text:
Department of Pre-University Education, Karnataka course PUC Karnataka Science Class 12
Share

# P Suppose a Charge +Q1 is Given to the Positive Plate and a Charge −Q2 to the Negative Plate of a Capacitor. What is the "Charge on the Capacitor"? - Physics

ConceptCombination of Capacitors

#### Question

Suppose a charge +Q1 is given to the positive plate and a charge −Q2 to the negative plate of a capacitor. What is the "charge on the capacitor"?

#### Solution

Given :

Charge on the positive plane = +Q_1

Charge on the negative plate = -Q_2

To calculate: Charge on the capacitor

Let ABCD be the Gaussian surface such that faces AD and BC lie inside plates X and Y, respectively.
Let q be the charge appearing on surface II. Then, the distribution of the charges on faces I, III and IV will be in accordance with the figure.

Let the area of the plates be A and the permittivity of the free space be ∈_0.

Now, to determine q in terms of Q1 and Q2, we need to apply Gauss's law to calculate the electric field due to all four faces of the capacitor at point P. Also, we know that the electric field inside a capacitor is zero.

Electric field due to face I at point P, E1 = (Q_1 - q)/(2∈_0A)

Electric field due to face II at point P, E2= (+q)/(2∈_0A)

Electric field due to face III at point P, E3 = (-q)/{2∈_0A)

Electric field due to face IV at point P, E4 = -((-Q_2+q)/(2∈_0A))      (Negative sign is used as point P lies on the LHS of face IV.)

Since point P lies inside the conductor,

E1 + E2 + E3 + E4 = 0

therefore Q_1-q+q-q-(-Q_2+q) = 0

⇒ q = (Q_1+Q_2)/2

Thus , the change on the capacitor is (Q_1+Q_2)/2, which is the charge on faces  II and III.

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Solution for Concepts of Physics - Vol. 2 (2018 to Current)
Chapter 9: Capacitors
Short Answers | Q: 1 | Page no. 163

#### Video TutorialsVIEW ALL [1]

Solution P Suppose a Charge +Q1 is Given to the Positive Plate and a Charge −Q2 to the Negative Plate of a Capacitor. What is the "Charge on the Capacitor"? Concept: Combination of Capacitors.
S

format: plain


text:
# 2017-09-05

### Rotationally Invariant per-sample mixing layer for AA

We have a layer that takes as input:

• A tensor of samples $$I[bs, h, w, spp, n_{in}]$$

• A tensor of per-pixel angles $$\theta[bs, h, w]$$

• A tensor of kernel weights $$K[k_h, k_w, n_{in}, n_{out}]$$

• An array of subpixel offsets (corresponding to the samples'$$xy$$ positions) $$p[bs, h, w, spp, 2]$$

And outputs a tensor of sample features $$O[bs, h, w, spp, n_{out}]$$.

The operator bilinearly interpolates into the kernel based on the sample's rotated spatial position. The kernel is centered at each sample's location.

$O[b, y, x, s', c_{out}] = \sum_{c_{in}} \sum_{s=1\ldots spp} I[b, y, x, s, c_{in}]K[rotate_{s'}(p[b, y, x, s], \theta[b, y, x]), c_{in}, c_{out}]$

This operator is pretty slow, because of the quadratic sample-sample interaction. We also have a layer that outputs per-pixel quantities instead: $$O[bs, h, w, n_{out}]$$.

Here's an example of learned kernels:

### Datasets

We use three independent test cases:

• rotated grayscale edges
• random flat triangles
• rotated sine waves.

The angle input is either learnable or hardcoded as: $\theta = \arctan\left(\frac{\frac{dI}{dy}}{\frac{dI}{dx}}\right)$

For all the results below, we use 1 hidden layer, 32 filters per layer. The filters have a receptive field of 5 pixels, and size $$25\times25$$. That is, a sub-pixel resolution of roughly $$\frac{1}{5}$$.

### FixedEdges

Noisy outputs, with dirty edge

### Sines

Fixed frequency, random angle. I forgot to output colors... But we get cleaner outputs.


text:
# Probability proof and graphs

Let $G = (V, E)$ be a graph with vertex set $V$ and edge set $E$. A subset $I$ of $V$ is called an independent set if for any two distinct vertices $u$ and $v$ in $I$, $(u, v)$ is not an edge in $E$.

Let $n$ and $m$ denote the number of vertices and edges in $G$, respectively, and assume that $m ≥ n/2$.

Consider the following algorithm, in which all random choices made are mutually independent:

Algorithm IndepSet(G):

Step 1: Set $H = G$.

Step 2: Let $d = 2m/n$. For each vertex $v$ of $H$, with probability $1−1/d$, delete the vertex $v$, together with its incident edges, from $H$.

Step 3: As long as the graph $H$ contains edges, do the following: Pick an arbitrary edge $(u, v)$ in $H$, and remove the vertex $u$, together with its incident edges, from $H$.

Step 4: Let $I$ be the vertex set of the graph $H$. Return $I$.

• Argue that the set $I$ that is returned by this algorithm is an independent set in G.

Any help appreciated. Have thought of anything even to get the question started over the past 6 hours.

The argument follows from Step 3. You need only to argue that none of the vertices in $I$ are adjacent, but if they were, then you would not have completed Step 3 - "As long as the graph $H$ contains edges..." - which only terminates when $H$ is completely disconnected. Note also that it removes edges by removing vertices (rather than just the edge itself), therefore given vertices $u$ and $v$ in $V(H)$, if $(u,v)$ is not in $E(H)$, it was not in $E(G)$ to begin with.
Therefore for every distinct pair of vertices $u$ and $v$ in $I$, the edge $(u,v)$ is not in $G$, hence $I$ is an independent set.


text:
# An unusual cubic representation problem

• Published in 2014
In the collection
For a non-zero integer $N$, we consider the problem of finding $3$ integers $(a, b, c)$ such that $N = \frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}.$ We show that the existence of solutions is related to points of infinite order on a family of elliptic curves. We discuss strictly positive solutions and prove the surprising fact that such solutions do not exist for $N$ odd, even though there may exist solutions with one of $a, b, c$ negative. We also show that, where a strictly positive solution does exist, it can be of enormous size (trillions of digits, even in the range we consider).

### BibTeX entry

@article{AnUnusualCubicRepresentationProblem,
title = {An unusual cubic representation problem},
author = {Andrew Bremner and Allan Macleod},
abstract = {For a non-zero integer $N$, we consider the problem of finding $3$ integers
$(a, b, c)$ such that
$N = \frac{\{}a{\}}{\{}b+c{\}} + \frac{\{}b{\}}{\{}c+a{\}} + \frac{\{}c{\}}{\{}a+b{\}}.$
We show that the existence of solutions is related to points of infinite order on a family of elliptic curves. We discuss strictly positive solutions and prove the surprising fact that such solutions do not exist for $N$ odd, even though there may exist solutions with one of $a, b, c$ negative. We also show that, where a strictly positive solution does exist, it can be of enormous size (trillions of digits, even in the range we consider).},
}


text:
Page:Popular Science Monthly Volume 74.djvu/85

The most remarkable change, shown in Table II., is that of Germany, which passed from the fourth place in 1789 to the first place in 1869, and nearly quadrupled its percentage of membership during that time. The diminution of membership in France is almost equally striking, while the change in Great Britain is slight. The four countries grouped in the last line but two and the corresponding differences are: Germany, ${\displaystyle {{\ce {+}}}}$ 19; United States, ${\displaystyle {{\ce {+}}}}$ 7; Austria, ${\displaystyle {{\ce {+}}}}$6; Scandinavia, ${\displaystyle {{\ce {+}}}}$ 4. The increase in Austria is largely due to recent membership in the Prussian Academy, as shown in Table I., and is perhaps


text:
# A cricketer scored 48 runs in the 7th innings. His average score increased by 4. Find his average after the 7th innings.

22 views
in Aptitude
closed
A cricketer scored 48 runs in the 7th innings. His average score increased by 4. Find his average after the 7th innings.
1. 25
2. 20
3. 23
4. 24

by (30.0k points)
selected

Correct Answer - Option 4 : 24

Given: A cricketer scored 48 runs in the 7th innings. His average score increased by 4.

Formula: Average of n numbers a1, a2, ... an = (a1 + a2 + ... + an)/n

Calculation: Let his average up to 7th innings be x

(6x + 48)/7 = x + 4

⇒ 6x + 48 = 7x + 28

⇒ 20 = x

So, his average after 7th innings is 20 + 4 = 24


text:
Did you miss your activation email?

• October 18, 2019, 07:38 PM
• Proudly celebrating 13 years online.
• Donate now to become a lifetime supporting member of the site and get a non-expiring license key for all of our programs.

### Show Posts

This section allows you to view all posts made by this member. Note that you can only see posts made in areas you currently have access to.

### Messages - paulobrabo [ switch to compact view ]

Pages: [1] 2 3 4next
1
##### General Software Discussion / Re: Macrium Reflet Free 6.0.684
« on: June 18, 2015, 03:19 AM »
Mmmmm now the free version has differential backup and auto-verify.

Looking good

2
##### General Software Discussion / Re: jv16 PowerTools - using Indiegogo to 'fund'' open-sourcing it
« on: July 29, 2014, 03:33 PM »
Now he took the money and disappeared, leaving behind his own child (jv16 PowerTools) just like this without a word and also abandoning all of us, users of his software and, worse, trying to still make more money by sending us emails proposing to buy platinum licences of the software, well knowing that people buying it will never receive the licences nor any support.

Here:
Developer Jouni Flemming is living in Thailand
http://www.macecraft...5&p=33784#p33784

Actually the developer of jv16 PowerTools (Jouni Flemming) is living in Thailand (since april 2014) as appears from the following link provided by member Vasek.

http://www.meetup.co...p/members/140922292/

Other members of the Macecraft staff (like Veera Peltonen) have been laid off.

Read this post of member BlackSteak.
http://www.macecraft...=1&t=5554#p33781

Nobody must doubt the jv16 PowerTools story is finished and there will never be an open source version of this software.

Jouni Flemming always wanted to be (very) rich (as appears from his own words in the following link).

http://jv16.org/

Now he took the money and disappeared, leaving behind his own child (jv16 PowerTools) just like this without a word and also abandoning all of us, users of his software and, worse, trying to still make more money by sending us emails proposing to buy platinum licences of the software, well knowing that people buying it will never receive the licences nor any support.

This could be qualified as swindle.

3
##### General Software Discussion / Re: TrueCrypt alternative
« on: June 22, 2014, 11:47 PM »
In the end I strongy suspect there'll be nothing at all mysterious or sinister behind any of this. I'm guessing they were simply hired by somebody, and were either required to ditch their old opus as a condition of employment/contract - or they did it on their own as a gesture of goodwill to whomever. Probably either Microsoft or Uncle Sam.
-40hz

I can't think of anything more sinister than that!

4
##### Mini-Reviews by Members / Re: RIPT (Ript) shareable scrapbook-clipping programme - Mini-Review
« on: April 15, 2014, 05:16 AM »

5
##### Living Room / Re: Anyone here using a standing desk?
« on: April 11, 2014, 02:24 AM »
Maybe it's since we're not perfectly healthy (who is?!)  that each of us should spend a lot of time and thought looking for an optimal solution for our own condition and way of working. The way we work is in the end the way we will (or wish) to be living in the foreseeable future.

There are no fit-all solutions, but there are paradigms that we should all weigh and examine deeply. The mind is weak, but the flesh wants to find a way!

Now that I think of it, in the early morning (before 6 a.m.) I do some writing lying down on my bed, using my netbook.  For some of us a mix of different solutions will maybe work better than a single one. We humans are not known for not being complicated.

6
##### Living Room / Re: Anyone here using a standing desk?
« on: April 10, 2014, 05:47 PM »
@paulobrabo - ^Well...I guess it's a good thing I said "most of the people" and not "all of the people" huh?
-40hz

Of course!  But it's always the damn exceptions that won't let you sleep!

7
##### Living Room / Re: Anyone here using a standing desk?
« on: April 10, 2014, 03:37 PM »
Most of the people who I've heard advocate for standing desks are noticeably athletic younger people with no disabilities or old injuries to deal with.

Like her:
(see attachment in previous post)
You know the type.
-40hz

I'm certainly not her, being otherwise lazy and closer to 50 than I have ever been – but I work on my standing desk at least 8 hours a day. I read the linked article some days ago because the title caught my interest; I thought I would find a good, sound medical reason the author had discovered to kill his standing desk... and in the end it was only the pain – certainly a good reason, but a very personal one, because I've never felt any.

My story goes the other way round because I had much pain in my back... until I started to work standing. I would suggest everyone interested to have a go: use a makeshift platform to work standing some hours a day for some days. I'm far from a paragon of health, but I just can't work sitting down anymore. It feels like I am literally chained to the chair, unauthorized to move and robbed of my most sacred personal freedoms

8
##### Living Room / Re: Evernote, the bug-ridden elephant.
« on: January 08, 2014, 02:13 PM »
I don't care for Evernote, I use it but very sparsely. But boy did I lose data using Simplenote (using both Resophnotes and Cintanotes) or what. Apparently you don't have to be the size of an elephant to be bug ridden.

9
##### General Software Discussion / Re: Cobian Backup
« on: January 08, 2014, 04:04 AM »
And the first version is a beta.....
-Contro

An incredibly stable beta, which I've been using for many, many years.

But to each his own, I'm sure you'll find a solution that fits you among the many available. The problem with asking for a software recommendation is that everyone works differently, and not everything works for everyone. Most of the times you'll have to try many things and discover for yourself which one of them suits you best.

You could start here:
http://www.techsuppo...-free-backup-program
And here:
http://www.techsuppo...ndations-reviews.htm

10
##### General Software Discussion / Re: Cobian Backup
« on: January 08, 2014, 01:47 AM »
I've used Cobian backup for many years, but I also feel it keeps using more and more resources.

I have tried many alternatives (there are thousands) but I'm settling with the simplicity of bvckup (fast, free):
http://www.bvckup.com
• Real-time, periodic or manual backups
Continuously monitor folders for changes and update their backup copies immediately after the originals are modified. Or run backups at fixed time intervals.
• Delta file copying
Reduce the amount of data being transferred by copying modified parts of the files only. This speeds up the backup, in many cases - dramatically.
• Precise file replication
Copy not only the file data, but also the attributes, timestamps, NTFS security and ownership information.
• Intelligent error handling
Rest assured that an issue with a specific file will not preclude the rest of the backup from completing. The program differentiates between file-specific and global errors and handles them differently.

Version 2, which won't be free but is currently in open beta, is even cooler and still tight:
http://www.bvckup2.com

Bvckup 2 is light, robust and simple to understand.
It is also incredibly fast.

Delta copying is a crown jewel of Bvckup 2. It detects and skips over unmodified parts of the files, cutting down processing time of larger files to a fraction.

If a backup goes to- or from- a removable storage device, Bvckup 2 will monitor for device removals and insertions and will run the backup only if the original device is present. It will also automatically adjust backup locations should the original device appear under a different drive letter.

Bvckup is not a two way sync. It doesn't compress, encrypt or FTP files. Nor does it come with a restore function. It does just one thing - it replicates the contents of one directory into another - and it does this exceptionally well.

All beta users are eligible for special upgrade pricing upon production release

I like when they make them lean and mean!

11
##### Living Room / Re: Best note-taking setup with tablet and keyboard?
« on: January 03, 2014, 06:42 AM »
Hehe we keep looking. The main advantage of the netbook for me is the size. It's my digital moleskine! As my main concern is writing, I would pick up a netbook over a tablet anytime.

I do a lot of writing, most of it txts (writemonkey!) synced through dropbox. I also have some Scrivener projects, synced through dropbox. As for notes, Wiznotes takes care of keeping them always synchronized among machines. I tried simplenote more than once, but I had constant synchronization woes and lost information I wish I hadn't.

I additionally backup all of these to the amazon servers with Cloudberry Backup.

12
##### Living Room / Re: Best note-taking setup with tablet and keyboard?
« on: January 03, 2014, 05:46 AM »
@Paulo
Which netbook do you have? All the Windows (XP and 7) netbooks I tried, were not instant-on.
-fgrieser

I have an old Samsung NC215PD1 Atom 2Gb 500Gb.

You are right, a hard start will take those Windows 7 usual seconds, but after the thing is booted you may close and reopen the lid and it's really start on. The battery lasts about 7 hours, so I rarely have to boot it up, just recharge it every now and then. I use it everywhere

13
##### Living Room / Re: Best note-taking setup with tablet and keyboard?
« on: January 02, 2014, 11:46 PM »
Hence netbooks, laptops etc. that require boot-up are not suitable.
-dr_andus

You must consider that nowadays most netbooks (like my little Samsung running Windows 7 Home) don't require boot-up at all. You just open the lid and start working. In fact I've chosen a netbook instead of a tablet because I use mine mostly for writing, and the sturdiness of the keyboard was priority one in my own list of requirements.

As for notetaking, I use Wiznote -- cloud-synced but with full local access.

14
##### Mini-Reviews by Members / Re: WizNote (a PIM from China) - Mini-Review + Provisional User Forum
« on: January 02, 2014, 02:56 AM »
I haven't messed about with the plugins at all (not trialled them yet)
-IainB

You should definitely give it try; most plugins are installed and activated by default.

15
##### Mini-Reviews by Members / Re: WizNote (a PIM from China) - Mini-Review + Provisional User Forum
« on: January 01, 2014, 03:37 AM »
I'm using this and I love it!

In my Windows 7 netbook Wiznote used to perform quite slow: 3-5 seconds for the main window to appear when I activated it.

I had better results after disabling some unused plugins and restarting the program.

Go Tools > Plugin Manager and disable all unnecessary plugins.

The list of plugins I have disabled:

• Copy to another account
• CHM Maker
• Import Evernote
• Outline
• Speech
• Markdown
• Zoom
• MathJax
• Blogtools

Don't forget to restart the program!

Much faster now

16
##### General Software Discussion / Re: CryptoLocker and CryptoPrevent
« on: November 22, 2013, 12:18 PM »
Indeed, the naming is confusing, but no – you don't have to have HitmanPro (which costs money) to have your files protected by HitmanPro.Alert (free). Alert will not clean your computer from infection (you may have to use another program for that, say Malwarebytes Free/Pro), but it won't let your files be encrypted, actually stopping the infection before it can do any harm.

As for updates, as Alert is behavior based and not signature based, that shouldn't be a big problem. From the website, about HitmanPro.Alert:

• Future proof technology does not rely on malware signatures.
• Compatible with all antivirus programs and runs alongside any other security software.

17
##### General Software Discussion / Re: CryptoLocker and CryptoPrevent
« on: November 20, 2013, 01:42 PM »

does that work okay with your anti-virus? - which anti-virus?
Sounds like you dont have HitmanPro anti-malware installed as well (?)
TIA :-)
-tomos

No, no HitmanPro anti-malware here, only the free .Alert thingie with Cryptolocker prevention. And yes, it works flawlessly with my Avast 2014 Free!

18
##### General Software Discussion / Re: CryptoLocker and CryptoPrevent
« on: November 20, 2013, 09:37 AM »
There's also the beta version of HitmanPro.Alert with Cryptoguard.

http://www.surfright.nl/en/cryptoguard

HitmanPro.Alert 2.5 contains a new feature, called CryptoGuard that monitors your file system for suspicious operations. When suspicious behavior is detected, the malicious code is neutralized and your files remain safe from harm.

CryptoGuard works silently in the background at the file system level, keeping track of processes modifying your personal files. CryptoGuard works autonomously, so no user interaction is required.

CryptoGuard works at the file system level and does not conflict with full disk encryption software like BitLocker, Sophos SafeGuard or TrueCrypt.

Free! I've installed this on my father's PC...   and now it's on mine too

19
##### Living Room / Re: Making a new page of "DonationCoder's Favorite Web Sites" - suggestions?
« on: September 08, 2013, 04:48 AM »
Freeware Guide!

http://www.freeware-guide.com/

20
##### Living Room / Re: Designers discuss the new Yahoo Logo: "Logo, Bullshit and Co., Inc."
« on: September 07, 2013, 01:56 PM »
I think she watched far too many episodes of Mad Men...
-40hz

Lol, and haven't we all?

Part of the problem is that the mathematical approach should not be used in this case. Bilateral symmetry and typography generally don't work well together. Typefaces are like... faces, and we have a keen eye for those. We all have seen those photo edits where a human face looks complete, but it becomes soon clear that one of the side of the head is just mirrored... and the final effect looks often somewhat unnatural and disturbing. The same general principle works for letters.

All letters in the new logo have perfect bilateral symmetry (if you cut them vertically, one side is identical to the other), and the effect is... imbalanced:

Compare to this one, made with Hermann Zapf's Optima (which certainly inspired the new Yahoo typeface). The "Y" and "A" have personality and weight, being asymmetrical in their vertical axis:

http://en.wikipedia.org/wiki/Optima

Let's say that the new logo is far from OPTIMAL

Yahoo's old logo had its problems, but at least it was very asymmetrical

21
##### Living Room / Re: Designers discuss the new Yahoo Logo: "Logo, Bullshit and Co., Inc."
« on: September 07, 2013, 04:13 AM »
Or maybe not

The alternative logo this guy created before the reveal isn't particularly great, but I love his reaction to the final design:

Is it playful? Bevels.

Is it simple? Bevels.

Is it original? Bevels.

Is it iconic? Bevels.

Is it meaningful? Bevels.

Is it timeless? Bevels.

Is it irreverent? Bevels.

Of irreverence and elegance
https://medium.com/i...-shapes/cba88884743c

22
##### Living Room / Re: Designers discuss the new Yahoo Logo: "Logo, Bullshit and Co., Inc."
« on: September 07, 2013, 03:50 AM »
Heh, I'm a lettering and logo designer and I wholeheartedly agree with the backslash: both the logo and the post-justification for it are terrible.

Specially bullshit is the "our logo doesn't have straight lines because there aren't straight lines in nature" reasoning. The curves are so subtle, and in the web the logo will be generally applied in such small sizes, that it doesn't make any difference. The screen will render and the eye will see straight lines in 90% of the cases.

Also: bevels???   The old Yahoo logo was less 1990 than that. The 29 in-joke logos have all the advantage of being straight, one color, no gradient, no shadow, no fake 3-D.

And let me stop at that

23
« on: March 20, 2013, 05:08 PM »

24
##### Living Room / How Google believes the internet *should not be read*
« on: March 18, 2013, 05:04 AM »

I use Reader A LOT - more than any other Google product, but I'm kind of grateful for the wake up call. It reminds me that Google won't hesitate before cancelling any other service, even one that feels as "natural" as, say, blogger. Blogging is declining in usage as much as Reader, I guess.

Sorry guys, but I've got to agree with Dave Winer on this one. By Google killing its own RSS, suddenly there's new competition for that software space again, and one less space that Google won't control or censor.
-zridling

This guy I mentioned before is even more on the spot, I'd say:

25
« on: March 16, 2013, 05:16 AM »
Two more:

As one example, many people now rely on social media as a primary news source.  In many cases–especially with “bi-directional” services like Facebook ($FB) or LinkedIn ($LKND) where people only connect with “friends”–social media only surfaces content from people who are likely to share common viewpoints.  Plus, those posts are culled by mysterious algorithms (such as the algorithm controlling Facebook’s newsfeed) that further reduce exposure to diverse viewpoints.


text:
# Mathematica plots a discontinuity in piecewise function that does not exist [duplicate]

This question already has an answer here:

I have the following function defined:

IntImpTri[r1_, r2_, r_] :=
Piecewise[{
{((4/((r2 - r1)^2)) ((r^2 - r1^2)/2 - r1 (r - r1))),
r >= r1 && r < ((r1 + r2)/2)},
{(1/2 - (2/((r2 - r1)^2)) (r^2 - ((r1 + r2)/2)^2) +
(4/((r2 - r1)^2)) r2 (r - ((r1 + r2)/2))),
r >= ((r1 + r2)/2) && r < r2},
{1, r >= r2}}, 0];

I am using Mathematica 9 and I do not understand why, when I try to plot this function, which is the integral function of a triangle pulse, the figure shows an interruption in the line.

If I try the following command: Plot[IntImpTri[0, 4, r], {r, -1, 5}], I get the following output:

There is a discontinuity around x=2 but the piecewise covers everything!

-

## marked as duplicate by whuber, Sjoerd C. de Vries, m_goldberg, Artes, Guess who it is.♦Apr 30 '13 at 23:56

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

I am using Mathematica under Unix... –  Andry Apr 30 '13 at 21:40
I am not sure exactly why it is missing this point (must be something with how Plot is decided to recurse), but try increasing the PlotPoints to specify how many initial sample points to use: Plot[IntImpTri[0, 4, r], {r, -1, 5}, PlotPoints -> 300] –  chuy Apr 30 '13 at 21:45
possible duplicate of Plot showing discontinuity where it shouldn't. Also a duplicate of mathematica.stackexchange.com/questions/19877/…. For more information, do a search. –  whuber Apr 30 '13 at 22:14

## 1 Answer

Plot[IntImpTri[0, 4, r], {r, -1, 5}, Exclusions -> None]

The problem is usually caused by discontinuities in the derivatives

-


text:
I'm a lecturer at the University of Cape Town in the department of Mathematics and Applied Mathematics. I teach mathematics both at undergraduate and at honours levels and my research interests lie in the intersection of applied mathematics and many other areas of science, from biology and neuroscience to fundamental particle physics and psychology.

## Using polynomials to solve differential equations

One of the aims of MAM1000W isn’t just to teach you individual mathematical topics, but over time to allow you to see the links between these subjects. Sometimes we do this explicitly, and sometimes you should notice the connections yourself simply by seeing one topic pop up in the middle of another. As I’ve written before, so much of it is about noticing patterns.

Today in class I gave a differential equation which wouldn’t be solvable by any of the methods we have looked at.

$y''(x)+\cos(x)y'(x)+e^xy(x)=x^2$

This is second order linear but its coefficients are not constant. We don’t have any way in to solve this. We actually wanted to solve this with the initial conditions $y(0)=1$ and $y'(0)=-1$.

Actually, that’s a lie. We didn’t want to solve it, but we wanted to get an approximation for the solution close to $x=0$. This is like saying: OK, so we have a differential equation for population dynamics, or climate change, or the heating of an object, and we don’t worry too much about the very far future, but we want to know what it’s going to do in the short term.…

 How clear is this post?

## How Behavior Spreads: The Science of Complex Contagions, by Damon Centola, a review

NB. This book was sent to me as a review copy.

The idea of this book is relatively simple, but the consequences are huge, and in fact some of the ideas are far more subtle and complex than they may first appear.

Essentially this book is based on a series of experiments which Damon Centola has run, which are all related to changes in behaviour which can be tracked, and made to occur, through a social network (in the broadest sense of the word). This is the study diffusion in a network.

The fundamentals of the research lie on two distinctions: One in the complexity of a contagion/behaviour, meaning how many connections with others who have the contagion/behaviour do you need until you adopt it, and the other in the topology of the social network, meaning loosely, how much like a street where each person only talks to their neighbours, versus a small world-network where there are a lot of disparate connections does the network look like.…

## Why did we choose that range for theta when doing trig substitutions?

Remember when we are doing a trig substitution, for instance for an integral with:

$\sqrt{a^2-x^2}$

We said that we should choose $x=a\sin\theta$, which seemed reasonable, but we also said that $-\frac{\pi}{2}\le\theta\le\frac{\pi}{2}$. Where did this last bit come from?

Well, we want a couple of things to hold true. The first is that any substitution that we make, we have to be able to undo. That is, we will substitute $x$ for a function of $\theta$ but in the end we need to convert back to $x$ and so to do that we have to be able to write the inverse function of, in this case $x=a\sin\theta$. The $\sin$ function is itself not invertible because it’s not one to one, so we have to choose a range over which it is one to one. We could choose $-\frac{\pi}{2}\le\theta\le\frac{\pi}{2}$ or we could choose $\frac{\pi}{2}\le\theta\le\frac{3\pi}{2}$ (amongst an infinite set of possibilities). That would also be invertible. However, remember that we are going to end up with a term of the form:

$\sqrt{1-\sin^2\theta}=\sqrt{\cos^2\theta}$

So if we want this to simplify, we had better choose our range of $\theta$ such that $\cos\theta$ is positive, so that we can write $\sqrt{\cos^2\theta}=\cos\theta$.…

## Integrals with sec and tan when the power of tan is odd

We went through an example in class today which was

$\int tan^6\theta \sec^4\theta d\theta$

In this case we took out two powers of sec and then converted all the other $\sec$ into $latex\ tan$, which left a function of tan times $sec^2\theta d\theta$. We wanted to do this because the derivative of $\tan$ is $\sec^2$ and so we can do a simple substitution. If we have an odd power of $\tan$, we can employ a different trick. Let’s look at:

$I=\int \tan^5\theta\sec^7\theta d\theta$.

Here, sec is an odd power and so we can’t employ the same trick as before. Now we want to convert everything to a function of $\sec$ and have only a factor which is the derivative of $\sec$ left over. The derivative of $\sec$ is $\sec\tan$, so let’s try and take this out:

$I=\int \tan^5\theta\sec^7\theta d\theta=\int \tan^4\theta\sec^6\theta (\sec\theta\tan\theta)d\theta$.

Now convert the $\tan$ into $\sec$ by $\tan^2\theta=\sec^2\theta-1$:

$I=\int (\sec^2\theta-1)^2\sec^6\theta (\sec\theta\tan\theta)d\theta=\int (\sec^{10}\theta-2\sec^8\theta+\sec^6\theta) (\sec\theta\tan\theta)d\theta$

where here we have just expanded out the bracket and multiplied everything out.…

## Fundamental theorem of calculus example

We did an example today in class which I wanted to go through again here. The question was to calculate

$\frac{d}{dx}\int_a^{x^4}\sec t dt$

We spot the pattern immediately that it’s an FTC part 1 type question, but it’s not quite there yet. In the FTC part 1, the upper limit of the integral is just $x$, and not $x^4$. A question that we would be able to answer is:

$\frac{d}{dx}\int_a^{x}\sec t dt$

This would just be $\sec x$. Or, of course, we can show that in exactly the same way:

$\frac{d}{du}\int_a^{u}\sec t dt=\sec u$

That’s just changing the names of the variables, which is fine, right? But that’s not quite the question. So, how can we convert from $x^4$ to $u$? Well, how about a substitution? How about letting $x^4=u$ and seeing what happens. This is actually just a chain rule. It’s like if I asked you to calculate:

$\frac{d}{dx} g(x^4)$.

You would just say: Let $x^4=u$ and then we have:

$\frac{d}{dx} g(x^4)=\frac{du}{dx}\frac{d}{du}g(u)=4x^3 g'(u)$.…

## Calculus for the ambitious, by Tom Korner, a review, by Henri Laurie

This is a lovely book: strong emphasis on ideas; a lively sense of humour; a sure logical touch; historical detail that is accurate, relevant, yet quirky (takes some doing!). What’s not to like?

Well, there’s this: it is not easy to decide whether to recommend the book to anybody who doesn’t already know calculus. I’ll return to that. Let me start by describing why this is such a good book.

Firstly, the light touch and the clarity, which together make it wonderfully accessible. Fans of Tom Korner, including yours truly, will be happy to hear that it it as good as his “The Pleasures of Counting” and “Fourier Analysis”, two of the best books on maths ever. Like them, it discusses applications, social context and history but always in a way that supports the maths, which remains the main focus.

Secondly, the balance between rigour and intuition is superbly judged and maintained.…

## The Recamán sequence

In case you have watched the following video about the Recamán sequence.

and want to play around with it in Mathematica. Here is my code for doing so:

nums = {0};

For[i = 1, i < 66, i++,
If[nums[[-1]] – i > 0 && Position[nums, nums[[-1]] – i] === {}, nums = Append[nums, nums[[-1]] – i],
nums = Append[nums, nums[[-1]] + i]]
]

{{#[[1]], 0}, #[[2]]} & /@ Partition[Riffle[Mean[#] & /@ Partition[Riffle[nums, nums[[2 ;;]]], 2],
Abs[Differences[nums]]/2], 2];

Show[Show[
Table[Graphics[Circle[%[[i, 1]], %[[i, 2]], {(i) \[Pi], (i + 1) \[Pi]}]], {i, Length[%]}], ImageSize -> 1000], Plot[0, {x, 0, 91}],
Axes -> True]

(You may have to copy this by hand rather than copy/paste.)

This produces the following rather beautiful graphic (and answers the question posed in the video):

Evidence away my dear Watson…evidence away.

 How clear is this post?

## Music by the Numbers, From Pythagoras to Schoenberg – By Eli Maor, a review

NB. I was sent this book as a review copy.

Music by the numbers leads us on a journey, as stated in the title, from Pythagoras to Schoenberg. In many ways the endpoint is stated early on, giving us clues that a revolution in mathematical thinking about musical scales will be encountered in the early twentieth century. Indeed the journey through musical practice, mathematics, physics and the biology of hearing is woven rather beautifully together, giving the account of our step by step explorations of tonal systems and their links to the physics of vibration. The development of calculus and the triumph of Fourier take as from the somewhat numerological and empiric realms of musical experimentation to the age of a true understanding of timbre – the way different instruments express harmonics and their overtones in different admixtures. A lot of emphasis is placed on the development of scales based on subtly different frequency ratios, which were developed over the years (particularly within European music, non-European music being given only very brief comment) to balance the physical, mathematical and aesthetic qualities of the various possible tunings of instruments.…

## Kovalevskaia research grants for female mathematicians in Southern African region

 How clear is this post?


text:
# Fukushima Management and Government Performance

1. ### NUCENG

916
This seems to be a high interest topic and nobady else started it so I will. If previous discussion is evidence of a future trend please put on your asbestos underwear before you post.

Before you start throwing knives, I will concede that there have been serious mistakes and defective communication during the past 6 weeks. There will have to be an accounting for those lapses. Keep in mind that the Japanese culture is also part of this. It doesn't excuse them, but it may be part of the problem which will be hard to change. Try to put yourself in their shoes during the early hours of this esvent. Be honest can you guarantee you could have prevented this?

I have sent the following in two private messages as my response to the general distrust and fear of the "nuclear industry." As part of that industry I have seen good people and bad, competent and incompetent, dedicated and lazy. In short they are human beings.

"So why should you trust these people to do the right thing? To me, it seems the public looks at the nuclear "industry" as a small group of old white guys sitting around a conference room in a skyscraper hundreds of miles away, trying to squeeze more profit out of a plant by cutting corners, threatening the workers, and lying to the government and the public.

The best argument I can offer is that the engineers and managers at nuclear plants LIVE there too. They have homes, children, and friends that they value and want to protect. Yes there have been cases where managers have retaliated against workers who have raised safety questions, but the reason we know that is that those managers have often been prosecuted or fired as a result. In general most of my colleagues were not reluctant to raise safety issues, partly because of whistle-blower protections, but mostly because they want to protect themselves, their families, and their communities."

I know there are evil people: Hitler, Stalin, Pol Pot, the Borgias, Charlie Manson. I can say confidently that I have never met one of those and I certainly have never worked with one. Okay, now I'll call the fire department to stand by. In the words of Breaker Morant "Shoot straight, you B******s.

### Staff: Mentor

This has been my experience as well. Folks at NPPs have a personal stake in the safe operation - namely their families, friends and neighbors.

3. ### clancy688

546
They did grave mistakes, both government and TEPCO. But still they are trying their damn best to resolve the situation.

People who are constantly bashing TEPCO and the government for their disaster response don't seem to realize that both gain nothing in actively hampering relief efforts.
In Germany you hear nothing, absolutely nothing positive regarding TEPCO and the japanese government. On the contrary, they are depicted as incompetent, lying fools who don't want to resolve anything. I'm seriously annoyed by that attitude of my people.

4. ### Dmytry

505
Well, the cutting corners happens. That's how the boral sheet swelling problem was solved. By cutting corners. :)

I would say, there are many entirely different classes involved:
Owners. They own this stuff. How they came to be this wealthy? Many, by investing.
White collar businesspeople who manage owner's investments, buying and selling stock etc.
White collar management of the company, in skyscrapers hundreds of miles away. Their job is to maximize profit. They're in a control of a big power utility - which has power lines, nuclear reactors, coal plants, etc. These guys have no clue and greatly exaggerate safety figures and believe in those figures.
Engineers of varying levels. That part may be very thin. There are engineers employed by the power company, and the engineers employed for regulation.
Technicians and low level workers. In Japan, very low level, judging by wages.
The list is by no means comprehensive or detailed.

I do not trust the management to do the right thing. And they run this show. They can screen for potential whistleblowers (with some euphemism such as testing for 'teamwork attitude').

On the topic of trust - if only it was so simple. The psychological research shows that people tend to shy away the responsibility and choose inaction.
Watch this - the people's behaviour - unrelated to nuclear power, but so related to the trust:
http://abcnews.go.com/WhatWouldYouDo/story?id=6613617&page=1
(notably, not a single person did the right thing - calling the police and informing the woman)
http://en.wikipedia.org/wiki/Milgram_experiment
It takes a lot of willpower, a lot of guts to stand out and blow the whistle. Those qualities can be screened against when hiring if they interfere with profitability, and its very easy to say that it is about team work, or about background, or what ever. Military types - I really can't trust military types. Who would willingly join organization where you're being bossed around all the time, with very strict hierarchy?

It is all nice to say that so far nuclear power did not claim many lives - but imagine that Japan was not about 25% nuclear but 75% nuclear, at the time of tsunami, with same quality of power plants. It is kind of obvious enough that 3 Fukushimas at once would be far worse than 3 times Fukushima, as a: it'd be dominated by worst case out of 9 reactors and 12 spent fuel pools, b: there would be far fewer resources for handling it.

Last edited: Apr 24, 2011
5. ### NUCENG

916
Dmytry, I have reordered this to address similar things together. I hope I haven't distorted your position.

I'll accept that there are investors. I don't think any US nuclear utility is privately owned. That is because until recently utilities were strictly regulated. Executives responsible for operation of nuclear plants are required to sign correspondence with the NRC under Oath and Affirmation which puts them under penalty of law for the completeness and accuracy of the content. I have never seen one of them that doesn't take that seriously.

Yep I see the humor- cutting corners Hee Hee.

As to cutting corners or squeezing the plant for profits, every plant has two or sometimes more resident NRC inspectors constantly watching for signs of equipment, personnel, maintenance and safety. NRC conducts frequent team inspections and reviews the hundreds of reports and submittals required each year. Then there is INPO, the Institute of Nuclear Power Operations, conducting surveillance of plant conditions, operating excellence, safety, procedural compliance and use of operating experiences from other plants. There is NEIL, the insurer, looking for conditions which would decrease plant reliability and safety. Neil insurance rates are set accordingly. We have Owners groups, the Electrical Power Research Institute (EPRI), the Nuclear Energy Institute (NEI) working to share improvements and efforts to address issues. Plant Managers and Operators are Licensed and can be held individually responsible for negligence or misconduct. Professional Engineers have standards and ethics to meet or they can lose their licenses. Add to those steps, procedures for just about everything, second checking and independent verification of everything from valve positioning, to surveillance testing, to annalysis. Add formal corrective action programs. How long would a coverup last? In the United States technicians and laborers in the nuclear industry are well paid.

This list, too, is not comprehensive and I'm sure others can add more examples.

I can't argue that those things happened. But you pointed out these events were not related to nuclear power in the US. You won't accept this, but my experience is that trust is justified in people I have known in the industry.

Actually once a person blows the whistle he, or she, is protected by law from retribution, harrassment, or retaliation. This protection has been more abused by the people that have applied for this protection than the managers and companies. When a manager or executive or supervisor is found to have violared these protections he can be banned from work in the industry or even jailed. Also he is immediately vulnerable to civil suits.

Your statements above are self-contradictory. You say it takes courage to stand up for what is right and then reject military veterans who are most likely to have exactly that kind of courage and discipline.

As bad as the current tragedy is, I agree that would be worse. I'm hoping we can learn from this event and make that less likely.

Last edited by a moderator: Apr 25, 2011
6. ### IowaNewbie

10
While I agree there is regulation and regular inspection, I do have questions about this. Are the resident NRC inspectors paid for by NRC or by the Plant payroll? We have seen other regulated industries where regulators are accountable to federal agencies, but are payrolled by the industries. In situations like this, the question of accountability becomes one of 'Who puts the food on your family's table?"

Also, it is in the best interest of the NRC for nuclear plants to continue in the US. If all nuclear plants were phased out in the US - so would many of the commission's employment positions. Again, "Who puts the food on your family's table?"

Now pretty much replace NRC with INPO, NEIL, EPRI, NEI. If all those agencies/orgs/companies/panels/etc are 100% completely independent of the nuclear plants and the decisions those plants make - fantastic - that's one set of safeguards that are working. But we know that without those nuclear plants - they would be downsized and/or die off.

Some corners are cut in every industry every day - because they are seen 'less detrimental' than others that could be cut. We also know that the good-ol' boy network exists in every industry: as in "Bob, I'll give you 2 days to bring this back up to snuff ... I'll be back and I'll write up whatever I see. " It's all human nature. And the further the Executive Board lives from the industry they manage - the more likely they are to be open to (or to think up) cost- and corner- cutting ideas.

In a perfect world - with perfect people - nuclear power is the perfect choice. But almost nothing in our human experience is perfect.

7. ### NUCENG

916
NRC inspectors, including the resident inspectors are paid federal employees. NRC is partially funded by fes from the industry and partly out of apportions from Congress. Commissioners are appointed by the President and Confirmed by the US Senate.

The other organizations are funded by the industry. Admittedly that raises a possibility of colusion or inflence. I don't know what you do for a living, but let me ask you this, "Do you try to give an honest day's work. Do you try to do the right thing?" The fact that you are here asking questions means that you care. Would it really surprise you that most people in the nuclear industry have the same answers to those questions?

8. ### IowaNewbie

10
I work in technical theatre and political data management. Yes, I agree that most do have the same "Yes" answers to those questions.

But then speaking of theatre ... "Spiderman" Broadway musical, comes to mind when there are safety questions in that industry. The only people that have been hurt are those involved in the show, by the decisions that have been made. They all have appeared to have followed industry and legal guidelines - yet ...

Do I need to go into political officials and their examples?

It's about bad judgment not bad intent. And sometimes, bad judgment isn't known until after the ramifications of the decisions have come full-force. And that is really what we are dealing with here - when not dealing with very rare instances of collusion. Problem is - with theatre - bad judgment usually just closes a show ... but with nuclear power - the results can end up like Chernobyl or Fukushima.

Bringing this back to Fukushima - that is what appears to have occurred in light with this disaster - bad judgment, not necessarily collusion. There were a few bad judgments prior to, including not having diesel generators at high enough elevation. But much of what will be considered (or already considered) bad judgments in reaction to the disaster - initial dismissal of concerns, slow to evacuate or inappropriate evacuation, not having robots at-the-ready (because they decided not to build any years ago), not air-dropping enough personal rad monitors for staff on site until caught by the press, etc etc etc ...

They all appear intended well - but if we look at the delay of salt water cooling decision - why was it delayed?  - they were trying to hedge their bets and not 'ruin' their reactor. What really should have been the first thought? "Damn the torpedoes and full steam ahead" - or - "Damn the reactor - get that water in there and cool it down ... NOW."

9. ### Dmytry

505

Last edited: Apr 25, 2011
10. ### Dmytry

505
Also, consider Chernobyl. Nobody was being evil there. The experiment was important to safety. To surviving 2 minutes right after blackout, when decay heat is very bad, while backup generators start. To the best knowledge of people responsible, at the time, it was safe to perform outside the specified parameters.
Graphite tipped control rods were graphite tipped to increase control range and to increase fuel burn-up in the bottom part of core. Not because someone wanted to blow up a reactor.
End result: worst accident in the history. Maybe to be de-rated to second worst in a year time when Fukushima is properly investigated.

Consider the Fukushima. Nobody wanted to build unsafe reactors. Yet it so happened - and they never funded their own equivalent of KHG or INTRA because they grossly over-estimated safety of their plants, they have grossly underestimated the tsunami, they had electrical stuff in the floodable basement. To prevent this takes something more than simple naive notion of honesty and good will.
To prevent this, takes being honest with oneself - and a lot of people are very dishonest with themselves. People routinely deceive themselves. Especially when it comes to safety. It is so easy not to think uncomfortable things. There's nobody in this whole world whom I really trust not to self deceive at all. Not even myself. Everyone is prone to self deception. And there's very, very few people who i trust to think - seriously think - to see if their action is moral or immoral. I don't trust people to recognize immorality of actions their consider, when it is in the slightest mentally demanding. When the immorality is in the slightest non straightforward. When one can make oneself believe that its ok.

http://www.fotuva.org/feynman/challenger-appendix.html
Managers believing in one in 100 000 figures.

Last edited: Apr 25, 2011
11. ### Danuta

100
Even disregarding every other glaringly negligent thing I think TEPCO is guilty of, at least I would have taken this into account:

Tectonic setting---Pacific "Ring of Fire", same as Japan
Chilean earthquake and tsunami---May 22, 1960
Earthquake magnitude---9.5, strongest ever recorded
Tsunami classification---earthquake generated 25 meter waves

And Japan is much more seismically active than Chile. Furthermore, the Fuku plant is built on Japan"s most seismically active coast(east). The Chilean mega-earthquake was only 50 years ago.

Let's start with this little bit of TEPCO's logic-and-probability defiance, before all else.

Last edited: Apr 25, 2011
12. ### Danuta

100
So what? It is the DUTY of both government and the power company that owns the thing to do their damn best to resolve the problem. You want someone to give them a medal for persisting to fix their grave mistakes maybe? High risk behaviour=Maximum profits=Taking the searing heat if TSHTF. I don't know how much money they saved through corner cutting but estimates for the clean up go from conservative billions to perhaps more realistic trillions of yen. Not quite living up to the nuclear industry's spiel about "clean and economical", is it?

Last edited: Apr 25, 2011
13. ### ascot317

65
See, "trying one's best" might not be sufficient, because it's limited by one's abilities.

I'm quite sure the tech guys at the plant do the best to their abilities. Their abilities are the result of their training and intelligence. They're (probably) trained to maintain and run a nuclear plant. They're, however, not trained to deal with the current situation. And they're weren't exactly equipped for it, either. Plastic bags instead of rubber boots, dosimeters instead of proper counters, and only one for a group of people?

Tepco's managers might try to do their best, too. But then, they're managers, whose job it is to run a company efficiently. A disaster managers can deal with is when their company is in financial problems. However, this problem goes well beyond that. If they don't have an engineering/physics background, they will have little understanding of the current situation (and they likely won't even see it that way!). Yet, they're the ones who have to decide.
They usually have advisors: lawyers and engineers (hopefully more of the latter). However, due to the Japanese culture, these subordinates are in a peculiar situation. They might not be able to express their opinion as freely as needed. And if they do, their bosses might just say "Hai, so desu" ("Yes, so it is", but often more like, "yeah, whatever").

The problem is, the guys who really have the skills to deal with such a difficult situation are usually stuck in between the tech guys and the top management.

And most of these guys seem to be stuck within their "box", too. Do you guys still remember the lab results showing quantities of 134I? These were declared "faulty" by someone, saying "the reactors are shut down, how would something go critical"?

The decision not to accept foreign high-tech-help (most of the accepted help is rather low-tech) is a similar issue. They could have had highly specialised robots driving through the plants weeks ago. Instead, they taped a counter to a pimped EOD-robot. They could have had a lab with trained staff on site. Instead, it takes hours to even reach a lab. And in that lab, workers apparently have trouble with their job. They find highly active debris (300-900mSv/h) and put it away, without further analyzing it. Driving water samples to a lab works, but not concrete debris.

The disaster management we're seeing here is a problem.

People seldomly step down when they notice their own incompetence. And they even more seldomly notice their incompetence themselves.

14. ### NUCENG

916
Danuta, it looks like you have done your homework. The Valdivia is the most intense earthquake ever recorded. Your numbers for maximum runup of the tsunami are what I found too and 9.5 or 9.6 for Magnitude.

Runup in Hawaii was about 12 m.

Runup in Honshu was 5.5 m (close to the 5.7 m design basis at Fukushima.

Now we have a 9.0 Magnitude earthquake off Honshu and locally a 14 m runup at the Fukushima.

Scientists tell you that the difference in runup locally between Valdivia and the recent Japanese earthquake is due to the fact that Japan has a longer shoal area off its east coast compared to Chile which has a very short shoaling area on its west coast causing much higher amplification of waves coming ashore.

Dmytry, please join in on this as well. You have asked me to address hypothetical conditions. Now its my turn.I am going to ask you to be an engineer.

What height should the wall be at the Onagawa plant which is still operating? I will ask you to explain your answer only in terms of spending money on this wall versus building additional breakwalls and special shelters and warning systems along the coast where perople were killed by this tsunami. If you choose to build the wall to 15 m (just over the size of this tsunami you will be able to save an additional 500 lives in a similar event. If you chose to build it to 25 m to match the Chile tsunami the number of lives saved drops to 400.

This is not a trick question. There are real consequences to design choices. Budgets are not unlimited. If this is unfair assume that each meter costs only one life. Or even easier. Each meter of wall height means that there will be another \$500,000 in property damage that won't be prevented.

Now once you pick your height for the wall, and it has been built, a scientist comes up to you and shows you this report:

http://www.es.ucsc.edu/~ward/papers/single.pdf

He tells you that he has used this method and he came up with a vulnerability to a landslide tsunami in New Zealand that had not been mapped before. He predicts that there have been 68 landslides in that area over 20 million years that could produce a tsunami of 35 meters on the coast of Honshu. He estimates that there is a now a 1:5,000 per year possibility of a similar slide. If you decide not to do anything he tells you he will take it to the regulators and the press. What do you do now?

I know this situation I'm asking you to think about is hypothetical, but it is fair, because it is similar to the choice of a 5.7 m wall at Fukushima based on a historical maximum runup of 5.5 m. If they knew of a probability of a tsunami greater than that, you are now in the same position they were.

Dmytry, Danuta, You both care deeply about nuclear safety or you wouldn't be here. So do I. and so do 99.9% of my colleagues. (I can't put any more 9s on that because I don't know everybody in the industry.

Dmytry doesn't trust us. That is good. Watch us like a hawk. In the US we have lots of people and organizations opposed to nuclear power who watch everything we do. If you don't live in the US, I hope that is true where you are as well.

15. ### Dmytry

505
http://en.wikipedia.org/wiki/Historic_tsunamis
tsunamis as tall as 50 meters happened in Japan during recorded history. I don't know where you got historical maximum runup of 5.5 meters? Are you confusing open-sea height with run-up?
edit: best yet. Some place was hit by 30 meters tsunami as recently as in 1993.

At very least: maximum runup on the entire coast over recorded history (NOT just at the reactor site), times 2 for safety factor (takes care of various discoveries such as what you linked). Maybe recalculated run-up for particular near-coast geometry, but only if the fluid simulation model can be trusted not to underestimate.
The resulting run-up height would be well over 50 meters.

Probably, that figure would make construction of nuclear power plant impossible at that location. Probably it would have to be built higher uphill, and have some sort of artificial lake for coolant water reserve + pumps to pump water in. Expensive.
The management would never allow that. The plant has to be build no matter what, and there is a limited budget. The height would be absolute minimum they can get away with. Something like smallest possible estimate of maximum recorded historical run-up on this particular single location, with a tiny safety factor. Then, if you choose a location that was never hit by strong tsunami due to quake never happening near it, you can get away with minimal protection, even though that location is not necessarily any safer than a location which was hit by some really tall tsunami a few hundred years ago.

For the city - well, well, I'd let sides present their argument, I'd inform people of the historical tsunamis (which can be VERY tall), I'd rather the people decide, do they want to together pay for the wall, or do they want to go without the wall. The problem with city is that it already exists. Also, it is not a communism there in Japan. No central planning. It's one group of people responsible for building a safe NPP, and another group responsible for adding a wall for existing city, and you have no business using pre-existing risks to justify the risk you add when you construct a nuclear power plant. In my eyes, if you have an inclination to use pre-existing risks to justify the extra risk you are responsible for, you are not to be trusted with safety.
The ordinary immoral person is so due to ability to justify own actions and see them as moral. "Looking at big picture" is a common theme.

Last edited: Apr 25, 2011
16. ### Danuta

100
What height should the walls be at Fuku and Onagawa. That is the engineering question.

Thank goodness this is a forum and I don't have to write up a few hundred pages of this and that, as would be mandatory in any industry. My answer is hence brief. I would not build a nuclear power station the likes of Fuku or Onagawa on the eastern shore of Japan where they stand now. You couldn't make me. (although I've always wanted an Italian villa of my own, but we won't go there). All other calculations are useless then.

Dmytry is right about historical maximum for Japanese coastal tsunami being 50 meters, even more, but every nuclear industry person I spoke to kept telling me that was looooong ago in the 1700's and the probability of it happening again could not realistically be taken into account. So I mentioned something more recent. No one from the industry likes to bring up the Chilean quake.

Last edited: Apr 25, 2011
17. ### Dmytry

505
For more recent, 30 meters in 1933 .
http://en.wikipedia.org/wiki/1933_Sanriku_earthquake
and if you read the list of tsunamis on that page, there's awful lot MUCH taller than 5.5 meters. My understanding is that the maximum is localized and it is thus easy to find spots with small local historical maximum (either due to lack of nearby quake or lack of historical recording), which are nonetheless not necessarily any safer.
There may also be safer spots due to geometry, but verifying that a spot is safe, with back-then computing technology, would have been very expensive. It is very expensive even now.
Fluid simulation is complicated, and fluid simulation that is guaranteed not to underestimate, is very difficult - I do not even know how you'd assure that. Software also costs money and it could be cheaper to just assume maximum * safety factor than to obtain more accurate estimate that can be trusted.

Last edited: Apr 25, 2011
18. ### NUCENG

916
Non-responsive. If I can summarize your answer You will impose absolute protection standards for the nuclear plant, but the general population will simply be told they are at risk. Really? And you call ME immoral? Your answer is that they can all die as long as they don't die from radiation.

Instead of answering that question and showing that you understand that there are limits to how much risk we can eliminate, you choose the Kobeyashi Maru way out by changing the question and calling me names.

You sit there telling us how simple the answers are and that the reason the problems exist is that we can't be trusted. Everybody is wrong except Dmytry. That is the definition of intellectual dishonesty.

19. ### NUCENG

916
Also non-responsive. See my response to Dmytry. I am not trying to tell you there is nothing to improve in managing and operating nuclear power plants. I am trying to help you understand how complicated decisions can become. Hindsight is 20/20 and the people in the cheap seats always know better than the coach on the field.

20. ### Danuta

100
Nuceng, I would never have agreed to build those reactors where they stand. Neva'. Nor would a lot of people. One reason why I run my own business is so nobody can tell me to do what I don't want to do and threaten me with loss of my job if I don't do it. Been there. I think I know how complicated decisions can become without your helping me understand. I have never been in the cheap seats, by the way, so I hope you are not referring to me.

Edit: Seriously, who would put six reactors in close proximity of each other smack dab in the middle of the world's earthquake and tsunami central? On earthquake and tsunami central's eastern shore no less!! NOT ME.

Last edited: Apr 25, 2011


text:
Implementing T9 with 1 MB RAM

Recommended Posts

Hi guys, i would like to talk about what i'm going to code, cause i need some suggestions :) Embedded platform, RAM<1MB avaible, cpu < 100 Mhz. I'm gonna write a T9 for that embedded system, but i'm sure i will encounter problems with the ram: i need to use as less RAM as i can, cause i need all the ram for the main program. What i would do: Load the dictionary into the RAM, then use some simple string comparing to find the nearest 4/5 words. But this is a problem: the dictionary could be very big, using too much RAM. Any ideas on another way to do this?

Share on other sites
db on file ordered.
binary search (on file) and load only needed data in real time.

Share on other sites
Quote:
 Original post by feal87db on file ordered.binary search (on file) and load only needed data in real time.

I forgot to say that the "disk" is a memory stick, and access to it is damn slow

Share on other sites
Quote:
Original post by roby65
Quote:
 Original post by feal87db on file ordered.binary search (on file) and load only needed data in real time.

I forgot to say that the "disk" is a memory stick, and access to it is damn slow

i've done a similiar app for an old (dr.dos only) PDT from symbol,and works fast. speed is not necessary, seeks times are. do a check

Share on other sites
Quote:
 Original post by feal87i've done a similiar app for an old (dr.dos only) PDT from symbol,and works fast. speed is not necessary, seeks times are. do a check

So, should i load words from file everytime the user types anything?

Share on other sites
Quote:
Original post by roby65
Quote:
 Original post by feal87i've done a similiar app for an old (dr.dos only) PDT from symbol,and works fast. speed is not necessary, seeks times are. do a check

So, should i load words from file everytime the user types anything?

Yep,only the needed words (5-6) using a binary search on file.

Share on other sites
Instead of a full blown dictionary (that is, if you really mean something like a c++-map, c#-dictionary, of similar associative arrays/containers), you could build something like this (pseudo-code), with keys only:

const num_letters = ...;Entry {    Entry *next[num_letters];};

yielding a structure like

              +-------A--------+          +---B---+        +---L---+          E       N        L       P          R       O        E       H          R       R        G       A          A       M        O          T       A        R          I       L        I          O                C          N

Unsupported letters would just be NULL, and if you are careful, lookup per Entry is O(const).

If even this key-only structure is too much, you could still cut it off at some level (i.e. for very long or uncommon words) and then load from disk.

Not trivial, but then you are not on a trivial system. Also don't forget that 1 MiB = 1024 KiB = 1048576 Byte, i.e., if you do it non-naive, then that's plenty of space.

sidenote: You are aware of that T9 is a patented "idea"?

Share on other sites
What phresnel is talking about is called a trie.

Share on other sites
If you have some cycles to waste, you can also make it more compact:

struct Letters {        bool a:1, b:1, c:1, d:1, e:1, f:1, g:1;        bool h:1, i:1, j:1, k:1, l:1, m:1, n:1;        bool o:1, p:1, q:1, r:1, s:1, t:1, u:1;        bool v:1, w:1, x:1, y:1, z:1;};struct Node {        Letters letters;        Node *children;};

This would be 8 bytes per node on x86.

E.g., when you have a node with a, k, x set, then children[0] would be your a node, children[1] would be your k node, children[2] would be your x node.

Of course you should add some helper functions to that structure, like size(), char operator[](size_t), etc, otherwise your code gets scrambled ;)

Quote:
 Original post by alvaroWhat phresnel is talking about is called a trie.

Tbh, I didn't know that it has a name :D

Create an account

Register a new account

• Forum Statistics

• Total Topics
628367
• Total Posts
2982279

• 10
• 9
• 13
• 24
• 11


text:
# Two Normal Subgroups Intersecting Trivially Commute Each Other

## Problem 196

Let $G$ be a group. Assume that $H$ and $K$ are both normal subgroups of $G$ and $H \cap K=1$. Then for any elements $h \in H$ and $k\in K$, show that $hk=kh$.

## Proof.

It suffices to show that $h^{-1}k^{-1}hk \in H \cap K$.
In fact, if this it true then we have $h^{-1}k^{-1}hk=1$, and thus $hk=kh$.

Since $h\in H$ and $H$ is a normal subgroup of $G$, we see that the conjugate $k^{-1}hk\in H$.
Thus we have
$h^{-1}k^{-1}hk =h^{-1}(k^{-1}hk)\in H. \tag{*}$

Also, since $k^{-1}\in K$ and $K$ is a normal subgroup of $G$, we have the conjugate $h^{-1}k^{-1}h\in K$.
Hence, we see that
$h^{-1}k^{-1}hk =(h^{-1}k^{-1}h)k\in K. \tag{**}$

From (*) and (**), we see that the element $h^{-1}k^{-1}hk$ is in both $H$ and $K$, hence in $H\cap K$ as claimed.

### More from my site

• Abelian Normal Subgroup, Intersection, and Product of Groups Let $G$ be a group and let $A$ be an abelian subgroup of $G$ with $A \triangleleft G$. (That is, $A$ is a normal subgroup of $G$.) If $B$ is any subgroup of $G$, then show that $A \cap B \triangleleft AB.$   Proof. First of all, since $A \triangleleft G$, the […]
• If a Sylow Subgroup is Normal in a Normal Subgroup, it is a Normal Subgroup Let $G$ be a finite group. Suppose that $p$ is a prime number that divides the order of $G$. Let $N$ be a normal subgroup of $G$ and let $P$ be a $p$-Sylow subgroup of $G$. Show that if $P$ is normal in $N$, then $P$ is a normal subgroup of $G$.   Hint. It follows from […]
• Two Quotients Groups are Abelian then Intersection Quotient is Abelian Let $K, N$ be normal subgroups of a group $G$. Suppose that the quotient groups $G/K$ and $G/N$ are both abelian groups. Then show that the group $G/(K \cap N)$ is also an abelian group.     Hint. We use the following fact to prove the problem. Lemma: For a […]
• Conjugate of the Centralizer of a Set is the Centralizer of the Conjugate of the Set Let $X$ be a subset of a group $G$. Let $C_G(X)$ be the centralizer subgroup of $X$ in $G$. For any $g \in G$, show that $gC_G(X)g^{-1}=C_G(gXg^{-1})$.   Proof. $(\subset)$ We first show that $gC_G(X)g^{-1} \subset C_G(gXg^{-1})$. Take any $h\in C_G(X)$. Then for […]
• Group Generated by Commutators of Two Normal Subgroups is a Normal Subgroup Let $G$ be a group and $H$ and $K$ be subgroups of $G$. For $h \in H$, and $k \in K$, we define the commutator $[h, k]:=hkh^{-1}k^{-1}$. Let $[H,K]$ be a subgroup of $G$ generated by all such commutators. Show that if $H$ and $K$ are normal subgroups of $G$, then the subgroup […]
• Commutator Subgroup and Abelian Quotient Group Let $G$ be a group and let $D(G)=[G,G]$ be the commutator subgroup of $G$. Let $N$ be a subgroup of $G$. Prove that the subgroup $N$ is normal in $G$ and $G/N$ is an abelian group if and only if $N \supset D(G)$.   Definitions. Recall that for any $a, b \in G$, the […]
• Any Subgroup of Index 2 in a Finite Group is Normal Show that any subgroup of index $2$ in a group is a normal subgroup. Hint. Left (right) cosets partition the group into disjoint sets. Consider both left and right cosets. Proof. Let $H$ be a subgroup of index $2$ in a group $G$. Let $e \in G$ be the identity […]
• The Preimage of a Normal Subgroup Under a Group Homomorphism is Normal Let $G$ and $G'$ be groups and let $f:G \to G'$ be a group homomorphism. If $H'$ is a normal subgroup of the group $G'$, then show that $H=f^{-1}(H')$ is a normal subgroup of the group $G$.   Proof. We prove that $H$ is normal in $G$. (The fact that $H$ is a subgroup […]

#### You may also like...

##### Abelian Normal Subgroup, Intersection, and Product of Groups

Let $G$ be a group and let $A$ be an abelian subgroup of $G$ with $A \triangleleft G$. (That is,...

Close


text:
# How to use hfill and underbrace together

I'm basically trying to achieve what was answered in How to make nested table span all underlying cells but this time with an horizontal brace under 1 2 3. But as soon as I use \underbrace, 1 2 3 collaps. It seems like \underbrace is cancelling the effect of \hfill.

-

\documentclass{article}
\begin{document}
\noindent
\makebox[0.75\textwidth]{left\hfill right}\\
$\underbrace{\makebox[0.75\textwidth]{1\hfill2\hfill3}}_{abc}$

\end{document}

and the same with a tabular of an unknown width:

\documentclass{article}
\newsavebox\TBox
\begin{document}

\savebox\TBox{%
\begin{tabular}{lcr}
left & & right\\
l & center & r\\
\end{tabular}}

\noindent\usebox\TBox\\
$\underbrace{\makebox[\wd\TBox]{\kern\tabcolsep% l\hfill2\hfill r\kern\tabcolsep}}_{abc}$

\end{document}

-
Sorry, your answer is useless to me because I'm inside of a table. And I cannot use \textwidth a I don't know the number of cells in advance. –  Dejan Jan 4 '12 at 10:19
@Dejan: see edited answer –  Herbert Jan 4 '12 at 10:35

To keep the width of the "box" that contains the "1 2 3" elements from collapsing, you could use the \makebox[<width>]{<text>} command. To use this command, you have to tell LaTeX how wide this box should be. In the MWE below, I create a length variable, \tabularwidth, to store the value of the box's intended width. In addition, I use the tabular* rather than the tabular environment in order to instruct LaTeX to set the width of the tabular environment to the same value.

\documentclass{article}
\usepackage{amsmath}
\newlength\tabularwidth
\setlength\tabularwidth{0.5\textwidth} %% or whatever value you want
\begin{document}
\noindent
\begin{tabular*}{\tabularwidth}{l@{\extracolsep{\fill}}r}
some text & more text \\
\multicolumn{2}{l}{$\underbrace{ \makebox[\tabularwidth]{1 \hfill 2 \hfill 3}}_{\text{abc}}$} \\
\end{tabular*}
\end{document}

Addendum: If you can't (or don't want to) set the width of the tabular environment in advance and prefer to go with whatever width LaTeX comes up with when it goes about constructing the tabular environment, you may want to proceed as follows. You first construct an "invisible box" of the same width as the material that's supposed to get the underbrace material, and you then save the resulting box's width as a length parameter. Finally, this length parameter is used in the subsequent construction of the actual tabular environment. The revised MWE looks like this:

\documentclass{article}
\usepackage{amsmath}
\newlength\UBwidth % "UB" stands for "underbrace"
\newsavebox\UBbox

\begin{document}

% use TeX's \savebox command to construct a box whose width is of interest
\savebox\UBbox{%
\begin{tabular}{lr}
some text & more text \\ % assume this is the relevant line of the table
\end{tabular}}
\setlength\UBwidth{\wd\UBbox} % save width of \UBbox

\noindent
\begin{tabular}{lr}
some text & more text \\
\multicolumn{2}{l}{$\underbrace{ \makebox[\UBwidth]{1 \hfill 2 \hfill 3}}_{\text{abc}}$} \\
\end{tabular}
\end{document}

If this approach seems a bit convoluted to you, rest assured that I agree with you. However, taking this approach (or some other method that generates the width) is required because LaTeX does not provide a simple mechanism for retrieving a tabular environment's overall width (or the width of any non-empty subset of columns of a tabular environment) in "real time," i.e., while the tabular environment is still being built up. Incidentally, that's also why, in my first answer, I suggested you take the tabular* rather than the tabular approach...

-
I would prefer that Tex determines the optimal width of the table instead of me. I'm creating the tex code dynamically so I cannot know in advance. Is there a solution that works without having to specify the table width? –  Dejan Jan 4 '12 at 10:22
@Dejan: I'm writing an addendum to my answer to address this follow-up question. –  Mico Jan 4 '12 at 11:21
Thank you very much for your efforts. However, my case is in reality even more complicated as the multicolumns do not necessarily span all columns. The multicolumns can be anywhere in the table having any count of columns. Also, the columns are not equal sized. –  Dejan Jan 4 '12 at 15:48
@Dejan: In this case, I suggest you either edit/augment your original question or post a new question with more specific information about the work you need to get done. By the way, the code I posted does not require the underlying columns to be of equal width. –  Mico Jan 4 '12 at 17:20


text:
• ### An algorithm for the reconstruction of high-energy neutrino-induced particle showers and its application to the ANTARES neutrino telescope(1703.02432)

June 28, 2017 astro-ph.HE
A novel algorithm to reconstruct neutrino-induced particle showers within the ANTARES neutrino telescope is presented. The method achieves a median angular resolution of $6^\circ$ for shower energies below 100 TeV. Applying this algorithm to 6 years of data taken with the ANTARES detector, 8 events with reconstructed shower energies above 10 TeV are observed. This is consistent with the expectation of about 5 events from atmospheric backgrounds, but also compatible with diffuse astrophysical flux measurements by the IceCube collaboration, from which 2 - 4 additional events are expected. A 90% C.L. upper limit on the diffuse astrophysical neutrino flux with a value per neutrino flavour of $E^2\cdot \Phi^{90\%} = 4.9 \cdot 10^{-8}$ GeV $\cdot$ cm$^{-2} \cdot$ s$^{-1} \cdot$ sr$^{-1}$ is set, applicable to the energy range from 23 TeV to 7.8 PeV, assuming an unbroken $E^{-2}$ spectrum and neutrino flavour equipartition at Earth.
• ### Stacked search for time shifted high energy neutrinos from gamma ray bursts with the ANTARES neutrino telescope(1608.08840)

Oct. 20, 2016 astro-ph.HE
A search for high-energy neutrino emission correlated with gamma-ray bursts outside the electromagnetic prompt-emission time window is presented. Using a stacking approach of the time delays between reported gamma-ray burst alerts and spatially coincident muon-neutrino signatures, data from the Antares neutrino telescope recorded between 2007 and 2012 are analysed. One year of public data from the IceCube detector between 2008 and 2009 have been also investigated. The respective timing profiles are scanned for statistically significant accumulations within 40 days of the Gamma Ray Burst, as expected from Lorentz Invariance Violation effects and some astrophysical models. No significant excess over the expected accidental coincidence rate could be found in either of the two data sets. The average strength of the neutrino signal is found to be fainter than one detectable neutrino signal per hundred gamma-ray bursts in the Antares data at 90% confidence level.
• ### Murchison Widefield Array Limits on Radio Emission from ANTARES Neutrino Events(1603.02271)

March 7, 2016 astro-ph.HE
We present a search, using the Murchison Widefield Array (MWA), for electromagnetic counterparts to two candidate high energy neutrino events detected by the ANTARES neutrino telescope in 2013 November and 2014 March. These events were selected by ANTARES because they are consistent, within 0.4 degrees, with the locations of galaxies within 20 Mpc of Earth. Using MWA archival data at frequencies between 118 and 182 MHz, taken ~20 days prior to, at the same time as, and up to a year after the neutrino triggers, we look for transient or strongly variable radio sources consistent with the neutrino positions. No such counterparts are detected, and we set a 5 sigma upper limit for low-frequency radio emission of ~1E37 erg/s for progenitors at 20 Mpc. If the neutrino sources are instead not in nearby galaxies, but originate in binary neutron star coalescences, our limits place the progenitors at z > 0.2. While it is possible, due to the high background from atmospheric neutrinos, that neither event is astrophysical, the MWA observations are nevertheless among the first to follow up neutrino candidates in the radio, and illustrate the promise of wide-field instruments like MWA to detect electromagnetic counterparts to such events.
• ### A Search for Time Dependent Neutrino Emission from Microquasars with the ANTARES Telescope(1402.1600)

Feb. 7, 2014 astro-ph.HE
Results are presented on a search for neutrino emission from a sample of six microquasars, based on the data collected by the ANTARES neutrino telescope between 2007 and 2010. By means of appropriate time cuts, the neutrino search has been restricted to the periods when the acceleration of relativistic jets was taking place at the microquasars under study. The time cuts have been chosen using the information from the X-ray telescopes RXTE/ASM and Swift/BAT, and, in one case, the gamma-ray telescope Fermi/LAT. Since none of the searches has produced a statistically significant signal, upper limits on the neutrino fluences are derived and compared to the predictions from theoretical models.
• ### Search for muon neutrinos from gamma-ray bursts with the ANTARES neutrino telescope using 2008 to 2011 data(1307.0304)

Nov. 6, 2013 hep-ph, astro-ph.HE
A search for muon neutrinos in coincidence with gamma-ray bursts with the ANTARES neutrino detector using data from the end of 2007 to 2011 is performed. Expected neutrino fluxes are calculated for each burst individually. The most recent numerical calculations of the spectra using the NeuCosmA code are employed, which include Monte Carlo simulations of the full underlying photohadronic interaction processes. The discovery probability for a selection of 296 gamma-ray bursts in the given period is optimised using an extended maximum-likelihood strategy. No significant excess over background is found in the data, and 90% confidence level upper limits are placed on the total expected flux according to the model.
• ### AMADEUS - The Acoustic Neutrino Detection Test System of the ANTARES Deep-Sea Neutrino Telescope(1009.4179)

Oct. 9, 2012 astro-ph.IM
The AMADEUS (ANTARES Modules for the Acoustic Detection Under the Sea) system which is described in this article aims at the investigation of techniques for acoustic detection of neutrinos in the deep sea. It is integrated into the ANTARES neutrino telescope in the Mediterranean Sea. Its acoustic sensors, installed at water depths between 2050 and 2300 m, employ piezo-electric elements for the broad-band recording of signals with frequencies ranging up to 125 kHz. The typical sensitivity of the sensors is around -145 dB re 1V/muPa (including preamplifier). Completed in May 2008, AMADEUS consists of six "acoustic clusters", each comprising six acoustic sensors that are arranged at distances of roughly 1 m from each other. Two vertical mechanical structures (so-called lines) of the ANTARES detector host three acoustic clusters each. Spacings between the clusters range from 14.5 to 340 m. Each cluster contains custom-designed electronics boards to amplify and digitise the acoustic signals from the sensors. An on-shore computer cluster is used to process and filter the data stream and store the selected events. The daily volume of recorded data is about 10 GB. The system is operating continuously and automatically, requiring only little human intervention. AMADEUS allows for extensive studies of both transient signals and ambient noise in the deep sea, as well as signal correlations on several length scales and localisation of acoustic point sources. Thus the system is excellently suited to assess the background conditions for the measurement of the bipolar pulses expected to originate from neutrino interactions.
• ### Search for Relativistic Magnetic Monopoles with the ANTARES Neutrino Telescope(1110.2656)

Aug. 29, 2012 astro-ph.HE
Magnetic monopoles are predicted in various unified gauge models and could be produced at intermediate mass scales. Their detection in a neutrino telescope is facilitated by the large amount of light emitted compared to that from muons. This paper reports on a search for upgoing relativistic magnetic monopoles with the ANTARES neutrino telescope using a data set of 116 days of live time taken from December 2007 to December 2008. The one observed event is consistent with the expected atmospheric neutrino and muon background, leading to a 90% C.L. upper limit on the monopole flux between 1.3E-17 and 8.9E-17 cm-2.s-1.sr-1 for monopoles with velocity beta greater than 0.625.
• ### Search for Cosmic Neutrino Point Sources with Four Years of Data from the ANTARES Telescope(1207.3105)

July 21, 2012 hep-ex, astro-ph.HE
In this paper, a time integrated search for point sources of cosmic neutrinos is presented using the data collected from 2007 to 2010 by the ANTARES neutrino telescope. No statistically significant signal has been found and upper limits on the neutrino flux have been obtained. Assuming an $E_{\nu}^{-2}$ spectrum, these flux limits are at $1-10\times10^{-8}$ GeV cm$^{-2}$ s$^{-1}$ for declinations ranging from $-90^{\circ}$ to 40$^{\circ}$. Limits for specific models of RX J1713.7-3946 and Vela X, which include information on the source morphology and spectrum, are also given.
• ### The Positioning System of the ANTARES Neutrino Telescope(1202.3894)

July 16, 2012 astro-ph.IM, astro-ph.HE
The ANTARES neutrino telescope, located 40km off the coast of Toulon in the Mediterranean Sea at a mooring depth of about 2475m, consists of twelve detection lines equipped typically with 25 storeys. Every storey carries three optical modules that detect Cherenkov light induced by charged secondary particles (typically muons) coming from neutrino interactions. As these lines are flexible structures fixed to the sea bed and held taut by a buoy, sea currents cause the lines to move and the storeys to rotate. The knowledge of the position of the optical modules with a precision better than 10cm is essential for a good reconstruction of particle tracks. In this paper the ANTARES positioning system is described. It consists of an acoustic positioning system, for distance triangulation, and a compass-tiltmeter system, for the measurement of the orientation and inclination of the storeys. Necessary corrections are discussed and the results of the detector alignment procedure are described.
• ### Measurement of Atmospheric Neutrino Oscillations with the ANTARES Neutrino Telescope(1206.0645)

July 2, 2012 hep-ex
The data taken with the ANTARES neutrino telescope from 2007 to 2010, a total live time of 863 days, are used to measure the oscillation parameters of atmospheric neutrinos. Muon tracks are reconstructed with energies as low as 20 GeV. Neutrino oscillations will cause a suppression of vertical upgoing muon neutrinos of such energies crossing the Earth. The parameters determining the oscillation of atmospheric neutrinos are extracted by fitting the event rate as a function of the ratio of the estimated neutrino energy and reconstructed flight path through the Earth. Measurement contours of the oscillation parameters in a two-flavour approximation are derived. Assuming maximum mixing, a mass difference of $\Delta m_{32}^2=(3.1\pm 0.9)\cdot 10^{-3}$ eV$^2$ is obtained, in good agreement with the world average value.
• ### A method for detection of muon induced electromagnetic showers with the ANTARES detector(1106.0426)

Feb. 29, 2012 astro-ph.IM, astro-ph.HE
The primary aim of ANTARES is neutrino astronomy with upward going muons created in charged current muon neutrino interactions in the detector and its surroundings. Downward going muons are background for neutrino searches. These muons are the decay products of cosmic-ray collisions in the Earth's atmosphere far above the detector. This paper presents a method to identify and count electromagnetic showers induced along atmospheric muon tracks with the ANTARES detector. The method is applied to both cosmic muon data and simulations and its applicability to the reconstruction of muon event energies is demonstrated.
• ### Measurement of the Group Velocity of Light in Sea Water at the ANTARES Site(1110.5184)

Feb. 13, 2012 hep-ex
The group velocity of light has been measured at eight different wavelengths between 385 nm and 532 nm in the Mediterranean Sea at a depth of about 2.2 km with the ANTARES optical beacon systems. A parametrisation of the dependence of the refractive index on wavelength based on the salinity, pressure and temperature of the sea water at the ANTARES site is in good agreement with these measurements.
• ### Acoustic and optical variations during rapid downward motion episodes in the deep north-western Mediterranean Sea(1111.6482)

Nov. 28, 2011 physics.geo-ph, astro-ph.IM
An Acoustic Doppler Current Profiler (ADCP) was moored at the deep-sea site of the ANTARES neutrino telescope near Toulon, France, thus providing a unique opportunity to compare high-resolution acoustic and optical observations between 70 and 170 m above the sea bed at 2475 m. The ADCP measured downward vertical currents of magnitudes up to 0.03 m s-1 in late winter and early spring 2006. In the same period, observations were made of enhanced levels of acoustic reflection, interpreted as suspended particles including zooplankton, by a factor of about 10 and of horizontal currents reaching 0.35 m s-1. These observations coincided with high light levels detected by the telescope, interpreted as increased bioluminescence. During winter 2006 deep dense-water formation occurred in the Ligurian subbasin, thus providing a possible explanation for these observations. However, the 10-20 days quasi-periodic episodes of high levels of acoustic reflection, light and large vertical currents continuing into the summer are not direct evidence of this process. It is hypothesized that the main process allowing for suspended material to be moved vertically later in the year is local advection, linked with topographic boundary current instabilities along the rim of the 'Northern Current'.
• ### Search for Neutrino Emission from Gamma-Ray Flaring Blazars with the ANTARES Telescope(1111.3473)

Nov. 15, 2011 astro-ph.HE
The ANTARES telescope is well-suited to detect neutrinos produced in astrophysical transient sources as it can observe a full hemisphere of the sky at all times with a high duty cycle. Radio-loud active galactic nuclei with jets pointing almost directly towards the observer, the so-called blazars, are particularly attractive potential neutrino point sources. The all-sky monitor LAT on board the Fermi satellite probes the variability of any given gamma-ray bright blazar in the sky on time scales of hours to months. Assuming hadronic models, a strong correlation between the gamma-ray and the neutrino fluxes is expected. Selecting a narrow time window on the assumed neutrino production period can significantly reduce the background. An unbinned method based on the minimization of a likelihood ratio was applied to a subsample of data collected in 2008 (61 days live time). By searching for neutrinos during the high state periods of the AGN light curve, the sensitivity to these sources was improved by about a factor of two with respect to a standard time-integrated point source search. First results on the search for neutrinos associated with ten bright and variable Fermi sources are presented.


text:
0

# How to disable or enable Player's ShiftLock with a script(not changing StarterPlayer properties)?

So I tried to disable or enable player's shiftlock for a gun system, but I can't find the way to do it(I tried changing the camera CFrame, making the Humanoid.AutoRotate false, but it didn't work as I wanted to.) Is there a way to do it?

game.StarterPlayer.Shiftlock = true


text:
93-164 Gallavotti Giovanni
Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable hamiltonian systems. A review. (217K, TeX) Jun 6, 93
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

Abstract. THIS IS A CORRECTED VERSION OF A PREVIOUSLY POSTED PAPER. Rotators interacting with a pendulum via small, velocity independent, potentials are considered. If the interaction potential does not depend on the pendulum position then the pendulum and the rotators are decoupled and we study the invariant tori of the rotators system at fixed rotation numbers: we exhibit cancellations, to all orders of perturbation theory, that allow proving the stability and analyticity of the dipohantine tori. We find in this way a proof of the KAM theorem by direct bounds of the $k$--th order coefficient of the perturbation expansion of the parametric equations of the tori in terms of their average anomalies: this extends Siegel's approach, from the linearization of analytic maps to the KAM theory; the convergence radius does not depend, in this case, on the twist strength, which could even vanish ({\it "twistless KAM tori"}). The same ideas apply to the case in which the potential couples the pendulum and the rotators: in this case the invariant tori with diophantine rotation numbers are unstable and have stable and unstable manifolds ({\it "whiskers"}): instead of studying the perturbation theory of the invariant tori we look for the cancellations that must be present because the homoclinic intersections of the whiskers are {\it "quasi flat"}, if the rotation velocity of the quasi periodic motion on the tori is large. We rederive in this way the result that, under suitable conditions, the homoclinic splitting is smaller than any power in the period of the forcing and find the exact asymptotics in the two dimensional cases ({\it e.g.} in the case of a periodically forced pendulum). The technique can be applied to study other quantities: we mention, as another example, the {\it homoclinic scattering phase shifts}.

Files: 93-164.src( desc , 93-164.tex )


text:
## shaniehh one year ago Assume a and b are nonzero rational numbers and c and d are irrational numbers. For each of the following expressions, determine whether the result is irrational, rational, or both. Justify your answers.

1. shaniehh

Part A: ac + d Part B:|dw:1441585678410:dw| Part C: b^2(c + d)

2. SolomonZelman

$$4b\sqrt{3+c}$$ ?

3. shaniehh

is that a question

4. SolomonZelman

5. shaniehh

i dont really know it says to find out if they are rational

6. SolomonZelman

Well, $$\sqrt{3+c}$$ would NOT be rational if c is irrational.

7. SolomonZelman

and you know that: (non-zero rational) × (irrational)=irrational

8. SolomonZelman

if c<-3 then you get an imaginary output (with an irrational real part)