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• May 04, 2015, 10:13:26 PM

### Author Topic: Special Snowflake Stories  (Read 6311086 times)

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#### alkira6

• Hero Member
• Posts: 1013
##### Re: Special Snowflake Stories
« Reply #21675 on: June 17, 2013, 11:10:45 AM »
When my ex bought a car off Craigslist, he didn't have checks for his account so what he did was after he'd test-driven the car, he and the seller went to the local branch of X bank and seller watched while my ex withdrew the money in a mix of 100s and a cashier's check.  The seller accepted that the money had come from the bank so it was likely genuine.  I did the same thing when I bought a house (trailer) for around 4k - met at the bank, etc.  I would never accept anything over a $20 at a garage sale either! That's what I did in college when I bought my car - test drove, took it to a garage to be checked out, and then we drove to the bank to get the money from the teller, who also signed the receipt for the sale for us. #### magicdomino • Super Hero! • Posts: 5133 ##### Re: Special Snowflake Stories « Reply #21676 on: June 17, 2013, 11:24:42 AM » Re:$100 bills and garage sales

I, personally, would never accept a $100 bill from anyone at a garage sale, even if I had lots of change. Or even if I were selling something on Craigslist. In fact, when I place ads on Craigslist for things, I always write, "Cash only. No$100's."

$100's are the most counterfeited bills out there. I'd be extremely suspicious of someone trying to pay for a small item with one of them. That was my first thought. #### Kimblee • I look good in white.... • Super Hero! • Posts: 6832 • "Hugs don't go Boom." "They don't? Since when?" ##### Re: Special Snowflake Stories « Reply #21677 on: June 17, 2013, 11:56:17 AM » Yes the old garage sale SS's. Who think their being very clever and daring by behaving as a pumpkin to get that extra saving they can rave about. When I married my dh we ended up with 2 washing machines, so we decided to sell his and keep my newer one. I just wanted it gone so I posted it in the paper for$80, great price for a 2nd hand machine that even students could purchase it.

In comes SS she thinks she will hardball me and scoop it up for a bargain on behalf of her son.  Claimed the hoses at the back were cut off and it didn't work.  I ensured her the hoses were not cut off that is how they are, and the machine works fine (it was clear where she was headed).  She demanded to see it in action very rudely, so I got out the extension cord to show her it's working state.  She then demanded to buy it cheaper as it's obviously been used and why were we selling it.  At that point I just inform her the price is the price I stated, and that it's no longer available for her to buy good day.

While she was gaping another car pulled up and another lady came on behalf of her child, who was moving out for the first time.  She was pleasant to deal with and wanted to purchase it straight away, so done deal.  She had the money out and paid me and we loaded it into her car.  The first lady just spluttered and informed me that she was first and should get it.  I informed her I can sell to whomever I please and had already asked her to leave my property, have a pleasant day.

Sold a pair of baby swings (needed repairs - I had the parts order sheet with them) to a lady buying them for her church nursery (building in construction for at least two months) while the guy with twins was still "negotiating" a reduced price "since they didn't work".  Well - his twins would be older, larger, and all that by the time the parts came in - the church nursery wasn't going to be ready for babies to use the swings for at least two months - I was happy with the asking price & she was happy to find two baby swings for half price (even after she ordered the parts - price was cheaper for TWO than just one replacement part).

Guy with twins at home had to keep looking.....those twins are over 25 by now....wonder if their Dad still remembers the "swings that got away"?  I'm pretty sure the swings in the church nursery have had to be replaced by now.....

I was a bit SS at a garage sale. The mention of baby swings brought back my shame. (I get no pass for being 12, right?)

My cousins (2 years and 3 months) had just moved in with us when their mom was in an accident and my mom agreed to take them in. And by my mom took them in, i mean, on all weekends and afterschool, clear to the moment I got into the the car the next day to go to school, *I* raised them. (My stepdad was in the hospital, Mom didn't have much of a choice. To be fair, she did take us to the hospital on weekends, where i got to tend two babies in a hospital... you know, for a change in scenery i guess?)

We got a baby swing brand new, but if had batteries and i hated it. At a garage sale I saw something I wanted, with a price i could afford; one of those older crank up swings, working, for $5. Only problem, a man was dikkering over the price, trying to get the owner to take a dollar. So i rab over with my littler cousin on my hip, the older holding the back of my jeans and said "I'll give you five right now." handed him my money, grabbed the swing and "ran" (okay, limped/pulled it) back to the car, pulling it into the backseat (three rows of seats, carseats in 2nd row, me and swing in 3rd) and shutting the door while i strapped in the kids/the man who wanted it for a dollar yelled at me through the glass. The owner was laughing though. He was a SS too I guess. The swing now belongs to my other cousin and STILL works. She has made it clear that when i have kids, i'm on my own if i want it back, because she's claiming adverse possesion rights, due to having had it in her house for over five years. She promises she'll provide a getaway vehicle if i want to swoop in and buy another one though. http://www.etsy.com/shop/Sassycelticmoon <a href="http://knitmeter.com/" title="Get Your Own KnitMeter">[/url] #### wheeitsme • Hero Member • Posts: 4119 ##### Re: Special Snowflake Stories « Reply #21678 on: June 17, 2013, 12:00:14 PM » Good lord. And I'm guessing there wasn't even a smidgen of shame or self-awareness to go with that pronouncement. Quote Then there was the guy who showed up about 15 minutes into the sale with a 100 dollar bill and wanted to buy a one dollar item. While I had change, I didn't have change for that much money that early in the morning. He asked me where he was supposed to get change for the other garage sales and I suggested that he stop at the local Quik Mart and ask them. He did manage to find a dollar bill to pay for the item. The hundred dollar bill nitwits can be the bane of my existence at the library. They get one or more hundred dollar bills and then as far as I can tell their first reaction is that they must immediately come to the library to pay their 75 cent overdue fee. We'll take it if we can manage to give change without too much hassle, but some of them get a bunch of fives, ones and even quarters back. The ones who insist, at least. If we don't have enough tens and twenties, most of the people who "only have a hundred" will miraculously manage to come up with something smaller. I've had more than one person tell me that their bank gave them the hundred and they just want to break it. Why they didn't request smaller bills from, say, the person who gave them the hundred, who works in the big building full of money, I have no idea. I've never been able to think of a way to ask that wouldn't sound like I was calling the patron a nimrod. I got a$100 bill for my birthday (I'm over 40 and my Dad is not a shopper, LOL).  And when I went to the big box building store this weekend and bought $12 worth of stuff, I asked if they would be able to take it. I asked. And I told them that if they couldn't, I would pay with my debit. The cashier said that she thought she could, opened her drawer and confirmed that it wouldn't be a problem. And that's the polite way to do it #### siamesecat2965 • Super Hero! • Posts: 9395 ##### Re: Special Snowflake Stories « Reply #21679 on: June 17, 2013, 12:11:00 PM » Good lord. And I'm guessing there wasn't even a smidgen of shame or self-awareness to go with that pronouncement. Quote Then there was the guy who showed up about 15 minutes into the sale with a 100 dollar bill and wanted to buy a one dollar item. While I had change, I didn't have change for that much money that early in the morning. He asked me where he was supposed to get change for the other garage sales and I suggested that he stop at the local Quik Mart and ask them. He did manage to find a dollar bill to pay for the item. The hundred dollar bill nitwits can be the bane of my existence at the library. They get one or more hundred dollar bills and then as far as I can tell their first reaction is that they must immediately come to the library to pay their 75 cent overdue fee. We'll take it if we can manage to give change without too much hassle, but some of them get a bunch of fives, ones and even quarters back. The ones who insist, at least. If we don't have enough tens and twenties, most of the people who "only have a hundred" will miraculously manage to come up with something smaller. I've had more than one person tell me that their bank gave them the hundred and they just want to break it. Why they didn't request smaller bills from, say, the person who gave them the hundred, who works in the big building full of money, I have no idea. I've never been able to think of a way to ask that wouldn't sound like I was calling the patron a nimrod. I got a$100 bill for my birthday (I'm over 40 and my Dad is not a shopper, LOL).  And when I went to the big box building store this weekend and bought $12 worth of stuff, I asked if they would be able to take it. I asked. And I told them that if they couldn't, I would pay with my debit. The cashier said that she thought she could, opened her drawer and confirmed that it wouldn't be a problem. And that's the polite way to do it I've also done this, usually at the grocery store or other big box store, when I'm spending quite a bit, so my change coming back will be minimal. But if i wasn't spending that much, I'd still ask, and if they said no, I'd pay another way. #### PeterM • Hero Member • Posts: 3321 ##### Re: Special Snowflake Stories « Reply #21680 on: June 17, 2013, 12:17:18 PM » Has anyone ever asked someone who makes that "I'll take my business elsewhere!" or "I won't be back!" statement why exactly they think they're important enough that anyone in the world would care? I'd be curious to hear the answer, though I imagine it'd really come down to the usual boring arrogance. I've always been either an uninvolved bystander or working when I've heard it, so I've never been able to ask. I've said it, actually. Not because I think my business alone is important enough to matter -- just the opposite, actually. No one's ever going to notice if Shopper X or Shopper Y just stop shopping at the store. They won't know if it's because of some policy the shopper hates, because they moved somewhere else, or whatever. So if there's ever a policy or behavior that's honestly bad enough to make me not willing to shop at that store again, I figure the best thing to do is inform the store exactly that. If you never tell them, they'll have no idea it's because of the policy, and if enough people leave because of it, maybe they'll change it. That's a good point, and an example of the acceptable way to pull the "Never shopping here again" card. I was thinking specifically of the SSes who try to use it as a weapon as they flounce off, fully expecting to be stopped and begged for forgiveness. I don't understand why they think anyone particularly wants their business - especially at a one-time even like a garage sale, as someone pointed out - but I must concede that as a general rule SSes who flounce are not the most self-aware or introspective people in the world. #### Outdoor Girl • Super Hero! • Posts: 14993 ##### Re: Special Snowflake Stories « Reply #21681 on: June 17, 2013, 12:21:09 PM » Re:$100 bills and garage sales

I, personally, would never accept a $100 bill from anyone at a garage sale, even if I had lots of change. Or even if I were selling something on Craigslist. In fact, when I place ads on Craigslist for things, I always write, "Cash only. No$100's."

$100's are the most counterfeited bills out there. I'd be extremely suspicious of someone trying to pay for a small item with one of them. That was my first thought. At least where I am, I've heard that$20s are the most (or used to be before we got the new polymer bills) counterfeited bill because people were a lot less likely to look closely at a $20. That's what everybody gets out of the bank machine, right? But the issue with$100s being counterfeit is that the merchant/seller is out a lot more money if it is counterfeit.
After cleaning out my Dad's house, I have this advice:  If you haven't used it in a year, throw it out!!!!.
Ontario

#### Hazmat

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##### Re: Special Snowflake Stories
« Reply #21682 on: June 17, 2013, 12:28:48 PM »

Good lord. And I'm guessing there wasn't even a smidgen of shame or self-awareness to go with that pronouncement.

Quote
Then there was the guy who showed up about 15 minutes into the sale with a 100 dollar bill and wanted to buy a one dollar item.  While I had change, I didn't have change for that much money that early in the morning.  He asked me where he was supposed to get change for the other garage sales and I suggested that he stop at the local Quik Mart and ask them.  He did manage to find a dollar bill to pay for the item.

The hundred dollar bill nitwits can be the bane of my existence at the library. They get one or more hundred dollar bills and then as far as I can tell their first reaction is that they must immediately come to the library to pay their 75 cent overdue fee. We'll take it if we can manage to give change without too much hassle, but some of them get a bunch of fives, ones and even quarters back. The ones who insist, at least. If we don't have enough tens and twenties, most of the people who "only have a hundred" will miraculously manage to come up with something smaller.

I've had more than one person tell me that their bank gave them the hundred and they just want to break it. Why they didn't request smaller bills from, say, the person who gave them the hundred, who works in the big building full of money, I have no idea. I've never been able to think of a way to ask that wouldn't sound like I was calling the patron a nimrod.

I got a $100 bill for my birthday (I'm over 40 and my Dad is not a shopper, LOL). And when I went to the big box building store this weekend and bought$12 worth of stuff, I asked if they would be able to take it.  I asked.  And I told them that if they couldn't, I would pay with my debit.  The cashier said that she thought she could, opened her drawer and confirmed that it wouldn't be a problem.

And that's the polite way to do it
Indeed.  Last week i needed a part for my motorcycle, I all had was $100 bill and 2 singles. Went they told me at the bike shop it would be$22 total, and since it was early morning in a cash only shop, I asked if they could take it, or should i go to my bank 2 blocks away to get change.  Of course the answer was yes, if I wouldn't mind changing it (although i think he would have taken it, I didn't want to take all his change).
A guest is a jewel on the cushion of hospitality. -Nero Wolfe

Indiana

#### Shalamar

• Hero Member
• Posts: 1520
##### Re: Special Snowflake Stories
« Reply #21683 on: June 17, 2013, 12:34:18 PM »
I'm the Social Committee rep for my floor in the company, and I often sell raffle tickets and whatnot on behalf of the committee.  These tickets are usually $1 or$3, some small amount.  I've lost count of the number of people who try to give me a twenty and then look bewildered when I say "Um, I don't have enough change, can you please find something smaller?"    I'm not sure where they got the idea that I have a cash drawer hidden at my desk.

#### artk2002

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##### Re: Special Snowflake Stories
« Reply #21684 on: June 17, 2013, 12:41:27 PM »
Re: $100 bills and garage sales I, personally, would never accept a$100 bill from anyone at a garage sale, even if I had lots of change. Or even if I were selling something on Craigslist.  In fact, when I place ads on Craigslist for things, I always write, "Cash only.  No $100's."$100's are the most counterfeited bills out there.  I'd be extremely suspicious of someone trying to pay for a small item with one of them.

"No bills larger than $20." I agree that using a$100 to pay for a small price item is a warning sign that they're trying to pass a counterfeit bill. It's exactly the kind of anonymous transaction that can help hide the counterfeiter. It would be interesting to see the reaction if someone said "Sure, I'll take that $100. I'd like to see a photo ID, please." Twenty years from now you will be more disappointed by the things that you didn't do than by the ones you did do. So throw off the bow lines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. -Mark Twain #### heartmug • Hero Member • Posts: 2491 ##### Re: Special Snowflake Stories « Reply #21685 on: June 17, 2013, 12:42:54 PM » Re:$100 bills and garage sales

I, personally, would never accept a $100 bill from anyone at a garage sale, even if I had lots of change. Or even if I were selling something on Craigslist. In fact, when I place ads on Craigslist for things, I always write, "Cash only. No$100's."

$100's are the most counterfeited bills out there. I'd be extremely suspicious of someone trying to pay for a small item with one of them. That was my first thought. POD. When I last held a yard sale I would not accept$100 bills no matter how much you were buying.  2 people tried it.  Lady handed me it for a $20 bookcase and I said "There is a grocery store exactly 2 miles straight down the street (one block over) - you can't miss it. " I held it for her for 1/2 hour and she came back with a$20.  Later a young couple came wanting to buy around $25 worth of stuff. I gave them the same line and they never came back. One option in a tug of war with someone is just to drop the rope. #### Virg • Super Hero! • Posts: 5892 ##### Re: Special Snowflake Stories « Reply #21686 on: June 17, 2013, 12:48:32 PM » LadyClaire wrote: "Well, I'd turned my text tone off when I went to bed the other night..only to be jolted awake by my phone ringing at 12:15 a.m. It was co-worker...because I "hadn't answered her texts" that she'd sent me at 11:30 p.m. These were not work related texts, BTW, and nothing important." I'd block her number entirely. If anyone at work complained, I would simply tell them that she keeps sending non-work related texts and calls at late hours. artk2002 wrote: "It would be interesting to see the reaction if someone said "Sure, I'll take that$100. I'd like to see a photo ID, please.""

The fridge logic in this is that someone who's knowingly passing counterfeit currency is probably skilled enough to have a fake ID that would pass muster.  I'd rather just say no and not have to deal with any issues.

Virg

#### jedikaiti

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##### Re: Special Snowflake Stories
« Reply #21687 on: June 17, 2013, 12:50:09 PM »

"Well, I'd turned my text tone off when I went to bed the other night..only to be jolted awake by my phone ringing at 12:15 a.m. It was co-worker...because I "hadn't answered her texts" that she'd sent me at 11:30 p.m. These were not work related texts, BTW, and nothing important."

I'd block her number entirely.  If anyone at work complained, I would simply tell them that she keeps sending non-work related texts and calls at late hours.

Absolutely. Or assign a silent ringtone to that number.
What part of v_e = \sqrt{\frac{2GM}{r}} don't you understand? It's only rocket science!

"The problem with re-examining your brilliant ideas is that more often than not, you discover they are the intellectual equivalent of saying, 'Hold my beer and watch this!'" - Cindy Couture

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##### Re: Special Snowflake Stories
« Reply #21688 on: June 17, 2013, 01:06:04 PM »

"Well, I'd turned my text tone off when I went to bed the other night..only to be jolted awake by my phone ringing at 12:15 a.m. It was co-worker...because I "hadn't answered her texts" that she'd sent me at 11:30 p.m. These were not work related texts, BTW, and nothing important."

I'd block her number entirely.  If anyone at work complained, I would simply tell them that she keeps sending non-work related texts and calls at late hours.

Absolutely. Or assign a silent ringtone to that number.

I did that the next morning, as soon as my head was clear enough to figure it out.

#### Elfmama

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##### Re: Special Snowflake Stories
« Reply #21689 on: June 17, 2013, 01:09:34 PM »
Well, in a store you would expect to be able to get change for a large bill.  But asking at a yard sale or a craft fair or a flea market if they have change for $100, first thing in the morning? Either SS or someone trying to pass off a counterfeit. You might lose a sale if it's just SSness, but you'll lose a lot more, all day long, when you don't have change for$5.
« Last Edit: June 17, 2013, 01:14:25 PM by Elfmama »
~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~
It's true. Money can't buy happiness.  You have to turn it
into books first.
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# How many similar binary search trees are made from different permutations?

If I have numbers ranging from 1 to n, and I generate all the permutations of these numbers. Now, I create Binary search tree from these permutations. For a value n i want to know how many BSTs would have same structure. for example for n=3; we have:

1,2,3

1,3,2

2,1,3

2,3,1

3,1,2

3,2,1

In this 2,1,3 and 2,3,1 produce same BST. So for 3 answer is 2.

I have figured out that if I take 3 numbers, and the root is less than one number and greater than other, then the sequence produced is same. ie. for n=9

2,1,3, 5,4,6 8,7,9 and 2,3,1 5,6,4 8,9,7 produce same BST.

• Can you deduce your answer from the number of possible BSTs on $n$ elements? – Yuval Filmus Dec 31 '17 at 15:24
• Is it somehow related to Catalan number? – Rajeev Pandey Dec 31 '17 at 15:30
• This is very likely. – Yuval Filmus Dec 31 '17 at 17:17
• Why is your answer 2 (for n=3)? In that case you have five possible binary trees and six permutations? Are you looking for the trees that have a unique permutation? – Hendrik Jan Jan 1 '18 at 13:45
• No I'm looking for trees that have same structure. 2,1,3 and 3,1,2 have same structure – Rajeev Pandey Jan 1 '18 at 14:42

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# Schedule of the Workshop "Picard-Fuchs Equations and Hypergeometric Motives"

## Monday, March 26

 10:15 - 10:50 Registration & Welcome coffee 10:50 - 11:00 Opening remarks 11:00 - 12:00 Frits Beukers: Some supercongruences of arbitrary length 12:00 - 13:45 Lunch break 13:45 - 14:45 Alexander Varchenko: Solutions of KZ differential equations modulo p 15:00 - 16:00 Bartosz Naskręcki: Elliptic and hyperelliptic realisations of low degree hypergeometric motives 16:00 - 16:30 Tea and cake 16:30 - 17:30 Roberto Villaflor Loyola: Periods of linear algebraic cycles in Fermat varieties afterwards Reception

## Tuesday, March 27

 09:30 - 10:30 Mark Watkins: Computing with hypergeometric motives in Magma 10:30 - 11:00 Group photo and coffee break 11:00 - 12:00 Madhav Nori: Semi-Abelian Motives 12:00 - 13:45 Lunch break 13:45 - 14:45 Wadim Zudilin: A q-microscope for hypergeometric congruences 15:00 - 16:00 Masha Vlasenko: Dwork Crystals and related congruences 16:00 - 16:30 Tea and cake

## Wednesday, March 28

 09:30 - 10:30 Jan Stienstra: Zhegalkin Zebra Motives, digital recordings of Mirror Symmetry 10:30 - 11:00 Coffee break 11:00 - 12:00 R. Paul Horja: Spherical Functors and GKZ D-modules 12:00 - 13:45 Lunch break 13:45 - 14:45 Duco van Straten: Frobenius structure for Calabi-Yau operators 15:00 - 16:00 Kiran S. Kedlaya: Frobenius structures on hypergeometric equations: computational methods 16:00 - 16:30 Tea and cake

## Thursday, March 29

 09:30 - 10:30 Danylo Radchenko: Goursat rigid local systems of rank 4 10:30 - 11:00 Coffee break 11:00 - 12:00 Damian Rössler: The arithmetic Riemann-Roch Theorem and Bernoulli numbers 12:00 - 13:45 Lunch break 13:45 - 14:45 Robert Kucharczyk: The geometry and arithmetic of triangular modular curves 15:00 - 16:00 John Voight: On the hypergeometric decomposition of symmetric K3 quartic pencils 16:00 - 16:30 Tea and cake

# Abstracts

## Frits Beukers: Some supercongruences of arbitrary length

In joint work with Eric Delaygue it is shown that truncated hypergeometric sums with parameters ½,...,½ and 1,...,1 and evaluated at the point 1 are equal modulo p to Dwork's unit-root eigenvalue modulo p2. Congruences modulo p follow directly from Dwork's work, the fact that the congruence holds modulo p2 accounts for the name 'supercongruence'.

Recorded Talk

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## R. Paul Horja: Spherical Functors and GKZ D-modules

Some classical mirror symmetry results can be recast using the more recent language of spherical functors. In this context, I will explain a Riemann-Hilbert type conjectural connection with the GKZ D-modules naturally appearing in toric mirror symmetry.

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## Kiran S. Kedlaya: Frobenius structures on hypergeometric equations: computational methods

Current implementations of the computation of L-functions associated to hypergeometric motives in Magma and Sage rely on a p-adic trace formula. We describe and demonstrate (in Sage) an alternate approach based on computing the right Frobenius structure on the hypergeometric equation. This gives rise to a conjectural formula for the residue at 0 of this Frobenius structure in terms of p-adic Gamma functions, related to Dwork's work on generalized hypergeometric functions.

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## Robert Kucharczyk: The geometry and arithmetic of triangular modular curves

In this talk I will take a closer look at triangle groups acting on the upper half plane. Except for finitely many special cases, which are highly interesting in themselves, these are non-arithmetic groups. However, a notion of congruence subgroup is well-defined for these, and there are natural moduli problems that are classified by quotients of the upper half plane by such subgroups, giving rise to models over number fields. These curves have much to do with very classical mathematics, and they build a bridge between the hypergeometric world and the world of Shimura varieties. This is ongoing joint work with John Voight, who is also present at this conference.

Recorded talk

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## Bartosz Naskręcki: Elliptic and hyperelliptic realisations of low degree hypergeometric motives

In this talk we will discuss what are the so-called hypergeometric motives and how one can approach the problem of their explicit construction as Chow motives in explicitely given algebraic varieties. The class of hypergeometric motives corresponds to Picard-Fuchs equations of hypergeometric type and forms a rich family of pure motives with nice L-functions. Following recent work of Beukers-Cohen-Mellit we will show how to realise certain hypergeometric motives of weights 0 and 2 as submotives in elliptic and hyperelliptic surfaces. An application of this work is the computation of minimal polynomials of hypergeometric series with finite monodromy groups and proof of identities between certain hypergeometric finite sums, which mimics well-known identities for classical hypergeometric series. This is a part of the larger program conducted by Villegas et al. to study the hypergeometric differential equations (special cases of differential equations '"coming from algebraic geometry'") from the algebraic perspective.

Recorded talk

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joint work with Deepam Patel

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## Danylo Radchenko: Goursat rigid local systems of rank 4

I will talk about certain rigid local systems of rank 4 considered by Goursat, with emphasis on explicit constructions and examples. The talk is based on joint work with Fernando Rodriguez Villegas.

Recorded Talk

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## Damian Rössler: The arithmetic Riemann-Roch theorem and Bernoulli numbers

(with V. Maillot) We shall show that integrality properties of the zero part of the abelian polylogarithm can be investigated using the arithmetic Adams-Riemann-Roch theorem. This is a refinement of the arithmetic Riemann-Roch theorem of Bismut-Gillet-Soulé-Faltings, which gives more information on denominators of Chern classes than the original theorem. We apply this theorem to the Poincaré bundle on an abelian scheme and and the final calculation involves a variant of von Staudt’s theorem.

On a canonical class of Green currents for the unit sections of abelian schemes. Documenta Math. 20 (2015), 631–668

Recorded Talk

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## Jan Stienstra: Zhegalkin zebra motives, digital recordings of Mirror Symmetry

I present a very simple construction of doubly-periodic tilings of the plane by convex black and white polygons. These tilings are the motives in the title. The vertices and edges in the tiling form a quiver (=directed graph) which comes with a so-called potential, provided by the polygons. Dual to this graph one has the bipartite graph formed by the black/white polygons and the edges in the tiling. We deform this structure by putting weights on the edges and connect this with representations of the Jacobi algebra of the quiver with potential and with the Kasteleyn matrix of the bi-partite graph.

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## Duco van Straten: Frobenius structure for Calabi-Yau operators

This is a report on joint work in progress with P. Candelas and X. de la Ossa on the (largly conjectural) computation of Euler factors from Calabi-Yau operators. The method uses Dworks deformation method starting from a simple Frobenius matrix at the MUM-point that involves a p-adic version of ζ(3). We give some new applications, in particular to the determination of congruence levels.

Top

## Alexander Varchenko: Solutions of KZ differential equations modulo p

Polynomial solutions of the KZ differential equations over a finite field Fp will be constructed as analogs of multidimensional hypergeometric solutions.

Top

## Roberto Villaflor Loyola: Periods of linear algebraic cycles in Fermat varieties

In this talk we will show how a theorem of Carlson and Griffiths can be used to compute periods of linear algebraic cycles inside Fermat varieties of even dimension. As an application we prove that the locus of hypersurfaces containing two linear cycles whose intersection is of low dimension, is a reduced component of the Hodge locus in the underlying parameter space. Our method can be used to verify similar statements for other kind of algebraic cycles (for example complete intersection algebraic cycles) by means of computer assistance. This is joint work with Hossein Movasati.

Recorded Talk

## Masha Vlasenko: Dwork crystals and related congruences

In the talk I will describe a realization of the p-adic cohomology of an affine toric hypersurface which originates in Dwork's work and give an explicit description of the unit-root subcrystal based on certain congruences for the coeficients of powers of a Laurent polynomial. This is joint work with Frits Beukers.

Recorded Talk

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## John Voight: On the hypergeometric decomposition of symmetric K3 quartic pencils

We study the hypergeometric functions associated to five one-parameter deformations of Delsarte K3 quartic hypersurfaces in projective space. We compute all of their Picard–Fuchs differential equations; we count points using Gauss sums and rewrite this in terms of finite field hypergeometric sums; then we match up each differential equation to a factor of the zeta function, and we write this in terms of global $L$-functions. This computation gives a complete, explicit description of the motives for these pencils in terms of hypergeometric motives.

This is joint work with Charles F. Doran, Tyler L. Kelly, Adriana Salerno, Steven Sperber, and Ursula Whitcher.

Recorded Talk

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## Mark Watkins: Computing with hypergeometric motives in Magma

We survey the computational vistas that are available for computing with hypergeometric motives in the computer algebra system Magma. Various examples that exemplify the theory will be highlighted.

Recorded Talk

Top

## Wadim Zudilin: A q-microscope for hypergeometric congruences

By examining asymptotic behavior of certain infinite basic ($q$-) hypergeometric sums at roots of unity (that is, at a "$q$-microscopic" level) we prove polynomial congruences for their truncations. The latter reduce to non-trivial (super)congruences for truncated ordinary hypergeometric sums, which have been observed numerically and proven rarely. A typical example includes derivation, from a q-analogue of Ramanujan's formula $$\sum_{n=0}^\infty\frac{\binom{4n}{2n}{\binom{2n}{n}}^2}{2^{8n}3^{2n}}\,(8n+1)=\frac{2\sqrt{3}}{\pi},$$ of the two supercongruences $$S(p-1)\equiv p\biggl(\frac{-3}p\biggr)\pmod{p^3} \quad\text{and}\quad S\Bigl(\frac{p-1}2\Bigr) \equiv p\biggl(\frac{-3}p\biggr)\pmod{p^3},$$ valid for all primes $p>3$, where $S(N)$ denotes the truncation of the infinite sum at the $N$-th place and $(\frac{-3}{\cdot})$ stands for the quadratic character modulo $3$.


text: It’s important to first think about the model that we will fit to address these questions. MEDV). The default setting is N, the number of input variables selected in the Step 1 of 2 dialog. Now we define the dependent and independent variables. Included and excluded predictors are shown in the Model Predictors table. From a marketing or statistical research to data analysis, linear regression model have an important role in the business. RSS: The residual sum of squares, or the sum of squared deviations between the predicted probability of success and the actual value (1 or 0). In the following example, we will use multiple linear regression to predict the stock index price (i.e., the dependent variable) of a fictitious economy by using 2 independent/input variables: 1. B1X1= the regression coefficient (B1) of the first independent variable (X1) (a.k.a. We’ll call these numbers. In addition to these variables, the data set also contains an additional variable, Cat. On the XLMiner ribbon, from the Data Mining tab, select Predict - Multiple Linear Regression to open the Multiple Linear Regression - Step 1 of 2 dialog. Select Deleted. We want to predict Price (in thousands of dollars) based on Mileage (in thousands of miles). When this option is selected, the Studentized Residuals are displayed in the output. Solve via QR Decomposition 6. For a variable to leave the regression, the statistic's value must be less than the value of FOUT (default = 2.71). However, the relationship between them is not always linear. Call Us Check to see if the "Data Analysis" ToolPak is active by clicking on the "Data" tab. When this checkbox is selected, the DF fits for each observation is displayed in the output. Nearly normal residuals: Check a Q-Q plot on the standardized residuals to see if they are approximately normally distributed. This is an overall measure of the impact of the ith datapoint on the estimated regression coefficient. Select Variance-covariance matrix. All predictors were eligible to enter the model passing the tolerance threshold of 5.23E-10. It allows the mean function E()y to depend on more than one explanatory variables Multiple Linear Regression Equation • Sometimes also called multivariate linear regression for MLR • The prediction equation is Y′= a + b 1X 1 + b 2X 2 + b 3X 3 + ∙∙∙b kX k • There is still one intercept constant, a, but each independent variable (e.g., X 1, X 2, X 3) has their own regression coefficient Cp: Mallows Cp (Total squared error) is a measure of the error in the best subset model, relative to the error incorporating all variables. Statistics play a critical hand in determining the relationship among different variables. Example 9.9. When this checkbox is selected, the collinearity diagnostics are displayed in the output. MULTIPLE REGRESSION EXAMPLE For a sample of n = 166 college students, the following variables were measured: Y = height X1 = mother’s height (“momheight”) X2 = father’s height (“dadheight”) X3 = 1 if male, 0 if female (“male”) Our goal is to predict student’s height using the mother’s and father’s heights, and sex, where sex is If this option is selected, XLMiner partitions the data set before running the prediction method. Multiple Regression - Example. In the first decile, taking the most expensive predicted housing prices in the dataset, the predictive performance of the model is about 1.7 times better as simply assigning a random predicted value. Note: This portion of the lesson is most important for those students who will continue studying statistics after taking Stat 462. Multiple linear regression follows the same conditions as the simple linear model. Then the data set(s) are sorted using the predicted output variable value. On the XLMiner ribbon, from the Applying Your Model tab, select Help - Examples, then Forecasting/Data Mining Examples to open the Boston_Housing.xlsx from the data sets folder. The average error is typically very small, because positive prediction errors tend to be counterbalanced by negative ones. If this procedure is selected, Number of best subsets is enabled. XLMiner displays The Total sum of squared errors summaries for both the Training and Validation Sets on the MLR_Output worksheet. in the residuals so this condition is met. Some key points about MLR: In this lesson, you will learn how to solve problems using concepts based on linear regression. Home. An example of how useful Multiple Regression Analysis could be can be seen in determining the compensation of an employee. To answer this question, data was randomly selected from an Internet car sale site. In many applications, there is more than one factor that inﬂuences the response. In our example, code (allotted to each education) and year are independent variables, whereas, salaryis dependent variable. Multiple Regression worked example (July 2014 updated) 1. Best Subsets where searches of all combinations of variables are performed to observe which combination has the best fit. The critical assumption of the model is that the conditional mean function is linear: E(Y|X) = α +βX. the effect that increasing the value of the independent varia… This data set has 14 variables. For every one thousand mile increase in Mileage for a Jaguar car, we expect Price will decrease by 0.6203 (0.48988 + 0.13042) thousands of dollars ($620.30) (holding all other variables constant). Linear Regression with Multiple Variables. We show below how we can obtain one of these $$p$$-values (for CarTypeJaguar) in R directly: We, therefore, have sufficient evidence to reject the null hypothesis for Mileage and the intercept on Porche compared to the intercept on BMW (which is also significant), assuming the other terms are in the model. REGRESSION ANALYSIS July 2014 updated Prepared by Michael Ling Page 1 QUANTITATIVE RESEARCH METHODS SAMPLE OF REGRESSION ANALYSIS Prepared by Michael Ling 2. The next step is to create the regression model as an instance of LinearRegression and fit it with .fit(): model = LinearRegression (). The test is based on the diagonal elements of the triangular factor R resulting from Rank-Revealing QR Decomposition. A simple linear regression equation for this would be $$\hat{Price} = b_0 + b_1 * Mileage$$. Lift Charts and RROC Curves (on the MLR_TrainingLiftChart and MLR_ValidationLiftChart, respectively) are visual aids for measuring model performance. where $${SE}_i$$ represents the standard deviation of the distribution of the sample coefficients. In der Statistik ist die multiple lineare Regression, auch mehrfache lineare Regression (kurz: MLR) oder lineare Mehrfachregression genannt, ein regressionsanalytisches Verfahren und ein Spezialfall der linearen Regression.Die multiple lineare Regression ist ein statistisches Verfahren, mit dem versucht wird, eine beobachtete abhängige Variable durch mehrere unabhängige Variablen zu erklären. For example, a modeler might want to relate the weights of individuals to their heights using a linear regression model. The default setting is N, the number of input variables selected in the. If this procedure is selected, FOUT is enabled. Anything to the left of this line signifies a better prediction, and anything to the right signifies a worse prediction. We see that the (Intercept), Mileage and CarTypePorche are statistically significant at the 5% level, while the others are not. It tells in which proportion y varies when x varies. Multiple Linear Regression is performed on a data set either to predict the response variable based on the predictor variable, or to study the relationship between the response variable and predictor variables. Recall that these sample coefficients are actually random variables that will vary as different samples are (theoretically, would be) collected. This bars in this chart indicate the factor by which the MLR model outperforms a random assignment, one decile at a time. We can use the lm function here to fit a line and conduct the hypothesis test. The greater the area between the lift curve and the baseline, the better the model. Solution: Solving the two regression equations we get mean values of X and Y . Articulate assumptions for multiple linear regression 2. A linear regression model that contains more than one predictor variable is called a multiple linear regression model. An example data set having three independent variables and single dependent variable is used to build a multivariate regression model and in the later section of the article, R-code is provided to model the example data set. The scatterplot below shows the relationship between mileage, price, and car type. Outside: 01+775-831-0300. Parameters and are referred to as partial re… Select ANOVA table. After the model is built using the Training Set, the model is used to score on the Training Set and the Validation Set (if one exists). Noah can only work 20 hours a week. This table assesses whether two or more variables so closely track one another as to provide essentially the same information. Solve via Singular-Value Decomposition Also work out the values of the regression coefficient and correlation between the two variables X and Y. From a marketing or statistical research to data analysis, linear regression model have an important role in the business. Say, there is a telecom network called Neo. How can he find this information? Note: If you only have one explanatory variable, you should instead perform simple linear regression. The RSS for 12 coefficients is just slightly higher than the RSS for 13 coefficients suggesting that a model with 12 coefficients may be sufficient to fit a regression. Multiple Linear Regression is performed on a data set either to predict the response variable based on the predictor variable, or to study the relationship between the response variable and predictor variables. DFFits provides information on how the fitted model would change if a point was not included in the model. Linear Regression with Multiple Variables. example b = regress (y,X) returns a vector b of coefficient estimates for a multiple linear regression of the responses in vector y on the predictors in matrix X. The model describes a plane in the three-dimensional space of , and . Let $$x_1 = [1, 3, 4, 7, 9, 9]$$ ... Really what is happening here is the same concept as for multiple linear regression, the equation of a plane is being estimated. Standardized residuals are obtained by dividing the unstandardized residuals by the respective standard deviations. Data Mining. The following example Regression Model table displays the results when three predictors (Opening Theaters, Genre_Romantic Comedy, and Studio_IRS) are eliminated. Probability is a quasi hypothesis test of the proposition that a given subset is acceptable; if Probability < .05 we can rule out that subset. It is used to discover the relationship and assumes the linearity between target and predictors. XLMiner offers the following five selection procedures for selecting the best subset of variables. A description of each variable is given in the following table. Linear regression answers a simple question: Can you measure an exact relationship between one target variables and a set of predictors? For the given lines of regression 3X–2Y=5and X–4Y=7. 4.8. Many of simple linear regression examples (problems and solutions) from the real life can be given to help you understand the core meaning. This data set has 14 variables. linear regression model is an adequate approximation to the true unknown function. Economics: Linear regression is the predominant empirical tool in economics. The following example illustrates XLMiner's Multiple Linear Regression method using the Boston Housing data set to predict the median house prices in housing tracts. Note that an interpretation of the observed intercept can also be done: we expect a BMW car with zero miles to have a price of$56,290.07. For example, it is used to predict consumer spending, fixed investment spending, inventory investment, purchases of a country’s exports, spending on imports, the demand to hold liquid assets, labour demand, and labour supply. Multivariate Linear Regression. We should be a little cautious of this prediction though since there are no cars in our sample of used cars that have zero mileage. It is also a method that can be reformulated using matrix notation and solved using matrix operations. The preferred methodology is to look in the residual plot to see if the standardized residuals (errors) from the model fit are randomly distributed: There does not appear to be any pattern (quadratic, sinusoidal, exponential, etc.) Linear Regression Real Life Example #1. On the Output Navigator, click the Collinearity Diags link to display the Collinearity Diagnostics table. Typically, Prediction Intervals are more widely utilized as they are a more robust range for the predicted value. This residual is computed for the ith observation by first fitting a model without the ith observation, then using this model to predict the ith observation. 2013 [Chapter 1 and Chapter 4]). 2. Select. Under Residuals, select Standardized to display the Standardized Residuals in the output. Likewise, the numbers in front of the “x’s” are no longer slopes in multiple regression since the equation is not an equation of a line anymore. When this is selected, the covariance ratios are displayed in the output. © 2020 Frontline Systems, Inc. Frontline Systems respects your privacy. To estim… We need to also include in CarType to our model. When you have a large number of predictors and you would like to limit the model to only the significant variables, select Perform Variable selection to select the best subset of variables. The null model is defined as the model containing no predictor variables apart from the constant. 2013 [Chapter 1 and Chapter 4]). Since CarType has three levels: BMW, Porche, and Jaguar, we encode this as two dummy variables with BMW as the baseline (since it occurs first alphabetically in the list of three car types). Model link to display the Regression Model table. The formula for a multiple linear regression is: 1. y= the predicted value of the dependent variable 2. Solution: Regression coefficient of X on Y (i) Regression equation of X on Y (ii) Regression coefficient of Y on X (iii) Regression equation of Y on X. Y = 0.929X–3.716+11 = 0.929X+7.284. So, he collects all customer data and implements linear regression by taking monthly charges as the dependent variable and tenure as the independent variable. While one could compute these observed test statistics by “hand”, the focus here is on the set-up of the problem and in understanding which formula for the test statistic applies. However, since there are several independent variables in multiple linear analysis, there is another mandatory condition for the model: Non-collinearity: Independent variables should show a minimum of correlation with each other. Multiple Linear Regression is one of the regression methods and falls under predictive mining techniques. Sequential Replacement in which variables are sequentially replaced and replacements that improve performance are retained. A good guess is the sample coefficients $$B_i$$. As a result, any residual with absolute value exceeding 3 usually requires attention. This tutorial is divided into 6 parts; they are: 1. More precisely, do the slopes and intercepts differ when comparing mileage and price for these three brands of cars? Ist die multiple lineare regression gegenüber der einfachen genauer? 1. Example 9.10 When this option is selected, the Deleted Residuals are displayed in the output. As the tenure of the customer i… Interpret the Regression Results Now, we can easily compare t… In Analytic Solver Platform, Analytic Solver Pro, XLMiner Platform, and XLMiner Pro V2015, a new pre-processing feature selection step has been added to prevent predictors causing rank deficiency of the design matrix from becoming part of the model. One of the more commonly applied principles of this discipline is the Multiple Regression Analysis, which is used when reviewing three or more measurable variables.When translated in mathematical terms, Multiple Regression Analysis means that there is a dependent variable, referred to as Y. The Sum of Squared Errors is calculated as each variable is introduced in the model, beginning with the constant term and continuing with each variable as it appears in the data set. Inside USA: 888-831-0333 Forward Selection in which variables are added one at a time, starting with the most significant. More than one variable: multiple linear regression (MLR) 4.11. This also creates a baseline interaction term of BMW:Mileage, which is not specifically included in the model but comes into play by setting Jaguar and Porche equal to 0: $\hat{Price} = b_0 + b_1 * Mileage + b_2 * Porche + b_3 * Jaguar + b_4 Mileage*Jaguar + b_5 Mileage*Porche.$. Step 3: Create a model and fit it. In linear models Cooks Distance has, approximately, an F distribution with k and (n-k) degrees of freedom. The total sum of squared errors is the sum of the squared errors (deviations between predicted and actual values), and the root mean square error (square root of the average squared error). When this option is selected, the fitted values are displayed in the output. Remember that in order to use the shortcut (formula-based, theoretical) approach, we need to check that some conditions are met. Problem Statement . Select DF fits. The chemist examines 32 pieces of cotton cellulose produced at different settings of curing time, curing temperature, formaldehyde concentration, and catalyst ratio. 2013. I run a company and I want to know how my employees’ job performance relates to their IQ, their motivation and the amount of social support they receive.


text:
Opuscula Math. 30, no. 4 (2010), 507-525
http://dx.doi.org/10.7494/OpMath.2010.30.4.507

Opuscula Mathematica

# On some impulsive fractional differential equations in Banach spaces

JinRong Wang
W. Wei
YanLong Yang

Abstract. This paper deals with some impulsive fractional differential equations in Banach spaces. Utilizing the Leray-Schauder fixed point theorem and the impulsive nonlinear singular version of the Gronwall inequality, the existence of $$PC$$-mild solutions for some fractional differential equations with impulses are obtained under some easily checked conditions. At last, an example is given for demonstration.

Keywords: fractional differential equations with impulses, nonlinear impulsive singular version of the Gronwall inequality, $$PC$$-mild solutions, existence.

Mathematics Subject Classification: 45N05, 93C25.

Full text (pdf)

JinRong Wang, W. Wei, YanLong Yang, On some impulsive fractional differential equations in Banach spaces, Opuscula Math. 30, no. 4 (2010), 507-525, http://dx.doi.org/10.7494/OpMath.2010.30.4.507

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## Tuesday, August 23, 2011

### Once more: gravity is not an entropic force

Archil Kobakhidze of the University of Melbourne (where my uncle has taught maths since the late 1960s) released his new paper on the arXiv,
Once more: gravity is not an entropic force
He repeats and refines his arguments from his September 2010 paper, Gravity is not an entropic force (Phys Rev D 83, 2011), and he kindly cites your humble correspondent's January 2010 blog entry, Why gravity can't be entropic, as the first source of the argument that an entropic force predicts the disappearance of interference patterns that are however beautifully seen in neutron interferometry (see e.g. Nesvizhevsky et al. in Nature 2002: PDF free for a recent paper in this research direction that began in the mid 1970s: PDF) - a point that Kobakhidze (as far as I know) realized independently of me.

What motivated him to write another paper was, among other things, an April 2011 preprint, On gravity as an entropic force, by Masud Chaichian, Markku Oksanen, and Anca Tureanu. This paper contains some invalid criticism of Kobakhidze's paper which is why Kobakhidze decided to explain the flaw in a new preprint.

The authors of the flawed preprint used at least two (but related) invalid arguments in their attempts to resuscitate Erik Verlinde's theory. One of them was the claim that Verlinde's theory produces the "right classical limit". When this classical limit is quantized, one obtains the right quantum theory, including the neutron interference. However, this argument incorrectly assumes that quantum physics is uniquely determined by a classical limit. It's not. If you take the classical limit C of a quantum theory Q and "quantize" C again, you don't necessarily get Q.

In particular, when we talk about the distance-dependent entropy, it's a feature of a physical theory that holds both in the quantum theory Q and in the classical limit C. And in the quantum theory, it automatically destroys the interference patterns because there exists no one-to-one way how to link microstates at different separations (because their numbers differ). So there can't exist any quantum theory that preserves the interference but that still produces a classical limit with a distance-dependent entropy.

Kobakhidze looks at a particular method used by the three authors to mask the error in their paper: they try to hide the distance-dependent character of the number of microstates - which is the very defining feature of Verlinde's proposal - by using different conventions for coarse-graining at different distances. Of course, this is just a trick to fool themselves (as well as insufficiently careful readers of their paper). If one uses a self-consistent description and a fixed definition of the entropy, the entropy simply does depend on the distance between the gravitating bodies (such as the Earth and the neutrons) and the interference pattern disappears.

In my opinion, Kobakhidze also tries to present Verlinde's proposal in a maximally comprehensible, no-nonsense way. Instead of accepting the usual potential force as found by Newton,
$\vec F = -m \vec \nabla \Phi,$ one must adopt an entropic force that depends on a temperature and an entropy,
$\vec F = T \vec \nabla S.$ The temperature should be associated with the Unruh temperature which depends on the gravitational acceleration. This assumption is very problematic and probably inconsistent by itself because different pairs of bodies would have different temperatures which means that they couldn't be in a thermal equilibrium.

Moreover, everyone knows that the actual temperature of the Sun - and the temperature of all degrees of freedom on the Surface of the Sun - is 6000 °C and has nothing to do with tiny temperatures associated with the Sun by Verlinde.

Fine. Ignore that the temperatures in the real situations would be highly non-constant which would lead to a huge heat transfer and irreversibility. Kobakhidze writes down what the formula for entropy $$S = S(r)$$ as a function of the distance has to be,
$S = 2\pi m \log(r/r_{\rm Verlinde}).$ I've integrated his formula for $$\vec \nabla S$$. An unknown distance scale, $$r_{\rm Verlinde}$$, really has to be added as well which is almost certainly another inconsistency but that's not the way how Kobakhidze shows that Verlinde's theory is falsified by the observations.

Lisa Randall's new book on particle physics and philosophy of science, Knocking on Heaven's Door, will be released on September 20th. Pre-order now: I've read it thrice, it's great.

Kobakhidze realizes that the number of microstates depends on the distance. But in agreement with his previous paper, he still assumes that the neutron may be associated with a wave function. If you try to do so, however, the momentum operator in quantum mechanics inevitably contains a non-Hermitian piece which takes care of the separation of the wave function among many microstates when the number of microstates goes up:
$\hat p = -i \frac{\partial}{\partial r} - 2\pi i m.$ Well, this is too optimistic because the relative phases between all the microstates would be undetermined and would evolve chaotically because of small differences in the energy between the macroscopically indistinguishable microstates - which would eliminate any trace of quantum coherence. But even if you assume that the quantum coherence is preserved, you get totally wrong new and very large terms in the Schrödinger equation that will obviously predict that the neutron interferometry experiments should see something completely different than what they do see.

The author describes some wrong predictions of Verlinde's theory for the neutron in the gravitational field in some detail. At any rate, the conclusion is that the neutron interferometry experiments in the Earth's gravitational field falsify all forms of "gravity as an entropic force" hypotheses.

Challenge

If you think that Verlinde's proposal has not been falsified, just explain the neutron interferometry experiments with his theory! Define some microstates so that the entropy depends on the distance according to Verlinde's description. And then try to derive the usual Schrödinger equation for the neutron in the external potential - which has been experimentally observed to govern the neutrons - from your original Hamiltonian for the neutron-Earth system by defining the state $$|h\rangle$$ for the neutron at height $$h$$ as a linear combination of your many microstates (whose density depends on the height $$h$$).

In advance, I can assure you that your attempts will fail. The very meaning of the entropic force is that the coherence is lost whenever the force acts, so the information about the relative phases of the neutron's wave function will disappear. Try it and if you fail - and you will surely fail - please stop with the nonsensical suggestions that Verlinde's proposal could still be OK in some way. Its very fundamental assumptions contradict some experimentally established pillars of modern physics.

If you couldn't have figured this simple thing out for more than 1 year, it's pretty painful, but if you will fail to do so for 2 or more years, it will be even more painful. ;-)

1. This reminds me of Garrett Lisi's E8 theory to some extent. I noticed that Woit has on entry on his "Not Even Wrong" blog to the effect that Verlinde has been awarded some big grant money to continue his work:

"\$6.5 Million for Entropic Gravity"http://www.math.columbia.edu/~woit/wordpress/?p=3781

So it seems that even if experts can be confident that he is wrong, Verlinde has a short-term victory.

2. Why in the world would one even suggest to associate the temperatures of the atoms of gravitating objects with the "temperature" of the microscopic degrees of freedom that cause gravity in the case of entropic gravity???

The universe is clearly far, far away from equilibrium with regard to the effective temperature of the real vacuum. By the time it will get to that equilibrium, all notions of space and time will be gone and there will be no observers left to amuse themselves about physics.

As far as Kobakhidze's derivation of the (in his eyes) correct Schroedinger equation is concerned... Schroedinger quantum mechanics is not even a self-consistent theory of quantum systems. It has nothing to say about fields and it does not treat gravity as a field. It treats gravity as a CLASSICAL potential. Kobakhidze's argument is basically nonsense in, nonsense out (in that he pretends that one can say anything about gravitation by using non-relativistic single particle quantum mechanics) and nature tells him so by agreeing completely with Verlinde's hand-waving and disagreeing with his.

Now, if someone would be so nice to show me a quantum field theoretical derivation of neutron wave functions formulated in a quantum field theory of gravity that incorporates Verlinde's argument and that still predicts the wrong outcome, then, maybe, I would be convinced. Until then I go with the experimental proof, which clearly states that Verlinde's hands wave far more successfully than Kobakhidze's.

And why entropic forces would immediately destroy coherence is also not clear to me. I talk a lot to people, which means that the entropic forces which transport the sound waves from my mouth to their ears work quite well without destroying short term coherence in sound waves. They retain both their amplitude and phase over quite some distance. And anybody who has done atomic spectroscopy knows that random em fields acting on atoms do not automatically destroy line spectra, they merely modify them, leading to line broadening and changes in transition probabilities. How much coherence gets destroyed is all a matter of scales. The effective scale of a neutron scattering experiment is far, far, far away from the scale on which entropic gravity emerges from microscopic degrees on freedom holographic screens... and by the time the neutrons get to react to them, the collective sum of all those interactions behaves like a Newtonian potential.

3. Sorry, your comment is pure crackpottery.

Whenever some degrees of freedom do interact with the rest so that this interaction matters - and it surely matters if one wants to use this behavior to explain huge effects such as the gravitational attraction - then they inevitably do converge to equilibrium.

It's pure crackpottery for you to suggest that they don't thermalize and/or that their temperature isn't really temperature and can't be measured. The temperature is always the same thing. The entropy is always the same thing, too. You can't have it both ways. You either try to use these temperatures and entropy to explain something - but then you also have to accept that these crazy new terms in the temperature and entropy also have other consequences that instantly falsify the model - or you preserve your sanity in realizing that there's no extra temperature or entropy coming from a nonzero gravitational potential.

I won't even discuss your utterly idiotic comments about Schrodinger's equations being inapplicable or bad or whatever rubbish you are writing. I wouldn't be doing anything else if I had to respond to every paragraph written by every crank of your type. Schrodinger's equation works perfectly, even in the presence of the gravitational potential as has been tested since the 1970s by neutron interferometry etc.


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Q

# Using the property of determinants and without expanding, prove that determinant 1 bc a(b+c) 1 ca b(c+a) 1 ab c(a+b) = 0 Ex 4.2 Q : 2

Q : 4           Using the property of determinants and without expanding, prove that

$\dpi{100} \begin{vmatrix}1 &bc &a(b+c) \\1 &ca &b(c+a) \\1 &ab & c(a+b) \end{vmatrix}=0$

Views

We have determinant:

$\triangle = \begin{vmatrix} 1 &bc &a(b+c) \\ 1& ca &b(c+a) \\ 1& ab &c(a+b) \end{vmatrix}$

Applying $C_{3} \rightarrow C_{2} + C_{3}$ we have then;

$\triangle = \begin{vmatrix} 1 &bc & ab+bc+ca \\ 1& ca &ab+bc+ca \\ 1& ab &ab+bc+ca \end{vmatrix}$

So, here column 3 and column 1 are proportional.

Therefore, $\triangle = 0$.

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# Washburn's equation

In physics, Washburn's equation describes capillary flow in a bundle of parallel cylindrical tubes; it is extended with some issues also to imbibition into porous materials. The equation is named after Edward Wight Washburn;[1] also known as Lucas–Washburn equation, considering that Richard Lucas[2] wrote a similar paper three years earlier, or the Bell-Cameron-Lucas-Washburn equation, considering J.M. Bell and F.K. Cameron's discovery of the form of the equation fifteen years earlier.[3]

## Derivation

For wet-out flow, it is

${\displaystyle L^{2}={\frac {\gamma Dt}{4\eta }}}$

where ${\displaystyle t}$ is the time for a liquid of dynamic viscosity ${\displaystyle \eta }$ and surface tension ${\displaystyle \gamma }$ to penetrate a distance ${\displaystyle L}$ into the capillary whose pore diameter is ${\displaystyle D}$. In case of a porous materials many issues have been raised both about the physical meaning of the calculated pore diameter ${\displaystyle D}$[4] and the real possibility to use this equation for the calculation of the contact angle of the solid.[5] The equation is derived for capillary flow in a cylindrical tube in the absence of a gravitational field, but is sufficiently accurate in many cases when the capillary force is still significantly greater than the gravitational force.

In his paper from 1921 Washburn applies Poiseuille's Law for fluid motion in a circular tube. Inserting the expression for the differential volume in terms of the length ${\displaystyle l}$ of fluid in the tube ${\displaystyle dV=\pi r^{2}dl}$, one obtains

${\displaystyle {\frac {\delta l}{\delta t}}={\frac {\sum P}{8r^{2}\eta l}}(r^{4}+4\epsilon r^{3})}$

where ${\displaystyle \sum P}$ is the sum over the participating pressures, such as the atmospheric pressure ${\displaystyle P_{A}}$, the hydrostatic pressure ${\displaystyle P_{h}}$ and the equivalent pressure due to capillary forces ${\displaystyle P_{c}}$. ${\displaystyle \eta }$ is the viscosity of the liquid, and ${\displaystyle \epsilon }$ is the coefficient of slip, which is assumed to be 0 for wetting materials. ${\displaystyle r}$ is the radius of the capillary. The pressures in turn can be written as

${\displaystyle P_{h}=hg\rho -lg\rho \sin \psi }$
${\displaystyle P_{c}={\frac {2\gamma }{r}}\cos \phi }$

where ${\displaystyle \rho }$ is the density of the liquid and ${\displaystyle \gamma }$ its surface tension. ${\displaystyle \psi }$ is the angle of the tube with respect to the horizontal axis. ${\displaystyle \phi }$ is the contact angle of the liquid on the capillary material. Substituting these expressions leads to the first-order differential equation for the distance the fluid penetrates into the tube ${\displaystyle l}$:

${\displaystyle {\frac {\delta l}{\delta t}}={\frac {[P_{A}+g\rho (h-l\sin \psi )+{\frac {2\gamma }{r}}\cos \phi ](r^{4}+4\epsilon r^{3})}{8r^{2}\eta l}}}$

### Washburn's constant

The Washburn constant may be included in Washburn's equation.

It is calculated as follows:

${\displaystyle {\frac {10^{4}\left[\mathrm {\frac {\mu m}{cm}} \right]\left[\mathrm {\frac {N}{m^{2}}} \right]}{68947.6\left[\mathrm {\frac {dynes}{cm^{2}}} \right]}}=0.1450(38)}$[6][7]

## Applications

### Inkjet printing

The penetration of a liquid into the substrate flowing under its own capillary pressure can be calculated using a simplified version of Washburn's equation:[8][9]

${\displaystyle l=\left[{\frac {r\cos \theta }{2}}\right]^{\frac {1}{2}}\left[{\frac {\gamma }{\eta }}\right]^{\frac {1}{2}}t^{\frac {1}{2}}}$

where the surface tension-to-viscosity ratio ${\displaystyle \left[{\tfrac {\gamma }{\eta }}\right]^{\frac {1}{2}}}$ represents the speed of ink penetration into the substrate.

### Food

According to physicist and igNobel prize winner Len Fisher, the Washburn equation can be extremely accurate for more complex materials including biscuits.[10][11] Following an informal celebration called national biscuit dunking day, some newspaper articles quoted the equation as Fisher's equation.[12]

## References

1. ^ Edward W. Washburn (1921). "The Dynamics of Capillary Flow". Physical Review. 17 (3): 273. Bibcode:1921PhRv...17..273W. doi:10.1103/PhysRev.17.273.
2. ^ Lucas, R. (1918). "Ueber das Zeitgesetz des Kapillaren Aufstiegs von Flussigkeiten". Kolloid Z. 23: 15. doi:10.1007/bf01461107.
3. ^ Bell, J.M. & Cameron, F.K. (1906). "The flow of liquids through capillary spaces". J. Phys. Chem. 10: 658–674. doi:10.1021/j150080a005.
4. ^ Dullien, F. A. L. (1979). Porous Media: Fluid Transport and Pore Structure. New York: Academic Press. ISBN 0-12-223650-5.
5. ^ Marco, Brugnara; Claudio, Della Volpe; Stefano, Siboni (2006). "Wettability of porous materials. II. Can we obtain the contact angle from the Washburn equation?". In Mittal, K. L. Contact Angle, Wettability and Adhesion. Mass. VSP.
6. ^ Micromeritics, "Autopore IV User Manual", September (2000). Section B, Appendix D: Data Reduction, page D-1. (Note that the addition of 1N/m2 is not given in this reference, merely implied)
7. ^ Micromeritics, "A new method of interpolation and smooth curve fitting based on local procedures", Journal of the Association of Computing Machinery (1970). Volume 17(4), pp.589-602.
8. ^ Oliver, J. F. (1982). "Wetting and Penetration of Paper Surfaces". 200: 435–453. doi:10.1021/bk-1982-0200.ch022. ISSN 1947-5918.
9. ^ Leelajariyakul, S.; Noguchi, H.; Kiatkamjornwong, S. (2008). "Surface-modified and micro-encapsulated pigmented inks for ink jet printing on textile fabrics". Progress in Organic Coatings. 62 (2): 145–161. doi:10.1016/j.porgcoat.2007.10.005. ISSN 0300-9440.
10. ^ "The 1999 Ig Nobel Prize Ceremony". http://www.improbable.com. Improbable Research. Retrieved 2015-10-07. Len Fisher, discoverer of the optimal way to dunk a biscuit. External link in |website= (help)
11. ^ Barb, Natalie (25 November 1998). "No more flunking on dunking". http://news.bbc.co.uk. BBC News. Retrieved 2015-10-07. External link in |website= (help)
12. ^ Fisher, Len (11 February 1999). "Physics takes the biscuit". http://www.nature.com. Nature. Retrieved 2015-10-07. Washburn will be turning in his grave to learn that the media have renamed his work the "Fisher equation". External link in |website= (help)


text:
# Ferric oxide crystallises in a hexagonal close-packed array of oxide ions with two out of every three octahedral holes occupied by ferric ions. Derive the formula of the ferric oxide.

$\begin{array}{1 1}Fe_2O_3\\Fe_3O_2\\FeO\\Fe_4O_3\end{array}$

Suppose the number of oxide ions ($O^{2-})$ in the packing = N
$\therefore$ As 2/3$^{rd}$ of the octahedral voids are occupied by ferric ions,therefore number of ferric ions present.
$\Rightarrow \large\frac{2}{3}$$\times N=\large\frac{2N}{3} Ratio of Fe^{3+} : O^{2-}=\large\frac{2N}{3}$$ : N$
$\Rightarrow 2 : 3$
Hence,the formula of ferric oxide =$Fe_2O_3$


text:
Ir al contenido principal

## Due November 9

### Problem 1

The fixed points of a continuous $f:\mathbb B^n\to\mathbb B^n$ might not be interior.

### Problem 2

The Brouwer fixed point theorem is false for the open ball.

### Problem 3

Let $K\subset\R^n$ be compact and convex, and $f:K\to K$ continuous. Then f has a fixed point.

### Problem 4

Let $K\subset\R^n$ be compact and convex with $C^1$ boundary, $x_0\in K$, and $b:K\setminus\{x_0\}\to\partial K$ given by the intersection point of the line from $x_0$ to $x$, on the side of $x$. Then $b\in C^1$.

Note that, if $x_0$ is an interior point of $K$, then $b$ is a retraction from $K\setminus\{x_0\}$ onto $\partial K$.


text:
# 8.2 | Applications to Geometry

Let $$f$$ be a continuous function defined on $$[a,b],$$ and let $$P=\{x_0,x_1, \ldots, x_n \}$$ be a regular partition of $$[a,b].$$ The arc length of the graph of $$f$$ from $$P(a,f(a))$$ to $$Q(b,f(b))$$ is
$$L = \lim_{n \rightarrow \infty} \sum_{k=1}^ \infty d(P_{k-1},P_k)$$
if the limit exists.
Let $$f$$ be smooth on $$[a,b].$$ Then the arc length of the graph of $$f$$ from $$P(a,f(a))$$ to $$Q(b,f(b))$$ is
$$L = \int_a^b \sqrt{1+ [f'(x)]^2} \; dx.$$
Let $$f$$ be smooth on $$[a,b].$$ The arc length function $$s$$ for the graph of $$f$$ is defined by
$$s(x) = \int_a^x \sqrt{1 + [f'(t)]^2} \; dt$$
with domain $$[a,b].$$
The surface area of the surface of revolution obtained by revolving the graph of $$y = f(x)$$ from $$x =a$$ to $$x = b$$ about the $$x$$-axis is given by
$$s = \int_a^b 2 \pi f(x) \sqrt{1+[f'(x)]^2} \; dx$$