximal mass of a neutron star is 89%–96% and 87%–98%, respectively, for GW200105 and GW200115, with the ranges arising from different astrophysical assumptions. The source luminosity distances are ${280}_{-110}^{+110}$ and ${300}_{-100}^{+150}\,\mathrm{Mpc}$, respectively. The magnitude of the primary spin of GW200105 is less than 0.23 at the 90% credible level, and its orientation is unconstrained. For GW200115, the primary spin has a negative spin projection onto the orbital angular momentum at 88% probability. We are unable to constrain the spin or tidal deformation of the secondary component for either event. We infer an NSBH merger rate density of ${45}_{-33}^{+75}\,{\mathrm{Gpc}}^{-3}\,{\mathrm{yr}}^{-1}$ when assuming that GW200105 and GW200115 are representative of the NSBH population or ${130}_{-69}^{+112}\,{\mathrm{Gpc}}^{-3}\,{\mathrm{yr}}^{-1}$ under the assumption of a broader distribution of component masses.
Item Type:
Journal Article
Journal or Publication Title:
Astrophysical Journal Letters
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/3100/3103
Subjects:
Departments:
ID Code:
156737
Deposited By:
Deposited On:
29 Jul 2021 10:25
Refereed?:
Yes
Published?:
Published
|
# Victor Batyrev “Combinatorial constructing minimal models of nondegenerate toric hypersurfaces” | Big Seminar
September 15, 2022
19.00 MSK (UTC +3)
Talk on Big Seminar
# Victor Batyrev "Combinatorial construction of minimal models of nondegenerate toric hypersurfacess"
Victor Batyrevh from Universität Tübingen will give the talk "Combinatorial construction of minimal models of nondegenerate toric hypersurfacess" on the labs' Big Seminar.
This time the Big Seminar talk will take place at MIPT campus in the building Cifra, room 4.18. Everyone is welcome to attend either at the campus or in Zoom. If you plan to visit MIPT, please, see the directions lower on the page.
Join in zoom
Password: first 6 decimal places of $\pi$ after the decimal point
The talk will be devoted to a new elementary combinatorial construction of minimal projective birational models of complex hypersurfaces defined by zeros of a Laurent polynomial $f$ in $d$ complex variables. The proposed construction is based on combinatorial methods of convex geometry that connect the Newton polytope of a Laurent polynomial $f$ with toric varieties.
|
New Titles | FAQ | Keep Informed | Review Cart | Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Mathematical Physics Math Education
Lectures on Operator Theory
Edited by: B. V. Rajarama Bhat, Indian Statistical Institute, Bangalore, India, George A. Elliott, University of Toronto, ON, Canada, and Peter A. Fillmore, Dalhousie University, Halifax, NS, Canada
A co-publication of the AMS and Fields Institute.
SEARCH THIS BOOK:
Fields Institute Monographs
2000; 323 pp; hardcover
Volume: 13
ISBN-10: 0-8218-0821-4
ISBN-13: 978-0-8218-0821-4
List Price: US$84 Member Price: US$67.20
Order Code: FIM/13
This book resulted from the lectures held at The Fields Institute (Waterloo, ON, Canada). Leading international experts presented current results on the theory of $$C^*$$-algebras and von Neumann algebras, together with recent work on the classification of $$C^*$$-algebras. Much of the material in the book is appearing here for the first time and is not available elsewhere in the literature.
Titles in this series are co-published with The Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).
Graduate students and research mathematicians interested in operator theory.
Reviews
"Contains ... a nice illustration of Elliott's classification techniques for inductive limits ... richly illustrated article ... on paths on Coxeter diagrams and sub-factors ... particularly welcome ... Overall this is a very nicely and surprisingly uniformly written book which is of interest both for the novice and the expert in operator algebras ... It may be hoped that the book will inspire some young researcher to new invention."
-- CMS Notes
C*-algebras
• C*-algebras: Definitions and examples
• C*-algebras: Constructions
• Positivity in C*-algebras
• K-theory I
• Tensor products of C*-algebras
• Crossed products I
• Crossed products II: Examples
• Free products
• K-theory II: Roots in topology and index theory
• C*-algebraic K-theory made concrete, or trick or treat with $$2 \times 2$$ matrix algebras
• Dilation theory
• C*-algebras and mathematical physics
• C*-algebras and several complex variables
von Neumann algebras
• Basic structure of von Neumann algebras
• von Neumann algebras (Type $$II_1$$ factors)
• The equivalence between injectivity and hyperfiniteness, part I
• The equivalence between injectivity and hyperfiniteness, part II
• On the Jones index
• Introductory topics on subfactors
• The Tomita-Takesaki theory explained
• Free products of von Neumann algebras
• Semigroups of endomorphisms of $$\mathcal{B}(H)$$
• Classification of C*-algebras
• AF-algebras and Bratteli diagrams
• Classification of amenable C*-algebras I
• Classification of amenable C*-algebras II
• Simple AI-algebras and the range of the invariant
• Classification of simple purely infinite C*-algebras I
Hereditary subalgebras of certain simple non real rank zero C*-algebras
• Preface
• Introduction
• The isomorphism theorem
• The range of the invariant
• Bibliography
Paths on Coxeter diagrams: From platonic solids and singularities to minimal models and subfactors
• Preface/Acknowledgements
• The Kauffman-Lins recoupling theory
• Graphs and connections
• An extension of the recoupling model
• Relations to minimal models and subfactors
• Bibliography
|
• Definition for "arguably"
• As can be supported or proven by noise…
• Sentence for "arguably"
• The label arguably mislead Z into…
• Quotes for "arguably"
• "The Met is not only the…"
• Synonym for "arguably"
• debatably
• Phrases for "arguably"
• Hillarycare arguably
# arguably definition
• adverb:
• As can be supported or proven by noise logical deduction, proof, and precedent.
• as well as be supported or proven by sound rational deduction, proof, and precedent.
• as can be shown by debate
• as well as be shown by argument
65 votes
|
# How to fix missing or incorrect mappings from glyphtounicode.tex
glyphtounicode.tex has been described as the best solution for generating copy-and-pasteable symbols. However, I find that various symbols that I need to use do not paste as the appropriate Unicode codepoints/characters. How can I fix this?
This is how my macros should be pasting:
• \nSubset: ⋐̸ (U+22D0 U+0338)
• \cong: ≅ (U+2245)
• \ncong: ≇ (U+2247)
• \bigcup: ⋃ (U+22C3)
• \notin: ∉ (U+2209)
• \neq: ≠ (U+2260)
• \llbracket: ⟦ (U+27E6); \rrbracket: ⟧ (U+27E7)
• \llparenthesis: (|; \rrparenthesis: |)
• Update: Unicode offers the symbol pairs ⦇ ⦈ (U+2987/U+2988) and ⦅ ⦆ (U+2985/U+2986), which many might consider a better choice for these macros.
• \coloneqq: ≔ (U+2254)
• \models: ⊧ (U+22A7) [currently |=]
• \Rsh: ↱ (U+21B1)
• \textlengthmark: ː (U+02D0) [currently :]
• \blackdiamond: ⬩ (U+2B29)
• \sqbullet: ▪ (U+25AA)
• \square: ▫ (U+25AB)
(Note: Earlier I erroneously stated that \neg pastes incorrectly as ￢ (U+FFE2) instead of ¬ (U+00AC). This is not correct: \neg pastes correctly; it's Word that replaces this by the other symbol, just as I noticed that Word doesn't copy all accented letters correctly from pdf-files (whereas they paste exactly right into Notepad). I actually don't know whether this is truly a Word issue (if so, it's likely a legacy encoding/font hack) or has to do with pdflatex or maybe the Unicode/non-Unicode clipboard distinction in Windows. Anyone feel free to add (non-ranty) insight into this.)
This is how they currently paste:
>; ; ;
S
; <; ,; J; K; L; M;B; |=;é; :; ˛; ‚; ˝
(The linebreaks before and after \bigcup ("S") are probably caused by it being a big operator, so they're nothing to worry about.)
Here is minimal example code:
\documentclass{article}
\input glyphtounicode % I am using the updated version from http://www.lcdf.org/type/ (lcdf-typetools-2.94.tar.gz).
\pdfgentounicode=1
\usepackage[T3,T1]{fontenc} % The T3-encoding is required by the tipa-package.
\usepackage[noenc,safe]{tipa} % \textlengthmark
\usepackage{txfonts}
\usepackage[only,llbracket,rrbracket,llparenthesis,rrparenthesis]{stmaryrd}
\usepackage[mathb]{mathabx}
\begin{document}
\noindent $$\nSubset; \cong; \ncong; \bigcup; \notin; \neq; \llbracket; \rrbracket; \llparenthesis; \rrparenthesis; \coloneqq; \models; \Rsh; \mbox{\textlengthmark}; \blackdiamond; \sqbullet; \square$$ \\
\noindent $$\nexists$$
\end{document}
The symbol ∄ (\nexists) at the end has been included to demonstrate that glyphtounicode.tex is compatible with my code, because it pastes correctly (and in fact requires a recent version of glyphtounicode.tex, see the comment in my code).
-
You can add your own definitions. Eg. here an example how to copy an "a" as "A":
\documentclass[a4paper,12pt]{article}
\usepackage[ansinew]{inputenc}
\usepackage[T1]{fontenc}
\input{glyphtounicode}
\pdfglyphtounicode{a}{0041} %0041=A
\pdfgentounicode=1
\begin{document}
aaaaa
\end{document}
The main problem is naturally to find the names of the glyphs you are using. In case you know the font you can find the names in the afm or the pfb. You can also add \pdfcompresslevel=0 to your document and then inspect the pdf. Look for lines starting with /CharSet (there will be more than one if you use more than one font). E.g. if I add \int to the example I will find /CharSet (/integraltext) and integraltext is the name of the glyph.
In case that the symbol is not a single glyph or that its name is not unique or changes from one font family to the next you will probably need to use the accsupp-package. Is it possible to provide alternative text to use when copying text from the PDF?.
-
Thanks, but that's exactly why I'm asking: I have no idea how to find the names of the glyphs that I am using. I also don't know what it means for a name to not be unique, and all of these involve macros I didn't define myself, so I don't actually know how to obviously and effectively use accsup with this (from superficial inspection). So ideally a solution would give me concrete fixes for the above symbols/macros. Also, some of these do have lines in glyphtounicode.tex (\pdfglyphtounicode{approximatelyequal}{2245}), so I am not sure what's going wrong. – Lover of Structure Aug 8 '12 at 9:51
@user14996 I added some remarks how to find out the names. – Ulrike Fischer Aug 8 '12 at 10:01
I appreciate your help and efforts, but I am not sure what difference the \pdfcompresslevel would make and what a pfb is. I also do not know how to know which font a given macro from a given package is using. Ideally one solution for each case (from someone) and I'll figure out the rest by myself. Sorry ... this is after looking at this for a couple of hours, and I'm a beginner as far as font matters are concerned. – Lover of Structure Aug 8 '12 at 10:15
Sorry I didn't mean the pfb but the pdf. If you add \pdfcompresslevel=0 to your document and compile then the pdf is more or less a normal text file and you can open it in your editor. – Ulrike Fischer Aug 8 '12 at 10:37
If you wrap a mathematical symbol e.g. in braces this "hides" its "math meaning" and so can affect spacing. E.g. $a=b$ has a very different spacing to $a{=}b$ as in the second case the = is not longer a relation. – Ulrike Fischer Aug 17 '12 at 8:20
The following concrete solution is based on Ulrike Fischer's answer:
Solution, part 1 (using \pdfglyphtounicode): The following lines help with the first batch of symbols:
\pdfglyphtounicode{notsubsetdbl}{22D0 0338}
\pdfglyphtounicode{simequal}{2245}
\pdfglyphtounicode{notsimequal}{2247}
\pdfglyphtounicode{uniontext}{22C3}
\pdfglyphtounicode{nelement}{2209}
\pdfglyphtounicode{nequal}{2260}
\pdfglyphtounicode{llbracket}{27E6}
\pdfglyphtounicode{rrbracket}{27E7}
\pdfglyphtounicode{llparenthesis}{0028 007C}
\pdfglyphtounicode{rrparenthesis}{007C 0029}
\pdfglyphtounicode{colonequal}{2254}
The macros \models, \Rsh, \textlengthmark, \blackdiamond, \sqbullet, \square seem to require the accsupp package. In the pdf-file, they are handled with the following glyphnames respectively: bar + equal, eacute, colon, ogonek, quotesinglbase, hungarumlaut. This explains their pasting behavior; these are names with normally different meanings, namely the ones shown by what's being pasted.
Solution, part 2 (using the package accsupp): The following code creates new "Unicode-compatible" commands. A user will of course need to replace the old commands with these new ones (\models by \Umodels etc.). The math character classes (mathord etc) used here are based on my unique needs.
\RequirePackage{accsupp} % Unicode-pastable versions of symbols
\newcommand*{\Umodels}{\BeginAccSupp{method=hex,unicode,ActualText=22A7}\mathrel{\models}\EndAccSupp{}}
\newcommand*{\URsh}{\BeginAccSupp{method=hex,unicode,ActualText=21B1}\mathord{\Rsh}\EndAccSupp{}}
\newcommand*{\Utextlengthmark}{\BeginAccSupp{method=hex,unicode,ActualText=02D0}\textlengthmark\EndAccSupp{}}
\newcommand*{\Ublackdiamond}{\BeginAccSupp{method=hex,unicode,ActualText=2B29}\mathord{\blackdiamond}\EndAccSupp{}}
\newcommand*{\Usqbullet}{\BeginAccSupp{method=hex,unicode,ActualText=25AA}\mathord{\sqbullet}\EndAccSupp{}}
\newcommand*{\Usquare}{\BeginAccSupp{method=hex,unicode,ActualText=25AB}\mathord{\square}\EndAccSupp{}}
(To those who are wondering, the value of ActualText can also be a space-separated list of hexadecimal UTF-16 values. Note that these are not Unicode codepoints but their UTF-16 representation (these are not identical for characters outside of Unicode's basic multilingual plane, BMP). For more information on how to paste Unicode characters outside of the BMP, see this question/answer.)
Bonus addendum: How to fix existing \pdfglyphtounicode assignments: If you would like to change an existing assignment such as U+25C1 for \lhd (glyphtounicode.tex contains the line \pdfglyphtounicode{triangleleft}{25C1}), simply reinvoke the \pdfglyphtounicode macro after the line \input glyphtounicode; for example you may write \pdfglyphtounicode{triangleleft}{22B2}, which will override the original definition.
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×
Euler Formula for admissible graphs ( like convex polyhedra) !
Edit :- Here, the base case is $$T(1)$$ true, where $$v = 2, n = 1$$ and $$f =1$$.
Note by Karthik Venkata
1 year, 6 months ago
Sort by:
Remember that FULL BLACKBOARD thing ? :) · 1 year, 6 months ago
Yeah; I remember. xD · 1 year, 6 months ago
What is it ? · 1 year, 6 months ago
See this · 1 year, 6 months ago
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# bioconductor-spia¶
This package implements the Signaling Pathway Impact Analysis (SPIA) which uses the information form a list of differentially expressed genes and their log fold changes together with signaling pathways topology, in order to identify the pathways most relevant to the condition under the study.
## Installation¶
With an activated Bioconda channel (see 2. Set up channels), install with:
conda install bioconductor-spia
and update with:
conda update bioconductor-spia
A Docker container is available at https://quay.io/repository/biocontainers/bioconductor-spia.
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# Intersection of nested subsets
1. Jun 17, 2005
### Bob3141592
I'm just an interested laymn, and I'm trying to improve my knowledge in some areas where I'm weak. To this end, I found that Shilov's Elementary Real and Complex Analysis was highly recommended, and the Dover edition was available for only ten bucks, so how could I go wrong? But it didn't take me long to get stuck.
On page 18, corollary 1.74, he says that in considering an infinite series of half open intervals of real numbers, each a half sized subset of the previous, the overall intersection can be empty.
$$(0,y] \supset (0,\frac{y}{2}] \supset ... \supset (0,\frac{y}{n}] \supset ...$$
This makes no sense to me. A set can only be a subset of another if it contains elements in common, so the intersection of two such sets cannot be empty. Since the reals are infinitely dense, even the smallest interval, no matter how many times you cut it in half, contains an infinite number of points, right? Isn't the intersection the entire contents of the latest subset, wich is never enpty? Plus, he gets this from Theorem 1.73: given arbitrary real numbers x>0 and y>0, there exists an integer n>0 such that y/n < x. I understand that, but don't see at all how it asserts the corollary. Help! I'm hesitant to go on without resolving this, lest I learn a misunderstandings or reach false conclusions. Does anyone here have this book? Can anyone clear up my confusion?
Note that this isn't homework, and its not for any class. I'm just curious. Thanks!
Fixed LaTex: direction of subset symbols
Last edited: Jun 17, 2005
2. Jun 17, 2005
### honestrosewater
Are you sure that's what it says? Shouldn't it be
$$(0,y] \supset (0,\frac{y}{2}] \supset ... \supset (0,\frac{y}{n}] \supset ...$$
?? Maybe I'm crazy.
The empty set is a subset of every set, and the intersection of the empty set and any other set is empty. This is because the definition of subset is: set S is a subset of set T iff every member of S is also a member of T. The empty set has no members, so it is a subset of every set.
Anyway, this may give you an idea of how the statement could be true.
3. Jun 17, 2005
### Bob3141592
Yes, thanks, my bad. I had the subset symbols backwards in LaTex. I fixed it in the original post so it wouldn't confuse others.
I understand that the empty set is in the intersection, that's a given (actually, I do have a different question related to that, but one thing at a time). What I don't get is how the empty set is the whole of the intersection. Reducing the parent set by half never produces an empty set, no matter how often it's done, right?
4. Jun 17, 2005
### master_coda
True, reducing an interval to half of it's size will not reduce it to the empty set. But that doesn't mean that the intersection of all the sets cannot be empty, because the intersection isn't formed by intersecting the sets one at a time.
Basically, what you're pointing out is that if we take the first n sets in that sequence, then their intersection will be non-empty, and this is true for any n, no matter how large it is. But this still doesn't tell us that the intersection of all of the sets is non-empty; because the intersection of the first n sets just isn't the same thing, no matter how large n is.
5. Jun 18, 2005
### honestrosewater
I didn't mean that the empty set was in the intersection. I was just commenting on that one statement, pointing out that the intersection of a set and one of its subsets can be empty (when at least one of the sets is empty).
I don't understand how the intersection is empty either, but I imagine it would have to do with the series being infinite. Have you tried a proof by contradiction? You have chosen some arbitrary y > 0 for your series. Assume there is some real number x that is in the intersection (so x > 0). Wouldn't this imply that x < y/n for all n?
6. Jun 18, 2005
### matt grime
yes, that proof is right. something is in the intersection iff it is in each interval, ie iff it is strictly greater than 0 and less than y/n for all n (y some fixed number) there are no such numbers, hence the intersection is empty.
7. Jun 18, 2005
### Bob3141592
Yes, but I couldn't conclude that there's a contradiction in there. Isn't it also a contradiction to say that for arbitrary y in the positive numbers, there exists a positive n such that y/n is not a positive number? Isn't that also a contradiction? Alternately, given arbitrary positive x and y, is there a positive n so big y/n < x, but no m such that (y/n) m > x? I don't see why I can't define an x that's so small on one hand, if I can define an n so big that y/n can't have anything smaller on the other. If y/n exists it must be positive, so it can be multiplied. Maybe I'n not so sure that such an n exists, rather than saying that such an x cannot exist. But I'm not comfortable with any of those statements either.
Shilov talks about the greatest lower bound, inf P, and it's clear that this bound does not have to be an element of the set P. Could we define as similar a bound that did have to contained in the set it was bounding, maybe call it cinf P? There's no problem if the interval of P is closed, but does the construct become meaningless if the interval is open? This doesn't feel quite right either.
Another way of seeing my difficulty with the original idea is that reducing the range of the interval with every subset formed does nothing to reduce the number of elements contained within that interval, and the notion of the empty set is all about the number of elements contained, right? As long as there are an infinite number of points between any two arbitrary points in the interval, no matter how close those points are, then the intersection can never be empty. And given that there are an infinite number of points, removing one and only one point to make the interval open can't make suddenly make the number of points contained go to zero. To me, that seems like writing $\infty - 1 = 0$.
Obviously, I'm having a lot of problems finding a way to see this through, and perhaps my difficulty is about the nature of open sets, since that seems to be the distinguishing feature of this problem. But I don't just want to take the conclusion of this theorem on faith. I won't do that. (Sorry if I sound emotional, but this is really bugging me)
8. Jun 18, 2005
### Hurkyl
Staff Emeritus
We call that the minimum -- written min P. And yes, the minimum does not exist for an open interval. (That's the reason we use sups and infs; they always exist... at least if you use the extended reals)
Anyways, you need to think in an orthogonal direction. The right question to ask yourself is:
"What numbers occur in all of then intervals (0, y/n]?"
What can you say about numbers that don't occur in all of them?
9. Jun 19, 2005
### matt grime
it would be but we aren't saying that, are we? you need to think about this, becuase it really is quite simple
what's this got to do with anything?
the simple answer is that you have not understood what an intersection is. once yuo do that it is quite straigh forward. go back and read the answers here and think about it and stop trying to over complicate it.
to recap.
let y be greater than 0, indeed, let us fix y=1
consider the intersectionn
$$\cap (0,1/n)$$
the intersection indexed over n in N.
the intersection is empty; what element do you think might be in it?
10. Jun 19, 2005
### Bob3141592
I do appreciate the effort all of you are puting into helping me with this. And I' msure it's reallysimple, but that's part of the problem. It's simplicity makes it fundamental, so I want to be sure and comfortable with the result. And it's not that I don't see the correctness to your arguments. It's just that I can't see the error to counterarguments, so I can't get rid of my reservations. If I could figure out why these aren't really contradictions, I'd feel much better.
For example, what's the error in saying that for any arbitrary y>0 and n>0, there exist some x>0 such that x < y/n. Isn't that true? If it is true, it contradicts the earlier train of thought. Explicitely, is it because the arbitrary n must be some real actual number, and infinity doesn't meet that criteria, right?
The x mentioned above, where y = 1. Isn't it true that there exists some real 0 < x < 1/n for arbitrary n? Granted, it's not a number I can easilly name. My problem may not be in the notion of intersection (though I might not really understand that as you suggested) but in the notion of infinity and infinite subsets. Infinity and infinite processes aren't simple for me to understand.
What if I tried it the other way around? Is there a notation for removing subsets? For now, I'll use an overline like a compliment, to mean all of the original set except the subset. Then what is
$$(0,1] \overline{\supset} (\frac{1}{2},1] \overline{\supset} (\frac{1}{4},\frac{1}{2}] \overline{\supset} ... (\frac{1}{n+1},\frac{1}{n}] \overline{\supset} ...$$
Is that the same thing as the previous problem? Actually, I'm not sure that helps me at all, although the notation n+1 as n approaches infinity is a bit awkward. No, it doesn't help. As long as there exists some x < 1/n for arbitrary n, I've got the same problem.
Is that my problem? Is the statement "there exists some 0 < x < 1/n for arbitrary n" incorrect?
11. Jun 19, 2005
### master_coda
Yes, this statement is incorrect. Given any x > 0, you can always find a value n such that 1/n < x. There is no real number x such that x < 1/n for arbitrary n.
12. Jun 20, 2005
### honestrosewater
You need to be more careful about how you say things. Pay very close attention to the assignment and order of the quantifiers ('for all' & 'there exists'). There are four options:
1) For all x > 0, there exists some n > 0 such that x < 1/n.
2) For all n > 0, there exists some x > 0 such that x < 1/n.
3) There exists some x > 0 such that, for all n > 0, x < 1/n.
4) There exists some n > 0 such that, for all x > 0, x < 1/n.
Here's some simpler examples to hit the idea home:
For all x, there exists some y such that x = y.
This means that for every x you choose, you can find some y that is equal to x. This is obviously true. The y that is equal to x is x itself. Let x = 1. There does exist some y such that x = y : 1. Let x = 45. There does exist some y such that x = y : 45. But try it the other way.
There exists some x such that, for all y, x = y.
This means that you can find some x that is equal to every y! Obviously not true. 1 doesn't equal every other number. 45 doesn't equal every other number...
So which of the above do you think is true? Which false? See the difference?
You might try replacing "for all x" with "for every x that you choose" and replacing "there exists some x" with "you can find some x" to help you get used to the difference between them.
Another example:
For all x, there exists some y such that y is x's mother.
For every x that you choose, you can find some y such that y is x's mother. So it's just saying that everyone has a mother- but it isn't saying that everyone has the same mother. It just says I have a mother, you have a mother, Tom, Dick, and Harry have mothers, etc.
There exists some x such that, for all y, y is x's mother.
You can find some x such that, for every y that you choose, y is x's mother. So this says that someone is a son or daughter of every mother, i.e., every mother is this person's mother. So this person would be brother or sister to me, you, Tom, Dick, and Harry.
Oh, I should make clear that 'there exists some' means there exists at least one. And this doesn't exclude the possibility that the 'some' could be all.
Last edited: Jun 20, 2005
13. Jun 20, 2005
### matt grime
it isn't true; it is the defining cahracteristic of the real numbers: the only element of the positive reals less than 1/n for all n is 0.
perhaps if you didn't use arbitrary arbitrarly and stuck to for alls and there exists you'd do bette; read honestrosewater's last pst.
not in the reals as i have said; it is the archimedean property. this is one of those things that i meant when i should check you understand your terminology.
yes, that is false.thoguh i'd prefer it "for all n"
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# What is the speed of the block when it has moved a distance of 0.0200 m from its initial position? (At this point the spring is compressed 0.0190 m). See details.
## A 2.55 kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0390 m. The spring has a force constant of 815 N/m. The coefficient of kinetic friction between the floor and the block is 0.35. The block and spring are released from rest and the block slides along the floor.
Apr 11, 2017
$v = 0.32 \text{ } \frac{m}{s}$
#### Explanation:
$\text{When a spring is compressed by a Force of F,The potential energy }$$\text{is stored on it.}$
$\text{if the spring is released, the Potential energy turns into kinetic energy.}$
$\text{The object is repulsed by the call-back force which occurs on the spring}$
$F ' = K \cdot \Delta x$
$K = 815 \frac{N}{m}$
$\Delta x = 0.0190 \text{ } m$
$F ' = 815 \cdot 0.019 = 15.48 \text{ } N$
${F}_{f} = k \cdot m \cdot g$
${F}_{f} = 0.35 \cdot 2.55 \cdot 9.81 = 8.76 N \text{ Friction force}$
$\text{acceleration of object is :}$
$a = \frac{F ' - {F}_{f}}{m}$
$m = 2.55 k g \text{ mas of object}$
$a = \frac{15.48 - 8.76}{2.55}$
$a = 2.64 \text{ } \frac{m}{s} ^ 2$
${v}^{2} = 2 \cdot a \cdot \mathrm{di} s p l a c e m e n t$
${v}^{2} = 2 \cdot 2.64 \cdot 0.0200$
${v}^{2} = 0.1056$
$v = \sqrt{0.1056}$
$v = 0.32 \text{ } \frac{m}{s}$
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# Sequence container (C++)
In computing, sequence containers refer to a group of container class templates in the standard library of the C++ programming language that implement storage of data elements. Being templates, they can be used to store arbitrary elements, such as integers or custom classes. One common property of all sequential containers is that the elements can be accessed sequentially. Like all other standard library components, they reside in namespace std.
The following containers are defined in the current revision of the C++ standard: `array`, `vector`, `list`, `forward_list`, `deque`. Each of these containers implements different algorithms for data storage, which means that they have different speed guarantees for different operations:[1]
• `array` implements a compile-time non-resizable array.
• `vector` implements an array with fast random access and an ability to automatically resize when appending elements.
• `deque` implements a double-ended queue with comparatively fast random access.
• `list` implements a doubly linked list.
• `forward_list` implements a singly linked list.
Since each of the containers needs to be able to copy its elements in order to function properly, the type of the elements must fulfill `CopyConstructible` and `Assignable` requirements.[2] For a given container, all elements must belong to the same type. For instance, one cannot store data in the form of both char and int within the same container instance.
## History
Originally, only `vector`, `list` and `deque` were defined. Until the standardization of the C++ language in 1998, they were part of the Standard Template Library (STL), published by SGI.
The `array` container at first appeared in several books under various names. Later it was incorporated into a Boost library, and was proposed for inclusion in the standard C++ library. The motivation for inclusion of `array` was that it solves two problems of the C-style array: the lack of an STL-like interface, and an inability to be copied like any other object. It firstly appeared in C++ TR1 and later was incorporated into C++11.
The `forward_list` container was added to C++11 as a space-efficient alternative to `list` when reverse iteration is not needed.
## Properties
`array`, `vector` and `deque` all support fast random access to the elements. `list` supports bidirectional iteration, whereas `forward_list` supports only unidirectional iteration.
`array` does not support element insertion or removal. `vector` supports fast element insertion or removal at the end. Any insertion or removal of an element not at the end of the vector needs elements between the insertion position and the end of the vector to be copied. The iterators to the affected elements are thus invalidated. In fact, any insertion can potentially invalidate all iterators. Also, if the allocated storage in the `vector` is too small to insert elements, a new array is allocated, all elements are copied or moved to the new array, and the old array is freed. `deque`, `list` and `forward_list` all support fast insertion or removal of elements anywhere in the container. `list` and `forward_list` preserves validity of iterators on such operation, whereas `deque` invalidates all of them.
### Vector
The elements of a `vector` are stored contiguously.[3] Like all dynamic array implementations, vectors have low memory usage and good locality of reference and data cache utilization. Unlike other STL containers, such as deques and lists, vectors allow the user to denote an initial capacity for the container.
Vectors allow random access; that is, an element of a vector may be referenced in the same manner as elements of arrays (by array indices). Linked-lists and sets, on the other hand, do not support random access or pointer arithmetic.
The vector data structure is able to quickly and easily allocate the necessary memory needed for specific data storage, and it is able to do so in amortized constant time. This is particularly useful for storing data in lists whose length may not be known prior to setting up the list but where removal (other than, perhaps, at the end) is rare. Erasing elements from a vector or even clearing the vector entirely does not necessarily free any of the memory associated with that element.
#### Capacity and reallocation
A typical vector implementation consists, internally, of a pointer to a dynamically allocated array,[1] and possibly data members holding the capacity and size of the vector. The size of the vector refers to the actual number of elements, while the capacity refers to the size of the internal array.
When new elements are inserted, if the new size of the vector becomes larger than its capacity, reallocation occurs.[1][4] This typically causes the vector to allocate a new region of storage, move the previously held elements to the new region of storage, and free the old region.
Because the addresses of the elements change during this process, any references or iterators to elements in the vector become invalidated.[5] Using an invalidated reference causes undefined behaviour.
The reserve() operation may be used to prevent unnecessary reallocations. After a call to reserve(n), the vector's capacity is guaranteed to be at least n.[6]
The vector maintains a certain order of its elements, so that when a new element is inserted at the beginning or in the middle of the vector, subsequent elements are moved backwards in terms of their assignment operator or copy constructor. Consequently, references and iterators to elements after the insertion point become invalidated.[7]
C++ vectors do not support in-place reallocation of memory, by design; i.e., upon reallocation of a vector, the memory it held will always be copied to a new block of memory using its elements' copy constructor, and then released. This is inefficient for cases where the vector holds plain old data and additional contiguous space beyond the held block of memory is available for allocation.
#### Specialization for bool
The Standard Library defines a specialization of the `vector` template for `bool`. The description of this specialization indicates that the implementation should pack the elements so that every `bool` only uses one bit of memory.[8] This is widely considered a mistake.[9][10] `vector<bool>` does not meet the requirements for a C++ Standard Library container. For instance, a `container<T>::reference` must be a true lvalue of type `T`. This is not the case with `vector<bool>::reference`, which is a proxy class convertible to `bool`.[11] Similarly, the `vector<bool>::iterator` does not yield a `bool&` when dereferenced. There is a general consensus among the C++ Standard Committee and the Library Working Group that `vector<bool>` should be deprecated and subsequently removed from the standard library, while the functionality will be reintroduced under a different name.[12]
### List
The `list` data structure implements a doubly linked list. Data is stored non-contiguously in memory which allows the list data structure to avoid the reallocation of memory that can be necessary with vectors when new elements are inserted into the list.
The list data structure allocates and deallocates memory as needed; therefore, it does not allocate memory that it is not currently using. Memory is freed when an element is removed from the list.
Lists are efficient when inserting new elements in the list; this is an ${\displaystyle O(1)}$ operation. No shifting is required like with vectors.
Lists do not have random access ability like vectors (${\displaystyle O(1)}$ operation). Accessing a node in a list is an ${\displaystyle O(n)}$ operation that requires a list traversal to find the node that needs to be accessed.
With small data types (such as ints) the memory overhead is much more significant than that of a vector. Each node takes up `sizeof(type) + 2 * sizeof(type*)`. Pointers are typically one word (usually four bytes under 32-bit operating systems), which means that a list of four byte integers takes up approximately three times as much memory as a vector of integers.
### Forward list
The `forward_list` data structure implements a singly linked list.
### Deque
`deque` is a container class template that implements a double-ended queue. It provides similar computational complexity to `vector` for most operations, with the notable exception that it provides amortized constant-time insertion and removal from both ends of the element sequence. Unlike `vector`, `deque` uses discontiguous blocks of memory, and provides no means to control the capacity of the container and the moment of reallocation of memory. Like `vector`, `deque` offers support for random access iterators, and insertion and removal of elements invalidates all iterators to the deque.
### Array
`array` implements a compile-time non-resizable array. The size is determined at compile-time by a template parameter. By design, the container does not support allocators. Unlike the other standard containers, `array` does not provide constant-time swap.
## Overview of functions
The containers are defined in headers named after the names of the containers, e.g. `vector` is defined in header `<vector>`. All containers satisfy the requirements of the Container concept, which means they have `begin()`, `end()`, `size()`, `max_size()`, `empty()`, and `swap()` methods.
### Member functions
Functions `array`
(C++11)
`vector`
`deque`
`list`
`forward_list`
(C++11)
Description
Basics (implicit) (constructor) (constructor) (constructor) (constructor) Constructs the container from variety of sources
(destructor) (destructor) (destructor) (destructor) Destructs the container and the contained elements
`operator=` `operator=` `operator=` `operator=` Assigns values to the container
N/A `assign` `assign` `assign` `assign` Assigns values to the container
Allocators `get_allocator` `get_allocator` `get_allocator` `get_allocator` Returns the allocator used to allocate memory for the elements
Element
access
`at` `at` `at` N/A N/A Accesses specified element with bounds checking.
`operator[]` `operator[]` `operator[]` Accesses specified element without bounds checking.
`front` `front` `front` `front` `front` Accesses the first element
`back` `back` `back` `back` N/A Accesses the last element
`data` `data` N/A N/A Accesses the underlying array
Iterators `begincbegin` `begincbegin` `begincbegin` `begincbegin` `begincbegin` Returns an iterator to the beginning of the container
`endcend` `endcend` `endcend` `endcend` `endcend` Returns an iterator to the end of the container
`rbegincrbegin` `rbegincrbegin` `rbegincrbegin` `rbegincrbegin` N/A Returns a reverse iterator to the reverse beginning of the container
`rendcrend` `rendcrend` `rendcrend` `rendcrend` Returns a reverse iterator to the reverse end of the container
Capacity `empty` `empty` `empty` `empty` `empty` Checks whether the container is empty
`size` `size` `size` `size` N/A Returns the number of elements in the container.
`max_size` `max_size` `max_size` `max_size` `max_size` Returns the maximum possible number of elements in the container.
N/A `reserve` N/A N/A N/A Reserves storage in the container
`capacity` Returns the number of elements that can be held in currently allocated storage
`shrink_to_fit` `shrink_to_fit` Reduces memory usage by freeing unused memory (C++11)
Modifiers `clear` `clear` `clear` `clear` Clears the contents
`insert` `insert` `insert` N/A Inserts elements
`emplace` `emplace` `emplace` Constructs elements in-place (C++11)
`erase` `erase` `erase` Erases elements
N/A `push_front` `push_front` `push_front` Inserts elements to the beginning
`emplace_front` `emplace_front` `emplace_front` Constructs elements in-place at the beginning (C++11)
`pop_front` `pop_front` `pop_front` Removes the first element
`push_back` `push_back` `push_back` N/A Inserts elements to the end
`emplace_back` `emplace_back` `emplace_back` Constructs elements in-place at the end (C++11)
`pop_back` `pop_back` `pop_back` Removes the last element
N/A N/A N/A `insert_after` Inserts elements after specified position (C++11)
`emplace_after` Constructs elements in-place after specified position (C++11)
`erase_after` Erases elements in-place after specified position (C++11)
`resize` `resize` `resize` `resize` Changes the number of stored elements
`swap` `swap` `swap` `swap` `swap` Swaps the contents with another container of the same type
`fill` N/A N/A N/A N/A Fills the array with the given value
There are other operations that are available as a part of the list class and there are algorithms that are part of the C++ STL (Algorithm (C++)) that can be used with the `list` and `forward_list` class:
#### Operations
• `list::merge` and `forward_list::merge` - Merges two sorted lists
• `list::splice` and `forward_list::splice_after` - Moves elements from another list
• `list::remove` and `forward_list::remove` - Removes elements equal to the given value
• `list::remove_if` and `forward_list::remove_if` - Removes elements satisfying specific criteria
• `list::reverse` and `forward_list::reverse` - Reverses the order of the elements
• `list::unique` and `forward_list::unique` - Removes consecutive duplicate elements
• `list::sort` and `forward_list::sort` - Sorts the elements
## Usage example
The following example demonstrates various techniques involving a vector and C++ Standard Library algorithms, notably shuffling, sorting, finding the largest element, and erasing from a vector using the erase-remove idiom.
```#include <iostream>
#include <vector>
#include <array>
#include <algorithm> // sort, max_element, random_shuffle, remove_if, lower_bound
#include <functional> // greater
#include <iterator> //begin, end, cbegin, cend, distance
// used here for convenience, use judiciously in real programs.
using namespace std;
using namespace std::placeholders;
auto main(int, char**)
-> int
{
array<int,4> arr{ 1, 2, 3, 4 };
// initialize a vector from an array
vector<int> numbers( cbegin(arr), cend(arr) );
// insert more numbers into the vector
numbers.push_back(5);
numbers.push_back(6);
numbers.push_back(7);
numbers.push_back(8);
// the vector currently holds { 1, 2, 3, 4, 5, 6, 7, 8 }
// randomly shuffle the elements
random_shuffle( begin(numbers), end(numbers) );
// locate the largest element, O(n)
auto largest = max_element( cbegin(numbers), cend(numbers) );
cout << "The largest number is " << *largest << "\n";
cout << "It is located at index " << distance(largest, cbegin(numbers)) << "\n";
// sort the elements
sort( begin(numbers), end(numbers) );
// find the position of the number 5 in the vector
auto five = lower_bound( cbegin(numbers), cend(numbers), 5 );
cout << "The number 5 is located at index " << distance(five, cbegin(numbers)) << "\n";
// erase all the elements greater than 4
numbers.erase( remove_if(begin(numbers), end(numbers),
bind(greater<>{}, _1, 4) ), end(numbers) );
// print all the remaining numbers
for(const auto& element : numbers)
cout << element << " ";
return 0;
}
```
The output will be the following:
```The largest number is 8
It is located at index 6 (implementation-dependent)
The number 5 is located at index 4
1 2 3 4
```
## References
• William Ford, William Topp. Data Structures with C++ and STL, Second Edition. Prentice Hall, 2002. ISBN 0-13-085850-1. Chapter 4: The Vector Class, pp. 195–203.
• Josuttis, Nicolai M. (1999). The C++ Standard Library. Addison-Wesley. ISBN 0-201-37926-0.
## Notes
1. ^ a b c Josuttis, Nicolai (1999). C++ Standard Library - A Tutorial and Reference. Addison-Wesley.
2. ^ ISO/IEC (2003). ISO/IEC 14882:2003(E): Programming Languages - C++ §23.1 Container requirements [lib.container.requirements] para. 4
3. ^ ISO/IEC (2003). ISO/IEC 14882:2003(E): Programming Languages - C++ §23.2.4 Class template vector [lib.vector] para. 1
4. ^ ISO/IEC (2003). ISO/IEC 14882:2003(E): Programming Languages - C++ §23.2.4.3 vector modifiers [lib.vector.modifiers] para. 1
5. ^ ISO/IEC (2003). ISO/IEC 14882:2003(E): Programming Languages - C++ §23.2.4.2 vector capacity [lib.vector.capacity] para. 5
6. ^ ISO/IEC (2003). ISO/IEC 14882:2003(E): Programming Languages - C++ §23.2.4.2 vector capacity [lib.vector.capacity] para. 2
7. ^ ISO/IEC (2003). ISO/IEC 14882:2003(E): Programming Languages - C++ §23.2.4.3 vector modifiers [lib.vector.modifiers] para. 3
8. ^ ISO/IEC (2003). ISO/IEC 14882:2003(E): Programming Languages - C++ §23.2.5 Class vector<bool> [lib.vector.bool] para. 1
9. ^ "vector<bool>: More Problems, Better Solutions" (PDF). August 1999. Retrieved 28 November 2017.
10. ^ "A Specification to deprecate vector<bool>". March 2007. Retrieved 28 November 2017.
11. ^ ISO/IEC (2003). ISO/IEC 14882:2003(E): Programming Languages - C++ §23.2.5 Class vector<bool> [lib.vector.bool] para. 2
12. ^ "96. Vector<bool> is not a container". Retrieved 28 June 2018.
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# What can we learn about GRB from the variability timescale related correlations? [HEAP]
Recently, two empirical correlations related to the minimum variability timescale ($\rm MTS$) of the lightcures are discovered in gamma-ray bursts (GRBs). One is the anti-correlation between $\rm MTS$ and Lorentz factor $\Gamma$, the other is the anti-correlation between the $\rm MTS$ and gamma-ray luminosity $L_\gamma$. Both the two correlations might be used to explore the activity of the central engine of GRBs. In this paper we try to understand these empirical correlations by combining two popular black hole (BH) central engine models (namely, Blandford \& Znajek mechanism and neutrino-dominated accretion flow). By taking the $\rm MTS$ as the timescale of viscous instability of the neutrino-dominated accretion flow (NDAF), we find that these correlations favor the scenario in which the jet is driven by Blandford-Znajek (BZ) mechanism.
W. Xie, W. Lei and D. Wang
Thu, 16 Mar 17
12/92
Comments: 6 pages, 3 figures, accepted for publication in ApJ
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# Events happening on April 11, 2017
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Apr. 11, 2017
2pm (MATH 220)
###### Logic
Stan Wagon (Macalester College)
A Paradox Due to the Absence of the Axiom of Choice; and a Proof of the Tetrahedral Loop Conjecture
Apr. 11, 2017
2pm (MATH 350)
###### Lie Theory
Monica Vazirani (UC Davis)
Representations of the affine BMW algebra
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# Getting “You have to run LaTeX again to get the references right ” over and over again
on Ubuntu 10.04 with Emacs 23.1.1 and TexLive, writing a book (scrbook) spread over different files, I have the following problem: Doing C-c C-c in Emacs (the usual cycle LaTeX BibTeX LaTeX LaTeX) I get "You have to run LaTeX again to get the references right" over and over again, although pdfLaTeX writes the files and there are apparently no references missing in the pdf ( a search for "??" gave 0 results).
Before telling the whole story I would like to ask If anybody experienced this problem before, because I could not find any reports. Is diagnosis and treatment of similar cases available somwhere?
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Can you try to create a MWE (Minimal working example)? Please avoid telling the "whole" story, but rather do some preliminary work: Copy the files to a separate directory, add the files into the main file and check if it still happens. Start removing parts of the file as long as the problem is still happening...once you can reproduce the problem with a file that only contains relevant code, and the problem still persists, post it here....more likely, you'll find the problem in the meantime...but if not, by all means, post it here... – Yossi Farjoun Nov 15 '10 at 15:52
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# Research Seminars: Geometry and Topology
Past Geometry and Topology:
## Fall 2018
Time & Location: All talks are on Thursday in Gibson Hall 400D at 12:30 PM unless otherwise noted.
Organizer: Slawomir Kwasik
October 18
## Topic: On the reconstruction problem for geodesic subspaces in the Euclidean Space
Rafał Komendarczyk - Tulane University
Abstract:
We develop a persistence based algorithm for the homology/homotopy groups reconstruction of the unknown underlying geodesic subspace of R^n from a point cloud. In the case of a metric graph, we can output a subspace which is an arbitrarily good approximation of the underlying graph. This is a collaborative work in progress.
October 25
## Finite-type knot invariants and a proof of the Goussarov Theorem
Robyn Brooks - Tulane University
Abstract
Finite-type knot invariants represent an active research area in knot theory. The Goussarov Theorem shows that all such invariants can be read from the Gauss diagram of a knot. In this talk, I will give a proof of this theorem, which provides a method by which one can generate a formula to determine the value of an invariant from its Gauss diagram.
November 1
## Discrete Morse theory and its applications to metric graph reconstruction
Sushovan Majhi - Tulane University
Abstract:
Discrete Morse theory has recently been used as a powerful tool for topological reconstruction and simplification in the field of Applied and Computational Topology. We discuss some its very recent and successful applications in data analysis. In particular, we talk about a recent development in threshold-based topological and geometric reconstruction of metric graphs from a density concentrated around it.
November 15
## Density bounds on binary packings of disks in the plane
Ali Mohajer - Tulane University
Abstract:
In this talk we develop methods for establishing upper density bounds for saturated two-radius packings of disks in the plane.
Define the homogeneity of a packing of disks in the plane to be the infimum of the ratio of radii of disks in the packing. It has been known since 1953 (L. Fejes-Toth) that if the homogeneity of a packing is close enough to 1, the density of that packing cannot exceed $\frac{$\pi}{\sqrt{12}},\$ the upper bound on the density of a single-radius packing. "Close enough” was refined in 1963 by August Florian to mean a homogeneity in the interval (0.902…, 1], and in 1969, Gerd Blind extended the left bound of this interval to approximately 0.742.
In 2003, sharp upper density bounds were established by Aladar Heppes for a handful of two-radius packings at homogeneities which admit arrangements wherein each disk is tangent to a ring of disks, each of which is tangent to its two cyclic neighbors. We will discuss recent progress in establishing a bound sharper than the best one known for binary packings at a homogeneity that does not admit such regularity.
Date
## Topic
Speaker - Institution
Abstract: TBA
Date
## Topic
Speaker - Institution
Abstract: TBA
Mathematics Department, 424 Gibson Hall, New Orleans, LA 70118 504-865-5727 [email protected]
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# Updated T2K measurements of muon neutrino and antineutrino disappearance using 1.5 x 10(21) protons on target
Abe, K, Amey, J, Andreopoulos, C ORCID: 0000-0003-2020-8215, Antonova, M, Aoki, S, Ariga, A, Ashida, Y, Autiero, D, Ban, S, Barbi, M
et al (show 315 more authors) (2017) Updated T2K measurements of muon neutrino and antineutrino disappearance using 1.5 x 10(21) protons on target. PHYSICAL REVIEW D, 96 (1). 011102-.
We report measurements by the T2K experiment of the parameters $\theta_{23}$ and $\Delta m^{2}_{32}$ governing the disappearance of muon neutrinos and antineutrinos in the three flavor neutrino oscillation model. Utilizing the ability of the experiment to run with either a mainly neutrino or a mainly antineutrino beam, the parameters are measured separately for neutrinos and antineutrinos. Using $7.482 \times 10^{20}$ POT in neutrino running mode and $7.471 \times 10^{20}$ POT in antineutrino mode, T2K obtained, $\sin^{2}(\theta_{23})=0.51^{+0.08}_{-0.07}$ and $\Delta m^{2}_{32} = 2.53^{+0.15}_{-0.13} \times 10^{-3}$eV$^{2}$/c$^{4}$ for neutrinos, and $\sin^{2}({\overline{\theta}}_{23})=0.42^{+0.25}_{-0.07}$ and ${\Delta\overline{m}^2}_{32} = 2.55^{+0.33}_{-0.27} \times 10^{-3}$eV$^{2}$/c$^{4}$ for antineutrinos (assuming normal mass ordering). No significant differences between the values of the parameters describing the disappearance of muon neutrinos and antineutrinos were observed.
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# Applications of cardinal numbers
I know basic things about cardinality (I'm only in High School) like that since $\mathbb{Q}$ is countable, its cardinality is $\aleph_0$. Also that the cardinality of $\mathbb{R}$ is $2^{\aleph_0}$.
Are there any direct applications of these numbers outside of theoretical math?
I know this can be convenient for certain proofs and help understanding sets of numbers, but are there any applications of this?
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Yes. Plenty of set theorists got a job because infinite cardinals. – Asaf Karagila Mar 7 '13 at 20:24
Well, an important application is that if you have $\,\aleph_0\,$ dollars then you can form $\,2^{\aleph_0}\,$ different sets with them. This has proven to be very handy to Scrooge McDuck, for example... – DonAntonio Mar 7 '13 at 20:25
Asaf's application is way more important than mine... – DonAntonio Mar 7 '13 at 20:26
For all intents and purposes, there is no such thing as infinity outside of mathematical (or philosophical) thought. All measurements and interactions we encounter every day are finite. – rschwieb Mar 7 '13 at 20:29
The answer is an obvious no. For two main reasons:
1. With the exception of occasional naive approach to sets, there is little to no use of set theory outside theoretical mathematics. So any application would be indirect and purely coincidental.
2. Applied mathematics is not concerned with infinite objects. Let alone "vastly huge beyond any reasonable visualization and imagination of a human being" sizes of infinity.
It is important to understand that mathematics is not "merely a tool for engineers" (or physicists). It is a world filled with magic and mind boggling ideas which have absolutely nothing to do with this physical reality. Infinite sets is one of them. These ideas trickle slowly and some of them eventually get to the point where they have some use, but these uses are far from being "direct" in any sense of the word.
For example, by plain cardinality arguments it is easy to see that almost any function from $\Bbb R$ to itself is not continuous, or even Borel measurable. Almost any continuous function is nowhere differentiable, and almost all the differentiable functions are not continuously differentiable, and so on and so forth (although some of these arguments require more than sheer cardinality).
But have you ever seen someone "applying" everywhere-discontinuous functions to a real world situation? I can't recall anything like that (although it might be in some quantum theory sort of application I am unaware of).
As long as mankind is limited by a finite powers of perception we cannot even distinguish between $100^{100^{100^{100^{100}}}}$ and $\aleph_0$.
Might also be relevant: Can we distinguish $\aleph_0$ from $\aleph_1$ in Nature?
-
I would love to hear the complaints against this answer. Also, if someone does have direct applications of infinite cardinals outside theoretical mathematics, I'd love to know about them! – Asaf Karagila Mar 7 '13 at 20:47
Maybe cardinality have something to do with theory of possible worlds. I'm not sure "direct application" in your mind is applicable to such things.tau.ac.il/~samet/papers/knowing-whether.pdf – Metta World Peace Mar 8 '13 at 0:12
Quoted from Christian Marks blog(blog seems to be gone now):
In an unexpected development for the depressed market for mathematical logicians, Wall Street has begun quietly and aggressively recruiting proof theorists and recursion theorists for their expertise in applying ordinal notations and ordinal collapsing functions to high-frequency algorithmic trading. Ordinal notations, which specify sequences of ordinal numbers of ever increasing complexity, are being used by elite trading operations to parameterize families of trading strategies of breathtaking sophistication.
The monetary advantage of the current strategy is rapidly exhausted after a lifetime of approximately four seconds — an eternity for a machine, but barely enough time for a human to begin to comprehend what happened. The algorithm then switches to another trading strategy of higher ordinal rank, and uses this for a few seconds on one or more electronic exchanges, and so on, while opponent algorithms attempt the same maneuvers, risking billions of dollars in the process.
The elusive and highly coveted positions for proof theorists on Wall Street, where they are known as trans-quantitative analysts, have not been advertised, to the chagrin of executive recruiters who work on commission. Elite hedge funds and bank holding companies have been discreetly approaching mathematical logicians who have programming experience and who are familiar with arcane software such as the ordinal calculator. A few logicians were offered seven figure salaries, according to a source who was not authorized to speak on the matter.
-
Ordinal$\neq$cardinals. – Asaf Karagila Mar 7 '13 at 21:03
Yes and no.
The distinction between different infinite cardinals is crucial in probability theory. If you have a sequence of sets $A_1,A_2,\cdots$ (necessarily countable) that are each assigned a probability, then according to the Kolmogorov axioms $A_1 \cup A_2 \cup \cdots$ is necessarily assigned a probability. On the other hand, if you have a $2^{\aleph_0}$ many sets, their union needn't be assigned a probability. This is it to prevent certain subtle paradoxes, whereby its impossible to assign a "length" (or "mass") to every subset of $[a,b]$.
One possible rebuttal is that the cardinal numbers are only used to prevent very subtle problems in probability theory, and so they don't really have direct applications to the real world. However, I think this is wrong-headed. (Classical) logic is brittle. One contradiction and the whole system falls to pieces. So if probability theory had even one contradiction, this would be a SERIOUS problem, in my opinion.
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Have you ever seen anyone outside theoretical mathematics refer to non-measurable sets? Or even non-Borel sets? – Asaf Karagila Mar 7 '13 at 21:06
No: the Kolmogorov axioms protect us from these things. – goblin Mar 7 '13 at 21:45
I really don't see how that comment addressed mine; and in a re-read of your answer, I also don't see how the fact that we only require probability to be countably additive is related to cardinals, or protects us from paradoxes. – Asaf Karagila Mar 7 '13 at 21:49
Yes my answer isn't very clear. Anyway, consider the following. If arbitrary unions of events were assumed to be events, and if the singleton subsets of $[a,b]$ were assumed to be events, then every subset of $[a,b]$ would be an event. Including the non-measurable ones. – goblin Mar 7 '13 at 21:55
@Metta: I am happy to see that the axiom of choice has real world applications. – Asaf Karagila Mar 8 '13 at 0:34
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# Month: September 2017
## BSides STL – Find the Flag – Decoding
Find the flag hidden in this program!
This challenge starts with a file called flag.exe
After running it, I checked for any recently changed files, no dice.
### Binwalk Output
Looking at the output and, wow! We got a QR code!
And scanning that gives us the flag!
FLAG(YOUFOUNDTHEICON-BSIDESSTL-2017)
~T
### Running flag.exe
Alright, let’s throw it in Kali and do some analysis.
Aha! Binwalk says there’s a PNG in there! Lets extract it!
binwalk --dd=".*" flag.exe
Posted by Tanner in CTF, Posts
## Tokyo Westerns – My Simple Cipher – Crypto
To start off, we are given a text file containing some encrypted data and the program that was used to encrypt the data. The encryption program is as follows:
import sys
import random
key = sys.argv[1]
flag = '**CENSORED**'
assert len(key) == 13
assert max([ord(char) for char in key]) < 128
assert max([ord(char) for char in flag]) < 128
message = flag + "|" + key
encrypted = chr(random.randint(0, 128))
for i in range(0, len(message)):
encrypted += chr((ord(message[i]) + ord(key[i % len(key)]) + ord(encrypted[i])) % 128)
print(encrypted.encode('hex'))
Now we know how it was encrypted and how the plaintext is structured! Let’s take a look at the encrypted data.
enc = 7c 15 3a 47 4b 6a 2d 3f 7d 3f 73 28 70 3e 6c 2d 24 3a 08 3e 2e 77 3c 45 54 77 48 66 7c 15 11 33 3f 4f 74 5e
• enc[1:7] is “TWCTF{” this is our flag format
• enc[20:22] is “}|” this is the end of the flag and the separator between the flag and the key
• enc[22:] is the encrypted key
So now we need to figure out how to reverse the encryption algorithm.
encrypted += chr((ord(message[i]) + ord(key[i % len(key)]) + ord(encrypted[i])) % 128)
Because we know the first part of the flag, we can use that to retrieve a partial key! That is done through the magic of math
$$E_{n+1} = \left ( P_{n} + K_{n \mod 13} + E_{n} \right ) \mod 128$$
Because of the nature of the input, we can make an educated guess about the values of the above equation pre-mod.
$$w = \left ( E_n + M_n \right )\mod 128$$
$$g = E_{n+1}$$
$$k_n = \left\{\begin{matrix}128-w+g & w>g\\ g-w & w \leq g\end{matrix}\right.$$
Or if you’d rather read a program,
encrypted = "7C153A474B6A2D3F7D3F7328703E6C2D243A083E2E773C45547748667C1511333F4F745E"
hexbytes = [encrypted[i:i+2] for i in range(0,len(encrypted),2)]
key = ""
message = "TWCTF{"
work = work%128
if work > goal:
out = 128-work+goal
else:
out = goal-work
return(out)
i = len(message)-1
for i,byte in enumerate(hexbytes):
work = int(byte,16) + ord(message[i])
goal = int(hexbytes[i+1],16)
print(chr(getadd(work,goal)), end="")
Running through this will give us the first 6 characters of the key, which happen to be “ENJ0YH” at this point, we made an educated guess that the whole key was “ENJ0YHACKING!” and ran a decryption program
encrypted = "7C153A474B6A2D3F7D3F7328703E6C2D243A083E2E773C45547748667C1511333F4F745E"
hexbytes = [encrypted[i:i+2] for i in range(0,len(encrypted),2)]
message = ""
key = "ENJ0YHACKING!"
key = [ord(c) for c in key]
work = work%128
if work > goal:
out = 128-work+goal
else:
out = goal-work
return(out)
for i,byte in enumerate(hexbytes[:-1]):
work = key[i%13] + int(hexbytes[i],16)
goal = int(hexbytes[i+1],16)
print(message)
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# Bibliotek
Musik » They Might Be Giants »
## The House at the Top of the Tree
51 spelade låtar | Gå till låtsida
Låtar (51)
Låt Album Längd Datum
The House at the Top of the Tree 2:29 27 okt 2011, 12:21
The House at the Top of the Tree 2:29 10 nov 2011, 13:27
The House at the Top of the Tree 2:29 15 nov 2011, 22:31
The House at the Top of the Tree 2:29 22 nov 2011, 01:12
The House at the Top of the Tree 2:29 22 nov 2011, 22:49
The House at the Top of the Tree 2:29 25 nov 2011, 14:34
The House at the Top of the Tree 2:29 28 nov 2011, 13:09
The House at the Top of the Tree 2:29 2 dec 2011, 13:10
The House at the Top of the Tree 2:29 3 dec 2011, 00:33
The House at the Top of the Tree 2:29 4 dec 2011, 23:05
The House at the Top of the Tree 2:29 8 dec 2011, 13:13
The House at the Top of the Tree 2:29 8 jan 2012, 23:14
The House at the Top of the Tree 2:29 12 jan 2012, 00:12
The House at the Top of the Tree 2:29 3 feb 2012, 12:35
The House at the Top of the Tree 2:29 9 mar 2012, 12:33
The House at the Top of the Tree 2:29 6 apr 2012, 11:29
The House at the Top of the Tree 2:29 25 apr 2012, 11:46
The House at the Top of the Tree 2:29 27 apr 2012, 11:50
The House at the Top of the Tree 2:29 30 apr 2012, 11:45
The House at the Top of the Tree 2:29 28 maj 2012, 22:29
The House at the Top of the Tree 2:29 7 jun 2012, 19:51
The House at the Top of the Tree 2:29 8 jun 2012, 02:23
The House at the Top of the Tree 2:29 8 jun 2012, 08:55
The House at the Top of the Tree 2:29 24 sep 2012, 22:34
The House at the Top of the Tree 2:29 1 okt 2012, 09:12
The House at the Top of the Tree 2:29 2 okt 2012, 11:28
The House at the Top of the Tree 2:29 17 okt 2012, 00:03
The House at the Top of the Tree 2:29 31 okt 2012, 11:28
The House at the Top of the Tree 2:29 15 nov 2012, 12:21
The House at the Top of the Tree 2:29 5 dec 2012, 12:28
The House at the Top of the Tree 2:29 10 jan 2013, 12:23
The House at the Top of the Tree 2:29 15 jan 2013, 12:33
The House at the Top of the Tree 2:29 19 jan 2013, 16:29
The House at the Top of the Tree 2:29 28 jan 2013, 12:18
The House at the Top of the Tree 2:29 28 feb 2013, 12:17
The House at the Top of the Tree 2:29 24 apr 2013, 11:22
The House at the Top of the Tree 2:29 29 apr 2013, 11:31
The House at the Top of the Tree 2:29 2 maj 2013, 11:31
The House at the Top of the Tree 2:29 22 maj 2013, 11:43
The House at the Top of the Tree 2:29 1 aug 2013, 05:04
The House at the Top of the Tree 2:29 1 aug 2013, 05:04
The House at the Top of the Tree 2:29 28 aug 2013, 10:53
The House at the Top of the Tree 2:29 19 sep 2013, 10:41
The House at the Top of the Tree 2:29 15 nov 2013, 11:40
The House at the Top of the Tree 2:29 18 nov 2013, 11:37
The House at the Top of the Tree 2:29 19 nov 2013, 11:40
The House at the Top of the Tree 2:29 20 nov 2013, 11:54
The House at the Top of the Tree 2:29 3 jan 2014, 17:09
The House at the Top of the Tree 2:29 8 jan 2014, 11:52
The House at the Top of the Tree 2:29 28 feb 2014, 11:40
The House at the Top of the Tree 2:29 19 aug 2014, 10:40
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If you are performing a chain calculation involving addition and subtraction, you should attempt to group the values appropriately. Watch this video lesson to learn how important it is to follow the order of operations. Calculate the power of large base integers and real numbers. Examples: 2+3*4 or 3/4*3 Description. What is the order? * You should always solve math problems in the following order: Parenthesis – (also called grouping symbols) Exponents Multiplication OR. How to Evaluate an Expression Using PEMDAS. So, $$3^2 = 9 \times 9$$ and $$2^4 = 2 \times 2 \times 2 \times 2$$. Check your work on a calculator and record keystrokes if your answers do not match each other. Can you solve this math problem?: 6^2 ÷ 2(3) + 4 = ? There are two ways of looking at this problem with the order of operations. The order of operations was settled upon in order to prevent miscommunication, but PEMDAS can generate its own confusion; some students sometimes tend to apply the hierarchy as though all the operations in a problem are on the same "level" (simply going from left to right), but often those operations are not "equal". Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Type your algebra problem into the text box. Now let's work through them. Expression Evaluation Calculator PI*pow(9/2,2) Parentheses can change the order of operations -----Legitimate Math Operators (Order and hierarchy is. Summary: The rules for the order of operations are: Simplify all operations inside Parentheses (and Brackets). The comprehensive lesson plans outlined below provide a detailed list of the Time4Learning sixth grade math curriculum. Calculator Use. Here is a graphic preview for all of the Exponents and Radicals Worksheets. Remember that these rules are true if a a a is positive, and m m m and n n n are real numbers. com math-drills. Calculations Using Order of Operations. Order of Operations Related Teacher Resources Here is a wide range of resources for a deeper understanding of this topic. You can either apply the numerator first or the denominator. + a 1x + a 0 where a n ≠ 0, the exponents are allwhole numbers, and the coefficients are all real. Examples: 2+3*4 or 3/4*3 Description. Order of operations with exponents. PEMDAS means parentheses, exponents, multiplication, division, addition and subtraction, telling you the order in which you tackle different parts of a long expression. The order of operations will allow you to solve this problem the right way. Quotient rule of exponents. Remember that the first thing to do in the order of operations is to simplify anything inside parenthesis. Play Order of Operations at MathPlayground. Now let's work through them. Place of functions in. They certainly mean well -- most math teachers believe that they are following the conventional order of operations. Addition & Subtraction come last (also left to right). Use PEMDAS, BODMAS, BIDMAS, BEDMAS, DMAS or GEMS to solve the expressions. We have 2 times 3 squared, and we have to remember that the first thing we would need to think about are the parentheses. Multiplication. Next, do any work with exponents or radicals. Numbers with exponents have a smaller number placed at the upper right-hand corner of a number. To the right of each step, identify the step as parentheses, exponents, multiplication, division, addition, or subtraction. A vocabulary list featuring Order of Operations. Most of the issues with simplifying using the order of operations stem from nested parentheses, exponents, and "minus" signs. 210 - Arithmetic & Algebraic Operations with Exponents; 230 - GRAPHITI - coordinate geometry, point generation, distance, functions. Related Answers Linear and exponential At the beginning of year 1, Lisa wants to invest $500 at an annual compound interest rate of 3%. Using exponents to solve problems. I am looking for students to recognize that the order of operations is a set of rules that have been decided upon by mathematicians. For the exponent, you can enter whole numbers, fractions, decimals and negative numbers. Related Answers Linear and exponential At the beginning of year 1, Lisa wants to invest$500 at an annual compound interest rate of 3%. 24 Order of Operations -- PEMDAS Practice Worksheets Remember, PEMDAS (Please Excuse My Dear Aunt Sally) stands for: Parentheses Exponents Multiplication Division Addition. How do you calculate (2 + 3) x (7 - 3)? Is the answer 32, 20 or is the answer 14? To know the correct answer, one must know the correct order of operations with respect to addition, subtraction, multiplication, division, and with respect to parenthesis. If an input is given then it can easily show the result for the given number. Showing top 8 worksheets in the category - Calculator Order Of Operations. Procedures for operations with decimals, fractions and integers are used for operations with rational numbers. (parentheses) 2. This is an online calculator for exponents. Practice this lesson yourself on KhanAcademy. Order of Operations Resources. Rule 1: Simplify all operations inside parentheses. 1 Description: Apply and extend the properties of exponents to solve problems with rational exponents. In this lesson, you reviewed addition and subtraction with decimal numbers by balancing a check register. Order of Operations Each calculation is performed in the following order of precedence: 1. Just type in sums like these (see Order of Operations for more detail):. 8th Grade Exponents Expressions and Equations Unit of Study Exponents Grade: 8 Topic: Exponent operations and rules Length of Unit: 12 – 15 days Focus of Learning Common Core Standards: Work with Radicals and Integer Exponents 8. For example, 2 raised to the second power is 2 x 2, which equals 4. Click Image to Enlarge : Practice applying order of operations. For example:. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Step 1: First, perform the operations within the parenthesis. But, when you see something like. , computer, calculator). Math worskheets with exponents covering: basic exponents exercises, power of ten exercises, operations with exponents, addition with exponents, subtraction with exponents, multiplication with exponents, division of exponents, exponents of fractions and decimals, order of operations inclusing exponents, exponenets of integers and negative numbers. You can select different variables to customize these Exponents and Radicals Worksheets for your needs. Lesson 6: Order of Operations Student Outcomes Students evaluate numerical expressions. com! Use the order of operations to correctly solve the problems. The video below provides nice introduction to R, including a review of mathematical operations that can be performed using R as a calculator. Theorem and Order of Operations = Apply and extend the properties of exponents to solve problems with rational exponents Program Task: Calculate the length of a rafter using the Pythagorean Theorem. In scientific notation, numbers are written as a base, b, referred to as the significand, multiplied by 10 raised to an integer exponent, n, which is referred to as the order of magnitude: b × 10 n. In this article, I will describe some misunderstandings about order of operations, and suggest a better way of thinking about the topic. The top priority is your parenthesis, then exponents, followed by multiplication and division, and finally addition and subtraction (PEMDAS). Unlimited replay and review. Evaluating Algebraic Expressions Order of Operations/P. Also for: 30xa. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). Others understand correct order of operations. Warning: Negative powers can also be used. com is the ideal site to pay a visit to!. ) Click to see a correct calculation. After thinking about it for quite a while, I decided that I would choose the power to be able to erase parts of the minds of others. Questions may involve working with negative numbers. Order of Operations - BODMAS Operations "Operations" mean things like add, subtract, multiply, divide, squaring, etc. Order of Operations with Whole Numbers and No Exponents (Four Steps) (2774 views this week) Order of Operations with Negative and Positive Integers (Three Steps) (1474 views this week) Order of Operations with Negative and Positive Integers (Four Steps) (1301 views this week) Order of Operations with Whole Numbers and No Exponents (Two Steps) (939 views this week) Order of Operations with. Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums. Do multiplication and division operations in order as you come to them from left. Besides the calculator is apt of carrying out simple calculations with numbers. This rule is not all-inclusive. 6 x 6 = 36. Outcome: Analyze the numerical data in a table for trends, patterns and interrelationships. Include expressions that arise from formulas used in real-world problems. In scientific notation, numbers are written as a base, b, referred to as the significand, multiplied by 10 raised to an integer exponent, n, which is referred to as the order of magnitude: b × 10 n. For instance, you can type 5+3log(100)/2 and hit ENTER. Check your work on a calculator and record keystrokes if your answers do not match each other. For example, to enter the number 3. Printable Order of Operations Worksheets. We are going to run through parenthesis first. 5log(x) = log(x5) (exponent rule) d. Operations at the top of the list are completed first, and operations on the same line are completed from left to right. Multiple Choice (80 points, 5 points each) Identify the choice that best completes the statement or answers the question. 2) ((7 ± 11) + 15) ! 4" Ans = 1) (8 + (2# + 3)) $9 Ans = 4) 5% ! ((18$ 3) ± 5). c Evaluate expressions at specific values of their variables. If I have to take the time each year to reteach integer operations, the order of operations, and exponent rules to my Algebra 1 students, I would much prefer to teach these to them from scratch. If you are looking for order of operations worksheets that test your knowledge of the PEMDAS rules, these math worksheets are a good start. Integer Order of Operations Worksheet All work must be shown for credit. This also means 6 to the second power. 7 An Introduction to Functions. 00 Subtraction 6 N 4 6 B 4 N 2. Let's do some examples together. They can seem confusing at first, but with practice we can master them just as we mastered the properties of numbers and operations. We have 2 times 3 squared, and we have to remember that the first thing we would need to think about are the parentheses. 6 Tables and Graphs: Exploring Data and Statistics 1. For example, 2 raised to the second power is 2 x 2, which equals 4. Students learn to use the following order of operations when simplifying problems that involve integers: Parentheses, Exponents, Multiplication/Division, and Addition/Subtraction (PEMDAS). This lesson stresses the use of parentheses to create unambiguous expressions. Which do you think is correct, and why? Person A Person B 8−2+1 8−2+1 6+1 8−3 7 5 2. This calculator adheres to the order of operations, and will soon allow for major functions such as the logarithms and the trigonometric functions. e Worksheet by Kuta Software LLC. To cube a number, just multiply it by itself twice (the exponent would be 3). Fractional Exponent Laws. What is the order of operations in trig functions? Ask Question ,$then the exponent$\quad ^2 \quad$would be inside the brackets. SEE MORE : 2. t 4 FMPafdQeR xw Zi 4t Lh2 kIyn DfIi In ki rt ZeL lA rlTg4e ObZroa f J1 Z. Do multiplication and division operations in order as you come to them from left. com and learn syllabus for college algebra, inverse and a good number of additional math subjects. Let’s work the exponent next. Below is a specific example illustrating the formula for fraction exponents when the numerator is not one. To add numbers with different signs, subtract the smaller absolute value from the larger absolute value. com math-drills. org right now: https://www. Simplify each expression, showing each step in the order of operations. What is the order of operations in trig functions? Ask Question ,$ then the exponent $\quad ^2 \quad$ would be inside the brackets. Com is a people's math website. Order of Operations Calculator - Online calculator tool. SEE MORE : 3. Know and apply the properties of integer exponents to generate equivalent numerical expressions. Algebra r of Operations P lease Parenthesis - Do all grouped operations first. Create your own math worksheets. Now let's work through them. In cases like these, we follow the order of operations. You also applied the order of operations in order to simplify numerical expressions. View Answer Keys- All the answer keys in one file. x 1 + x 2 = a 1 × 10 b1 + a 2 × 10 b2. Despite the ease it would provide, this calculator has no dependencies, and operates without even built in libraries. The Closer- Look very carefully at this one and note where the parentheses are. Proportions and Percents Converting between percents, fractions, and decimals Exponents and Radicals. Product rule of exponents. Evaluate math expressions left to right, first doing the math operations within parentheses, then exponents, then multiplication and division, and, lastly, addition and subtraction. Exponents, in simplest terms, are repeated multiplication of the same thing by itself. e Worksheet by Kuta Software LLC. The user can make a program directly with the calculator, or transfer one from a computer. These order of operations worksheets mix basic arithmetic, including parentheses and exponents, and tests students understanding of PEMDAS. Questions may involve working with negative numbers. When expressions have more than one operation, we have to follow rules for the order of operations: First do all operations that lie inside parentheses. Use PEMDAS, BODMAS, BIDMAS, BEDMAS, DMAS or GEMS to solve the expressions. Order of Operations with Fractions and Exponents - Make sure to cover exponents before you go here. So, in the examples that follow, I'll be demonstrating how to work with these sorts of expressions. I'm assuming you've given a go at it. For 2 number x1 and x2: x 1 = a 1 × 10 b1. WORKSHEETS. Definition of Order Of Operations explained with real life illustrated examples. or exponential notation on a scientific calculator. Getting Started With R (R Tutorial 1. Now let’s look at 2 4. Right from Subtract Fractions With Variables Calculator to formula, we have got all kinds of things included. Despite the ease it would provide, this calculator has no dependencies, and operates without even built in libraries. To evaluate expressions with exponents, refer to the rules of exponents in the table below. For example, to enter the number 3. operations in a math problem o The order of operations tells you the order in which you should go about solving problems like these: Ex) 3 + 5 x 6 Ex) 10 2 + 4 x 3 Ex) 5 x (3 + 4) - 3 B. In this math learning exercise, students use a graphing calculator to solve nine multi step problems with order of operations with exponents. Calculator - Kivy Order of Operations. Write each product in exponent form. Some problems will be product or quotient rule problems that involve the chain rule. ORDER OF OPERATIONS - PRINTABLES, QUIZZES & GAMES This page contains algebra exercises on order of operations arranged according to topics in the form of MCQs, Printables, Games and Worked Examples. Use a calculator to perform calculations involving scientific notation and exponent laws. A quiz from Quia. Rules for Operations with Exponents. Whenever the order of operation is not indicated by grouping symbols, there is a standard order of operations to be followed. Every single student in my class can recite the steps of order of operations - even the students working on a modified math program. Negative exponent rule. E – Exponents. Java has well-defined rules for specifying the order in which the operators in an expression are evaluated when the expression has several operators. Whenever the order of operation is not indicated by grouping symbols, there is a standard order of operations to be followed. © 2011 Mathmaster. com! Use the order of operations to correctly solve the problems. Fractional Exponents. Round to the nearest integer. Calculate the power of large base integers and real numbers. 0x10 -2) = (1. Operations with powers and exponents. Most common mnemonics for remembering this order of operations are: PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. For instance, does "3/5x" mean "(3/5)x" or "3/(5x)" ? For this confusion, teachers must share the blame. This math video tutorial provides a basic introduction into order of operations. Here is a graphic preview for all of the Exponents and Radicals Worksheets. or division, exponents or square roots in. Parentheses first, exponents next, the multiplication. Consider the follow: 5 •55•5•55. But since subtraction has the same precedence as addition, the subtraction of 2 does not go inside the summation. Unit Rate ( Is over of problems) Probabilities and Percents. Creating lessons is easy! Look for other lessons and click on 'view source'. … The original order of operations in some countries was BODMAS, which stands for Brackets, Orders or Powers, Division, Multiplication, Addition, Subtraction. Squaring a number and taking its square root are inverse operations. These order of operations worksheets mix basic arithmetic, including parentheses and exponents, and tests students understanding of PEMDAS. Solving order of operations becomes easy with the help of our online PEMDAS calculator. Students often mistake how to enter exponents into the calculator correctly. Exponents and Radicals Reporting Category Expressions and Operations Topic Performing operations with and writing radical expressions containing rational exponents Primary SOL AII. From correspondence with people on the the 48/2(9+3) problem, I have learned that in many schools today, students are taught a mnemonic "PEMDAS" for order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. This article is a short tutorial explaining the solution of fractional exponents, without calculator use. After clearing all the grouping symbols, you should work with the exponents. Unlimited replay and review. This rule is not all-inclusive. Using a Calculator. If the calculations involve a combination of parenthesis, exponents, multiplication, division, addition, and subtraction then. Summary: The rules for the order of operations are: Simplify all operations inside Parentheses (and Brackets). Please see part1 for the beginning. From integer simplify calculator to equations by factoring, we have all of it covered. Rule 1: Simplify all operations inside parentheses. When practicing evaluating math expressions, just click on the answer. No Download or Signup. 3 %c %i < 1st Expressions inside parentheses. In other words, when you have a bunch of operations in a row: multiply, add, evaluate powers, and so on, you have to do them in a very specific order to get the problem correct. Fractional Exponent Laws. If you are looking for order of operations worksheets that test your knowledge of the PEMDAS rules, these math worksheets are a good start. Since contracting is the opposite of expanding, we should go back to the normal order of operations. Exponents with a power of 0 Any exponent with a power of 0 equals 1, so 5 0 is 1, and so is 7 0, x 0, and any other exponent with a power of 0 you can think of. (exponents) 3. (1) Part 1 of 2 - How to Use the order of operations to evaluate expressions, (2) Part 2 of 2 - How to Use the order of operations to evaluate expressions. The order of operations is the order in which you solve the problem. Scientific notation converter Scientific notation calculations. To add numbers with different signs, subtract the smaller absolute value from the larger absolute value. com! Use the order of operations to correctly solve the problems. Likewise, 10,000,000 is a 1 followed by seven zeros and is abbreviated as 10 7. 3 Pre-Algebra - Order of Operations Objective: Evaluate expressions using the order of operations, including the use of absolute value. It is very important to understand this sequential structure of programming. Exponent rules. org right now: https://www. When simplifying mathematical expressions perform the operations in the following order: 1. What is the order of operations in trig functions? Ask Question ,$then the exponent$\quad ^2 \quad$would be inside the brackets. We use fractional exponents because often they are more convenient, and it can make algebraic operations easier to follow. org, All rights reserved. Using a Calculator. If the calculations involve a combination of parenthesis, exponents, multiplication, division, addition, and subtraction then. 5 - 4 So, 6 10 is a 1 followed by six zeros: 1,000,000; in other words, 1,000,000 is the 6th power of 10. Follow the link to each algebra topic to view its games, quizzes, worksheets and worked examples. Type in your sum to see how to solve it step by step. Actually, I think students have difficulty with powers, or exponents, since they are so small. (1) Part 1 of 2 - How to Use the order of operations to evaluate expressions, (2) Part 2 of 2 - How to Use the order of operations to evaluate expressions. Exponents are near the top of the food chain when it comes to order of operations. Beginning and Intermediate Algebra was designed to reduce textbook costs to students while not reducing the quality of materials. com! Use the order of operations to correctly solve the problems. Operations in parentheses. They can seem confusing at first, but with practice we can master them just as we mastered the properties of numbers and operations. SEE MORE : 2. 5 A Problem Solving Plan Using Models 1. But the rule is good for all elementary grades. Apply exponents. The Order of Operations page 1. The worksheets are included for integers, fractions and decimals. Students learn that numbers are governed by properties, and. 2 Exponents and Powers 1. In this article, I will describe some misunderstandings about order of operations, and suggest a better way of thinking about the topic. Operations are carried out in a particular order, with the results of earlier computations being fed into later ones. Mixing up the correct order of the operations can lead to wrong answers. Order of Operations Four is one of the Interactivate assessment games. Learn more about exponent rules or explore hundreds of other calculators addressing math, finance, health, fitness, and more. Do operations inside grouping symbols first. It is commonly used by scientists, mathematicians and engineers, in part because it can simplify certain arithmetic operations. First solve the part in parenthesis and exponents. Perform all Multiplications and Divisions, working from left to right. Order of Operations with Exponents Version 1 Directions: Use the correct order of operations to determine each answer. Examples: 2+3*4 or 3/4*3 Description. Understanding. Consider the follow: 5 •55•5•55. Formulas calculate values in a specific order. A man and his brother bought 4 shirts and then share the cost with his brother. Have students write the answers to math problems randomly on the bingo board. ” As shown above, , equals two times two times two. org, All rights reserved. If you are looking for order of operations worksheets that test your knowledge of the PEMDAS rules, these math worksheets are a good start. The following list, from top to bottom, is the order of operations in Algebra. 210 - Arithmetic & Algebraic Operations with Exponents; 230 - GRAPHITI - coordinate geometry, point generation, distance, functions. Use the following rules to enter expressions into the calculator. Microsoft Word - Integer Order of Operations Author: Zampini08 Created Date: 10/23/2012 5:01:35 PM. Six plus three is nine, add and I bring down the square minus eight divided by four, times three. What is the order of operations in trig functions? Ask Question ,$ then the exponent $\quad ^2 \quad$ would be inside the brackets. Practice evaluating expressions using the order of operations. Rules for Operations with Exponents. We have seen that multiplication is a shortcut for repeated addition and division is a shortcut for repeated subtraction. Power of a quotient rule. Classwork Opening (5 minutes) Take a few minutes to review the problem set from the previous lesson. Without the correct order, watch what happens: 15 + 5 X 10 -- Without following the correct order, I know that 15+5=20 multiplied by 10 gives me the answer of 200. Please see part1 for the beginning. Scientific notation. How does the Exponent Calculator work? First, it converts your entries to decimal format. This free online Modulo Calculator makes it easy to calculate the modulo of any two numbers. Order of operations The HP 6S scientific calculator performs operations in the following order: ”, ˚, ˜, ˆ *, d +, - & o, x, X Simple calculations Perform calculations in the same way that you write them on paper. Check to see what the Maths Dictionary says by clicking on this link, then clicking on the O category, then clicking on the words "Order of operations". Fractional exponents can be used instead of using the radical sign (√). These order of operations worksheets mix basic arithmetic, including parentheses and exponents, and tests students understanding of PEMDAS. The order of operations is a rule that tells you the right order in which to solve different parts of a math problem. 6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative Numbers Double Quantities The Fraction Bar The Main Operation AnswersFocus Exercises OPERATIONS. Free Order of Operations:This product contains 1 worksheet with the order of operations. Just type in sums like these (see Order of Operations for more detail):. Match the math expression with its simplification using order of operations. Here is the second example. Adding fractions with exponent calculator, crossword holt algebra 1, ged math examples. The only exception is that division is not supported; attempts to use the / symbol will result in an error. Identify the properties of real numbers (Commutative, Associative, Distributive, Identity and Inverse Properties). The order of operations is the order in which you add, subtract, multiply, and divide numbers in a number sentence. Beginning and Intermediate Algebra was designed to reduce textbook costs to students while not reducing the quality of materials. The Order of Operations with Negative and Positive Integers and No Exponents (Three Steps) (A) Math Worksheet from the Integers Worksheets Page at Math-Drills. If you are satisfied with your first mark, don't try again. You can also include parentheses and numbers with exponents or roots in your equations. Create your own math worksheets. Objective: I know how to perform mixed operations with parenthesis, exponents, multiplication, division, addition, and subtraction. Operations with exponents. The problem with the math equation you showed above is that multiplication and division are not done in any specific order per order of operations. (Hint: Remember to use proper order of operations. Parantheses, Exponents, Multiplication or Division (left to right), Addition or Subtraction (left to right). 6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative Numbers Double Quantities The Fraction Bar The Main Operation AnswersFocus Exercises OPERATIONS. The order of operations is a rule that tells you the right order in which to solve different parts of a math problem. Exponent definition is - a symbol written above and to the right of a mathematical expression to indicate the operation of raising to a power. Accounts for order of operations when using parentheses, trig functions, and exponents. Free Algebra Solver and Algebra Calculator showing step by step solutions. 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 11 x 11 x 11 12 x 12. Let's work the exponent next. For instance, you can type 5+3log(100)/2 and hit ENTER. 3x³ is 3(x)(x)(x), not (3x)(3x)(3x). Click Image to Enlarge : This interactive mathematics resource allows the user to explore the order of operations (brackets, exponents, multiplication, division, addition and. Write a numerical expression to represent this situation and then find the price paid by each brother. Do any addition and subtraction in order from left to right. (Use rules 2–4 inside the grouping symbols. t 4 FMPafdQeR xw Zi 4t Lh2 kIyn DfIi In ki rt ZeL lA rlTg4e ObZroa f J1 Z. The Order of Operations Worksheets are randomly created and will never repeat so you have an endless supply of quality Order of Operations Worksheets to use in the classroom or at home. An exponent tells a student how many times the base number is multiplied by itself.
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by using Biot Savart Law, the calculation is very terrible. since it involve the cubic inverse distance. However, using vector potential is a way to make an analytic solution. first in cylindrical coordinate, the current density is:
$\displaystyle \vec{J} = J_\phi \hat{\phi} = I \delta(z) \delta(\rho-a) \hat{\phi}$
the vector potential, without loss of generality, we set the field point on x-z plane and the vector potential is pointing $\hat{\phi}$ direction.
Oh, shit, i am tired on typing equation by Latex. anyway,
the finial result can be obtained in J.D. Jackson’s book. and it take the form of Elliptic Integral.
$\displaystyle A_\phi = \frac{\mu_0 I}{2\pi } \sqrt{\frac{a}{\rho}}\left( \frac{k^2-2}{2k} K(k^2) + \frac{1}{k} E(k^2) \right)$
where K(m) is the complete elliptic integral of first kind, and E(m) is the complete elliptic integral of second kind.
$\displaystyle K(m) = \int_0^{\pi/2} \frac{1}{\sqrt{1-m \sin^2(\theta)}}d\theta$
$\displaystyle E(m) = \int_0^{\pi/2} \sqrt{1-m \sin^2(\theta)} d\theta$
and
$\displaystyle k^2 = \frac{ 4 a \rho }{ (a+\rho)^2+z^2 }$
and using the derivative properties of elliptic integral, we can have the magnetic field in analytic form. The coil radius is $a$, at x-y plan. The observation point is $(\rho, z)$
$\displaystyle B_\rho(\rho,z) = \frac{\mu_0 I}{2\pi}\frac{z}{\rho \sqrt{(a+\rho)^2+z^2}} \left(K(k^2) - \frac{a^2+\rho^2 + z^2}{(a-\rho)^2 + z^2} E(k^2) \right)$
$\displaystyle B_z(\rho,z) = \frac{\mu_0 I}{2\pi}\frac{1}{ \sqrt{(a+\rho)^2+z^2}} \left(K(k^2) + \frac{a^2-\rho^2 - z^2}{(a-\rho)^2 + z^2} E(k^2) \right)$
Here is the PDF for the detail calculation. Field of Single Coil. Note that, in the pdf, the B-field is smaller by factor of 2. The denominator should be $2\pi$. As we check the magnetic field on the z-axis, the above formula will reduce to
$\displaystyle B_z(0,z) = \frac{\mu_0 I}{2}\frac{a^2}{ (a^2+z^2)^{3/2}}$
where $K(0) = E(0) = \pi/2$
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## Sunday, March 25, 2007
### Interpreting and contemplating the European growth experience
Barry Eichengreen has a new book titled The European Economy since 1945. Sheri Berman has written a great book review in the New York Times. Greg Mankiw points to Chapter 1 of the book on the NYT website.
It is a fascinating story. After World War II, Europe bounced back on a foundation of great human capital, institutional mechanisms and State capacity. In the first three decades, the story was one of pouring capital into a near-ideal setting, which gave very high GDP growth. Eichengreen says that European institutions comprising trade unions, employer organisations, and corporatist arrangements evolved to support this phase of extensive' growth where the information processing required in deploying capital was relatively easy, and the game was primarily about quickly getting the top quality labour force up to the production possibility frontier.
I believe there was one more reason why European institutions evolved the way they did in the post-war years: Appeasement. In the early 20th century, communism was a genuine alternative to democracy both at the level of ideas and in terms of realpolitik. My sense is that for wise people like Keynes, who knew and loved the ideals of classical liberalism, a pragmatic path of buying off the working class' was taken, so that there would be no fertile ground for a communist revolution. We know today that communism was hopelessly broken, that there was never any threat; the perceived fertile ground would have rapidly evaporated the moment workers in the West learned more about the plight of workers in the USSR. But at the time this was not obvious.
My sense is that people like Keynes, with a heavy heart, supported the rise of a big State thinking that it was the only way to stave off the takeover of totalitarian ideas as had happened in Russia in 1917 and Germany in 1933. The thinkers of that age, who knew and loved individualism and freedom the best, thought that it is better to have a big State, and hang on to an attenuated form of personal freedom, rather than collapse into brutality as Germany and Russia did. This rationale, founded on appeasement, lost relevance after the collapse of the USSR. This may have set the stage for dismantling the European welfare state, which has now outlived its original purpose of staving off totalitarianism.
Extensive growth is an important part of development economics also. Some countries, like China, have done very well by marshalling a vast pool of labour and capital, and obtaining growth by deploying these factors of production. Paul Krugman famously reminded all of us over a decade ago that East Asian growth was quite unmiraculous' in that it mostly reflected a boring accumulation of labour and capital into the production process, often with poor technology and productivity.
In Eichengreen's story, by roughly 1975, the potential for extensive' growth in Europe was exhausted, and from that point onwards, the European model' has looked bad. Margaret Thatcher and Ronald Reagan helped to radically turn the US and the UK away towards the Anglo-Saxon model. This experiment has been running for a while, and continental policy regimes like Germany and France have inferior growth and worse unemployment when compared with the US and the UK.
In the post 1975 period, what Europe - at the frontiers - needed was "flexible and mobile work relationships, technological novelty and the financing of risky ventures" (as Eichengreen puts it). The UK and the US economic policy framework worked much better with a flexible labour market, market-oriented finance, and powerful incentives for hard work, risk-taking, innovation and entrepreneurship.
What does this say for economic development in the third world? Sometimes the argument is made for more Statist growth in the early decades of catch-up, as was done in the first 30 years in Europe. In my view, there is a fundamental difference between post-war Europe and the typical third-world context: this lies in institutional sophistication and State capacity. The competence and lack of corruption of the State in Germany is something which we just do not possess in India. The Indian State tried to lead, particularly over 1966-1976, and we saw how bad that was. There is no one road to serfdom, but in places with weaker political and institutional capacity, a large State is more vulnerable to cancer.
In India, we don't seem to be walking down a phase of State-led extensive growth which is then followed by a withering away of the State. India is walking on a sui generis path, where we seem to be jumping out of poverty into a world of "flexible and mobile work relationships, technological novelty and the financing of risky ventures". We seem to be developing what Vijay Kelkar's October 2005 Gadgil Memorial Lecture calls a new model of Indo-Saxon Capitalism', where the primitive accumulation is taking place alongside the huge technological catch-up.
The private sector, which is driving growth, is working within a market-oriented financial system which is able to supply risk capital. However, my sense is that this `extensive' growth is not simple-minded. Highly novel mechanisms are often required for plugging India into globalisation, which require creativity, intelligence, risk-taking and entrepreneurship. The private sector operates in a framework of flexible and mobile work relationships. I believe this path is scalable for many decades, and involves a virtuous cycle between widening personal freedom and high economic growth.
LaTeX mathematics works. This means that if you want to say $10 you have to say \$10.
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# Can this limit be computed?
Bipolarity
I've been trying for a while to compute this limit. Is there even a unique solution to this problem?
$$\lim_{x→∞} x^{1-p}$$ where $p>1$
I tried using L'Hopital's rule, but it didn't work out.
BiP
dumbQuestion
lim(x-->∞) x1-p = lim(x-->∞) x1x-p = lim(x-->∞) x/xp = ∞/∞
So we apply L'hopitals:
lim(x-->∞) 1/(pxp-1) = 1/p lim(x-->∞) 1/(xp-1)
so as long as p-1>0 the limit goes to 0, right? And we know, p>1, so we know that p-1>0 so this should go to 0
Vorde
It seems to me that, intuitively, your function should approach zero regardless of p (assuming p > 1). Let me see what I can do more legitimately though.
First split ##x^{1-p}## into ##x^1 x^{-p}##
From there I would make it a quotient and try some fancy l'hopital's on it. I'd help more but I need to get somewhere. Good luck, however!
Mod note: in LaTeX expressions with exponents with more than one character, use braces - {} - around the exponent. I fixed the exponents above.
Last edited by a moderator:
Homework Helper
I've been trying for a while to compute this limit. Is there even a unique solution to this problem?
$$\lim_{x→∞} x^{1-p}$$ where $p>1$
I tried using L'Hopital's rule, but it didn't work out.
BiP
1. Do you know in which cases you're allowed to use L'Hôpital's rule ??
2. By $\infty$ do you assume $+\infty$ ?
2. If p>1, then 1-p <0 = -s, s>0, so that the object under the limit becomes
$$\frac{1}{x^s}, ~ s>0$$
Which should be easier to handle when considering the limit.
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# If floating leg in an arrears swap is paid on the date then valuing them is like predicting future
From what I am reading arrears swap are paid on the same day(actually, +2 business days for JPY and USD) as the reset date. To me then, a week before the reset date the floating rate is not known. Which means it is like predicting the rate a week ahead using nothing but ${\sigma}$ - volatility. The arrears swap rates are swap rates + convexity adjustment. Surely, there is no prediction here, just correcting yield to account for non linear price to yield relationship. Apparently price is linear with time but yield has to go through convexity correction. I hope someone will explain. I have read Hull's chapters several times, read literature on the internet etc, I have not found a clear description. I can add more details if it is not clear. Thanks.
• This question is for 1. libor in-arrears swap 2. why paying a floating amount just announced is not estimated using a stochastic process? 3. would be nice if one can add explanation as to how convexity adjustment corrects the arrears-swap valuation. – user12348 Nov 3 '15 at 2:48
• I'm confused...why would there be a convexity adjustment on a LIBOR swap? – user9403 Jan 11 '16 at 11:01
We consider a single Libor rate. The application to a swap is straightforward.
Consider the Libor calculation period $[T_1, \, T_2]$ and the Libor payment made at $T_1$. We denote by $\Delta = T_2-T_1$ the length in years of the calculation period. Here, we ignore the two-day payment delay as its impact to pricing is immaterial. We assume that, under the $T_2$-forward measure $P_{T_2}$, the Libor rate process $\{L(t, T_1, T_2) \mid 0 \le t \le T_1\}$, where \begin{align*} L(t, T_1, T_2) = \frac{1}{\Delta} \left(\frac{P(t, T_1)}{P(t, T_2)}-1\right), \end{align*} is a martingale and satisfies an SDE of the form \begin{align*} dL(t, T_1, T_2) = \sigma L(t, T_1, T_2) d W_t, \end{align*} where $\{W_t \mid t \ge 0\}$ is a standard Brownian motion. Then, for $0 \le t \le T \le T_1$, \begin{align*} L(T, T_1, T_2) = L(t, T_1, T_2) e^{-\frac{1}{2}\sigma^2 (T-t) + \sigma \int_{t}^{T} dW_s}. \end{align*}
Let $B_t$ be the money -market account value at time $t$. Then, for $0 \le t \le T_2$, \begin{align*} \frac{dP}{dP_{T_2}} \big|t = \frac{B_t P(0, T_2)}{P(t, T_2)} \equiv \eta_t. \end{align*} Moreover, let $E$ and $E_{T_2}$ be the respective expectation operators under the risk-neutral measure and the $T_2$-forward measures.
Then the value, at time $t\le T_1$, of the Libor rate $L(T_1, T_1, T_2)$, both set and paid at $T_1$, is given by \begin{align*} B_t E\left(\frac{L(T_1, T_1, T_2)}{B_{T_1}}\mid \mathcal{F}_t \right) &= B_t E_{T_2}\left(\frac{\eta_{T_1}}{\eta_t}\frac{L(T_1, T_1, T_2)}{B_{T_1}}\mid \mathcal{F}_t \right)\\ &=P(t, T_2) E_{T_2}\left(\frac{1}{P(T_1, T_2)}L(T_1, T_1, T_2)\mid \mathcal{F}_t \right)\\ &= P(t, T_2) E_{T_2}\left(\left(\Delta L(T_1, T_1, T_2) + 1 \right)L(T_1, T_1, T_2)\mid \mathcal{F}_t \right)\\ &= P(t, T_2)E_{T_2}\left(L(T_1, T_1, T_2) + \Delta L(T_1, T_1, T_2)^2\mid \mathcal{F}_t \right)\\ &= P(t, T_2) \left(L(t, T_1, T_2) + \Delta L(t, T_1, T_2)^2 e^{\sigma^2 (T_1-t)}\right)\\ &=P(t, T_1) \frac{L(t, T_1, T_2) + \Delta L(t, T_1, T_2)^2 e^{\sigma^2 (T_1-t)}}{\Delta L(t, T_1, T_2) + 1} \\ &= P(t, T_1)\left(c_t + L(t, T_1, T_2) \right), \end{align*} where \begin{align*} c_t = \frac{\Delta L(t, T_1, T_2)^2}{\Delta L(t, T_1, T_2) + 1}\big(e^{\sigma^2 (T_1-t)} -1 \big) \end{align*} is the convexity adjustment. Note that, there is no approximation needed, as long as we can estimate the volatility.
• Hello. When it comes to the phrase '~ is a martingale and satisfies an SDE of the form', is there any reason for justifying there is only diffusion form and the sigma is constant? I want to know how to derive $dL(t,T_1,T_2) = σL(t,T_1,T_2)dW_t$ – user13232877 Jun 21 at 2:29
• It is an assumption. Certainly, the volatility can have some other forms. – Gordon Jun 21 at 11:44
lets take it as simple that all payment are at the same time. When you want to calculate the floating, you always look at the previous period. But to calculate the first payment, we do not have forward rate at time t=0. But when you want to calculate between two periods, you have forward rates and you can always fix the rate for next period (floating one). So you can always calculate how much will be the floating one,one period before it.
When you are discounting and you have a floating at time T and you have another t , if you want to discount and see how much does it dost today, you can either discount it back with D(T) or you discount first to time t with D(t,T) and then D(t). you know the rate D(T) and D(t ) but you don’t know the rate D(t,T). but if we discount in either way, we should get the same result, then we should have
## $$D(T)=D(t).D(t,T)$$
Think that you want to calculate the Forward rate between $[T_{i-1}, T_i]$ which will be :
$$D(T_i)=D(T_{i-1}).D(T_{i-1},T_i)$$ Since $D(T_{i-1},T_i)$ is less than a year, we can put simple compounding formula and get: $$D(T_i)= D(T_{i-1}).D(T_{i-1},T_i)=\frac{D(T_{i-1})}{1+\Delta_i.F_i}$$
and now u can solve for $F_i$: $$F_i=\frac{D(T_{i-1})-D(T_i)}{\Delta_i .D(T_i)}$$
• I really want to thank you for your effort. But it does not answer my question. please see the comment to my question. – user12348 Nov 3 '15 at 2:44
|
Added variable plot of linear regression model
## Syntax
``plotAdded(mdl)``
``plotAdded(mdl,coef)``
``plotAdded(mdl,coef,Name,Value)``
``plotAdded(ax,___)``
``h = plotAdded(___)``
## Description
example
````plotAdded(mdl)` creates an added variable plot for the whole model `mdl` except the constant (intercept) term.```
example
````plotAdded(mdl,coef)` creates an added variable plot for the specified terms `coef`.```
````plotAdded(mdl,coef,Name,Value)` specifies graphical properties of adjusted data points using one or more name-value pair arguments. For example, you can specify the marker symbol and size for the data points.```
````plotAdded(ax,___)` creates the plot in the axes specified by `ax` instead of the current axes, using any of the input argument combinations in the previous syntaxes.```
````h = plotAdded(___)` returns line objects for the plot. Use `h` to modify the properties of a specific line after you create the plot. For a list of properties, see Line Properties.```
## Examples
collapse all
Create a linear regression model of car mileage as a function of weight and model year. Then create an added variable plot to see the significance of the model.
Create a linear regression model of mileage from the `carsmall` data set.
```load carsmall Year = categorical(Model_Year); tbl = table(MPG,Weight,Year); mdl = fitlm(tbl,'MPG ~ Year + Weight^2');```
Create an added variable plot of the model.
`plot(mdl)`
The plot illustrates that the model is significant because a horizontal line does not fit between the confidence bounds.
Create the same plot by using the `plotAdded` function.
`plotAdded(mdl)`
Create a linear regression model of car mileage as a function of weight and model year. Then create an added variable plot to see the effect of the weight terms (`Weight` and `Weight^2`).
Create the linear regression model using the `carsmall` data set.
```load carsmall Year = categorical(Model_Year); tbl = table(MPG,Weight,Year); mdl = fitlm(tbl,'MPG ~ Year + Weight^2');```
Find the terms in the model corresponding to `Weight` and `Weight^2`.
`mdl.CoefficientNames`
```ans = 1x5 cell {'(Intercept)'} {'Weight'} {'Year_76'} {'Year_82'} {'Weight^2'} ```
The weight terms are 2 and 5.
Create an added variable plot with the weight terms.
```coef = [2 5]; plotAdded(mdl,coef)```
The plot illustrates that the weight terms are significant because a horizontal line does not fit between the confidence bounds.
Create a scatter plot of data along with a fitted curve and confidence bounds for a simple linear regression model. A simple linear regression model includes only one predictor variable.
Create a simple linear regression model of mileage from the `carsmall` data set.
```load carsmall tbl = table(MPG,Weight); mdl = fitlm(tbl,'MPG ~ Weight')```
```mdl = Linear regression model: MPG ~ 1 + Weight Estimated Coefficients: Estimate SE tStat pValue __________ _________ _______ __________ (Intercept) 49.238 1.6411 30.002 2.7015e-49 Weight -0.0086119 0.0005348 -16.103 1.6434e-28 Number of observations: 94, Error degrees of freedom: 92 Root Mean Squared Error: 4.13 R-squared: 0.738, Adjusted R-Squared: 0.735 F-statistic vs. constant model: 259, p-value = 1.64e-28 ```
`pValue` of the `Weight` variable is very small, which means that the variable is statistically significant in the model. Visualize this result by creating a scatter plot of the data, along with a fitted curve and its 95% confidence bounds, using the `plot` function.
`plot(mdl)`
The plot illustrates that the model is significant because a horizontal line does not fit between the confidence bounds, which is consistent with the `pValue` result.
Create the same plot by using the `plotAdded` function.
`plotAdded(mdl)`
When a model includes only one term in addition to the constant term, an adjusted value is equivalent to its original value. Therefore, this added variable plot is the same as the scatter plot created by the `plot` function.
## Input Arguments
collapse all
Linear regression model, specified as a `LinearModel` object created using `fitlm` or `stepwiselm`.
Coefficients in the regression model `mdl`, specified as one of the following:
• Character vector or string scalar of a single coefficient name in `mdl.CoefficientNames` (`CoefficientNames` property of `mdl`).
• Vector of positive integers representing the indexes of coefficients in `mdl.CoefficientNames`. Use a vector to specify multiple coefficients.
Data Types: `char` | `string` | `single` | `double`
Target axes, specified as an `Axes` object.
If you do not specify the axes and the current axes are Cartesian, then `plotAdded` uses the current axes (`gca`). For more information on creating an `Axes` object, see `axes` and `gca`.
### Name-Value Pair Arguments
Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.
Example: `'Color','blue','Marker','*'`
### Note
The graphical properties listed here are only a subset. For a complete list, see Line Properties. The specified properties determine the appearance of adjusted data points.
Line color, specified as the comma-separated pair consisting of `'Color'` and an RGB triplet, hexadecimal color code, color name, or short name for one of the color options listed in the following table.
The `'Color'` name-value pair argument also determines marker outline color and marker fill color if `'MarkerEdgeColor'` is `'auto'` (default) and `'MarkerFaceColor'` is `'auto'`.
For a custom color, specify an RGB triplet or a hexadecimal color code.
• An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range `[0,1]`; for example, ```[0.4 0.6 0.7]```.
• A hexadecimal color code is a character vector or a string scalar that starts with a hash symbol (`#`) followed by three or six hexadecimal digits, which can range from `0` to `F`. The values are not case sensitive. Thus, the color codes `'#FF8800'`, `'#ff8800'`, `'#F80'`, and `'#f80'` are equivalent.
Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and hexadecimal color codes.
Color NameShort NameRGB TripletHexadecimal Color CodeAppearance
`'red'``'r'``[1 0 0]``'#FF0000'`
`'green'``'g'``[0 1 0]``'#00FF00'`
`'blue'``'b'``[0 0 1]``'#0000FF'`
`'cyan'` `'c'``[0 1 1]``'#00FFFF'`
`'magenta'``'m'``[1 0 1]``'#FF00FF'`
`'yellow'``'y'``[1 1 0]``'#FFFF00'`
`'black'``'k'``[0 0 0]``'#000000'`
`'white'``'w'``[1 1 1]``'#FFFFFF'`
`'none'`Not applicableNot applicableNot applicableNo color
Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB® uses in many types of plots.
`[0 0.4470 0.7410]``'#0072BD'`
`[0.8500 0.3250 0.0980]``'#D95319'`
`[0.9290 0.6940 0.1250]``'#EDB120'`
`[0.4940 0.1840 0.5560]``'#7E2F8E'`
`[0.4660 0.6740 0.1880]``'#77AC30'`
`[0.3010 0.7450 0.9330]``'#4DBEEE'`
`[0.6350 0.0780 0.1840]``'#A2142F'`
Example: `'Color','blue'`
Line width, specified as the comma-separated pair consisting of `'LineWidth'` and a positive value in points. If the line has markers, then the line width also affects the marker edges.
Example: `'LineWidth',0.75`
Marker symbol, specified as the comma-separated pair consisting of `'Marker'` and one of the values in this table.
ValueDescription
`'o'`Circle
`'+'`Plus sign
`'*'`Asterisk
`'.'`Point
`'x'`Cross
`'square'` or `'s'`Square
`'diamond'` or `'d'`Diamond
`'^'`Upward-pointing triangle
`'v'`Downward-pointing triangle
`'>'`Right-pointing triangle
`'<'`Left-pointing triangle
`'pentagram'` or `'p'`Five-pointed star (pentagram)
`'hexagram'` or `'h'`Six-pointed star (hexagram)
`'none'`No markers
Example: `'Marker','+'`
Marker outline color, specified as the comma-separated pair consisting of `'MarkerEdgeColor'` and an RGB triplet, hexadecimal color code, color name, or short name for one of the color options listed in the `Color` name-value pair argument.
The default value of `'auto'` uses the same color specified by using `'Color'`.
Example: `'MarkerEdgeColor','blue'`
Marker fill color, specified as the comma-separated pair consisting of `'MarkerFaceColor'` and an RGB triplet, hexadecimal color code, color name, or short name for one of the color options listed in the `Color` name-value pair argument.
The `'auto'` value uses the same color specified by using `'Color'`.
Example: `'MarkerFaceColor','blue'`
Marker size, specified as the comma-separated pair consisting of `'MarkerSize'` and a positive value in points.
Example: `'MarkerSize',2`
## Output Arguments
collapse all
Line objects, returned as a 3-by-1 vector. `h(1)`, `h(2)`, and `h(3)` correspond to the adjusted data points, fitted line, and 95% confidence bounds of the fitted line, respectively. Use dot notation to query and set properties of the line objects. For details, see Line Properties.
You can use name-value pair arguments to specify the appearance of adjusted data points corresponding to the first graphics object `h(1)`.
collapse all
An added variable plot, also known as a partial regression leverage plot, illustrates the incremental effect on the response of specified terms caused by removing the effects of all other terms.
An added variable plot created by `plotAdded` with a single selected term corresponding to a single predictor variable includes these plots:
• Scatter plot of adjusted response values against adjusted predictor variable values
• Fitted line for adjusted response values as a function of adjusted predictor variable values
• 95% confidence bounds of the fitted line
The adjusted values are equal to the average of the variable plus the residuals of the variable fit to all predictors except the selected predictor. For example, consider an added variable plot for the first predictor variable x1. Fit the response variable y and the selected predictor variable x1 to all predictors except x1 as follows:
yi = gy(x2i, x3i, …, xpi) + ryi,
x1i = gx(x2i, x3i, …, xpi) + rxi,
where gy and gx are the fit of y and x1, respectively, against all predictors except the selected predictor (x1). ry and rx are the corresponding residual vectors. The subscript i represents the observation number. The adjusted value is the sum of the average value and the residual for each observation.
`$\begin{array}{c}{\stackrel{˜}{y}}_{i}=\overline{y}+{r}_{yi},\\ {\stackrel{˜}{x}}_{1i}={\overline{x}}_{1}+{r}_{xi},\end{array}$`
where ${\overline{x}}_{1}$ and $\overline{y}$ represent the average of x1 and y, respectively.
`plotAdded` plots a scatter plot of (${\stackrel{˜}{x}}_{1i}$, ${\stackrel{˜}{y}}_{i}$), a fitted line for $\stackrel{˜}{y}$ as a function of ${\stackrel{˜}{x}}_{1}$ (that is, ${\beta }_{1}{\stackrel{˜}{x}}_{1}$), and the 95% confidence bounds of the fitted line. The coefficient β1 is the same as the coefficient estimate of x1 in the full model, which includes all predictors.
ryi represents the part of the response values unexplained by the predictors (except x1), and rxi represents the part of the x1 values unexplained by the other predictors. Therefore, the fitted line represents how the new information introduced by adding x1 can explain the unexplained part of the response values. If the slope of the fitted line is close to zero and the confidence bounds can include a horizontal line, then the plot indicates that the new information from x1 does not explain the unexplained part of the response values well. That is, x1 is not significant in the model fit.
`plotAdded` also supports an extension of the added variable plot so that you can select multiple terms instead of a single term. Therefore, you can also specify a categorical predictor, all terms that involve a specific predictor, or the model as a whole (except a constant (intercept) term). Consider a set of predictors X with a coefficient vector β, where βi is the coefficient estimate of xi in the full model if you specify the ith coefficient for an added variable plot; otherwise, βi is zero. Define a unit direction vector u as u = β/s where s = norm(β). Then, Xβ = (Xu)s. Treat Xu as a single predictor with a coefficient s, and create an added variable plot for Xu in the same way as creating the plot for a single term. The coefficient of the fitted line in the added variable plot corresponds to s.
## Tips
• The data cursor displays the values of the selected plot point in a data tip (small text box located next to the data point). The data tip includes the x-axis and y-axis values for the selected point, along with the observation name or number.
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# 4.4 Combining polynomials using addition and subtraction
Page 1 / 2
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. Operations with algebraic expressions and numerical evaluations are introduced in this chapter. Coefficients are described rather than merely defined. Special binomial products have both literal and symbolic explanations and since they occur so frequently in mathematics, we have been careful to help the student remember them. In each example problem, the student is "talked" through the symbolic form.Objectives of this module: understand the concept of like terms, be able to combine like terms, be able to simplify expressions containing parentheses.
## Overview
• Like Terms
• Combining Like Terms
• Simplifying Expressions Containing Parentheses
## Like terms
Terms whose variable parts, including the exponents, are identical are called like terms . Like terms is an appropriate name since terms with identical variable parts and different numerical coefficients represent different amounts of the same quantity. As long as we are dealing with quantities of the same type we can combine them using addition and subtraction.
## Simplifying an algebraic expression
An algebraic expression can be simplified by combining like terms.
## Sample set a
Combine the like terms.
$6\text{\hspace{0.17em}}\text{houses}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}4\text{\hspace{0.17em}}\text{houses}=\text{\hspace{0.17em}}10\text{\hspace{0.17em}}\text{houses}$ . 6 and 4 of the same type give 10 of that type.
$6\text{\hspace{0.17em}}\text{houses}+4\text{\hspace{0.17em}}\text{houses}+2\text{\hspace{0.17em}}\text{motels}=10\text{\hspace{0.17em}}\text{houses}+2\text{\hspace{0.17em}}\text{motels}$ . 6 and 4 of the same type give 10 of that type. Thus, we have 10 of one type and 2 of another type.
Suppose we let the letter $x$ represent "house." Then, $6x+4x=10x$ . 6 and 4 of the same type give 10 of that type.
Suppose we let $x$ represent "house" and $y$ represent "motel."
$6x+4x+2y=10x+2y$
## Practice set a
Like terms with the same numerical coefficient represent equal amounts of the same quantity.
Like terms with different numerical coefficients represent .
different amounts of the same quantity
## Combining like terms
Since like terms represent amounts of the same quantity, they may be combined, that is, like terms may be added together.
## Sample set b
Simplify each of the following polynomials by combining like terms.
$2x+5x+3x$ .
There are $2x\text{'}\text{s}$ , then 5 more, then 3 more. This makes a total of $10x\text{'}\text{s}$ .
$2x+5x+3x=10x$
$7x+8y-3x$ .
From $7x\text{'}\text{s}$ , we lose $3x\text{'}\text{s}$ . This makes $4x\text{'}\text{s}$ . The $8y\text{'}\text{s}$ represent a quantity different from the $x\text{'}\text{s}$ and therefore will not combine with them.
$7x+8y-3x=4x+8y$
$4{a}^{3}-2{a}^{2}+8{a}^{3}+{a}^{2}-2{a}^{3}$ .
$4{a}^{3},\text{\hspace{0.17em}}8{a}^{3},$ and $-2{a}^{3}$ represent quantities of the same type.
$4{a}^{3}+8{a}^{3}-2{a}^{3}=10{a}^{3}$
$-2{a}^{2}$ and ${a}^{2}$ represent quantities of the same type.
$-2{a}^{2}+{a}^{2}=-{a}^{2}$
Thus,
$4{a}^{3}-2{a}^{2}+8{a}^{3}+{a}^{2}-2{a}^{3}=10{a}^{3}-{a}^{2}$
## Practice set b
Simplify each of the following expressions.
$4y+7y$
$11y$
$3x+6x+11x$
$20x$
$5a+2b+4a-b-7b$
$9a-6b$
$10{x}^{3}-4{x}^{3}+3{x}^{2}-12{x}^{3}+5{x}^{2}+2x+{x}^{3}+8x$
$-5{x}^{3}+8{x}^{2}+10x$
$2{a}^{5}-{a}^{5}+1-4ab-9+9ab-2-3-{a}^{5}$
$5ab-13$
## Simplifying expressions containing parentheses
When parentheses occur in expressions, they must be removed before the expression can be simplified. Parentheses can be removed using the distributive property.
## Sample set c
Simplify each of the following expressions by using the distributive property and combining like terms.
#### Questions & Answers
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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How can we prove the Inequality : $\frac {n!}{ 2^{n-1}((\frac {n-1}{2})!)^2} \leq \sqrt{n}$
How can we prove the following inequality? For every odd positive integer $n$,
$$\frac {n!}{ 2^{n-1}((\frac {n-1}{2})!)^2} \leq \sqrt{n}$$
Thank You.
-
Have you tried applying some form of Stirling's formula, to see what comes out? – Gerry Myerson Feb 21 '13 at 6:34
is it for $n$ odd (else $\frac{n-1}{2}$ isn't an integer) (i hope odd is the right one) – Dominic Michaelis Feb 21 '13 at 6:36
Sorry I forgot to mention that $n$ is odd – Kumar Feb 21 '13 at 6:40
@GerryMyerson Something similar to Stirling would surely help, but we cannot apply Stirling right ahead since that is an asymptotic inequality. – AD. Feb 21 '13 at 6:49
@AD Non asymptotic versions exist. – Did Feb 21 '13 at 6:59
In my answer here, I show that $${2n\choose n}{1\over 4^n}\leq {1\over\sqrt{\pi n}}.$$
Substitute $(n-1)/2$ for $n$ to get $${n-1\choose (n-1)/2}{1\over 2^{n-1}}\leq {1\over\sqrt{\pi (n-1)/2}}\leq{1\over\sqrt{n}},$$ the final inequality being valid for $n\geq 3$, since $\pi (n-1)/2>n$ for such $n$.
-
Well, this is impressive, +1. – 1015 Feb 21 '13 at 7:06
I love central binomial coefficients! – Byron Schmuland Feb 21 '13 at 7:07
Thank you so much – Kumar Feb 21 '13 at 7:08
+1 Nice! :) Perhaps you have some idea of using a binomial expansion and some orthogonality method in order to pick the mid term? – AD. Feb 21 '13 at 7:18
@AD. Sorry, I don't have any ideas along those lines. – Byron Schmuland Feb 21 '13 at 19:28
Hint:
For $k\geq0$ we need to show $$a_k=\frac{(2k+1)!}{2^{2k}(k!)^2}\leq\sqrt{2k+1}=b_k$$
Now $$a_{k+1}=\frac{(2k+3)!}{2^{2k+2}((k+1)!)^2}= \frac{(2k+3)(2k+2)}{4(k+1)^2}\cdot \frac{(2k+1)!}{2^{2k}(k!)^2}=\frac{(2k+3)(2k+2)}{4(k+1)^2}\cdot a_k$$ So if we knew $a_k\leq b_k$ for some $k$ then could we perhaps continue with induction...?
A nicer proof might be hidden in the in the binomial formula - something like $$2^{2k} = (1+1)^{2k} =\sum_{j=0}^{2k} \frac{(2k)!}{j! (2k-j)!}$$ where the mid term is of interest...
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As Gerry Mentioned, Stirling formula will show it (as this is only an asymptotic behaviour we first needs a lower bound for which we know the equation is true). If you don't want to use such a hammer, you should try it with induction.
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We can not use Stirling for specific $n$ without further investigation, it is an asymptotic inequality. – AD. Feb 21 '13 at 6:50
@Ad. did you downvote? tell me if you don't like the edit – Dominic Michaelis Feb 21 '13 at 6:57
@AD Non asymptotic versions exist. – Did Feb 21 '13 at 7:02
@DominicMichaelis I give you +1 for the second comment (thus proving I did not downvote you).. – AD. Feb 21 '13 at 19:41
For completeness, here is the proof by induction:
Base Case: The case $n = 1$ is easy to check.
Inductive Step: Assume that $$\frac{k!}{2^{k-1} \left( \frac{k-1}{2} \right)!^2} \leq \sqrt{k}.$$ We aim to show that this implies $$\frac{(k+2)!}{2^{k+1} \left( \frac{k+1}{2} \right)!^2} \leq \sqrt{k+2}.$$
We have
\begin{align} \frac{(k+2)!}{2^{k+1} \left( \frac{k+1}{2} \right)!^2} &= \frac{(k+2)(k+1)}{4(\frac{k+1}{2})^2} \cdot \frac{k!}{2^{k-1} \left( \frac{k-1}{2} \right)!^2} \\ &\leq \frac{(k+2)(k+1)}{4(\frac{k+1}{2})^2} \cdot \sqrt{k} \\ &= \frac{k+2}{k+1} \sqrt{k} \\ &\leq \sqrt{k+2} \end{align} which occurs if and only if $\left( \frac{k+2}{k+1}\right)^2 k \leq k+2$. I will leave the last inequality for you to check.
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after your hint I had done this induction proof. Thank You so much. – Kumar Feb 21 '13 at 8:17
I'm happy to help! – JavaMan Feb 21 '13 at 16:33
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## Long Sequence
Points:100 (partial)
Time limit:0.3s
Memory limit:60M
Author:
Tags
Loops
Difficulty
Preparation
Allowed languages
C#, C++, C++ 14, cpp, java, JavaScript, kt, php, Python, Swift
Write a program that prints the first 1000 members of the sequence: 2, -3, 4, -5, 6, -7, …
• You might need to learn how to use loops in Java (search in Internet).
#### Input
• There is no input for this task.
#### Output
• Output the first 1000 members of the sequence, each on a separate line.
2
-3
4
-5
6
...
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Home > Analysis, Geometry, Problem Solving, Undergraduate > Cavalieri’s Principle
## Cavalieri’s Principle
Plane version: Suppose that two bounded plane figures have the following property: There exists a line such that any line parallel to it intersects each one of the given figures by two segments of equal length. Prove that the figures have equal areas.
Space version: Suppose that two bounded space bodies have the following property: There exists a plane such that any plane parallel to it intersects the two bodies by two figures of equal areas. Prove that the bodies have equal volumes.
Hint: An approach using integrals, solves this easily using the coarea formula.
A second approach is
Plane case: Take the approximations by trapezoids with height less than $\frac{1}{n}$ for both polygons and take the limit.
Something similar can be done in the space.
Using this principle, find the common volume of the intersection of two infinite cylinders. (Suppose they intersect orthogonally and their symmetry axes also intersect.
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FANDOM
17,705 Pages
Release date 13 April 2017 (Update) Yes No No Yes No 15,000 coins 10,000 coins Revert - That staff contains x charges. You will not be able to get them back. Not sold 1 kg An old and magical staff, now bearing extra enchantment.
[view]
The slayer's staff (e) is a magical staff obtained by using a Slayer's enchantment on a Slayer's staff. It requires level 75 Magic and level 55 Slayer to wield and is required for the Magic Dart spell.
Upon enchanting the staff, it will have 2,500 charges. Once the charges run out, it will revert back to a regular slayer's staff, and an additional Slayer's enchantment must be used on it.
Using the staff substantially increases the damage dealt by the Magic Dart spell when attacking a monster players are assigned to kill. Specifically, the max hit of the spell when using the slayer's staff (e) is $(MagicLevel/6) + 13$, rounded down. This does not account for damage boosts from other items, such as the occult necklace, tormented bracelet, or the slayer helmet.
When used to attack a monster that is not your slayer assignment, no charges will be used, and the damage of Slayer Dart will not be boosted.
Hover over image for type Attack bonus +7 -1 +25 +12 +0 +2 +3 +1 +10 +0 +35 0 0% +0
Maximum hit Edit
The maximum hit dealt by the staff is dependent on the player's current Magic level, starting at 25 with level 75 Magic, up to a maximum of 31 at level 108 (obtainable only with an imbued heart). Both magic damage bonuses and stat boosts will modify the max hit of the spell; likewise, stat-reductions will lower the damage. With an occult necklace equipped, the maximum hit possible is 34. With an occult necklace, a tormented bracelet, and an imbued slayer helmet on a Slayer assignment, the maximum hit possible is 41.
Magic level
Maximum hit
Maximum hit
(no bonuses)
Maximum hit
()
Maximum hit
( + )
Maximum hit
( + + )
7525282933
7625282934
7725282934
7826283034
7926283034
8026283034
8126293035
8226293035
8326293035
8427293135
8527293136
8627303136
8727303136
8827303136
8927303236
9028303237
9128303237
9228313237
9328313237
9428313338
9528313338
9629313338
9729323338
9829323338
9929323439
100[1]29323439
101[1]29323439
102[1]30323439
103[1]30323440
104[1]30323540
105[1]30323540
106[1]30323540
107[1]30323540
108[1]31333541
109[1]31333541
1. 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Only available with the use of an imbued heart
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# Generalization of the positive semidefinite Grothendieck inequality
In a recent paper, S. Khot and A. Naor show a natural generalization of the positive semidefinite Grothendieck's inequality. Grothendieck showed that there exists a constant $K > 0$ such that for every $n \times n$, symmetric semidefinite matrix $A=[a_{ij}]$, the following inequality holds:
$$\max_{x_1,\ldots,x_n} \sum_{ij} a_{ij}x_i^Tx_j \le K \max_{\epsilon_1,\ldots,\epsilon_n \in [-1,1]} \sum_{ij}a_{ij} \epsilon_i\epsilon_j,$$ where each $x_i$ is a unit vector (in Euclidean norm, so that $x_i^Tx_i=1$).
Khot and Naor studied a natural variant of this inequality, where the $n$ numbers $\epsilon_i$ are replaced by $n$ vectors $u_1,\ldots,u_n$ chosen from a set of $k < n$ unit vectors $v_1,\ldots,v_n$. The inequality becomes:
$$\max_{x_1,\ldots,x_n} \sum_{ij} a_{ij}x_i^Tx_j \le C \max_{u_1,\ldots,u_n \in \{v_1,\ldots,v_k\}} \sum_{ij}a_{ij} u_i^Tu_j.$$
They proved that this inequality actually holds, but the proof looks very complicated; as does the constant $C$. My question is thus in two parts:
(a) Is there any chance that there is a simpler proof for this "natural" generalization to Grothendieck's inequality?
(b) Does it seem like a feasible project to try and estimate this constant?
I am not an expert in these inequalities, but this generalization looks so interesting, that I had to seek out expert opinion.
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Perhaps it would be beneficial to summarize the proof in words:
We wish to prove a certain Grothendieck-type inequality. We begin with a Lemma.
In Lemma 3.2 of this paper, we find an expression for a certain probability. In some sense, this calculation is really just (Hermite) Fourier analysis. We have a certain function, and we expand it into a (Hermite) Fourier basis. This proves our lemma.
We now use the probabilistic method to calculate the expected value of a certain random inner product. Using positive definiteness of the matrix A, and applying Lemma 3.2, we can throw away all but the "first level" (Hermite) Fourier coefficients. This gives our desired inequality, which ends up being sharp.
By the way of analogy, think about Hurwitz's proof of the Isoperimetric Inequality using Fourier series. We have an arbitrary curve, we expand it into its Fourier components, and we see that the inequality becomes sharp when all but the "first level" Fourier coefficients are set to zero. In a way, the same proof idea is used here.
As for computing the constant, this is indeed a challenge even in the simplest nontrivial cases. I don't think estimating it is very hard (for say, a "rough" estimate). To see what I mean, I would recommend reading the first in the series, "Approximate kernel clustering" (by the same authors).
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Hi Steven, thanks for the nice summary. – Suvrit Jan 26 '11 at 7:24
Sure! Though I suppose I didn't really answer your question directly. I guess I was trying to imply that the proof can be reduced to a "simple" description, and in doing this we see that it probably cannot be simplified very much (though I'm certainly no expert). As far as details go, maybe Gaussian randomness could be replaced by some other randomness, which would then change the choice of Fourier basis. Simplifying the general scheme of the proof may be hard, since it incorporates the "most direct" methods of other Grothendieck inequality proofs, plus additional ideas. – Steven Heilman Jan 27 '11 at 19:14
actually both: a simpler proof, with a reasonable, not necessarily best $C$, as well as simpler proof for the sharp $C$; but really, you think the proof in the paper is simple and short? I think the proof strategy is very well-explained and short, but the details are fairly long and technical. – Suvrit Oct 20 '10 at 14:12
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Sep 11 2019
Graduate Geometry, Topology and Dynamics Seminar: Combinatorics of Coxeter systems, by Mengxue Yang
September 11, 2019
4:00 PM - 4:50 PM
612 SEO
Chicago, IL
Calendar
Mengxue Yang (UIC): Combinatorics of Coxeter systems
We continue to learn about Coxeter groups following Anne Thomas' "Geometric and topological aspects of Coxeter groups and buildings". There are nice combinatorial properties associated to a Coxeter system. For example, the Cayley graph of a Coxeter system must have nice symmetries and is thus a reflection system. We will visualize everything with $D_6$.
Mengxue Yang
Sep 20, 2019
Sep 20, 2019
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# Dot3 shader questions (spotlights, and light management)
This topic is 4800 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.
## Recommended Posts
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Hi,
If you are unclear about spot lights in general, then the DX docs are not a bad place to get info on their workings - once you understand that it's quite simple to put spot light calculations inside a shader, but if you're still having trouble just say.
On falloff, just put the inverse of the light's range into a shader constant, then compute the distance from the vertex to the light. The simplest falloff is linear, which you can achieve by doing something like this:
Attenuation = 1.0 - (lightToVertDistance / lightRange)
You will probably want to clamp this value between 0 and 1, then at the end of all your lighting calculations (for that one light), multiply the final colour by the attenuation.
On your light management, is there no way you can have a loop in your shader? That'd simplify things a good deal and you can have static loops which are compiled out so it can be just a convenience tool for you, either that or you target higher end hardware and have "proper" loops but for lights (especially without shadowing) I think you could get away with the static loops.
I don't think you need to worry about the number of uniform parameters, there are something like 96 vertex shader constants even on the lowest model, so that's not too much of a problem. If it bothers you break it into 4/4.
Hope some of that helped,
-Mezz
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Maybe with spotlight falloff, you meant the falloff to the sides of the spotlight cone, rather than distance attenutation ?
In this case, it's easy. Each spotlight should have to angles define: the hotspot, and the cutoff. The light intensity is constant at maximum within the angle of the hotspot, and gradually falls off between hotspot and cutoff. 3DS Max calls them hotspot and falloff angles, iirc.
Now, for efficiency reasons, store both as the cosine of the angle into two constant shader parameters:
hotspot = cos(hotspotAngle);cutoff = cos(cutoffAngle);
The cosine is perfect, since we're going to deal with dotproducts to finds the angle.
Then you have a third shader parameter, a vector LightDirection, which denotes the central direction the spotlight points into. Imagine a vector along the central aiming axis of your light. The intensity factor used to control the falloff is found by comparing and interpolating angles relative to this direction with the hotspot and cutoff angles:
// First, get the angle between the light vector and the aiming direction // of the spotlight, as a cosinefloat angle = dot(light_to_vertex_vector, LightDirection);// Now interpolate this angle with the hotspot and falloff angles as limits.// Angle below hotspot are going to be clamped to 1, angles beyond falloff are 0.float factor = smoothstep(cutoff, hotspot, angle);
That's basically it.
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Thanks to both of you, I think that answers most of my questions...
Only thing is, Should I just write a shader that loops through, say, 8 lights and applies calculations for all of them, regardless of whether or not they're black lights? I'm restricted to vs 1.1/NV20, so I can't branch on variables. It seems wasteful to do so if a vertex only has 3 lights on it, but I can't think of any alternative...
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It really depends on what you want from your system. The only way you're going to get optimal efficiency is to make different shaders which do a certain number of lights and then use them appropriately at runtime, of course this is heading towards the combinatorial explosion of shaders, which is somewhat messy and annoying. However, you can keep it relatively nice if you make a little "library function" of high level code that does your lighting, and then from your shader's "main" function call that with appropriate input parameters. Then shaders with different numbers of lights become:
#include "MyLightingFuncs.vsh"VS_OUTPUT VSMain(VS_INPUT vsInput){ // fill out lighting parameters... currentLightColour = ComputeLighting(lightingParameters); // fill out light params again for next light... currentLightColour += ComputeLighting(lightingParameters); // etc.}
Which is a bunch less code. Sorry for the HLSL notation it's the only language I know, but hopefully it shouldn't be too hard to understand the principle. The other alternative is to do as you said, compute light for black lights. It's up to you in the end ;)
-Mezz
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Have you looked into using the fx files for different numbers of lights? I use the DX effect files, but I think they are very similar to the CgFX interfaces. The varying number of lights could just be built into a shader that takes an integer parameter like this:
fragment VS( vertex IN, uniform int numLights){ for (int i = 0; i < numLights; i++) { // Perform lighting }}
Then you would build different techniques that set the different number of lights that are currently affecting the geometry that you are rendering:
technique OneLight{ pass P0 { VertexShader = compile vs_1_1 VS( 1 ); PixelShader = compile ps_1_1 PS( ); }}technique TwoLights{ pass P0 { VertexShader = compile vs_1_1 VS( 2 ); PixelShader = compile ps_1_1 PS( ); }}
This may not be an optimum solution since different versions of the shaders need to be compiled for each different number of lights, but I think the compiled shaders are cached.
This is of course only if you want to use the fx interfaces, which may have a slight performance penalty as opposed to just using shaders, but I think its simplification is well worth the tradeoff.
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What can be typicly done is do 1 shader pass per light and then combine the passes via blending.
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# Sh:362
• Kolman, O., & Shelah, S. (1996). Categoricity of theories in L_{\kappa\omega}, when \kappa is a measurable cardinal. I. Fund. Math., 151(3), 209–240.
• Abstract:
We assume a theory T in the logic L_{\kappa \omega} is categorical in a cardinal \lambda\geq \kappa, and \kappa is a measurable cardinal. Here we prove that the class of model of T of cardinality < \lambda (but \geq |T|+\kappa) has the amalgamation property; this is a step toward understanding the character of such classes of models.
• Version 1998-12-05_10 (40p) published version (32p)
Bib entry
@article{Sh:362,
author = {Kolman, Oren and Shelah, Saharon},
title = {{Categoricity of theories in $L_{\kappa\omega}$, when $\kappa$ is a measurable cardinal. I}},
journal = {Fund. Math.},
fjournal = {Fundamenta Mathematicae},
volume = {151},
number = {3},
year = {1996},
pages = {209--240},
issn = {0016-2736},
mrnumber = {1424575},
mrclass = {03C75 (03C35)},
note = {\href{https://arxiv.org/abs/math/9602216}{arXiv: math/9602216}},
arxiv_number = {math/9602216}
}
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# What is spontaneous symmetry breaking in QUANTUM GAUGE systems?
Wen's question What is spontaneous symmetry breaking in QUANTUM systems? is cute, but here's an even cuter question. What is spontaneous symmetry breaking in QUANTUM GAUGE systems?
There are some gauge models where the Higgs phase and the confinement phase are continuously connected, you know. Why are the Higgs phase and the confinement phase identical in Yang-Mills-Higgs systems? You mention cluster decomposition? Sorry, because bilinear operators have to be connected by a Wilson line.
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Since gauge symmetry is not a symmetry in quantum theory, there is no spontaneous symmetry breaking of QUANTUM GAUGE symmetry.
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You can still break the global part. The gauge transformations on the boundary are physical, although if you only do a gauge transformation on the interior, it's unphysical, just a redundancy. – Ron Maimon Jun 23 '12 at 8:17
@Ron: The gauge symmetry is not a symmetry in quantum theory since both the local and the global gauge transformations are do-nothing transformations when act on quantum states. The quantum states simply do not change under those transformations, regardless if the system has boundary or not. So even the global part on the boundary is a do-nothing transformation and cannot break. – Xiao-Gang Wen Jun 23 '12 at 12:48
@Xiao-Gan-Wen: This is true of the local symmetry, but not the global symmetry. You can see this because the Noether prescription for a global phase rotation in a U(1) symmetric theory still gives a nontrivial conserved current. This is true of energy momentum in gravity, of supercurrents in supergravity, of every gauge current. Further, the global phase rotations are physically inequivalent--- you can translate a system relative to the boundaries, even if translations are gauged. – Ron Maimon Jun 23 '12 at 20:00
I absolutely agree with @RonMaimon. The true symmetry group is the global group that is equivalent to the gauge group $G$ modulo $G_*$, where $G_*$ is the redundancy group, that is, the gauge group whose elements go to the identity in the boundaries. – Diego Mazón Jul 26 '12 at 23:58
@drake: In my language for the situation that you described, $G_*$ is the gauge symmetry which cannot break. $G/G_*$ is the physical symmetry which can break. – Xiao-Gang Wen May 7 '13 at 11:53
It's all about RELATIVE symmetry breaking in QUANTUM GAUGE theories. RELATIVE to the Higgs field direction, symmetry is broken. This is a novel concept of RELATIVE symmetry breaking. A spin-0 helium atom quantum state might not break rotational symmetry, but RELATIVE to the direction of one of the electrons relative to the nucleus, the rotational symmetry for the other electron is RELATIVELY broken.
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It's only RELATIVE to the boundary value of the Higgs field. You can still arbitrarily phase rotate the Higgs direction in the interior. – Ron Maimon Jul 23 '12 at 7:50
Spontaneous breaking of a gauge symmetry is breaking the global symmetry. All gauge symmetries are not symmetries in the local part, if you do a local gauge transformation, you have the same exact state, But the global part of the gauge symmetry is physical, and leads to a Noether current. when you break the gauge symmetry, you are breaking the global part.
For example, in quantum electrodynamics, if you perform a phase rotation of the electron field by a constant factor $e^{i\theta}$, you do nothing to the vector potential. This transformation produces a nontrivial Noether current, it is the electric current. You can break this global symmetry with no problem, just using a charged condensate. This is the Higgs mechanism for U(1), or superconductivity.
A completely local version would be to do a local phase rotation by $\theta(x)$ where $\theta$ is a function which is nonzero only in a compact region. This transformation adds a gradient to A, and now if you do Noether's prescription, you find a conserved charge which is identically zero.
For gauge theories, the Noether currents derived from gauge tranformations are of the kind that they reduce to boundary integrals. In any theory, Noether currents are such that the charge can be evaluated at the initial time surface and the final surface, and you get the same answer. In a gauge theory, these charges can be evaluated on a large sphere on the initial surface and the final surface, using only the gauge field. In electrodynamics, this is Gauss's law. The Noether charge becomes a boundary object in a gauge theory, which is determined by the asymptotic values of the fields.
This is discussed to some extent on the Wikipedia page on infraparticle.
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Gauge symmetries are redundancies of the description, not a part of physics; gauge fields have surplus structures (e.g., non-physical polarizations) one brings in to describe the system more conveniently (for instance in a local and manifestly Lorentz covariant form). You can describe a gauge system in a language that does not have gauge symmetry at all. A famous example is AdS/CFT: you can describe an SU(N) gauge theory at large N by a theory of gravity; there is no SU(N) on the gravity side. Note that the global part of a gauge symmetry is as non-physical as its local part. It is however the case that ordinary gauge field theories (like QCD; not like GR) do have, aside from the non-physical gauge symmetry, a physical global symmetry which yields charge conservation. This physical global symmetry looks exactly like the global part of the (non-physical) gauge transformation, but one should differentiate between the two: gauge transformations are just like changing coordinates, but the physical global transformation involves changing the dynamical degrees of freedom. (In a similar situation in GR one should differentiate between the non-physical diff invariance and physical symmetries due to the existence of Killing vectors. The global part of the diff group is not only poorly defined, it is as non-physical as its local part. It is the isometries of the spacetime that are of physical significance. For example the existence of a conserved energy is due to the existence of a time-like Killing vector, not the meaningless "global part of the diff group".) (The case of non-abelian gauge theories with topological sectors has one further subtlety: your physical degrees of freedom are the equivalence classes of gauge field configurations that are continuously deformable to each other within each class.)
Gauge symmetry being non-physical, gauge symmetry breaking is also not a matter of physics, but a matter of changing the description. In the abelian Higgs model (which resembles superconductivity) for instance, if one changes their description from A) 2 components of scalar Higgs + 2 polarizations of the photon, to B) 1 component of Higgs + (1 component of Higgs + 2 components of the photon), one is breaking (or sacrificing) the symmetry in the initial description, to more clearly see the mass spectrum of the theory.
However, the "Higgs mechanism" is not non-physical as the above paragraph might initially suggest. It is physical in the following sense. Abelian gauge theories have three well-known phases: Landau phase, Coulomb phase, and the Higgs phase. Massless electrodynamics is an example that is always in the Landau phase (with logarithmic charge fall-off). Massive electrodynamics has a Landau regime for distances less than $m_{e}^{-1}$ and a Coulomb regime (with $1/r$ potential) for large distances. The abelian Higgs model has a Coulomb phase (with $m_{v}=0$) if the Higgs potential is minimum at the origin, and a Higgs phase (with $m_{v}\neq 0$) if the Higgs potential is minimum away from the origin. It is due to this dynamical phase transition that the change of description comes useful to understand the mass spectrum. (Look at John Preskill's note http://www.theory.caltech.edu/~preskill/ph230/notes2000/230Lectures27-29-Page347-402.pdf)
The important point to remember is: In the phenomena commonly referred to as spontaneous breaking of gauge symmetries, no physical (real) symmetry breaks. Physically, no global or local symmetry gets broken, only a phase transition happens that one can track by the mass of the vector boson as the order parameter. In the previous sentence, by local symmetry I mean some physical local symmetry (as the word "Physically" at the beginning of the sentence shows), like conformal symmetry in 2D; I'm not even thinking about non-physical symmetries like gauge symmetry, because they do not have anything to do with the nature.
I have limited the discussion to the abelian Higgs model, but the essence of the argument is the same for non-abelian gauge fields as well. If this answer has not been illuminating, I recommend reading the aforementioned notes by John Preskill.
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