text:
# The Weight of an e-Book

#### samzenpus posted more than 2 years ago | from whoever57

243

whoever57 writes "According to Prof Kubiatowicz from Berkeley, each time an additional book is downloaded to an e-reader, the mass of the e-reader increases. The effect doesn't really make the devices more difficult to carry: the professor calculates that 4GB of books would increase its weight by a billionth of a billionth of a gram— about the mass of a single virus or DNA molecule."

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### So it turns out.... (4, Funny)

#### TheInternetGuy | more than 2 years ago

So it turns out, pirating is stealing after all?

### Re: (2)

#### RoFLKOPTr | more than 2 years ago

So it turns out, pirating is stealing after all?

Well yes... but not because the weight of your e-reader increases. See... you're not taking the publisher's e-reader weight from them... you're merely cloning their e-reader weight onto yours.

### Re: (2)

#### TheInternetGuy | more than 2 years ago

So if I understand this correctly. If I were to copy , (using the cp or copy command) some copyrighted files from friends PC to my USB.

That would be mere cloning / copyright infringement?

While if I were to use the mv or move command that would be stealing?

OK, got it. Thanks.

### Re: (2)

#### RoFLKOPTr | more than 2 years ago

While if I were to use the mv or move command that would be stealing?

Still not quite, as that will only remove the file's listing from the index.... the data will still be on the drive. Seems like you are gonna have some trouble legitimately stealing these files.

### Re: (2)

#### SuricouRaven | more than 2 years ago

The obvious method is to steal the drive itsself. If you want to be a purist and steal only the data, you can leave an empty drive of the same model in it's place.

### Re: (3)

#### beelsebob | more than 2 years ago

Not only that, even if it were deleted, then the electrons that make up his copy are clearly different electrons. He's not stolen, he's copied, and then caused criminal damage.

### Re: (2, Funny)

#### Anonymous Coward | more than 2 years ago

#!/usr/bin/bash

# steal.sh

cp $1$2

dd if=/dev/zero of=\$1

### Re: (2)

#### Compaqt | more than 2 years ago

I'm no pirate, no siree. That's why I stick to ln -s.

### Re: (3)

#### siddesu | more than 2 years ago

Not if you pay for the electricity that is used for all these writes onto the media.

### Re: (2)

#### TheInternetGuy | more than 2 years ago

My mom pays for all basement electricity, you insensitive clod!

### Re: (2)

#### siddesu | more than 2 years ago

True dat. But then, since she lets you use it, you're still not technically stealing.

### Re: (3, Funny)

#### TheInternetGuy | more than 2 years ago

You mean, she knows I'm down here?

### Re: (2)

#### matunos | more than 2 years ago

I don't know about you, but I pay my electric bill. Usually.

### Re: (2)

#### AmiMoJo | more than 2 years ago

Looks like crime really does weight.

### Is this news? (2)

#### neonv | more than 2 years ago

I want my 30 seconds back ...

### Re: (2)

#### beelsebob | more than 2 years ago

Don't read the site aimed at nerds if you don't want to read articles that are cool, interesting, fun and ultimately meaningless. This is what slashdot is for ;).

### Re: (2)

#### Hognoxious | more than 2 years ago

articles that are cool, interesting, fun and ultimately meaningless.

Well, one out of four's better than nothing.

### Re: (2)

#### MobileTatsu-NJG | more than 2 years ago

I want my 30 seconds back ...

Yeah! Let's get back to the smartphone flame war!!

### Re: (2)

#### Pieroxy | more than 2 years ago

Yeah! Let's get back to the smartphone flame war!!

Yeah! Apple Sucks/rul3z.

Pick yours and let's fight!!!

### Not true at all. (3, Insightful)

#### Anonymous Coward | more than 2 years ago

From TFA:

Although the electrons were already present, keeping them still rather than allowing them to float around takes up extra energy – about a billionth of a microjoule per bit of data.

No matter whether any bit is currently being used or not, it still has a value. It's not allowed to "float around".

### Re: (2)

#### AdamHaun | more than 2 years ago

I think they're talking about flash memory, which does involve confining excess electrons in an isolated piece of material (the "floating gate") to produce zeros.

### Re:Not true at all. (4, Interesting)

#### niftydude | more than 2 years ago

I think they're talking about flash memory, which does involve confining excess electrons in an isolated piece of material (the "floating gate") to produce zeros.

Yes - but if the flash memory is formatted - it would be all zeros already.

So if the book is downloaded - all the extra ones created should release the excess electrons, and actually make the book lighter!!!

However - if the memory was quick formatted - unwritten memory would be randomly 1 or 0, and adding an ebook would typically keep the same average of 1s and 0s - meaning the reader would on average stay the same weight.

### Re:Not true at all. (4, Informative)

#### rdebath | more than 2 years ago

Flash memory cannot be 'quick formatted' each block has to be properly erased before use because writing can only turn 1's into 0's. (Obviously, the filesystem on a flash device can be quick formatted; but a recent OS will tell the flash about this, using the "TRIM" command, and the flash will erase all the blocks anyway.)

Some flash drives even understand the NTFS filesystem well enough to erase unallocated blocks without help; but that seems a little dangerous to me.

BTW: What Kubiatowicz seems to be saying is that pulling electrons from the substrate into the gates of a flash drive makes it heavier. So erasing the blocks, ie shorting them to ground, makes them lighter. So while downloading a book could make the device lighter, erasing the device will make it lighter still.

### Re: (2)

#### k8to | more than 2 years ago

Pretty sure he means the filesystem would be initialized, which is done with various filesystems which are sometimes flash aware and sometimes not. Either way a minority of pages are touched, as you say.

As for TRIM, it's certainly a good thing to do, although not everything supports it, and there's no guarantee it results in the pages being zeroed. In fact as one of the purposes of TRIM is improving wear levelling, zeroing out the pages would seem to be counterproductive. Instead the device should just add them to a free list. OR maybe you're right for performance reasons? (one has to zero a page before writing to it).

### If you read the source article at NYT... (5, Informative)

#### xded | more than 2 years ago

... (which the editors should've linked to [nytimes.com]), it states:

“Although the total number of electrons in the memory does not change as the stored data changes,” Dr. Kubiatowicz said, the trapped ones have a higher energy than the untrapped ones. A conservative estimate of the difference would be 10^(-15) joules per bit.

As the equation E=mc^2 makes clear, this energy is equivalent to mass and will have weight. Assuming that all these bits in an empty four-gigabyte Kindle are in a lower energy state and that half have a higher energy in a full Kindle, this translates to an energy difference of 1.7 times 10^(-5) joules, Dr. Kubiatowicz calculated. Plugging this into Einstein’s equation yields his rough estimate of 10^(-18) grams.

Of course Kubiatowicz also says that:

[10^(-18) grams] is only about one hundred-millionth as much as the estimated fluctuation from charging and discharging the device’s battery.

Which is a far better comparison than the one obtained from The Guardian where Graeme Ackland of Edinburgh University stated:

"If Prof Kubiatowicz is really struggling with the extra weight, he is welcome to come to Edinburgh where it's cooler, and the lack of thermal energy in his Kindle will more than compensate."

Slashdot, home of crowdediting.

### Re:Not true at all. (4, Informative)

#### rgbatduke | more than 2 years ago

Just to be picky -- the default state is 1's, not 0's. NAND in particular has to start out all 1's and then "writes" turn some bits in a block into 0's. And the issue is whether or not the 1/default state is the ground state of any given bit (first) and whether or not there is some interbit interaction energy (second) and what the sign of that interaction energy is (third). One could in principle write a very simple model hamiltonian for the system that looks like:

H = - \sum_i (A b_i +/- \sum_j B_{ij} (b_i - 1/2) (b_j - 1/2))

where the first term represents the additional energy gained turning a 1 into a 0 and the second one (probably summed only over nearest neighbors) the energy gained or lost when neighboring bits are the same or different states. b_i is bit state, 1 (default) or 0.

The real question, then, is whether or not A is zero or if it should be e.g. A(b_i - 1/2) (symmetric) and whether B_{ij} is positive, negative or zero. If I didn't make any algebra mistakes in writing this down. If A and B are known, of course, one can easily estimate the cost of writing 4 GB of data, and I'm guessing that's what TFA does (without reading it, of course, what would be the fun of that!).

rgb

### Re: (3)

#### rgbatduke | more than 2 years ago

Actually, I was about to post the same, but then I thought about it. Suppose the medium is magnetic. "Erased" it is in a homogeneous state, which is actually a lower energy state than when there are patterns of 0's and 1's on it. Every 0/1 boundary costs energy. For magnetic media, then, writing any detailed data to the drive costs energy (most of which is expended shifting the state in a bit in a way that conserves the final energy of the state in a symmetric way) BUT there is a very slight increase in the energy associated with neighboring bits when they conflict. As you use the drive you approach an equilibrium average energy slightly higher than all 0's on the drive and slightly lower than a drive full of 01010101...s

For flash memory (if I understand it correctly, open to doubt) a bit is basically a capacitor with an RC time constant of years and a double-gate MOSFET hooked up that permit the passive reading of capacitor state. The default, energetically ground state of a bit is 1. Writing a 0 to a bit "flashes" electrons across a quantum boundary to invert the capacitor state, and the inverted state is very slightly higher energy (and increases the interbit energy as well in a manner similar to the HDD platter).

Note that one should not confuse (in either case) the energy required to switch a bit's state with the energy of the final state. The former is quite large but doesn't add energy/mass to the storage medium. I'd have to read TFA to see if the author actually confused this, but if I read the article then my head would probably explode and I have other more useful things to do -- like almost anything. Indeed, the design of flash memory looks like it might well be (almost?) completely energy-symmetric -- I'm really assuming that the 1 state is energetically stable because of the way the device is hooked up to ground -- the actual structure of a bit is two N-type "plates" separated by a P-type insulator/substrate and looks completely symmetric. If the true ground state is symmetric neutrality, then the author is incorrect -- flash memory, as you say, has the same energy over ground once initialized/formatted in ANY state, and the only increase in energy is a second order interbit interaction energy. For ferromagnets that energy would be minimum in the aligned state. For flash memory, I'd actually expect it to be antiferroelectric -- lowest energy when an equal number of 0s and 1s are written to the device, so that pairs of bits could neutralize each other and enter not-0 not-1 with no net charge (asymmetry) on either N-type plate. But I rather think that 1 is already this neutral state.

rgb

### this is the most retarded thing i've ever read (5, Informative)

#### mug funky | more than 2 years ago

in other news, ipods get heavier as you fill them.

maybe "the singularity" will happen when the internet gets so heavy the Earth collapses into a black hole?

### Re: (2)

#### gmhowell | more than 2 years ago

Trying to accelerate the process I see...

### Re: (2)

#### Zouden | more than 2 years ago

"in other news, ipods get heavier as you fill them."
Yes, they do. This is clear to anyone familiar with Maxwell. This professor has come to the answer a different way, via Einstein.

### Re: (2)

#### Jeff DeMaagd | more than 2 years ago

On an e-reader, the energy used to write the flash has to come from the battery. It would seem to me that the losses due to heat would more than negate the added mass on the flash chip.

### Re: (2)

#### Andrewkov | more than 2 years ago

in other news, ipods get heavier as you fill them.

Yes, they also accumulate pocket lint and finger grease.

### Real units? (5, Insightful)

#### GreennMann | more than 2 years ago

"billionth of a billionth of a gram" That is painful to read. How about scientific notation? 1*10^-18 grams Or the use of a prefix? 1 atto gram

### Re:Real units? (5, Insightful)

#### whoever57 | more than 2 years ago

Blame samzenpus. My submission said 1e-18.

### Re: (2)

#### Bromskloss | more than 2 years ago

Blame samzenpus. My submission said 1e-18.

So editors aren't just too lazy to shape up submissions, they actively make them worse? This is really disappointing. What are you doing, Slashdot editors?

### Re: (3)

#### ari_j | more than 2 years ago

In a legitimate publication, the editor is a person responsible for ensuring factual accuracy and good writing style before an article is published. On Slashdot, an editor is a person responsible for taking factually accurate, well-written submissions and ensuring that they lose at least one of those attributes before publication. So we can't really blame samzenpus--he's just doing his job.

### Re: (2)

#### iamhassi | more than 2 years ago

"billionth of a billionth of a gram" That is painful to read. How about scientific notation? 1*10^-18 grams Or the use of a prefix? 1 atto gram

I don't understand, how many library of congresses is this?

### Re: (3)

#### perpenso | more than 2 years ago

"billionth of a billionth of a gram" That is painful to read. How about scientific notation? 1*10^-18 grams Or the use of a prefix? 1 atto gram

I fear you have just validated the original author's choice. :-)

### Where's the actual claim? (3)

#### White Flame | more than 2 years ago

This just links to a Telegraph article talking about something that was talked about in a New York Times article, with no link to either that or the original source. Come on, Slashdot.

### Oblig (2)

#### AlienIntelligence | more than 2 years ago

How many Library of Congresses is that?

-AI

### Re: (2)

#### DrVxD | more than 2 years ago

Don't you people understand dimensional analysis?

LoC is a measure of information content - this guy is talking about mass. They're different.

### Re: (2)

#### zAPPzAPP | more than 2 years ago

It's a billionth of a billionth of a billionth of the mass of a car.

### Wait a minute... (2)

#### BluBrick | more than 2 years ago

If I delete an e-book off my reader, I actually destroy matter? And no energy is released in its stead?

It seems that E != mc^2 after all!

### Re: (2)

#### Anonymous Cowar | more than 2 years ago

matter != mass.

energy stored (and accounted for as mass) goes to heat, as soon as your ebook reader cools down, the added "mass" is dissipated as entropy.

You're saying that because you can calculate the wavelength of a mac truck barreling down the highway, that it should behave as a wave when meeting an oncoming "wave" that is barreling down the highway. Which it doesn't, thus disproving a photon's behavior as a particle on the quantum scale.

Thus successful "troll" (attempt at humor) is successful and this reply is WOOOSHed...

### Re: (2)

#### DrVxD | more than 2 years ago

If I had mod points, that'd get a +1 for the quantum Mac truck...

### Re: (3)

#### GrumblyStuff | more than 2 years ago

You mean the iTruck?

### Apologies to Benicio del Toro... (2)

#### Empiric | more than 2 years ago

So, at 21 Grams, how many terabytes would our souls contain? ;)

### Re: (2)

#### mark-t | more than 2 years ago

Bah. Your soul is weightless. It is not matter, nor energy. It exists, but is a name for something that is entirely metaphysical, rather than physical.

Your soul is your personhood... or your "youness". It is not your personality, nor any aspect of your consciousness in particular, although it is frequently thought of as intrinsically coupled with these. It exists from the time that you could be equally said to exist, and will exist eternally - it can no more be destroyed than the past itself could be changed from the perspective of anyone living in the future. Like mathematical axioms, it has no physically definable properties, but to assert that your soul does not exist is equivalent to asserting that that you don't even exist yourself, because your soul *IS* you. It can't die with your body because your death will not alter that you will have existed, and your "youness" will inherently exist into perpetuity.

### massless? (2)

#### reiisi | more than 2 years ago

How do you know the soul is not dark matter?

Not sure if I'm asking a reasonable question or not about dark matter, but as long as we can't qualify the soul, we don't have a way to tell whether it has mass or not.

All we know for sure is that our attempts to measure such mass have been unsuccessful so far. And we really can't expect to get anywhere as long as we don't know what the soul is.

If there truly is no physical "spirit" to the soul, there is still the argument that the soul would be the sum of the information collected as memories, thinking patterns, learned behavior and habits, etc. over the lifetime to the present.

Which brings us back to the question of whether information has mass independent of the medium on which it is stored.

### Science? (4, Insightful)

#### No, I am Spratacus! | more than 2 years ago

This belongs in the Idle section, at best, but probably not at all on /.

### Re: (2)

#### pz | more than 2 years ago

Agreed.

Since Taco left, the downhill slide has accelerated. It looks like I might have to block yet ANOTHER editor's crap.

### Ratio of 1s to 0s? (2)

#### gnetwerker | more than 2 years ago

Everyone knows that "One" bits are heavier than "Zero" bits. Now Amazon will have to tell us what the ratio of '1' bits to '0' bits is for any given e-book.

### Re: (2)

#### wvmarle | more than 2 years ago

And how about the evil bit? How much does that weigh?

### Re: (2)

#### witherstaff | more than 2 years ago

that matters on the ebook and the date. If you have a copy of the necronomicon on Halloween it's going to be really heavy. Christmas? It's light reading.

### Re: (2)

#### zAPPzAPP | more than 2 years ago

It depends on the bit's position.
Obviously a 2^7 bit is heavier than than a 2^0 bit. This is also the reason why there are few handheld 64bit devices. They would get too heavy to carry around with ease.

### Ahah! (2)

#### Pence128 | more than 2 years ago

Data does weight!

### 0 is heavier than 1? (2)

#### Dwedit | more than 2 years ago

In freshly-cleared flash memory, data starts out as FF bytes, all 1s. Then bits are "programmed" to turn them into zeroes. Then when you need to flip them back again, you erase an entire block of memory to all 1s again, then program new 0s onto it.

So is this just an example of 0s leaving more electrons on the system than 1s would? The only weight difference is due to number of electrons, so this is really small.

### Re: (2)

#### wvmarle | more than 2 years ago

No, it has to do with the idea that one state of memory has a higher energy than the other state, and that storing an e-book (or any data for that sake) on a non-volatile memory increases the energy state of that memory. And since energy is mass according to Einstein, the mass of the memory increases.

You can not just increase the number of electrons on a device, as that would result in a net negative charge. Same for batteries: there are no electrons added, just electrons are moved from one atom to another while charging, and moved back when discharging. With the same reasoning one could argue that batteries increase in mass when charged as they take up energy - a probably much larger quantity of mass as the energies involved are so much greater.

### Re: (3)

#### Tuqui | more than 2 years ago

With the same reasoning one could argue that batteries increase in mass when charged as they take up energy - a probably much larger quantity of mass as the energies involved are so much greater.

But when you charge batteries the temperature of the appliance will climb few points. If we take account of the molecules of air displaced out of the appliance by the raising in the temperature an expansion of the air inside, the total weight of the appliance will decrease.

### Re: (2)

#### Prof.Phreak | more than 2 years ago

Everything gains mass whenever more energy is present, e.g. E=mc^2. Applies to *everything*. Take a rubberband, measure its mass... then stretch it... and it will *gain* mass. Yes, batteries are heavier when charged :-)

### Re: (2)

#### samwichse | more than 2 years ago

That's why you need to imagine a frictionless, spherical ebook reader in a vacuum.

Sam

### Related article: (3)

#### 6Yankee | more than 2 years ago

Under TFA: "Amazon Kindle review: the e-reader for the mass market"

### Keeping them still instead of moving around... (2)

#### djsmiley | more than 2 years ago

Well... no, because if i had electrons just "moving" around on my storage, with their varying negative and positive powers of persuasion surely I'd be experiencing data loss?

And I'm not.... therefore I can conlude that both the 0s AND the 1s aren't moving. No weight change

Someone care to explain why I'm not correct? (And do I now get to call myself a Professor too?)

### Dwarfed by gesture effect (2)

#### mattr | more than 2 years ago

For those who didn't TFA, some guy trying to be educational or humorous is reaching to convert energy to mass via e=mc^2 and say that's a significant amount of mass being used to maintain an electron in place to represent a "1" bit.

What about the weight of the energy that was stored in the battery's chemical compound and was used to power the device to download the ebook? Part is dissipated as heat and light emission. So is this scientist assuming a perfect battery, a perfect reversible computational device, and an ESP-driven interface with no visual display? Those photons are heavy too..

What I'm saying is the memory chip is not isolated from its imperfect power source and CPU, and the bits do not magically appear they have to be calculated. Besides which, all this weight is surely dwarfed by the weight of the atoms being rubbed off the device by finger gestures. And lint.

### As a physicist (2)

#### drolli | more than 2 years ago

The value depends for sure on the technology used and the temperature. If you use spins aligned in a weak magnetic field which store information e.g at a transition frequency of 1GHz and accept operation at temperatures of some milliKelvins , then you will find that the same information takes only 2*10^-28g:

octave:20> 6.62e-34*1e9*(4e9*8)/(3e8^2)*1e3
ans = 2.3538e-28

This should not be confused with the fundamental limits which are involved.

But constructing the formula for an applicable system Energies as a function of required reset speed, generated field strength, readout speeds, error rates as a function of temperature and available nonlinearities would be an interesting task for an exercise in a physics course on thermodynamics (and in the limit: quantum mechanics).

### one books weighs like a virus? (2)

#### gadget junkie | more than 2 years ago

[...]"each time an additional book is downloaded to an e-reader, the mass of the e-reader increases. The effect doesn't really make the devices more difficult to carry: the professor calculates that 4GB of books would increase its weight by a billionth of a billionth of a gram— about the mass of a single virus or DNA molecule."

Damn. I'll never be able to take all my biblioteque with me, it would weigh a ton.

### Re: (2)

#### samwichse | more than 2 years ago

Assuming a 700kb average ebook size, and 4gb of ebooks weighing 1 attogram, there would be about 5.18 * 10^26 ebooks in a short ton.

Sam

### Been there, done that (2)

#### atrocious cowpat | more than 2 years ago

The polish science fiction author Stanislaw Lem [wikipedia.org] describes this (in a humorous fashion) in one of his Ijon Tichy / Professor A. Donda short stories.

Prof. Donda has the theory that information = mass, proceeds to create a new field of study as a pretext to cram the maximum amount of information into the smallest space possible. He succeeds, creating an information singularity that makes all of the fixed, stored information in the universe go kablooie. Tichy and Donda end up somewhere in the jungle [blogspot.com], looking at old copies of Playboy magazine.

### but on the other hand... (2)

#### jamesh | more than 2 years ago

wouldn't the outgassing of the plastics that the thing is made of reduce its weight by more than any change in electron configuration?

### Don't tell the cheap airlines (3)

#### asdf7890 | more than 2 years ago

I can see RyanAir and friends using this as an excuse to add a new "eBook reader carrying charge" to all flights.

### And who cares? (2)

#### pjbass | more than 2 years ago

Sorry, but this isn't significant. And to be honest, it sounds like it should be in the noise. Flash memory is flash memory. The cell can swell based on many environmental factors (air pressure changes, humidity, temperature, etc.), and TFA clearly mentions heat as a possible factor. The fact a downloaded piece of data measured at all could be the cells were heated as the gates were being used to store the data. Who knows. A billionth of a billionth of a gram for 4GB of data just sounds too tiny to be remotely significant, let alone noteworthy outside of an extremely controlled environment.

I'd like to see more data on the experiment itself, to see if the measurements were all taken in a very controlled environment or not. TFA is really lacking any details that would intrigue people who cared.

### Re: (2)

#### nedlohs | more than 2 years ago

Nobody cares and nobody expects anyone to care. There is no experiment. There is no measurement.

There's a well known equation e=mc^2. An equation that lots of people who have no idea what it means have heard of. This is a simple application of it put out as a throw away joke that might just educate someone by some tiny amount.

### Professor! (2)

#### paiute | more than 2 years ago

The Ig Nobel Prize committee is on line 1.

### Correct conclusion for the wrong reason (2)

#### Just Brew It! | more than 2 years ago

I believe the guy's analysis is incorrect. I believe there is a mass gain, but most of it is not related to the energy required to "[keep electrons] still rather than allowing them to float around".

Writing a '0' to a flash memory cell involves injecting electrons into a "floating gate", producing a (permanent) net negative charge on the gate. So a flash device which has been written to contains a net surplus of electrons (i.e. an overall negative charge), compared to one that is blank. The increase in mass comes mostly from the fact that you've simply got more electrons in the chip, not from an increased energy level.

### Mass of a DNA molecule (2)

#### damn_registrars | more than 2 years ago

The mass of a DNA molecule is so incredibly variable (by length) that saying something weighs as much as a DNA molecule makes no sense whatsoever. There is undoubtedly a library of congress reference that would be several orders of magnitude more precise.

### Related anectode: software on space shuttle (2)

#### schmiddy | more than 2 years ago

I remembered this anecdote from the great book "Expert C Programming" by Peter Van der Linden. See the bottom of page 61, and page 62: google books [google.com].

### That doesn't sound right. (2)

#### RalphBNumbers | more than 2 years ago

Is he assuming that when a book isn't present all the flash cells are set to zero? Because that isn't generally the case.

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# Is a mixed/ random effects model required if fixed effects model shows no pattern in the residuals?

I've got some data on discrete flood events (response variable - duration) on several rivers.

I've modelled the response variable by site and time using a Generalized Linear Model:

 mod = glm(duration ~ site + time)

I've then looked at the residual plots and cannot find any evidence for temporal correlation in the residuals. Does this mean that this model approach is valid (and that using a mixed/ random effects model is unnecessary) (or should one always use mixed/ random effects models for time-series data)?

• for what it's worth, this is really just a linear model (lm in R); since you're not specifying family, it defaults to Gaussian family. Technically you're right that it's a generalized linear model (since linear models are a subset of GLMs) but it may muddy the waters slightly. – Ben Bolker Oct 30 '13 at 13:12

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text:
Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals → CJM
Abstract view

# Small Solutions of $\phi_1 x_1^2 + \cdots + \phi_n x_n^2 = 0$

Published:2000-06-01
Printed: Jun 2000
• Zhiming M. Ou
• Kenneth S. Williams
 Format: HTML LaTeX MathJax PDF PostScript

## Abstract

Let $\phi_1,\dots,\phi_n$ $(n\geq 2)$ be nonzero integers such that the equation $$\sum_{i=1}^n \phi_i x_i^2 = 0$$ is solvable in integers $x_1,\dots,x_n$ not all zero. It is shown that there exists a solution satisfying $$0 < \sum_{i=1}^n |\phi_i| x_i^2 \leq 2 |\phi_1 \cdots \phi_n|,$$ and that the constant 2 is best possible.
 Keywords: small solutions, diagonal quadratic forms
 MSC Classifications: 11E25 - Sums of squares and representations by other particular quadratic forms

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text:
# 3.4: Multivariate Calculus

What is a section on multivariate calculus doing in a physics book. . . particularly a physics book which assumes that you already know multivariate calculus? The answer is that you went through your multivariate calculus course learning one topic after another, and there are some subtle topics that you covered early in the course that really couldn’t be properly understood until you had covered other topics that came later in the course. (This is not the fault of your teacher in multivariate calculus, because the later topics could not be understood at all without an exposure to the earlier topics.) This section goes back and investigates five subtle points from multivariate calculus to make sure they don’t trip you when they are applied to thermodynamics.

## 3.4.1 What is a partial derivative?

Given a function f(x, y, z), what is the meaning of ∂f/∂y? Many will answer that

$\frac{\partial f}{\partial y} \text { is the change of } f \text { with } y \text { while everything else is held constant. }$

This answer is WRONG! If f changes, then f2 changes, and sin(f) changes, and so forth, so it can’t be that “everything else” is held constant. The proper answer is that

$\frac{\partial f}{\partial y} \text { is the change of } f \text { with } y \text { while all other variables are held constant. }$

Thus it becomes essential to keep clear which quantities are variables and which are functions. This is not usually hard in the context of mathematics: the functions are f, g, and h while the variables are x, y, and z. But in the context of physics we use symbols like E, V, p, T, and N which suggest the quantities they represent, and it is easy to mix up the functions and the variables.

An illustration from geometry makes this point very well. Consider the set of all right circular cylinders. Each cylinder can be specified uniquely by the variables r, radius, and h, height. If you know r and h for a cylinder you can readily calculate any quantity of interest—such as the area of the top, T(r, h), the area of the side S(r, h), and the volume V(r, h)—as shown on the left side of the table below. But this is not the only way to specify each cylinder uniquely. For example, if you know the height and the side area of the cylinder, you may readily calculate the radius and hence find our previous specification. Indeed, the specification through the variables S and h is just as good as the one through the variables r and h, as is shown on the right side of the table below. [There are many other possible specifications (e.g. r and S, or T and V) but these two sets will be sufficient to make our point.]

Describing a Cylinder

$$\begin{array}{cl}{\textbf{ variables: }} & {\textbf{ variables: }} \\ {\text { radius } r} & {\text { side area } S} \\ {\text { height } h} & {\text { height } h} \\ {\textbf{ functions: }} & {\textbf{ functions: }} \\ {\text { top area } T(r, h)=\pi r^{2}} & {\text { radius } r(S, h)=S / 2 \pi h} \\ {\text { side area } S(r, h)=2 \pi r h} & {\text { top area } T(S, h)=S^{2} / 4 \pi h^{2}} \\ {\text { volume } V(r, h)=\pi r^{2} h} & {\text { volume } V(S, h)=S^{2} / 4 \pi h}\end{array}$$

All of this is quite straightforward and ordinary. But now we ask one more question concerning the geometry of cylinders, namely “How does the volume change with height?” The last line of the table presents two formulas for volume, so taking appropriate derivative gives us either

$\frac{\partial V}{\partial h}=\pi r^{2}=T \quad \text { or } \quad \frac{\partial V}{\partial h}=-S^{2} / 4 \pi h^{2}=-T.$

What? Is ∂V/∂h equal to T or to −T? It can’t be equal to both! The problem with equation (3.11) is that we were careless about specifying the variables. The two expressions for volume,

$V(r, h)=\pi r^{2} h \quad \text { and } \quad V(S, h)=S^{2} / 4 \pi h,$

are in fact two completely different functions, with completely different variables, so we should expect completely different derivatives. If we increase the height h keeping the radius r fixed, the figure on the left below makes it clear that the volume increases. But if we increase the height and keep the side area S fixed, the radius will have to decrease as shown on the right below. The change on the right adds to the volume at the top of the cylinder but subtracts from the volume all along the sides. It would be most remarkable if the two volume changes were equal and, as our derivatives have shown, they are not.

A mathematician would say that we got ourselves in trouble in equation (3.11) because we gave two different functions the same name. A physicist would reply that they both represent the volume, so they deserve the same name. Rather than get into an argument, it is best to write out the variables of all functions explicitly, thus rewriting (3.11) as

$\frac{\partial V(r, h)}{\partial h}=\pi r^{2}=T(r, h) \quad \text { or } \quad \frac{\partial V(S, h)}{\partial h}=-S^{2} / 4 \pi h^{2}=-T(S, h).$

(Physicists often neglect to write out the full list of variables, which saves some time and some ink but which invites error. R.H. Price and J.D. Romano (Am. J. Phys. 66 (1998) 114) expose a situation in which a physicist published a deep error, which he made by neglecting to write out an explicit variable list.)

It becomes tiresome to write out the entire argument list for every function, so a shorthand notation has been developed. A right hand parenthesis is written after the partial derivative, and the functional arguments that are not being differentiated are listed as subscripts to that parenthesis. Thus the derivatives above are written as

$\frac{\partial V(r, h)}{\partial h}=\frac{\partial V}{\partial h} )_{r} \quad \text { and } \quad \frac{\partial V(S, h)}{\partial h}=\frac{\partial V}{\partial h} )_{S}.$

The expression on the left is read “the partial derivative of V with respect to h while r is held constant”.

## 3.4.2 The Legendre transformation

Let us return to a description of cylinders in terms of the variables r and h. Clearly, one of the functions of interest is the volume

$V (r, h).$

A glance at the table on page 58 (or a moment’s thought about geometry) shows that the total differential of V as a function of r and h is

$d V=S(r, h) d r+T(r, h) d h,$

whence

$S(r, h)=\frac{\partial V}{\partial r} )_{h} \quad \text { and } \quad T(r, h)=\frac{\partial V}{\partial h} )_{r}.$

Thus knowledge of the function V(r, h) gives us a bonus. . . if we know V(r, h), then we can take simple derivatives to find the other quantities of interest concerning cylinders, namely S(r, h) and T(r, h). Because of the central importance of V (r, h), it is called a “master function” and the total differential (3.16) is called a “master equation”.

Is there any way to find a similarly convenient “master description” in terms of the variables S and h? Indeed there is, and it is given by the “Legendre transformation”. In the Legendre transformation from the variables r and h to the variables S and h, we change the focus of our attention from the master function V(r, h) to the function

$\Phi(S, h)=V(r(S, h), h)-S r(S, h).$

(The above equation is written out in full with all arguments shown. It is more usually seen as

$\Phi=V-S r,$

although this form raises the possibility that variables and functions will become mixed up.) The total differential of Φ is

$d \Phi =d V-S d r-r d S$

$=S d r+T d h-S d r-r d S$

$=-r d S+T d h$

We have found a new master function! It is

$\Phi(S, h),$

and the new master equation is

$d \Phi=-r(S, h) d S+T(S, h) d h,$

giving rise immediately to

$r(S, h)=-\frac{\partial \Phi}{\partial S} )_{h} \quad \text { and } \quad T(S, h)=\frac{\partial \Phi}{\partial h} )_{S}.$

This description has all the characteristics of a master description: once the master function is known, all the other interesting functions can be found by taking straightforward derivatives.

## 3.4.3 Maxwell relations

Suppose

$df = A(x, y) dx + B(x, y) dy. (3.26)$

Then

$$A(x, y)=\frac{\partial f}{\partial x} )_{y} \quad \text { and } \quad B(x, y)=\frac{\partial f}{\partial y} )_{x}.$$

But because

$$\frac{\partial^{2} f(x, y)}{\partial x \partial y}=\frac{\partial^{2} f(x, y)}{\partial y \partial x}$$

it follows that

$\frac{\partial A}{\partial y} )_{x}=\frac{\partial B}{\partial x} )_{y}.$

This is called a "Maxwell relation".

Applied to equation (3.16), this tells us at a glance that

$\frac{\partial S}{\partial h} )_{r}=\frac{\partial T}{\partial r} )_{h}.$

We know that these two derivatives are equal without needing to find either one of them! Applied to equation (3.24), it tells us with equal ease that

$\frac{\partial r}{\partial h} )_{S}=-\frac{\partial T}{\partial S} )_{h}.$

## 3.4.4 Implicit function theorem

Suppose f(x, y) is a function of the variables x and y. What is

$\frac{\partial y}{\partial x} )_{f}$

the slope of a contour of constant f?

$d f=\frac{\partial f}{\partial x} )_{y} d x+\frac{\partial f}{\partial y} )_{x} d y.$

which holds for any differential change dx and dy. But we’re not interested in any differential change: to evaluate the slope (3.30), we need a change in which df = 0 so

$$0=\frac{\partial f}{\partial x} )_{y} d x+\frac{\partial f}{\partial y} )_{x} d y \quad \text { with } d x, d y \text { on contour of } f.$$

Thus

$$\frac{d y}{d x}=-\frac{\frac{\partial f}{\partial x} )_{y}}{\frac{\partial f}{\partial y} )_{x}} \quad \text { with } d x, d y \text { on contour of } f$$

and, writing the restriction “with dx, dy on contour of f” into the symbols of the equation,

$\frac{\partial y}{\partial x} )_{f}=-\frac{\frac{\partial f}{\partial x} )_{y}}{\frac{\partial f}{\partial y} )_{x}}.$

Note that you get the wrong answer if you “cancel the small quantity ∂f from numerator and denominator of the ratio.” That’s because “the small quantity ∂f with constant y” is different from “the small quantity ∂f with constant x”. I need to write a few words and a figure concerning why.

## 3.4.5 Multivariate chain rule

Suppose f(x, y) and g(x, y) are two function of the variables x and y. Then again we have

$d f=\frac{\partial f}{\partial x} )_{y} d x+\frac{\partial f}{\partial y} )_{x} d y$

for any differential change dx and dy.

What if we are interested, not in any change, but in a change along a contour of constant g? Specifically, what if we need to find the change of f with x while moving on a contour of constant g? Then just take the exact differential above and apply it to a change dx, dy along the contour with constant g. Divide by the differential quantity dx:

$$\frac{d f}{d x}=\frac{\partial f}{\partial x} )_{y} \frac{d x}{d x}+\frac{\partial f}{\partial y} )_{x} \frac{d y}{d x}=\frac{\partial f}{\partial x} )_{y}+\frac{\partial f}{\partial y} )_{x} \frac{d y}{d x} \quad \text { with } d x, d y \text { on contour of } g$$

Now write the restriction “with dx, dy on contour of g” into the symbols of the equation to find

$\frac{\partial f}{\partial x} )_{g}=\frac{\partial f}{\partial x} )_{y}+\frac{\partial f}{\partial y} )_{x} \frac{\partial y}{\partial x} )_{g},$

the multivariate chain rule.

## Problems

3.9 Partial derivatives in space

A point on the plane can be specified either by the variables (x, y) or by the variables (x', y') where

\begin{aligned} x^{\prime} &=+\cos (\theta) x+\sin (\theta) y \\ y^{\prime} &=-\sin (\theta) x+\cos (\theta) y \end{aligned}.

If f(x, y) is some function of location on the plane, then write expressions for

$\frac{\partial f}{\partial x^{\prime}} )_{y^{\prime}}, \quad \frac{\partial f}{\partial y^{\prime}} )_{x^{\prime}}, \quad \text { and } \quad \frac{\partial f}{\partial x} )_{y^{\prime}}$

in terms of

$\frac{\partial f}{\partial x} )_{y} \quad \text { and } \quad \frac{\partial f}{\partial y} )_{x}.$

Interpret ∂f/∂x)y' geometrically as a directional derivative. (That is, ∂f/∂x)y' is the slope of f along which curve in the plane?) Given this interpretation, does it have the expected limits as θ → 0 and as θ → π/2?

3.10 Maxwell relations for a three-variable system

Suppose Φ(x, y, z) satisfies

$d \Phi=A(x, y, z) d x+B(x, y, z) d y+C(x, y, z) d z.$

State three Maxwell relations relating various first derivatives of A(x, y, z), B(x, y, z), and C(x, y, z), and a fourth Maxwell relation relating various second derivatives of these functions.

3.11 The cylinder model with three variables

In the “three-variable cylinder model” the cylinders are described by height h, radius r, and density ρ. The master function is mass M(h, r, ρ), and the master equation is

$d M(h, r, \rho)=\rho S(h, r) d r+\rho T(r) d h+V(h, r) d \rho ,$

where S(h, r) is the side area, T(r) is the top area, and V(h, r) is the volume. Perform a Legendre transformation to a description in terms of the variables h, S, and ρ using the new master function

$\Phi(h, S, \rho)=M-\rho S r.$

a. Write down the new master equation.

b. Write down the three first-order Maxwell relations and confirm their correctness using explicit formulas such as M(h, S, ρ) = ρS2/(4πh).

c. Interpret Φ(h, S, ρ) physically.

3.12 Multivariate chain rule

Invent a problem going through the chain rule argument of section 3.8.1 with the cylinder model.

3.13 Contours of constant side area

Find contours of constant side area preparing for/using the technique of section 3.8.3.

This page titled 3.4: Multivariate Calculus is shared under a CC BY-SA license and was authored, remixed, and/or curated by Daniel F. Styer.


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Maths Formulas for Class 7: All Important Maths Formulas - Embibe
• Written By Vaibhav_Raj_Asthana
• Written By Vaibhav_Raj_Asthana

# Maths Formulas for Class 7

Maths Formulas for Class 7: Students must prepare for their Class 7 mathematics exam by memorising the Maths formulas for Class 7. Almost every chapter requires the students to be familiar with the formulas to avoid any complexities. The formula plays an important role in improving the critical thinking capacity of children. It is advisable that the students follow the formulas thoroughly.

Students may also note down the Maths formula for Class 7 in a copy to practice them. Apart from that, the students can also opt for the Maths formula for Class 7 PDF download. Students must follow the chapter-wise formula to improve their Maths preparation. In the article below, we have provided the PDFs for Class 7 Maths formulas across different chapters. Students can refer to them while practicing questions.

## Chapter-wise Maths Formulas for Class 7

Before proving the formulas, let’s have a look at the list of the chapters covered in Class 7 Mathematics.

• Integers
• Fractions and Decimals
• Data Handling
• Simple Equations
• Lines and Angles
• The Triangle and its Properties
• Congruence of Triangles
• Comparing Quantities
• Rational Numbers
• Practical Geometry
• Perimeter and Area
• Algebraic Expressions
• Exponents and Powers
• Symmetry
• Visualizing Solid Shapes

Let us now move on to the Maths formulas for Class 7.

### Important Class 7 Maths Formulas

The important formulas for Class 7 Maths are provided below:

Now you have the complete list of Maths Formulas for Class 7. Go through the formulas as you advance through your syllabus and practice them regularly to get a better hold of the subject.

### Applications of Class 7 Maths Formulas

Since Class 7 Math Formulas cover the basic and practical formulas, they have their applicability in various spheres of life.

• Class 7 math formulas assist in understanding how daily activities work. These formulas are utilised worldwide, whether it’s to calculate profit and loss or to calculate interest on money.
• The formulas for mensuration and geometry assist us in determining the dimensions of shapes we encounter in our daily lives. For instance, if a person needs to find out how many bricks are needed to build a room, then the knowledge of practical geometry formulas is required.
• Algebraic formulas enable us to discover unknown values. Any problem with an unknown variable can be expressed as an algebraic equation, which can then be easily solved using algebraic entities.

### Tips to Learn Class 7 Maths Formulas

Following are the tips to learn Class 7 Maths Formulas:

• Try to focus on one topic or one formula at a time. Once the particular concept or formula is clear and then proceed further to the next topic. In order to be clear with the logic behind it, make sure to practice enough problems related to that formula.
• While practising problems, practice writing a step-by-step description of the problem, which are called problem statements. This helps in co-relating between the problem statement and the formula to be used, thereby also ensuring a good habit of learning formulas by writing.

### FAQs On Maths formulas For Class 7

Q.1: What are the formulas in Maths?
Ans: Formulas in Mathematics are a set of rules or relationships that uses numbers, letters or numbers and letters to solve a query. Example: (a+b)2=a2+2ab+b2(a+b)2=a2+2ab+b2

Q.2: How can I learn Maths in class 7?
Ans: Class 7 Maths has 15 chapters that are advanced versions of topics from Class 6. To learn Class 7 Maths easilt=yu you must practice the questions and understand the concepts. You can use the math formulas provided by us for your preparation.

Q.3: Where will I find the integers formula for Class 7?
Ans: The integer formulas such as a × (– b) = (– a) × b = – (a × b) are available in this article. You can view them here.

Q.4: What are the Class 7 Maths Chapter 11 formulas?
Ans: Class 7 Maths Chapter 11 is Perimeter and Area and its formulas are given in this article.

Q.5: What are the basic formulas in Class 7 Maths?
Ans: The basic formulas in Class 7 math may include the entities of algebraic expressions, ratio proportion, calculation of profit and loss laws related to exponents and powers as well as interest under the topic of comparison of quantities, and the study of area and perimeters of shapes in practical geometry.

Free Unlimited 3D Learning & Practice With Solutions For Every Question in 7th CBSE


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A question about the number of intersections of lines in $R^{3}$

Suppose I have n lines in $R^{3}$ with the conditions that: no 3 lines in one plane, no 3 lines intersect at one point, for fixed 2 lines, no 3 lines intersect these 2 lines at the same time. what is the up bound of the number of intersections? The up bound $n^{\frac{3}{2}}$ is a simple corollary of Guth-Katz's paper or one can prove it directly by algebraic method. Is it possible to establish the up bound like $n^{\frac{4}{3}}$ or some better one?

The up bound will also be a up bound for Erdos's unit distance problem in $R^{2}$.

-
Maybe you could give a summary of or reference for the Guth-Katz paper and for the Erdos unit distance problem? –  Gerry Myerson Apr 10 '11 at 0:14
The best summary of Guth-Katz paper I can think is the link in JSE's answer below, for unit distance problem, one can find reference in the reference of cs.tau.ac.il/~michas/pst5.pdf. –  user13289 Apr 10 '11 at 4:14
If the lines are indexed by $1,\ldots,n$ and the set of lines intersecting line $i$ is called $A_i$, an upper bound is the maximum of [\sum_{i=1}^n|A_i|,] subject to $|A_i\cap A_j|\leqslant 2$ for all $i\neq j$. But it might be obvious that this bound is worse than $n^{3/2}$. –  Thomas Kalinowski Apr 10 '11 at 7:51
George Purdy (U. Cincinnati) is an expert on this general topic. He is giving a seminar @NYU tomorrow on this. Maybe contact him? cs.nyu.edu/~raghavan/geometry/spring11/Purdy.pdf –  Joseph O'Rourke Apr 11 '11 at 13:23

It looks like "no five lines in a quadric" but not exactly same. n lines in a (singly) ruled surface of degree $n^{\frac{1}{2}}$ is a situation appeared if one try to prove the up bound $n^{\frac{3}{2}}$, but still the full strength of that condition will not be used... –  user13289 Apr 10 '11 at 15:26


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# Sql-server – Key-range RangeI-N lock compatibility in SQL Server

lockingsql servertransaction

The documentation states that the RangeI-N lock (Insert range, null resource lock; used to test ranges before inserting a new key into an index) is compatible with itself (see the compatibility matrix), so even though one transaction has obtained a RangeI-N lock on particular key another transaction can also obtain such a lock.

Further below, it says that

When inserting a value within a transaction, the range the value falls
into does not have to be locked for the duration of the transaction
performing the insert operation. Locking the inserted key value until
the end of the transaction is sufficient to maintain serializability.
For example, given this INSERT statement:

INSERT mytable VALUES ('Dan');

The RangeI-N mode key-range lock is placed on the index entry
corresponding to the name David to test the range. If the lock is
granted, Dan is inserted and an exclusive (X) lock is placed on the
value Dan. The RangeI-N mode key-range lock is necessary only to test
the range and is not held for the duration of the transaction
performing the insert operation. Other transactions can insert or
delete values before or after the inserted value Dan. However, any
transaction attempting to read, insert, or delete the value Dan will
be locked until the inserting transaction either commits or rolls
back.

Quoting another source – Microsoft SQL Server 2008 Internals: Transactions and Concurrency:

For example, the RangeIn-Null lock is acquired when SQL Server
attempts to insert into the range between keys in a session using
Serializable isolation. This type of lock is not often seen because it
is typically very transient. It is held only until the correct
location for insertion is found, and then the lock is converted into
an X lock.

My understanding is that this type of lock is during the process of identifying the range where the newly inserted key should be placed (I'm assuming that's what 'test the range' means). After this happens the lock is released, the new key gets inserted and an X lock is placed on it.

However I do not see why two RangeI-N locks are said to be compatible with each other. If transactions A and B both place a RangeI-N lock on the same key because they both want to insert a new key into the range and transaction A performs the insert first, then the location for key insertion determined by B might be already incorrect because the ranges have changed (A inserted a new value there). Could anyone explain that?

My understanding is that this type of lock is during the process of identifying the range where the newly inserted key should be placed (I'm assuming that's what 'test the range' means). After this happens the lock is released, the new key gets inserted and an X lock is placed on it.

RangeI-N lock is requested to test that insertion into key range will not interfere with another transaction that may potentially do some serializable operation incompatible with insertion (like reading for example).

During insertion of record into index database engine locates page, where key being inserted should be placed. Page and key locks are not used at this stage yet, only latches. Once page is located, engine starts acquiring locks necessary for performing insertion of record to the page. These are IX lock for the page located, then RangeI-N lock for the key next to key being inserted. Upon acquiring RangeI-N is not held, and next X lock for the key being inserted is requested. After necessary locks acquired, insertion of the record proceeds.

Say we have table and data

CREATE TABLE T
(
K int NOT NULL,
CONSTRAINT UQ_T UNIQUE CLUSTERED (K)
);

INSERT INTO T (K)
VALUES (1), (2), (9), (10);

Let's take result of the following query

SELECT K, %%lockres%% AS lockres
FROM T;

which is

K    lockres
---- ---------------
1    (8194443284a0)
2    (61a06abd401c)
9    (30b7763ed433)
10   (d08358b1108f)

(we will refer to it in the things that follow).

Then, say we have a query

SELECT COUNT(*)
FROM T
WHERE K BETWEEN 1 AND 9;

Running it under SERIALIZABLE isolation level results to the following locking footprint

To protect key range, database engine locks every key in this range with RangeS-S lock. Additionally, key next to the range is locked (this is necessary for non-unique index, but engine is doing it for unique index too). In this case, locks are placed on resources corresponding (according to result of the query taken earlier) to keys 1, 2, 9 and 10.

Non-concurrent insertion to the table

INSERT INTO T (K)
VALUES (3);

results to following locking footprint

Key 3 does not exists in the table, and so database engine requests RangeI-N lock on the resource (30b7763ed433) corresponding to key 9, which is next to 3 at the moment. Acquiring RangeI-N means that there is no incompatible serializable activity being performed, so engine proceeds and acquires X lock on the resource (98ec012aa510) corresponding to key 3. Then actual insertion happens and locks are released. Notice that there is no release of RangeI-N lock.

Running above SELECT and INSERT concurrently causes INSERT to wait until transaction performed serializable SELECT is active

because of RangeI-N incompatibility with RangeS-S. As soon as transaction performed SELECT ends INSERT will proceed.

This is what "test the range" means.

However I do not see why two RangeI-N locks are said to be compatible with each other.

RangeI-N locks compatibility is good, because of it allows concurrent insertions into key range.

Imagine we are doing

INSERT INTO T (K)
VALUES (4);

and

INSERT INTO T (K)
VALUES (6);

concurrently.

It may happen that at some moment both statements acquire RangeI-N on the resource (30b7763ed433) corresponding to key 9. But this is fine, because of then concurrency is controlled by X on the keys and by page latch further.


text:
# dtypes¶

DataFrame.dtypes

Return the dtypes in the DataFrame.

This returns a Series with the data type of each column. The result’s index is the original DataFrame’s columns.


text:
•
Sök i SwePub databas

# Träfflista för sökning "WFRF:(Egberts K) "

Sökning: WFRF:(Egberts K)

Sortera/gruppera träfflistan

NumreringReferensOmslagsbildHitta
11.
• Abdalla, H., et al. (författare)
• Simultaneous observations of the blazar PKS 2155-304 from ultra-violet to TeV energies
• 2020
• Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 639, s. 1-13
• Tidskriftsartikel (refereegranskat)abstract
• Here we report the results of the first ever contemporaneous multi-wavelength observation campaign on the BL Lac object PKS 2155-304 involving Swift, NuSTAR, Fermi-LAT, and H.E.S.S. The use of these instruments allows us to cover a broad energy range, which is important for disentangling the different radiative mechanisms. The source, observed from June 2013 to October 2013, was found in a low flux state with respect to previous observations but exhibited highly significant flux variability in the X-rays. The high-energy end of the synchrotron spectrum can be traced up to 40 keV without significant contamination by high-energy emission. A one-zone synchrotron self-Compton model was used to reproduce the broadband flux of the source for all the observations presented here but failed for previous observations made in April 2013. A lepto-hadronic solution was then explored to explain these earlier observational results.
•
12.
• Acero, F., et al. (författare)
• Prospects for Cherenkov Telescope Array Observations of the Young Supernova Remnant RX J1713.7-3946
• 2017
• Ingår i: Astrophysical Journal. - : Institute of Physics Publishing (IOPP). - 0004-637X .- 1538-4357. ; 840:2
• Tidskriftsartikel (refereegranskat)abstract
• We perform simulations for future Cherenkov Telescope Array (CTA) observations of RX J1713.7-3946, a young supernova remnant (SNR) and one of the brightest sources ever discovered in very high energy (VHE) gamma rays. Special attention is paid to exploring possible spatial (anti) correlations of gamma rays with emission at other wavelengths, in particular X-rays and CO/H I emission. We present a series of simulated images of RX J1713.7-3946 for CTA based on a set of observationally motivated models for the gamma-ray emission. In these models, VHE gamma rays produced by high-energy electrons are assumed to trace the nonthermal X-ray emission observed by XMM-Newton, whereas those originating from relativistic protons delineate the local gas distributions. The local atomic and molecular gas distributions are deduced by the NANTEN team from CO and H I observations. Our primary goal is to show how one can distinguish the emission mechanism(s) of the gamma rays (i.e., hadronic versus leptonic, or a mixture of the two) through information provided by their spatial distribution, spectra, and time variation. This work is the first attempt to quantitatively evaluate the capabilities of CTA to achieve various proposed scientific goals by observing this important cosmic particle accelerator.
•
13.
• Aliu, E., et al. (författare)
• Long-term TeV and X-ray Observations of the Gamma-ray Binary HESS J0632+057
• 2014
• Ingår i: Astrophysical Journal. - 0004-637X .- 1538-4357. ; 780:2
• Tidskriftsartikel (refereegranskat)abstract
• HESS J0632+057 is the only gamma-ray binary known so far whose position in the sky allows observations with ground-based observatories in both thenorthern and southern hemispheres. Here we report on long-term observations of HESS J0632+057 conducted with the Very Energetic Radiation Imaging Telescope Array System and High Energy Stereoscopic System Cherenkov telescopes and the X-ray satellite Swift, spanning a time range from 2004 to 2012 and covering most of the system's orbit. The very-high-energy (VHE) emission is found to be variable and is correlated with that at X-ray energies. An orbital period of 315(-4)(+6) days is derived from the X-ray data set, which is compatible with previous results, P = (321 +/- 5) days. The VHE light curve shows a distinct maximum at orbital phases close to 0.3, or about 100 days after periastron passage, which coincides with the periodic enhancement of the X-rayemission. Furthermore, the analysis of the TeV data shows for the first time a statistically significant (> 6.5 sigma) detection at orbital phases 0.6-0.9. Theobtained gamma-ray and X-ray light curves and the correlation of the source emission at these two energy bands are discussed in the context of the recent ephemeris obtained for the system. Our results are compared to those reported for other gamma-ray binaries.
•
14.
• Abramowski, A., et al. (författare)
• Discovery of variable VHE gamma-ray emission from the binary system 1FGL J1018.6-5856
• 2015
• Ingår i: Astronomy and Astrophysics Supplement Series. - 0365-0138 .- 1286-4846. ; 577
• Tidskriftsartikel (refereegranskat)abstract
• Re-observations with the HESS telescope array of the very high-energy (VHE) source HESS J1018-589 A that is coincident with the Fermi-LAT γ-ray binary 1FGL J1018.6-5856 have resulted in a source detection significance of more than 9σ and the detection of variability (χ$^2$/ν of 238.3/155) in the emitted γ-ray flux. This variability confirms the association of HESS J1018-589 A with the high-energy γ-ray binary detected by Fermi-LAT and also confirms the point-like source as a new VHE binary system. The spectrum of HESS J1018-589 A is best fit with a power-law function with photon index Γ = 2.20 \plusmn 0.14$_stat$ \plusmn 0.2$_sys$. Emission is detected up to ~20 TeV. The mean differential flux level is (2.9 \plusmn 0.4) \times 10$^-13$ TeV$^-1$ cm$^-2$ s$^-1$ at 1 TeV, equivalent to ~1% of the flux from the Crab Nebula at the same energy. Variability is clearly detected in the night-by-night light curve. When folded on the orbital period of 16.58 days, the rebinned light curve peaks in phase with the observed X-ray and high-energy phaseograms. The fit of the HESS phaseogram to a constant flux provides evidence of periodicity at the level of N$_sigma$\gt 3σ. The shape of the VHE phaseogram and measured spectrum suggest a low-inclination, low-eccentricity system with amodest impact from VHE γ-ray absorption due to pair production (τ \lsim 1 at 300 GeV).
•
15.
•
16.
• Aharonian, F., et al. (författare)
• Simultaneous observations of pks 2155-304 with hess, fermi, rxte, and atom : Spectral energy distributions and variability in a low state
• 2009
• Ingår i: Astrophysical Journal Letters. - 2041-8205. ; 696:2, s. L150-L155
• Tidskriftsartikel (refereegranskat)abstract
• We report on the first simultaneous observations that cover the optical, X-ray, and high-energy gamma-ray bands of the BL Lac object PKS 2155-304. The gamma-ray bands were observed for 11 days, between 2008 August 25 and 2008 September 6 (MJD 54704-54715), jointly with the Fermi Gamma-ray Space Telescope and the HESS atmospheric Cherenkov array, providing the first simultaneous MeV-TeV spectral energy distribution (SED) with the new generation of gamma-ray telescopes. The ATOM telescope and the RXTE and Swift observatories provided optical and X-ray coverage of the low-energy component over the same time period. The object was close to the lowest archival X-ray and very high energy (VHE; > 100 GeV) state, whereas the optical flux was much higher. The light curves show relatively little (similar to 30%) variability overall when compared to past flaring episodes, but we find a clear optical/VHE correlation and evidence for a correlation of the X-rays with the high-energy spectral index. Contrary to previous observations in the flaring state, we do not find any correlation between the X-ray and VHE components. Although synchrotron self-Compton models are often invoked to explain the SEDs of BL Lac objects, the most common versions of these models are at odds with the correlated variability we find in the various bands for PKS 2155-304.
•
17.
• Aharonian, F., et al. (författare)
• SIMULTANEOUS OBSERVATIONS OF PKS 2155-304 WITH HESS, FERMI, RXTE, AND ATOM : SPECTRAL ENERGY DISTRIBUTIONS AND VARIABILITY IN A LOW STATE
• 2009
• Ingår i: Astrophysical Journal Letters. - 2041-8205 .- 0004-637X .- 1538-4357. ; 696:2, s. L150-L155
• Tidskriftsartikel (refereegranskat)abstract
• We report on the first simultaneous observations that cover the optical, X-ray, and high-energy gamma-ray bands of the BL Lac object PKS 2155-304. The gamma-ray bands were observed for 11 days, between 2008 August 25 and 2008 September 6 (MJD 54704-54715), jointly with the Fermi Gamma-ray Space Telescope and the HESS atmospheric Cherenkov array, providing the first simultaneous MeV-TeV spectral energy distribution (SED) with the new generation of gamma-ray telescopes. The ATOM telescope and the RXTE and Swift observatories provided optical and X-ray coverage of the low-energy component over the same time period. The object was close to the lowest archival X-ray and very high energy (VHE; > 100 GeV) state, whereas the optical flux was much higher. The light curves show relatively little (similar to 30%) variability overall when compared to past flaring episodes, but we find a clear optical/VHE correlation and evidence for a correlation of the X-rays with the high-energy spectral index. Contrary to previous observations in the flaring state, we do not find any correlation between the X-ray and VHE components. Although synchrotron self-Compton models are often invoked to explain the SEDs of BL Lac objects, the most common versions of these models are at odds with the correlated variability we find in the various bands for PKS 2155-304.
•
18.
•
19.
• Abdalla, H., et al. (författare)
• Gamma-ray blazar spectra with HESS II mono analysis : The case of PKS2155-304 and PG1553+113
• 2017
• Ingår i: Astronomy and Astrophysics. - : EDP Sciences. - 0004-6361 .- 1432-0746. ; 600
• Tidskriftsartikel (refereegranskat)abstract
• Context. The addition of a 28 m Cherenkov telescope (CT5) to the H.E.S.S. array extended the experiment's sensitivity to lower energies. The lowest energy threshold is obtained using monoscopic analysis of data taken with CT5, providing access to gamma-ray energies below 100 GeV for small zenith angle observations. Such an extension of the instrument's energy range is particularly beneficial for studies of active galactic nuclei with soft spectra, as expected for those at a redshift >= 0.5. The high-frequency peaked BL Lac objects PKS 2155-304 (z = 0.116) and PG 1553 + 113 (0.43 < z < 0.58) are among the brightest objects in the gamma-ray sky, both showing clear signatures of gamma-ray absorption at E > 100 GeV interpreted as being due to interactions with the extragalactic background light (EBL). Aims. The aims of this work are twofold: to demonstrate the monoscopic analysis of CT5 data with a low energy threshold, and to obtain accurate measurements of the spectral energy distributions (SED) of PKS 2155-304 and PG 1553 + 113 near their SED peaks at energies approximate to 100 GeV. Methods. Multiple observational campaigns of PKS 2155 304 and PG 1553 + 113 were conducted during 2013 and 2014 using the full H.E.S.S. II instrument (CT1-5). A monoscopic analysis of the data taken with the new CT5 telescope was developed along with an investigation into the systematic uncertainties on the spectral parameters which are derived from this analysis. Results. Using the data from CT5, the energy spectra of PKS 2155 304 and PG 1553 + 113 were reconstructed down to conservative threshold energies of 80 GeV for PKS 2155 304, which transits near zenith, and 110 GeV for the more northern PG 1553 + 113. The measured spectra, well fitted in both cases by a log-parabola spectral model ( with a 5.0 similar to statistical preference for non-zero curvature for PKS 2155 304 and 4.5 sigma for PG 1553+113), were found consistent with spectra derived from contemporaneous Fermi-LAT data, indicating a sharp break in the observed spectra of both sources at E approximate to 100 GeV. When corrected for EBL absorption, the intrinsic H.E.S.S. II mono and Fermi-LAT spectrum of PKS 2155 304 was found to show significant curvature. For PG 1553+113, however, no significant detection of curvature in the intrinsic spectrum could be found within statistical and systematic uncertainties.
•
20.
• Abdalla, H., et al. (författare)
• HESS Limits on Linelike Dark Matter Signatures in the 100 GeV to 2 TeV Energy Range Close to the Galactic Center
• 2016
• Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 117:15
• Tidskriftsartikel (refereegranskat)abstract
• A search for dark matter linelike signals iss performed in the vicinity of the Galactic Center by the H.E.S.S. experiment on observational data taken in 2014. An unbinned likelihood analysis iss developed to improve the sensitivity to linelike signals. The upgraded analysis along with newer data extend the energy coverage of the previous measurement down to 100 GeV. The 18 h of data collected with the H.E.S.S. array allow one to rule out at 95% C.L. the presence of a 130 GeV line (at l = -1.5 degrees, b = 0 degrees and for a dark matter profile centered at this location) previously reported in Fermi-LAT data. This new analysis overlaps significantly in energy with previous Fermi-LAT and H.E.S.S. results. No significant excess associated with dark matter annihilations was found in the energy range of 100 GeV to 2 TeV and upper limits on the gamma-ray flux and the velocity weighted annihilation cross section are derived adopting an Einasto dark matter halo profile. Expected limits for present and future large statistics H.E.S.S. observations are also given.
•
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# Diodes & Rectifiers

Diode - General purpose rectifier, 1A, 1N400X
A semiconductor device which passes current in the forward direction (from anode to cathode), and blocks current in the opposite direction.
Starting at $0.15 Diode - standard recovery rectifier, 3A, 1000V, 1N5408 1N5408 Diode. Lead mounted standard recovery rectifiers are designed for use in power supplies and other applications having need of a device with the following features: • High Current to Small Size • High Surge Current Capability • Low Forward Voltage Drop$0.38
Diode - 1N34A Germanium, low leakage
The 1N34A Germanium diode is an old standby in electronics. Widely used for detecting the rectifying efficiency or for switching on a radio, TV or stereo etc.
$1.75 Diode - 1N5817, Schottky, High Switching Speed Schottky diode with low forward voltage drop and high switching speeds.$0.15
Diode - 1N914, Small Signal
The 1N914 is a small signal diode similar to the 1N4148 and is common in many older electronics. The 1N914 is general purpose and can be used in a multitude of different applications.
$0.18 Diode - small signal fast switching, 1N4148A A semiconductor device which passes current in the forward direction(from anode to cathode), and blocks current in the opposite direction. For extreme fast switches.$0.20
Diode - Zener, 1W, 5% Tolerance
A semiconductor device that, above a certain reverse voltage(the zener value) has a sudden rise in current. If forward biased, the diode is an ordinary rectifier. When reverse biased, it exhibits a sharp break in its current-voltage graph. Voltage across the diode remains essentially constant for any further increase of reverse current.
Starting at $0.20 Diode - Zener, 5 Watt, ±5% tolerance 5W zener diodes that are great for use in tube amps. These are commonly used to drop B+ voltages for tube modification compatibility or to create low power modes for the amp. A zener is a semiconductor device that, above a certain reverse voltage(the zener value) has a sudden rise in current. If forward biased, the diode is an ordinary rectifier. When reverse biased, it exhibits a sharp break in its current-voltage graph. Voltage across the diode remains essentially constant for any further increase of reverse current.$0.55
Diode - 1N60, Germanium, DO-7
1N60 point-contact germanium diodes in a DO-7 package. 1N60 diodes were used in many vintage electronics and also make for great clipping diodes in stompbox effects pedals.
$1.25 Diode - BAT41, Schottky, Small Signal The BAT41 is a schottky diode used in many DIY projects. General purpose metal to silicon diode featuring very low turn-on voltage and fast switching. This device has integrated protection against excessive voltage such as electrostatic discharges.$0.28
Bridge Rectifier - Single-phase, 3A 400V
A full wave rectifier with 4 elements in a bridge circuit so that DC voltage is obtained from one pair of junctions when an AC voltage is applied to another pair of junctions.
$0.95 Diode - 1N270, Germanium, DO-7 1N60 point-contact germanium diodes in a DO-7 package. 1N60 diodes were used in many vintage electronics and also make for great clipping diodes in stompbox effects pedals. The MXR® Distortion+ uses the 1N270$1.75
Diode - Hexfred, ultrafast soft recovery, 8A, 600V
High performance, ultrafast diodes. Improve efficiency, reduce noise, allow higher frequency operation.
$2.75 Diode - Small Signal Fast Switching, 1N4448 A semiconductor device which passes current in the forward direction(from anode to cathode), and blocks current in the opposite direction. Features • Silicon epitaxial planar diodes • Low power loss, high efficiency • Low leakage • Low forward voltage • High speed switching • High current capability • High reliability Used in a variety of Fender amps. Replacement for Fender part number 0006260049$0.15
Diode - 1N5818, Schottky, High Switching Speed, 30V, 10A
1N5818 schottky diode with low forward voltage drop and high switching speeds.
• Very small conduction losses
• Negligible switching losses
• Extremely fast switching
• Low forward voltage drop
• Avalanche capability specified
$0.15 Diode - Fast Recovery, 1A, 600V, 1N4937 A semiconductor device that, above a certain reverse voltage(the zener value) has a sudden rise in current. If forward biased, the diode is an ordinary rectifier. When reverse biased, it exhibits a sharp break in its current-voltage graph. Voltage across the diode remains essentially constant for any further increase of reverse current.$0.39
Diode - Silicon Rectifier, 3A, 400V, 1N5404
A semiconductor device which passes current in the forward direction(from anode to cathode), and blocks current in the opposite direction.
$0.35 Bridge Rectifier - Single-phase, 2A, In-line 2A bridge rectifier in an inline package ideal for PCB use. Features: • Low reverse leakage • Low forward voltage • High forward surge current capability Starting at$0.85
Diode - Hexfred, 16A, 600V, ultrafast
High performance, ultrafast diodes. Improve efficiency, reduce noise, allow higher frequency operation.
$2.92 Save 27% Originally:$4.00
Transistor - 2N5135, Silicon, TO-105 case, NPN
The 2N5135 is a silicon NPN transistor in a TO-105 case. This transistor is a close match to the rare 2N5133 but with higher voltage ratings and is in a larger package. The hFE range is less wide than the 2N5133 with more values in the range found in the batches used on vintage Big Muff pedals. The lower hFE range also makes these a great option for silicon fuzz pedals.
\$1.75


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## Applied Mathematics

•  Tamara Kolda, Sandia National Laboratories
•  Practical Leverage-Based Sampling for Low-Rank Tensor Decomposition; zoom link @ https://sites.google.com/view/minds-seminar/home
•  07/23/2020
•  2:30 PM - 3:30 PM
•

(Part of One World MINDS seminar: https://sites.google.com/view/minds-seminar/home)  Conventional algorithms for finding low-rank canonical polyadic (CP) tensor decompositions are unwieldy for large sparse tensors. The CP decomposition can be computed by solving a sequence of overdetermined least problems with special Khatri-Rao structure. In this work, we present an application of randomized algorithms to fitting the CP decomposition of sparse tensors, solving a significantly smaller sampled least squares problem at each iteration with probabilistic guarantees on the approximation errors. Prior work has shown that sketching is effective in the dense case, but the prior approach cannot be applied to the sparse case because a fast Johnson-Lindenstrauss transform (e.g., using a fast Fourier transform) must be applied in each mode, causing the sparse tensor to become dense. Instead, we perform sketching through leverage score sampling, crucially relying on the fact that the structure of the Khatri-Rao product allows sampling from overestimates of the leverage scores without forming the full product or the corresponding probabilities. Naive application of leverage score sampling is ineffective because we often have cases where a few scores are quite large, so we propose a novel hybrid of deterministic and random leverage-score sampling which consistently yields improved fits. Numerical results on real-world large-scale tensors show the method is significantly faster than competing methods without sacrificing accuracy. This is joint work with Brett Larsen, Stanford University.

## Contact

Department of Mathematics
Michigan State University


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## The one that got away: A unique eclipse in the young brown dwarf Roque 12

Scholz, Aleks ; Froebrich, Dirk ; Muzic, Koraljka ; Eislöffel, Jochen
arXiv e-prints
06/2020

#### ABSTRACT

We report the discovery of a deep, singular eclipse of the bona fide brown dwarf Roque 12, a substellar member of the Pleiades. The eclipse was 0.6mag deep, lasted 1.3h, and was observed with two telescopes simultaneously in October 2002. No further eclipse was recorded, despite continuous monitoring with Kepler/K2 over 70d in 2015. There is tentative ($2\sigma$) evidence for radial velocity variations of 5km/s, over timescales of three months. The best explanation for the eclipse is the presence of a companion on an eccentric orbit. The observations constrain the eccentricity to e>0.5, the period to P>70d, and the mass of the companion to to ~0.001-0.04Msol. In principle it is also possible that the eclipse is caused by circum-sub-stellar material. Future data releases by Gaia and later LSST as well as improved radial velocity constraints may be able to unambiguously confirm the presence of the companion which would turn this system into one of the very few known eclipsing binary brown dwarfs with known age.


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Equipped with the right applications, a computer can be of great help in virtually any domain of activity. When it comes to designing and precision, no other tool is as accurate as a computer. Moreover, specialized applications such as AutoCAD give you the possibility to design nearly anything ranging from art, to complex mechanical parts or even buildings.
Suitable for business environments and experienced users
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Create 2D and 3D objects
You can make use of basic geometrical shapes to define your objects, as well as draw custom ones. Needless to say that you can take advantage of a multitude of tools that aim to enhance precision. A grid can be enabled so that you can easily snap elements, as well as adding anchor points to fully customize shapes.
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Various export possibilities
Similar to a modern web browser, each project is displayed in its own tab. This comes in handy, especially for comparison views. Moreover, layouts and layers also play important roles, as it makes objects handling a little easier.
Sine the application is not the easiest to carry around, requiring a slightly sophisticated machine to properly run, there are several export options put at your disposal so that the projects itself can be moved around.
Aside from the application specific format, you can save as an image file of multiple types, PDF, FBX and a few more. Additionally, it can be sent via email, directly printed out on a sheet of paper, or even sent to a 3D printing service, if available.
To end with
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AutoCAD was originally developed and marketed by the company now known as Autodesk, Inc. The first AutoCAD was introduced on December 8, 1982. This version, which can be identified by the version number 1, did not include Revit. The first Revit was introduced on March 28, 1990 as version 2. This was followed by version 4 in March 1990, which is the version that introduced the ribbon-based user interface, before it was replaced by the ribbon-based interface introduced in AutoCAD R10 in August 1994. A new user interface was also introduced in AutoCAD R9.

In early

Autodesk Digital Designer: A virtual modeling software that allows users to create, edit and document 2D and 3D designs that can be printed out or displayed on a screen. It is available as a free download from Autodesk’s website.
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Search for ‘ACCOUNTING’
Click on ‘ACCOUNTING – ACCOUNTING for Autocad’
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[Role of age, sex and environmental factors in the pathogenesis of motor neuron disease: contribution of the environment?].
The pathogenesis of motor neuron diseases (MND) is still unknown. The case-control study using medical records linked to a questionnaire is not useful in this domain. To analyse the influence of environmental factors on the risk of MND. A population-based case-control study was conducted on a new cohort of cases (n = 50) and controls (n = 136). Medical records were collected in a database. Each subject was questioned on exposure to occupational and environmental risk factors. All suspected factors were recorded in the database, except those that were common (e.g. smoking). The database was validated and duplicates were eliminated. Each subject was given a score of exposure. Individual risks were compared between case and control groups using univariate analysis and multivariate analysis including occupational factors and age. In the multiple logistic regression analysis, factors with p Q:

Prove $f$ is $1$ to $1$

I have a function which given by $f(x)=\frac{1}{2}x$ if $x\in \Bbb Q$ and $f(x)=x$ if $x\in \Bbb R-\Bbb Q$. I need to prove that this function is $1$ to \$

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Place your cursor on a point on a 2D drawing or type coordinates on the command line to jump to the point.

Place your cursor on a point on a 2D drawing or type coordinates on the command line to jump to the point.

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# Molecular Orbital Theory (Worksheets)

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.

## Q1.

Sketch the molecular orbital diagram of $$H_2^‐$$. Write the electron configuration of the ions interms of its molecular orbitals. Calculate the bond order.

## Q2

Sketch the molecular orbital diagram of $$H_2^+$$. Write the electron configuration of the ions interms of its molecular orbitals. Calculate the bond order.

## Q3.

Based on the previous two questions, which molecule is most stable? Why?

## Q4.

Sketch the molecular orbital diagram for the following molecules: $$B_2$$, $$N_2$$ and $$C_2$$.

This page titled Molecular Orbital Theory (Worksheets) is shared under a not declared license and was authored, remixed, and/or curated by Mark Draganjac.


text:
A. Airapetian, et al. (HERMES Collaboration)
Nucl.Phys. B842 (2011) 265–298
Publication year: 2011

Azimuthal asymmetries in exclusive electroproduction of a real photon from a longitudinally polarized deuterium target are measured with respect to target polarization alone and with respect to target polarization combined with beam helicity and/or beam charge. The asymmetries appear in the distribution of the real photons in the azimuthal angle ϕ around the virtual photon direction, relative to the lepton scattering plane. The asymmetries arise from the deeply virtual Compton scattering process and its interference with the Bethe-Heitler process. The results for the beam-charge and beam-helicity asymmetries from a tensor polarized deuterium target with vanishing vector polarization are shown to be compatible with those from an unpolarized deuterium target, which is expected for incoherent scattering dominant at larger momentum transfer. Furthermore, the results for the single target-spin asymmetry and for the double-spin asymmetry are found to be compatible with the corresponding asymmetries previously measured on a hydrogen target. For coherent scattering on the deuteron at small momentum transfer to the target, these findings imply that the tensor contribution to the cross section is small. Furthermore, the tensor asymmetry is found to be compatible with zero.


text:
## Statement

difficulty
A body moves describing a circular trajectory with constant linear and angular velocity equal to 3 m/s and 6π rad/s respectively. Determine its position vector when it has traveled exactly one meter.

## Solution

Data

v = 3 m/s

Resolution

If we apply the definitions of the angular magnitudes, we know that:

Now applying the definition of distance traveled based on the angular position and the radius:

Now that we know the radius and the angular position when the distance traveled is 1 m, we can determine the position vector using the following expression:

## Formulas worksheet

These are the main formulas that you must know to solve this exercise. If you are not clear about their meaning, we recommend you to check the theory in the corresponding sections. Furthermore, you will find in them, under the Formulas tab, the codes that will allow you to integrate these equations in external programs like Word or Mathematica.

Formulas
Related sections
$s=\phi ·R$
$\stackrel{\to }{r}=x·\stackrel{\to }{i}+y·\stackrel{\to }{j}=R·\mathrm{cos}\left(\phi \right)·\stackrel{\to }{i}+R·\mathrm{sin}\left(\phi \right)·\stackrel{\to }{j}$
$v=\omega ·R$


text:
Research interests: Abstract integral equations and operator semigroups. Integration, duality, and admissibility. Existence, stability, and bifurcation of parameter-dependent equilibria and periodic orbits. Methodological connections with control and economic dynamics.

For my work in mathematics I am kindly hosted by Utrecht University, The Netherlands. My PhD advisers are O. Diekmann and S.M. Verduyn Lunel.

## Contact information

You can contact me via email (can be used with my PGP key) or more email.
I have a profile on ResearchGate.

## Pre-prints and publications

S.G. Janssens, A class of abstract delay differential equations in the light of suns and stars. Part II, March 2020, arXiv:2003.13341 [math.DS, math.FA].
Presentation video and slides about this work for the third installment of the Delay Days, online, 1 October 2020.

M.M. Bosschaert, S.G. Janssens, Yu.A. Kuznetsov, Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations, March 2019, arXiv:1903.08276 [math.DS]. Accepted for publication in SIAM Journal on Applied Dynamical Systems.

S.G. Janssens, A class of abstract delay differential equations in the light of suns and stars. Part I, January 2019, arXiv:1901.11526 [math.DS, math.FA].
Presentation about this work for a day on Delay equations, theory and applications, Utrecht, 15 February 2019.

K. Dijkstra, S.A. van Gils, S.G. Janssens, Yu.A. Kuznetsov, S. Visser, Pitchfork-Hopf bifurcations in 1D neural field models with transmission delays, Phys. D 297 (2015), 88–101, DOI: 10.1016/j.physd.2015.01.004.

S.A. van Gils, S.G. Janssens, Yu.A. Kuznetsov, S. Visser, On local bifurcations in neural field models with transmission delays, J. Math. Biol. 66 (2013), no. 4-5, 837–887, DOI:10.1007/s00285-012-0598-6 and arXiv:1209.2849 [math.DS].

S.G. Janssens, On a Normalization Technique for Codimension Two Bifurcations of Equilibria of Delay Differential Equations, Master Thesis, Utrecht University, 2010, original or with updates (latest: 20 November 2018).

My master thesis was written under supervision of Yu.A. Kuznetsov with Odo Diekmann as co-supervisor. The updated version contains corrections and some new material – see the Summary of updates and corrections. It is available under a Creative Commons BY-NC-ND 4.0 International license.

## Site credits

I am a grateful user of various high quality programs that are part of the GNU project.
For online $\LaTeX$ formula typesetting with MathJax I use the Simpe MathJax plugin.


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# Is this possible in DirectX? (MSVC linking question)

This topic is 4731 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

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Hello - I want to link all the DirectX9 .libs into my engine .lib. The idea being that I can distribute my lib without the users having to have the DirectX SDK since they would be contained in my engine .lib It all works perfectly apart from I get 1000's of linker warnings when building the engine lib, all saying the same:
d3d9.lib(d3d9.dll) : warning LNK4006: _Direct3DCreate9@4 already defined in d3d9.lib(d3d9.dll); second definition ignored
d3d9.lib(d3d9.dll) : warning LNK4006: __imp__Direct3DCreate9@4 already defined in d3d9.lib(d3d9.dll); second definition ignored

etc...

Any help would be appreciated.

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First, users don't have to install the SDK -- they just install the runtime. Second, they will still need the DLLs, which means they have to install the runtime.

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Quote:
 Original post by JohnBoltonFirst, users don't have to install the SDK -- they just install the runtime. Second, they will still need the DLLs, which means they have to install the runtime.

I think the OP was refering to "user" as other developers, not the end user of a game.

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Yes sorry - user as in a user of my .lib :)

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Real function to entire functions - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T22:07:28Z http://mathoverflow.net/feeds/question/105918 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/105918/real-function-to-entire-functions Real function to entire functions unknown (google) 2012-08-30T09:23:58Z 2012-08-30T22:21:58Z
Let $g:[0,\infty) \rightarrow \mathbb{R}$ be an increasing function. Is there a way to construct an entire function $f(z)$ such that $f(x)=g(|x|)$ for all real $x$?
 http://mathoverflow.net/questions/105918/real-function-to-entire-functions/105925#105925 Answer by jbc for Real function to entire functions jbc 2012-08-30T10:54:18Z 2012-08-30T10:54:18Z
You certainly need some smoothness condition for this to be possible. In fact, the condition is that $f$ be extendable to an even, real-analytic function on the line which kind of makes the result a tautology since then $f$ has the form $\sum_{n=1}^\infty a_{2n} z^{2n}$.
 http://mathoverflow.net/questions/105918/real-function-to-entire-functions/105936#105936 Answer by Bazin for Real function to entire functions Bazin 2012-08-30T12:35:08Z 2012-08-30T22:21:58Z
You should keep in mind analytic continuation. Let $f:\mathbb R\rightarrow\mathbb R$ be a $C^\infty$ function ; if there exists an entire function extending $f$, then

(1) It is unique by analytic continuation,

(2) The function $f$ must be real-analytic.

Of course (2) is not sufficient: think about the real-analytic $x\mapsto\frac{1}{1+x^2}$, which does NOT have an entire extension, since by analytic continuation, that extension should coincide with $\mathbb C\ni z\mapsto \frac{1}{1+z^2}$, which has poles at $\pm i$. For a real-analytic $f$, you can formulate a criterion dealing with the size of derivatives. Such a function has an entire extension iff $$\forall R>0,\exists C_R,\forall n\in\mathbb N,\quad \vert f^{(n)}(0)\vert\le C_R\frac{n!}{R^n}.$$ On the other hand, real-analyticity of a $C^\infty$ $f$ on the real line is equivalent to $$\forall x\in \mathbb R,\exists r>0,\exists C>0, \exists R>0,\forall n\in\mathbb N,\quad \Vert f^{(n)}\Vert_{L^\infty(B(x,r))}\le C\frac{n!}{R^n}.$$